The document describes a method for tracking multiple maneuvering targets in infrared image sequences. It combines sequential probabilistic multiple hypothesis tracking (PMHT) with an interacting multiple model (IMM) approach. PMHT is first used to compute observation-to-target assignment probabilities and update target states for each dynamic model in the IMM. The IMM then computes a combined state estimate and predicts the target states for the next time step. This allows tracking of arbitrary target trajectories by explicitly modeling maneuvers as changes in the target's motion model. The algorithm reduces complexity compared to other multiple model PMHT approaches by using only observation association as missing data.
A REVIEW ON OPTIMIZATION OF LEAST SQUARES SUPPORT VECTOR MACHINE FOR TIME SER...ijaia
Support Vector Machine has appeared as an active study in machine learning community and extensively
used in various fields including in prediction, pattern recognition and many more. However, the Least
Squares Support Vector Machine which is a variant of Support Vector Machine offers better solution
strategy. In order to utilize the LSSVM capability in data mining task such as prediction, there is a need to
optimize its hyper parameters. This paper presents a review on techniques used to optimize the parameters
based on two main classes; Evolutionary Computation and Cross Validation.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
This document discusses using a learning automata approach to predict target locations in wireless sensor networks to reduce energy consumption and improve tracking accuracy. It proposes a learning automata based method that uses a target's movement history to predict its next location. Related works on target tracking techniques like tree-based, cluster-based, and prediction-based methods are summarized. Learning automata concepts are introduced. Simulation results are said to show the proposed method improves energy efficiency, reduces missed targets, and decreases transmitted packets compared to other methods.
Failure prediction of e-banking application system using adaptive neuro fuzzy...IJECEIAES
Problems often faced by IT operation unit is the difficulty in determining the cause of the failure of an incident such as slowing access to the internet banking url, non-functioning of some features of m-banking or even the cessation of the entire e-banking service. The proposed method to modify ANFIS with Fuzzy C-Means Clustering (FCM) approach is applied to detect four typical kinds of faults that may happen in the e-banking system, which are application response times, transaction per second, server utilization and network performance. Input data is obtained from the e-banking monitoring results throughout 2017 that become data training and data testing. The study shows that an ANFIS modeling with FCM optimized input has a RMSE 0.006 and increased accuracy by 1.27% compared to ANFIS without FCM optimization.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
Adaptive traffic lights based on traffic flow prediction using machine learni...IJECEIAES
This document discusses using machine learning algorithms to predict traffic flow and reduce congestion at intersections. It compares linear regression, random forest regressor, decision tree regressor, gradient boosting regressor, and K-neighbor regressor models on a UK road traffic dataset. All models performed well according to evaluation metrics, indicating they are suitable for an adaptive traffic light system. The system was implemented using a random forest regressor model and simulations showed it reduced traffic congestion by 30.8%, justifying its effectiveness.
This document proposes a semiblind channel estimation approach for MIMO-OFDM systems that combines training-based and blind techniques. It derives a linear prediction-based blind constraint and incorporates it into a training-based least squares cost function using a weighting factor. A perturbation analysis justifies the superiority of the semiblind solution and derives a closed-form expression for the mean square error of the blind constraint, facilitating the calculation of the optimal weighting factor. Computer simulations show the proposed semiblind approach achieves very high channel estimation accuracy compared to purely training-based or blind methods.
This document provides a literature review on beamforming techniques for 5G mobile communication systems. It discusses the objectives of focusing on beamforming techniques using a combination of the MUSIC and LMS algorithms in a new MLMS algorithm. It then reviews various beamforming algorithms such as LMS, TVLMS, MUSIC, and MLMS and compares their advantages and disadvantages. The document outlines future work plans to improve the MLMS algorithm by reducing iterations and convergence parameters to increase stability. It provides a work plan and references various literature on adaptive beamforming algorithms.
A REVIEW ON OPTIMIZATION OF LEAST SQUARES SUPPORT VECTOR MACHINE FOR TIME SER...ijaia
Support Vector Machine has appeared as an active study in machine learning community and extensively
used in various fields including in prediction, pattern recognition and many more. However, the Least
Squares Support Vector Machine which is a variant of Support Vector Machine offers better solution
strategy. In order to utilize the LSSVM capability in data mining task such as prediction, there is a need to
optimize its hyper parameters. This paper presents a review on techniques used to optimize the parameters
based on two main classes; Evolutionary Computation and Cross Validation.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
This document discusses using a learning automata approach to predict target locations in wireless sensor networks to reduce energy consumption and improve tracking accuracy. It proposes a learning automata based method that uses a target's movement history to predict its next location. Related works on target tracking techniques like tree-based, cluster-based, and prediction-based methods are summarized. Learning automata concepts are introduced. Simulation results are said to show the proposed method improves energy efficiency, reduces missed targets, and decreases transmitted packets compared to other methods.
Failure prediction of e-banking application system using adaptive neuro fuzzy...IJECEIAES
Problems often faced by IT operation unit is the difficulty in determining the cause of the failure of an incident such as slowing access to the internet banking url, non-functioning of some features of m-banking or even the cessation of the entire e-banking service. The proposed method to modify ANFIS with Fuzzy C-Means Clustering (FCM) approach is applied to detect four typical kinds of faults that may happen in the e-banking system, which are application response times, transaction per second, server utilization and network performance. Input data is obtained from the e-banking monitoring results throughout 2017 that become data training and data testing. The study shows that an ANFIS modeling with FCM optimized input has a RMSE 0.006 and increased accuracy by 1.27% compared to ANFIS without FCM optimization.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
Adaptive traffic lights based on traffic flow prediction using machine learni...IJECEIAES
This document discusses using machine learning algorithms to predict traffic flow and reduce congestion at intersections. It compares linear regression, random forest regressor, decision tree regressor, gradient boosting regressor, and K-neighbor regressor models on a UK road traffic dataset. All models performed well according to evaluation metrics, indicating they are suitable for an adaptive traffic light system. The system was implemented using a random forest regressor model and simulations showed it reduced traffic congestion by 30.8%, justifying its effectiveness.
This document proposes a semiblind channel estimation approach for MIMO-OFDM systems that combines training-based and blind techniques. It derives a linear prediction-based blind constraint and incorporates it into a training-based least squares cost function using a weighting factor. A perturbation analysis justifies the superiority of the semiblind solution and derives a closed-form expression for the mean square error of the blind constraint, facilitating the calculation of the optimal weighting factor. Computer simulations show the proposed semiblind approach achieves very high channel estimation accuracy compared to purely training-based or blind methods.
This document provides a literature review on beamforming techniques for 5G mobile communication systems. It discusses the objectives of focusing on beamforming techniques using a combination of the MUSIC and LMS algorithms in a new MLMS algorithm. It then reviews various beamforming algorithms such as LMS, TVLMS, MUSIC, and MLMS and compares their advantages and disadvantages. The document outlines future work plans to improve the MLMS algorithm by reducing iterations and convergence parameters to increase stability. It provides a work plan and references various literature on adaptive beamforming algorithms.
Trajectory Control With MPC For A Robot Manipülatör Using ANN ModelIJMER
In this study, in a computer the dynamic motion modelling of manipulator and control of
trajectory with an algorithm this has been tested. First after dynamic motion simulation of manipulator
has been made MPC Control. The result in this study we can observe that computed torque method gives
better results than MPC methods. So in trajectory control it is approved of using computed torque
method. In last part of this study the results are estimated forward development are exemined and
suggested. The model predictive control (MPC) technique for an articulated robot with n joints is
introduced in this paper. The proposed MPC control action is conceptually different with the trajectory
robot control methods in that the control action is determined by optimising a performance index over
the time horizon. A neural network (NN) is used in this paper as the predictive model.
A scalable collaborative filtering framework based on co-clusteringlau
This document summarizes a research paper that proposes a scalable collaborative filtering framework based on co-clustering. It introduces a dynamic collaborative filtering approach that supports new users, items, and ratings using incremental and batch versions of the co-clustering algorithm. Experimental results on a movie rating dataset show the co-clustering approach provides comparable prediction accuracy to SVD, NNMF, and correlation-based methods but with much lower computational effort.
Adaptive Variable Step Size in LMS Algorithm Using Evolutionary Programming: ...CSCJournals
The Least Mean square (LMS) algorithm has been extensively used in many applications due to its simplicity and robustness. In practical application of the LMS algorithm, a key parameter is the step size. As the step size becomes large /small, the convergence rate of the LMS algorithm will be rapid and the steady-state mean square error (MSE) will increase/decrease. Thus, the step size provides a trade off between the convergence rate and the steady-state MSE of the LMS algorithm. An intuitive way to improve the performance of the LMS algorithm is to make the step size variable rather than fixed, that is, choose large step size values during the initial convergence of the LMS algorithm, and use small step size values when the system is close to its steady state, which results invariable step size Least Mean square (VSSLMS) algorithms. By utilizing such an approach, both a fast convergence rate and a small steady-state MSE can be obtained. Although many VSSLMS algorithmic methods perform well under certain conditions, noise can degrade their performance and having performance sensitivity over parameter setting. In this paper, a new concept is introduced to vary the step size based upon evolutionary programming (SSLMSEV) algorithm is described. It has shown that the performance generated by this method is robust and does not require any presetting of involved parameters in solution based upon statistical characteristics of signal
Leader follower formation control of ground vehicles using camshift based gui...ijma
Autonomous ground vehicles have been designed for the purpose of that relies on ranging and bearing
information received from forward looking camera on the Formation control . A visual guidance control
algorithm is designed where real time image processing is used to provide feedback signals. The vision
subsystem and control subsystem work in parallel to accomplish formation control. A proportional
navigation and line of sight guidance laws are used to estimate the range and bearing information from the
leader vehicle using the vision subsystem. The algorithms for vision detection and localization used here
are similar to approaches for many computer vision tasks such as face tracking and detection that are
based color-and texture based features, and non-parametric Continuously Adaptive Mean-shift algorithms
to keep track of the leader. This is being proposed for the first time in the leader follower framework. The
algorithms are simple but effective for real time and provide an alternate approach to traditional based
approaches like the Viola Jones algorithm. Further to stabilize the follower to the leader trajectory, the
sliding mode controller is used to dynamically track the leader. The performance of the results is
demonstrated in simulation and in practical experiments.
Multi Object Tracking Methods Based on Particle Filter and HMMIJTET Journal
This document discusses multi-object tracking methods based on particle filtering and hidden Markov models. It provides an overview of particle filtering and how it can be used for object tracking by approximating the posterior distribution of objects in video frames. It also discusses how hidden Markov models can be used for prediction and tracking objects at the global layer. Specifically, it describes a multi-object tracking method that uses a coupled layer approach with a local layer tracked using particle filtering and a global layer tracked using a hidden Markov model. This improves tracking efficiency and reduces computational time compared to other recent multi-object trackers.
APPLYING DYNAMIC MODEL FOR MULTIPLE MANOEUVRING TARGET TRACKING USING PARTICL...IJITCA Journal
In this paper, we applied a dynamic model for manoeuvring targets in SIR particle filter algorithm for improving tracking accuracy of multiple manoeuvring targets. In our proposed approach, a color distribution model is used to detect changes of target's model . Our proposed approach controls
deformation of target's model. If deformation of target's model is larger than a predetermined threshold,then the model will be updated. Global Nearest Neighbor (GNN) algorithm is used as data association algorithm. We named our proposed method as Deformation Detection Particle Filter (DDPF) . DDPF
approach is compared with basic SIR-PF algorithm on real airshow videos. Comparisons results show that, the basic SIR-PF algorithm is not able to track the manoeuvring targets when the rotation or scaling is occurred in target' s model. However, DDPF approach updates target's model when the rotation or
scaling is occurred. Thus, the proposed approach is able to track the manoeuvring targets more efficiently
and accurately.
A SELECTIVE PAGING SCHEME BASED ON ACTIVITY IN CELLULAR MOBILE NETWORKS FOR R...ijwmn
This document presents a selective paging scheme based on activity for location management in cellular networks. An activity-based mobility model is used where mobile terminals move between cells according to daily activity patterns like going to work or school. A simulation is conducted with 49 cells, 100 mobile terminals, and schedules for moving between home, workplaces, colleges and fitness centers. The proposed scheme applies prediction-based selective paging at reporting centers to reduce paging cost without increasing location update cost. Simulation results are analyzed to compare the location management costs of the conventional and proposed schemes.
This document introduces a novel probabilistic tracking algorithm that uses variational Bayes to incorporate data association constraints and model-based track management. It models tracks using state space models like Kalman filters for linear complexity, rather than Gaussian processes which are cubic. A key innovation is retaining framing constraints of one measurement per track using a Bethe entropy approximation, enabling linear-time approximate inference. This allows tracking an unknown number of objects using a nonparametric extension of the Indian buffet process for track initiation and termination. The algorithm is demonstrated on radar and computer vision problems.
APPLYING DYNAMIC MODEL FOR MULTIPLE MANOEUVRING TARGET TRACKING USING PARTICL...IJITCA Journal
In this paper, we applied a dynamic model for manoeuvring targets in SIR particle filter algorithm for improving tracking accuracy of multiple manoeuvring targets. In our proposed approach, a color distribution model is used to detect changes of target's model. Our proposed approach controls deformation of target's model. If deformation of target's model is larger than a predetermined threshold, then the model will be updated. Global Nearest Neighbor (GNN) algorithm is used as data association algorithm. We named our proposed method as Deformation Detection Particle Filter (DDPF). DDPF approach is compared with basic SIR-PF algorithm on real airshow videos. Comparisons results show that, the basic SIR-PF algorithm is not able to track the manoeuvring targets when the rotation or scaling is occurred in target's model. However, DDPF approach updates target's model when the rotation or scaling is occurred. Thus, the proposed approach is able to track the manoeuvring targets more efficientlyand accurately.
VISUAL TRACKING USING PARTICLE SWARM OPTIMIZATIONcscpconf
The problem of robust extraction of visual odometry from a sequence of images obtained by an
eye in hand camera configuration is addressed. A novel approach toward solving planar
template based tracking is proposed which performs a non-linear image alignment for
successful retrieval of camera transformations. In order to obtain global optimum a biometaheuristic
is used for optimization of similarity among the planar regions. The proposed
method is validated on image sequences with real as well as synthetic transformations and
found to be resilient to intensity variations. A comparative analysis of the various similarity
measures as well as various state-of-art methods reveal that the algorithm succeeds in tracking
the planar regions robustly and has good potential to be used in real applications.
IRJET- Smart Railway System using Trip Chaining MethodIRJET Journal
This document proposes a smart railway system using trip chaining and big data analysis of passenger information from smart cards. The system would collect data like passenger name, age, travel time, source and destination stations from smart cards. It would then use k-means clustering to group passengers by age and travel patterns. A naïve bayes classifier would predict passenger counts at each station. This analysis of passenger data could help the railway department improve infrastructure and services based on demand.
MEASURING SIMILARITY BETWEEN MOBILITY MODELS AND REAL WORLD MOTION TRAJECTORIEScscpconf
Various mobility models have been proposed to represent the motion behaviour of mobile nodes in the real world. Selection of the most similar mobility model to a given real world environment is a challenging issue which has a significant impact on the quality of performance evaluation
of different network protocols. In this paper we propose a methodology for measurement of similarity between mobility models used in mobile networks simulation and real world mobility scenarios with different transportation modes. We explain our mobility metrics we have used for analysis of motion behavior of mobile nodes and a pre-processing method which makes our trajectories suitable for extraction and calculation of these metrics considering shape of the road networks and GPS noise. Then we use a feature selection method to find the most
discriminative features which are able to distinguish between trajectories with different transportation modes using a supervised learning and feature ranking method. Subsequently,
using our selected feature space we perform Fuzzy C-means Clustering to find the degree of similarity between each of our mobility models and real world trajectories with different
transportation modes. Our methodology can be used to select the most similar mobility model suitable for simulation of mobile network protocols (such as DTN and MANETs protocols) in a
particular real world area.
Measuring similarity between mobility models and real world motion trajectoriescsandit
Various mobility models have been proposed to represent the motion behaviour of mobile nodes
in the real world. Selection of the most similar mobility model to a given real world environment
is a challenging issue which has a significant impact on the quality of performance evaluation
of different network protocols. In this paper we propose a methodology for measurement of
similarity between mobility models used in mobile networks simulation and real world mobility
scenarios with different transportation modes. We explain our mobility metrics we have used for
analysis of motion behavior of mobile nodes and a pre-processing method which makes our
trajectories suitable for extraction and calculation of these metrics considering shape of the
road networks and GPS noise. Then we use a feature selection method to find the most
discriminative features which are able to distinguish between trajectories with different
transportation modes using a supervised learning and feature ranking method. Subsequently,
using our selected feature space we perform Fuzzy C-means Clustering to find the degree of
similarity between each of our mobility models and real world trajectories with different
transportation modes. Our methodology can be used to select the most similar mobility model
suitable for simulation of mobile network protocols (such as DTN and MANETs protocols) in a
particular real world area.
Experimental Framework for Mobility Anchor Point Selection Scheme in Hierarch...IDES Editor
Hierarchical Mobile IPv6 (HMIPv6) was designed to
support IP micro-mobility management in the next generation
Internet Protocol (IPv6) and the Next Generation Networks
(NGN) framework. The general idea behind this protocol is
the usage of Mobility Anchor Point (MAP) located at any level
router of network to support hierarchical mobility
management and seamless handover. Further, the distance
MAP selection in HMIPv6 causes MAP overloaded and increase
frequent binding update as the network grows. Therefore, to
address the issue in designing MAP selection scheme, we
propose an enhance distance scheme with a dynamic load
control mechanism (DMS-DLC). From the experimental
results we obtain that the proposed scheme gives better
distribution in MAP load and increase handover speed. In
addition a new proposed research framework was established
that uses the four stages model
New approach to calculating the fundamental matrix IJECEIAES
The estimation of the fundamental matrix (F) is to determine the epipolar geometry and to establish a geometrical relation between two images of the same scene or elaborate video frames. In the literature, we find many techniques that have been proposed for robust estimations such as RANSAC (random sample consensus), least squares median (LMeds), and M estimators as exhaustive. This article presents a comparison between the different detectors that are (Harris, FAST, SIFT, and SURF) in terms of detected points number, the number of correct matches and the computation speed of the ‘F’. Our method based first on the extraction of descriptors by the algorithm (SURF) was used in comparison to the other one because of its robustness, then set the threshold of uniqueness to obtain the best points and also normalize these points and rank it according to the weighting function of the different regions at the end of the estimation of the matrix ''F'' by the technique of the M-estimator at eight points, to calculate the average error and the speed of the calculation ''F''. The results of the experimental simulation were applied to the real images with different changes of viewpoints, for example (rotation, lighting and moving object), give a good agreement in terms of the counting speed of the fundamental matrix and the acceptable average error. The results of the simulation it shows this technique of use in real-time applications
IRJET - A Review on Pedestrian Behavior Prediction for Intelligent Transport ...IRJET Journal
This document reviews various techniques for predicting pedestrian behavior for intelligent transportation systems. It discusses algorithms that aim to predict pedestrian motion around crossroads to avoid potential collisions with vehicles. The document summarizes several papers that propose different methods for pedestrian behavior prediction, including the use of LSTM neural networks, goal-directed planning with deep neural networks, analyzing pedestrian-vehicle interaction behavior, using CNNs for pedestrian detection and direction prediction, predicting pedestrian intention at night using infrared cameras and fuzzy automata, and memory-based and physical modeling approaches.
An Alternative Genetic Algorithm to Optimize OSPF WeightsEM Legacy
This document presents a genetic algorithm approach to optimize OSPF routing weights. The algorithm aims to minimize maximum and average link utilization directly, unlike previous methods that minimized a convex cost function. It can find weights for both single and multiple shortest path routing. The genetic algorithm uses a chromosome encoding of link weights. It selects parents using rank selection and produces offspring using a reproduction strategy combining crossover and mutation. Additional mutation is applied to offspring not meeting certain conditions. The algorithm is tested on small networks and compared to MIP-based methods, showing results for larger networks with increasing traffic demands.
Q UANTUM C LUSTERING -B ASED F EATURE SUBSET S ELECTION FOR MAMMOGRAPHIC I...ijcsit
In this paper, we present an algorithm for feature selection. This algorithm labeled QC-FS: Quantum
Clustering for Feature Selection performs the selection in two steps. Partitioning the original features
space in order to group similar features is performed using the Quantum Clustering algorithm. Then the
selection of a representative for each cluster is carried out. It uses similarity measures such as correlation
coefficient (CC) and the mutual information (MI). The feature which maximizes this information is chosen
by the algorithm
1. The document presents a hybrid algorithm that combines Kernelized Fuzzy C-Means (KFCM), Hybrid Ant Colony Optimization (HACO), and Fuzzy Adaptive Particle Swarm Optimization (FAPSO) to improve clustering of electrocardiogram (ECG) beat data.
2. The algorithm maps data into a higher dimensional space using kernel functions to make clusters more linearly separable, addresses issues with KFCM being sensitive to initialization and prone to local minima.
3. It uses HACO to optimize cluster centers and membership degrees, and FAPSO to evaluate fitness values and optimize weight vectors, forming usable clusters for applications like ECG classification.
VISUAL TRACKING USING PARTICLE SWARM OPTIMIZATIONcsandit
The problem of robust extraction of visual odometry from a sequence of images obtained by an
eye in hand camera configuration is addressed. A novel approach toward solving planar
template based tracking is proposed which performs a non-linear image alignment for
successful retrieval of camera transformations. In order to obtain global optimum a biometaheuristic
is used for optimization of similarity among the planar regions. The proposed
method is validated on image sequences with real as well as synthetic transformations and
found to be resilient to intensity variations. A comparative analysis of the various similarity
measures as well as various state-of-art methods reveal that the algorithm succeeds in tracking
the planar regions robustly and has good potential to be used in real applications.
The document provides instructions for creating an account and submitting a request for writing assistance on the HelpWriting.net website. It outlines a 5-step process: 1) Create an account with a password and email; 2) Complete a 10-minute order form with instructions, sources, and deadline; 3) Review bids from writers and choose one; 4) Review the completed paper and authorize payment; 5) Request revisions to ensure satisfaction and receive a refund for plagiarized work.
Printable Writing Paper (28) By Aimee-Valentine-Art OnSara Parker
The document provides instructions for requesting an assignment writing service from HelpWriting.net. It outlines the 5-step process: 1) Create an account with a password and email. 2) Complete a 10-minute order form providing instructions, sources, and deadline. 3) Review bids from writers and choose one. 4) Review the completed paper and authorize payment if satisfied. 5) Request revisions until fully satisfied, and the company guarantees original, high-quality work or a full refund.
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In this study, in a computer the dynamic motion modelling of manipulator and control of
trajectory with an algorithm this has been tested. First after dynamic motion simulation of manipulator
has been made MPC Control. The result in this study we can observe that computed torque method gives
better results than MPC methods. So in trajectory control it is approved of using computed torque
method. In last part of this study the results are estimated forward development are exemined and
suggested. The model predictive control (MPC) technique for an articulated robot with n joints is
introduced in this paper. The proposed MPC control action is conceptually different with the trajectory
robot control methods in that the control action is determined by optimising a performance index over
the time horizon. A neural network (NN) is used in this paper as the predictive model.
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The Least Mean square (LMS) algorithm has been extensively used in many applications due to its simplicity and robustness. In practical application of the LMS algorithm, a key parameter is the step size. As the step size becomes large /small, the convergence rate of the LMS algorithm will be rapid and the steady-state mean square error (MSE) will increase/decrease. Thus, the step size provides a trade off between the convergence rate and the steady-state MSE of the LMS algorithm. An intuitive way to improve the performance of the LMS algorithm is to make the step size variable rather than fixed, that is, choose large step size values during the initial convergence of the LMS algorithm, and use small step size values when the system is close to its steady state, which results invariable step size Least Mean square (VSSLMS) algorithms. By utilizing such an approach, both a fast convergence rate and a small steady-state MSE can be obtained. Although many VSSLMS algorithmic methods perform well under certain conditions, noise can degrade their performance and having performance sensitivity over parameter setting. In this paper, a new concept is introduced to vary the step size based upon evolutionary programming (SSLMSEV) algorithm is described. It has shown that the performance generated by this method is robust and does not require any presetting of involved parameters in solution based upon statistical characteristics of signal
Leader follower formation control of ground vehicles using camshift based gui...ijma
Autonomous ground vehicles have been designed for the purpose of that relies on ranging and bearing
information received from forward looking camera on the Formation control . A visual guidance control
algorithm is designed where real time image processing is used to provide feedback signals. The vision
subsystem and control subsystem work in parallel to accomplish formation control. A proportional
navigation and line of sight guidance laws are used to estimate the range and bearing information from the
leader vehicle using the vision subsystem. The algorithms for vision detection and localization used here
are similar to approaches for many computer vision tasks such as face tracking and detection that are
based color-and texture based features, and non-parametric Continuously Adaptive Mean-shift algorithms
to keep track of the leader. This is being proposed for the first time in the leader follower framework. The
algorithms are simple but effective for real time and provide an alternate approach to traditional based
approaches like the Viola Jones algorithm. Further to stabilize the follower to the leader trajectory, the
sliding mode controller is used to dynamically track the leader. The performance of the results is
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In this paper, we applied a dynamic model for manoeuvring targets in SIR particle filter algorithm for improving tracking accuracy of multiple manoeuvring targets. In our proposed approach, a color distribution model is used to detect changes of target's model . Our proposed approach controls
deformation of target's model. If deformation of target's model is larger than a predetermined threshold,then the model will be updated. Global Nearest Neighbor (GNN) algorithm is used as data association algorithm. We named our proposed method as Deformation Detection Particle Filter (DDPF) . DDPF
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This document presents a selective paging scheme based on activity for location management in cellular networks. An activity-based mobility model is used where mobile terminals move between cells according to daily activity patterns like going to work or school. A simulation is conducted with 49 cells, 100 mobile terminals, and schedules for moving between home, workplaces, colleges and fitness centers. The proposed scheme applies prediction-based selective paging at reporting centers to reduce paging cost without increasing location update cost. Simulation results are analyzed to compare the location management costs of the conventional and proposed schemes.
This document introduces a novel probabilistic tracking algorithm that uses variational Bayes to incorporate data association constraints and model-based track management. It models tracks using state space models like Kalman filters for linear complexity, rather than Gaussian processes which are cubic. A key innovation is retaining framing constraints of one measurement per track using a Bethe entropy approximation, enabling linear-time approximate inference. This allows tracking an unknown number of objects using a nonparametric extension of the Indian buffet process for track initiation and termination. The algorithm is demonstrated on radar and computer vision problems.
APPLYING DYNAMIC MODEL FOR MULTIPLE MANOEUVRING TARGET TRACKING USING PARTICL...IJITCA Journal
In this paper, we applied a dynamic model for manoeuvring targets in SIR particle filter algorithm for improving tracking accuracy of multiple manoeuvring targets. In our proposed approach, a color distribution model is used to detect changes of target's model. Our proposed approach controls deformation of target's model. If deformation of target's model is larger than a predetermined threshold, then the model will be updated. Global Nearest Neighbor (GNN) algorithm is used as data association algorithm. We named our proposed method as Deformation Detection Particle Filter (DDPF). DDPF approach is compared with basic SIR-PF algorithm on real airshow videos. Comparisons results show that, the basic SIR-PF algorithm is not able to track the manoeuvring targets when the rotation or scaling is occurred in target's model. However, DDPF approach updates target's model when the rotation or scaling is occurred. Thus, the proposed approach is able to track the manoeuvring targets more efficientlyand accurately.
VISUAL TRACKING USING PARTICLE SWARM OPTIMIZATIONcscpconf
The problem of robust extraction of visual odometry from a sequence of images obtained by an
eye in hand camera configuration is addressed. A novel approach toward solving planar
template based tracking is proposed which performs a non-linear image alignment for
successful retrieval of camera transformations. In order to obtain global optimum a biometaheuristic
is used for optimization of similarity among the planar regions. The proposed
method is validated on image sequences with real as well as synthetic transformations and
found to be resilient to intensity variations. A comparative analysis of the various similarity
measures as well as various state-of-art methods reveal that the algorithm succeeds in tracking
the planar regions robustly and has good potential to be used in real applications.
IRJET- Smart Railway System using Trip Chaining MethodIRJET Journal
This document proposes a smart railway system using trip chaining and big data analysis of passenger information from smart cards. The system would collect data like passenger name, age, travel time, source and destination stations from smart cards. It would then use k-means clustering to group passengers by age and travel patterns. A naïve bayes classifier would predict passenger counts at each station. This analysis of passenger data could help the railway department improve infrastructure and services based on demand.
MEASURING SIMILARITY BETWEEN MOBILITY MODELS AND REAL WORLD MOTION TRAJECTORIEScscpconf
Various mobility models have been proposed to represent the motion behaviour of mobile nodes in the real world. Selection of the most similar mobility model to a given real world environment is a challenging issue which has a significant impact on the quality of performance evaluation
of different network protocols. In this paper we propose a methodology for measurement of similarity between mobility models used in mobile networks simulation and real world mobility scenarios with different transportation modes. We explain our mobility metrics we have used for analysis of motion behavior of mobile nodes and a pre-processing method which makes our trajectories suitable for extraction and calculation of these metrics considering shape of the road networks and GPS noise. Then we use a feature selection method to find the most
discriminative features which are able to distinguish between trajectories with different transportation modes using a supervised learning and feature ranking method. Subsequently,
using our selected feature space we perform Fuzzy C-means Clustering to find the degree of similarity between each of our mobility models and real world trajectories with different
transportation modes. Our methodology can be used to select the most similar mobility model suitable for simulation of mobile network protocols (such as DTN and MANETs protocols) in a
particular real world area.
Measuring similarity between mobility models and real world motion trajectoriescsandit
Various mobility models have been proposed to represent the motion behaviour of mobile nodes
in the real world. Selection of the most similar mobility model to a given real world environment
is a challenging issue which has a significant impact on the quality of performance evaluation
of different network protocols. In this paper we propose a methodology for measurement of
similarity between mobility models used in mobile networks simulation and real world mobility
scenarios with different transportation modes. We explain our mobility metrics we have used for
analysis of motion behavior of mobile nodes and a pre-processing method which makes our
trajectories suitable for extraction and calculation of these metrics considering shape of the
road networks and GPS noise. Then we use a feature selection method to find the most
discriminative features which are able to distinguish between trajectories with different
transportation modes using a supervised learning and feature ranking method. Subsequently,
using our selected feature space we perform Fuzzy C-means Clustering to find the degree of
similarity between each of our mobility models and real world trajectories with different
transportation modes. Our methodology can be used to select the most similar mobility model
suitable for simulation of mobile network protocols (such as DTN and MANETs protocols) in a
particular real world area.
Experimental Framework for Mobility Anchor Point Selection Scheme in Hierarch...IDES Editor
Hierarchical Mobile IPv6 (HMIPv6) was designed to
support IP micro-mobility management in the next generation
Internet Protocol (IPv6) and the Next Generation Networks
(NGN) framework. The general idea behind this protocol is
the usage of Mobility Anchor Point (MAP) located at any level
router of network to support hierarchical mobility
management and seamless handover. Further, the distance
MAP selection in HMIPv6 causes MAP overloaded and increase
frequent binding update as the network grows. Therefore, to
address the issue in designing MAP selection scheme, we
propose an enhance distance scheme with a dynamic load
control mechanism (DMS-DLC). From the experimental
results we obtain that the proposed scheme gives better
distribution in MAP load and increase handover speed. In
addition a new proposed research framework was established
that uses the four stages model
New approach to calculating the fundamental matrix IJECEIAES
The estimation of the fundamental matrix (F) is to determine the epipolar geometry and to establish a geometrical relation between two images of the same scene or elaborate video frames. In the literature, we find many techniques that have been proposed for robust estimations such as RANSAC (random sample consensus), least squares median (LMeds), and M estimators as exhaustive. This article presents a comparison between the different detectors that are (Harris, FAST, SIFT, and SURF) in terms of detected points number, the number of correct matches and the computation speed of the ‘F’. Our method based first on the extraction of descriptors by the algorithm (SURF) was used in comparison to the other one because of its robustness, then set the threshold of uniqueness to obtain the best points and also normalize these points and rank it according to the weighting function of the different regions at the end of the estimation of the matrix ''F'' by the technique of the M-estimator at eight points, to calculate the average error and the speed of the calculation ''F''. The results of the experimental simulation were applied to the real images with different changes of viewpoints, for example (rotation, lighting and moving object), give a good agreement in terms of the counting speed of the fundamental matrix and the acceptable average error. The results of the simulation it shows this technique of use in real-time applications
IRJET - A Review on Pedestrian Behavior Prediction for Intelligent Transport ...IRJET Journal
This document reviews various techniques for predicting pedestrian behavior for intelligent transportation systems. It discusses algorithms that aim to predict pedestrian motion around crossroads to avoid potential collisions with vehicles. The document summarizes several papers that propose different methods for pedestrian behavior prediction, including the use of LSTM neural networks, goal-directed planning with deep neural networks, analyzing pedestrian-vehicle interaction behavior, using CNNs for pedestrian detection and direction prediction, predicting pedestrian intention at night using infrared cameras and fuzzy automata, and memory-based and physical modeling approaches.
An Alternative Genetic Algorithm to Optimize OSPF WeightsEM Legacy
This document presents a genetic algorithm approach to optimize OSPF routing weights. The algorithm aims to minimize maximum and average link utilization directly, unlike previous methods that minimized a convex cost function. It can find weights for both single and multiple shortest path routing. The genetic algorithm uses a chromosome encoding of link weights. It selects parents using rank selection and produces offspring using a reproduction strategy combining crossover and mutation. Additional mutation is applied to offspring not meeting certain conditions. The algorithm is tested on small networks and compared to MIP-based methods, showing results for larger networks with increasing traffic demands.
Q UANTUM C LUSTERING -B ASED F EATURE SUBSET S ELECTION FOR MAMMOGRAPHIC I...ijcsit
In this paper, we present an algorithm for feature selection. This algorithm labeled QC-FS: Quantum
Clustering for Feature Selection performs the selection in two steps. Partitioning the original features
space in order to group similar features is performed using the Quantum Clustering algorithm. Then the
selection of a representative for each cluster is carried out. It uses similarity measures such as correlation
coefficient (CC) and the mutual information (MI). The feature which maximizes this information is chosen
by the algorithm
1. The document presents a hybrid algorithm that combines Kernelized Fuzzy C-Means (KFCM), Hybrid Ant Colony Optimization (HACO), and Fuzzy Adaptive Particle Swarm Optimization (FAPSO) to improve clustering of electrocardiogram (ECG) beat data.
2. The algorithm maps data into a higher dimensional space using kernel functions to make clusters more linearly separable, addresses issues with KFCM being sensitive to initialization and prone to local minima.
3. It uses HACO to optimize cluster centers and membership degrees, and FAPSO to evaluate fitness values and optimize weight vectors, forming usable clusters for applications like ECG classification.
VISUAL TRACKING USING PARTICLE SWARM OPTIMIZATIONcsandit
The problem of robust extraction of visual odometry from a sequence of images obtained by an
eye in hand camera configuration is addressed. A novel approach toward solving planar
template based tracking is proposed which performs a non-linear image alignment for
successful retrieval of camera transformations. In order to obtain global optimum a biometaheuristic
is used for optimization of similarity among the planar regions. The proposed
method is validated on image sequences with real as well as synthetic transformations and
found to be resilient to intensity variations. A comparative analysis of the various similarity
measures as well as various state-of-art methods reveal that the algorithm succeeds in tracking
the planar regions robustly and has good potential to be used in real applications.
Similar to A Combined PMHT And IMM Approach To Multiple-Point Target Tracking In Infrared Image Sequence (20)
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Cal State Northridge (CSUN) is a large public university located in Los Angeles County, California with over 41,000 students currently enrolled, making it one of the largest universities in the state. CSUN began in 1952 as a satellite campus for Cal State LA and became an independent university in 1958 under its original name of San Fernando Valley State College. Today CSUN offers over 200 degree programs and is known for its programs supporting underrepresented minority students and those with disabilities.
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2. 2 EURASIP Journal on Image and Video Processing
2. RELATED WORK AND OUR CONTRIBUTIONS
In this paper, we provide a solution to tracking multiple
nonmaneuvering and maneuvering point targets in a se-
quence of infrared images by combining the PMHT and the
IMM approaches [23]. In this combined approach, PMHT
is first used to compute the measurement-to-target assign-
ment probabilities and to update the target states for the cur-
rent scan of measurements, where each target state consists
of a collection of states, one for each model in the IMM. The
IMM is then used to compute a combined state estimate and
error covariance matrix for each target, and to predict for-
ward to the next scan, the collection of states for each target
based on a fixed transition probability matrix for the models
in the IMM. In the current paper, we explicitly model ma-
neuver as a change in target’s motion model. Inclusion of
IMM enables tracking of any arbitrary trajectory, and PMHT
helps to avoid the uncertainty about the observation origin.
In our approach, only validated observations are used to
calculate the observation centroid. Moreover, it uses only ob-
servation association as missing data, which simplifies E-step
and M-step [24] and consequently, it reduces the complexity
of the algorithm in comparison with augmented multimodel
PMHT algorithm [15]. In the later case, both observation as-
sociation and target association are treated as nuisance pa-
rameters or missing data, which increases the complexity of
the algorithm as it requires to explore all the possible config-
uration of observation association and target association.
A formulation, where IMM is used with PMHT, has
been investigated [25, 26]. It is important to note the ba-
sic differences between the proposed algorithm in this pa-
per and the one discussed [25, 26]. First, our methodol-
ogy which incorporates multiple models in the framework
of PMHT is quite different from the one discussed [25, 26].
The IMM-PMHT algorithm [25, 26] is similar to the multi-
model PMHT (MPMHT) [25, 26] except that the forward-
backward algorithm is replaced by the IMM. In the deriva-
tion of the algorithm, the key concern is how to apply the
IMM to the Kalman smoother, since the IMM supports only
a forward procedure (Kalman filter), and, therefore, the algo-
rithm uses an approximation to obtain the backward proba-
bility transition matrix. In our approach, PMHT is first used
to compute the measurement-to-target assignment probabil-
ities and to update the target states for the current scan of
measurements, where each target state consists of a collec-
tion of states, one for each model in the IMM. The IMM
is then used to compute a combined state estimate and er-
ror covariance matrix for each target, and to predict, for-
ward to the next scan, the collection of states for each tar-
get based on a fixed transition probability matrix for the
models in the IMM. Second, [25, 26] in order to apply the
IMM to the Kalman smoother, an assumption is made that
the maneuver mode switching process is a Markov process
when going backward, and the backward transition matrix
is the same as the usual (forward) transition matrix. Thus,
the IMM is done in the regular way except that filtering is
replaced by smoothing. In our formulation, we have explic-
itly modeled maneuver as a change in target’s motion model
rather than modeling it as an increase in the level of pro-
yt φ1
t|t−1 P1
t|t−1 φ2
t|t−1 P2
t|t−1
PMHT
model 1
PMHT
model 2
µt−1
φ1
t|t
P1
t|t
Lt
Model
probability
update
φ2
t|t
P2
t|t Combined state
estimate
µt
Mixing
φO1
t|t PO1
t|t
φO2
t|t PO2
t|t Φt|t
Pt|t
Time
update
model 1
Time
update
model 2
φ1
t+1|t P1
t+1|t φ2
t+1|t P2
t+1|t
Figure 1: PMHT + IMM algorithm for two models.
cess noise; and we clearly demonstrate the effectiveness of
such a methodology in our application. Inclusion of IMM
enables tracking of any arbitrary trajectory and PMHT helps
to avoid the uncertainty about the observation origin. The
flow chart of our proposed algorithm, as shown in Figure 1,
clearly explains our methodology. Finally, in our approach,
only validated observations are used to calculate the observa-
tion centroid. Moreover, it uses only observation association
as missing data, which simplifies E-step and M-step and con-
sequently, it reduces the complexity of the algorithm in com-
parison with augmented multimodel PMHT algorithm. In
[25, 26], both observation association and target association
are treated as nuisance parameters or missing data, which in-
creases the complexity of the algorithm as it requires to ex-
plore all the possible configuration of observation associa-
tion and target association.
For IMM, model probability is to be calculated, which
is based on likelihood of the observation and hence needs
an assignment of an observation to a target. Earlier IMM-
NN, IMM-MHT, IMM-PDAF, and IMM-JPDA ([27–34])
have been used for data assignment. Nevertheless, IMM-NN,
IMM-MHT, and IMM-PDAF have the same disadvantages
(mentioned earlier) of NN, MHT, and PDAF methods. To
reduce the computations, PDA has been replaced by JPDA
method with IMM filtering [31, 32]. As pointed out previ-
ously, with JPDA, also the complexity increases with the in-
crease in the number of targets and observations.
In our proposed solution, we overcome the above prob-
lems by using PMHT approach to calculate the centroid of
the observations. This centroid is then used to update the tar-
get’s state and to evaluate model probabilities. It is important
3. Mukesh A. Zaveri et al. 3
to note that it does not assign any particular observation to
a track. To simplify discussions, our variant of the combina-
tion of PMHT and IMM discussed in this paper is named as
PMHT + IMM.
3. PROPOSED PMHT + IMM ALGORITHM
In this section, the problem is described in multimodel
framework to track arbitrary trajectories of multiple-point
targets. The algorithm is divided into two major steps. In the
first step, namely, PMHT step, which is based on PMHT al-
gorithm [11], the centroid of the current observation set is
calculated for each target. The centroid of the observations
is then used to evaluate model likelihood and to update the
state for each model. It is followed by an IMM step, which
updates the combined state estimate and model probabil-
ity and predicts the state for the next time instant for each
model. It is assumed that the target tracks are independent
of each other. From one time instant to another time instant,
from observation to observation and from assignment to
assignment, independence is assumed. With these assump-
tions, PMHT algorithm, operating in batch mode [11], can
be used with only current set of observations. In the pro-
posed algorithm, there is no need to smooth target state in
batch mode, since all calculations are restricted to current
time instant only, and consequently, this reduces the com-
plexity of the algorithm.
Let Y and Φ denote the observation process and the state
process, respectively. Yt is a set of all observation set for time
t ≥ 1, where t is current time. Yt and Φt represent the re-
alization of the observation process and the state process at
time t. The observation vector
Yt =
yt(1), ..., yt
No
(1)
represents the received observation vector, where No is the
number of observations received. Similarly,
Φt =
Φt(1), ..., Φt
Nt
. (2)
Here, Nt is the total number of targets at time instant t, Φt(s)
(1 ≤ s ≤ Nt) represents the combined state vector for target
s, and φm
t (s) is the state vector of target s due to model m at
time t, where 1 ≤ m ≤ M. M is the total number of models
used to track that target. To overcome the uncertainty about
the observation origin, an assignment process K is used, and
Kt is a set of all its realizations for time t ≥ 1. Its realization
at time t is denoted by
Kt =
kt(1), ..., kt
No
, (3)
where Kt is an assignment vector and each element of vector
kt(j) = s indicates that target s produces observation j at
time t. The observation to track assignment probability Π at
time t is given by
Πt =
πt(1), ..., πt
Nt
. (4)
Here, πt(s) indicates the probability that an observation orig-
inates from the target s. This probability is independent of
the observation, that is,
πt(s) = p
kt(j) = s
∀j = 1, ..., No. (5)
It is assumed that one observation originates from one target
or clutter, which leads to the following constraint on assign-
ment probabilities:
Nt
s=1
πt(s) = 1. (6)
Each element of assignment vector Kt is independent, then
the probability of the associated event is
p
Kt
=
No
j=1
p
kt(j)
. (7)
Finally, the parameter is defined as
O
∆
= (Φ; Π). (8)
The assignment vector is treated as missing data and the
observation vector as incomplete data, and these together
form a complete data set X = (Y, K). With the incomplete
data formulation, EM algorithm [35, 36] is preferred in ob-
taining the solution for maximum likelihood (ML) estimate
or maximum a posteriori (MAP) estimate of the target state.
It consists of two steps: E-step and M-step. E-step evaluates
the expectation of log-likelihood of complete data using cur-
rent assignment probability and current state estimate of tar-
get. It estimates assignment probability as a by product. This
estimate is used in M-step, which estimates the state of the
target by maximizing the log-likelihood functional obtained
in E-step.
The estimate of O = (Φ; Π) at time t is given by Bayes’
rule:
p
O | Xt
= p
Φt; Πt
| Xt, Xt−1
=
p
Xt |
Φt; Πt
p
Xt | Xt−1
p
Φt; Πt
| Xt−1
,
(9)
where p(Xt | Xt−1) is a normalizing term, and using inde-
pendence assumption for assignment vector from one time
instant to another leads to
p
Φt; Πt
| Xt−1
= p
Φt; Πt
|
Φt−1
, (10)
where
Φt−1 represents the previous estimate;
p
O | Xt
=
p
Yt, Kt |
Φt; Πt
p
Xt | Xt−1
p
Φt; Πt
|
Φt−1
.
(11)
The previous estimate can be used as a priori knowledge.
Then MAP estimate of O is given by
Omap = arg max
(Φt;Πt)
log p
Yt, Kt |
Φt; Πt
+ log p
Φt; Πt
|
Φt−1
.
(12)
Two iterative steps are used to evaluate (12) and the descrip-
tion of the same follows.
4. 4 EURASIP Journal on Image and Video Processing
(1) Expectation (E-step)
Here, the expectation of the log-likelihood of the completed
data is evaluated. Basically, it is an evolution of conditional
expectation of Kt given the observation set Yt and the esti-
mated value of O at pth iteration,
O(p);
Q
O |
O(p)
= E log p
Yt, Kt | O
| Yt,
O(p)
=
Kt
log p
Yt, Kt | O
p
Kt | Yt,
O(p)
.
(13)
Independence assumption for each observation and assign-
ment gives,
Q
O |
O(p)
=
Kt
No
j=1
log p
yt(j) | Φt
k(j)
πt
k(j)
×
No
j=1
p
kt(j) | yt(j),
O(p)
.
(14)
Substituting (5) and summing over all possible configura-
tions of Kt, (14) can be rewritten as
Q
O |
O(p)
=
Nt
s=1
No
j=1
zt(s, j)
log πt(s)
+
Nt
s=1
No
j=1
log p
yt(j) | Φt(s)
zt(s, j),
(15)
where kt(j) ∈ [1, ..., Nt] and j ∈ [1, ..., No]. Here,
zt(s, j)
represents assignment weights for observation j and target s,
and it is defined as
zt(s, j) =
π
(p)
t (s)p
yt(j) | Φ
(p)
t (s)
Nt
i=1 π
(p)
t (i)p
yt(j) | Φ
(p)
t (i)
. (16)
(2) Maximization (M-step)
Using the previous estimate of the state as a priori and the
functional obtained in E-step, the estimate of the state is ob-
tained by maximizing
Φ
(p+1)
t = arg max
(Φt;Πt)
Q
O |
O(p)
+ log p
Φt; Πt
|
Φt−1
(17)
with respect to π(s) and Φ(s), s = 1, ..., Nt, respectively. The
value of Q(O |
O(p)) can be substituted from (15) and the
second term of (17) can be written as
p
Φt; Πt
|
Φt−1
=
Nt
s=1
p
Φ0(s)
p
Φt(s) |
Φt−1(s)
,
(18)
log p
Φt; Πt
|
Φt−1
=
Nt
s=1
log p
Φ0(s)
+ log p
Φt(s) |
Φt−1(s)
.
(19)
Here, Φ(s) represents the combined state vector of a tar-
get s. So, the parameter Φ(s) is the set of parameters
(φ1(s), φ2(s), ..., φM(s)), where φm(s) is the state vector of
target s due to model m. Again, each model m is indepen-
dent of the other m models. It leads to maximization of (17)
with respect to φm(s), for 1 ≤ m ≤ M. Maximization of (17)
with respect to π(s) gives
πt(s) =
1
No
No
j=1
zt(s, j), (20)
and with respect to Φ(s), that is, with respect to φm(s) for
each model m (1 ≤ m ≤ M), it results in Kalman filter-
ing (see the appendix). With Gaussian assumption for a state
φm
t (s) (1 ≤ m ≤ M, 1 ≤ s ≤ Nt), it is given by standard
Kalman equations that
φt|t−1 = f
φt−1|t−1
+ vt, (21)
where vt represents process noise having covariance Qp. The
observation yt(j) is given by
yt = h
φt|t−1
+ nt, (22)
where nt is an observation noise, assumed to be Gaussian
having covariance R.
Now, we describe the PMHT + IMM algorithm with the
help of the above formulation. The flow chart for the pro-
posed algorithm using two models for IMM is shown in
Figure 1. As the current set of observation Yt becomes avail-
able, the following two steps are performed at time instant t.
The observation set Yt is validated using combined state pre-
diction Φt|t−1 for a given target. PMHT step is evaluated for
each target, and for each model of a given target, sequentially.
After completion of PMHT step for each target, IMM step is
executed.
In the PMHT step, the assignment probabilities and cen-
troid of observations are calculated. These are used by IMM
step to update and predict the target state.
(1) PMHT step (PMHT model block in Figure 1).
For each target s (1 ≤ s ≤ Nt) and for each model m
(1 ≤ m ≤ M):
(a) initialize state
φm
t (s) =
φm
t|t−1(s) and covariance
Pm
t (s) = Pm
t|t−1(s)
φm
t|t−1(s) and Pm
t|t−1(s) represent pre-
viously predicted state and covariance, respectively;
(b) repeat the following steps at each iteration, till er-
ror converges to a fixed threshold value, that is,
φ
m(p−1)
t (s) −
φ
m(p)
t (s) ǫ.
(i) Calculate the assignment weights for each obser-
vation j = 1, ..., No for each target i = 1, ..., Nt
using (16).
(ii) Calculate the assignment probabilities for target
s using (20).
(iii) Calculate the centroid of observations (effective
observation):
ycm
t (s)
=
1
Noπ
m(p+1)
t (s)
No
j=1
z
m(p+1)
t (s, j)yt(j).
(23)
5. Mukesh A. Zaveri et al. 5
(iv) Calculate the effective observation noise covari-
ance matrix:
Rcm
t (s) =
Rm
t (s)
Noπ
m(p+1)
t (s)
. (24)
(v) State and state covariance updates:
y = ycm
t (s) − Hm
t (s)
φ
m(p)
t (s),
Sm
(s) = Hm
t (s)P
m(p)
t (s)
Hm
t (s)
T
+ Rcm
t (s),
(25)
likelihood of model1: Lm(s)=N [
y; 0, Sm(s)];
Km
g (s) = P
m(p)
t (s)
Hm
t (s)
T
Sm
(s)
−1
,
φ
m(p+1)
t (s) =
φ
m(p)
t (s) + Km
g (s)
y,
P
m(p+1)
t (s) = P
m(p)
t (s) − Km
g (s)Sm
(s)
Km
g (s)
T
.
(26)
At the end of PMHT step for each target s, for each
model m updated state
φm
t|t(s) and updated covariance,
Pm
t|t(s) are obtained.
(2) IMM step: for each target s (1 ≤ s ≤ Nt), repeat the
following steps.
(a) Model probability update (model probability update
block in Figure 1):
for each model m = 1, ..., M, calculate the model
probability using
µm
t (s) =
µm
t|t−1(s)Lm(s)
M
i=1 µi
t|t−1(s)Li(s)
. (27)
(b) Combined state and state covariance updates (com-
bined state estimate block in Figure 1):
Φt|t(s) =
M
m=1
φm
t|t(s)µm
t (s),
Pt|t(s) =
M
m=1
Pm
t|t(s) +
Φt|t(s) −
φm
t|t(s)
·
Φt|t(s) −
φm
t|t(s)
T
µm
t (s).
(28)
(c) For each model m = 1, ..., M, calculate the following.
(i) Model-conditional initialization (mixing) (mix-
ing block in Figure 1):
φ0m
=
M
i=1
φi
t|t(s)µi|m
,
P0m
=
M
i=1
Pi
t|t(s) +
φ0m
−
φi
t|t(s)
·
φ0m
−
φi
t|t(s)
T
µi|m
,
(29)
1 Note: likelihood of a model is calculated during the first iteration only for
given model and target.
where
µi|m
=
ξs
imµi
t(s)
µm
t+1|t
, µm
t+1|t =
M
i=1
ξs
imµi
t(s). (30)
Here ξim is the transition probability.
(ii) State and state covariance prediction (time up-
date model block in Figure 1):
φm
t+1|t(s) = Fm
t (s)
φ0m
,
Pm
t+1|t(s) = Fm
t (s)P0m
Fm
t (s)
T
+ Qm
t (s).
(31)
(d) Combined state and state covariance prediction:
Φt+1|t(s) =
M
m=1
φm
t+1|t(s)µm
t+1|t(s),
Pt+1|t(s) =
M
m=1
Pm
t+1|t(s) +
Φt+1|t(s) −
φm
t+1|t(s)
,
Φt+1|t(s) −
φm
t+1|t(s))T
µm
t+1|t(s).
(32)
The transition probability is initialized as
Ξ =
0.998 0.001
0.001 0.998
(33)
and initial model probability is set to µ = {0.5 0.5}. Initial
model probability for both models is set equally. These pa-
rameters are chosen based on the study reported in the lit-
erature and our exhaustive experimental investigations. The
transition probability matrix is initialized based on the fol-
lowing observation. The diagonal entries of the probability
matrix are related to the individual target dynamic models
used for tracking. Generally, the target dynamics is consis-
tent and therefore, it has a high probability that it will remain
in the same state. So, these diagonal entries are initially set
to high values. The nondiagonal entries represent the prob-
abilities of switching between different dynamic models as-
sociated with a target. In general, there is a low probability
that the target dynamics will change its state, that is, it will
switch from one target dynamic model to another, and con-
sequently, the nondiagonal entries are initially set to low val-
ues. Similarly, the model probabilities are also initialized with
equal probabilities. But, during the execution of algorithm
the model probabilities are updated automatically.
4. SIMULATION RESULTS
Synthetic IR images were generated using real-time temper-
ature data [37]. Intensity at different points in images is a
function of temperature, surface properties, and other envi-
ronmental factors. Based on exhaustive empirical study, we
have validated the close resemblance between synthetic IR
images and real IR images in airborne applications. Due to
the classified nature of the real IR images which we used for
our investigation, we are limited here to present our results
only for synthetic IR images.
6. 6 EURASIP Journal on Image and Video Processing
Trajectory
Trajectory crossover
1
2
Figure 2: Trajectory using SMM-PMHT model for ir44 clip :: crossover.
Trajectory
Trajectory diverage
1
2
Figure 3: Trajectory using CA-PMHT model for ir50 clip.
For simulation, the generated frame size is 1024 × 256
with a large target movement of ±20 pixels per frame. Many
video clips are simulated with different types of trajectories
to evaluate the performance of the proposed algorithm. Two
sets of clips have been generated: (i) the first clip set consist-
ing of maneuvering trajectories is generated using B-splines,
and it is quite important to note that these generated trajec-
tories do not follow any specific model; (ii) for the second
clip set, mixed trajectories are generated using constant ac-
celeration model for non-maneuvering trajectories and co-
sine and sine functions for nonlinear (maneuvering) trajec-
tories. The second case allows one to generate trajectories
with known models and known set of parameters to evaluate
the performance of the proposed algorithm. The nonlinear
function gives x and y positions of the target at each time
t. Extensive simulations have been done and simulation re-
sults for a few of the clips from these two different sets are
described here. It is assumed that each input clip is processed
with the target detection algorithm described in [38, 39]. At
each time instant, the output from the detection module is
treated as the observation set. As the tracking is done in an
image clip, the observation consists of x and y positions only.
For our case, t is discrete and also represents the frame num-
ber in an image clip. In general, the nonlinear functions are
of the following forms:
x(t) = αt
+ A ∗ tri fun (wt),
y(t) = B + A ∗ tri fun (wt),
(34)
where tri fun may be cosine or sine function α takes value
less than 1.0, and w is in radians.
Different values for the noise covariances are used:
(i) for the process and the observation to generate trajec-
tories and (ii) for the models used in tracking. This facilitates
the simulation of mismatch models, and thereby providing
realistic trajectories to evaluate different tracking algorithms.
For generating the nonmaneuvering and maneuvering tra-
jectories, the process noise variance and observation noise
variance for the position are set to 5.0 and 2.0. The process
noise variance value, for both the velocity and the accelera-
tion of the target in case of nonmaneuvering trajectories, is
set to 0.001. In our simulations, we have used constant accel-
eration (CA) and Singer’s maneuver model [40] (SMM) for
IMM. Both models have six state parameters, namely, posi-
tion, velocity, and acceleration for x and y. For tracking pur-
poses, in our simulations, the model observation noise vari-
ance for the position is set to 9.0 for both models. For all
trajectories, the tracking filters are initialized using positions
of the targets in the first two frames.
First, we have experimented with only CA (CA-PMHT)
and only SMM (SMM-PMHT) algorithms, that is, approach
proposed [14] for batch mode length set to 1, for different
trajectories in IR clips. Figure 2 represents the tracked trajec-
tories in an IR image clip using one particular type of model,
that is, SMM. It shows a crossover of trajectories and fails
to track the targets. Figure 3 depicts the failure of CA model
to track a target. But our proposed PMHT + IMM method
is able to track the target for these IR clips as shown in Fig-
ures 4 and 5, respectively. In Figures 2–9, the real trajectory
is shown with a solid line, whereas the predicted trajectory is
shown using a dotted line.
Figures 6 and 7 present results for target tracking in clut-
ter using the proposed method. It is important to note that
for the same IR clips, both CA-PMHT and SMM-PMHT fail
to track the targets simultaneously.
Figure 8 represents the variation with time in the like-
lihood of a model and consecutively the model probability,
for different trajectories for the clip ir50 with 0.03% clutter,
7. Mukesh A. Zaveri et al. 7
Trajectory
True trajectory
Predicted trajectory
1
2
Figure 4: Trajectory using PMHT + IMM model for ir44 clip at frame number 57.
True traj.
Predicted trajectory
1
2
Trajectory
Figure 5: Trajectory using PMHT + IMM model for ir50 clip at frame number 44.
respectively. Actually, it depicts the likelihood of a model for
a given target and matches with the result obtained for ir50
clip in Figure 7. These results lead to a conclusion that using
our proposed PMHT + IMM algorithm, it is possible to track
arbitrary trajectories.
Figure 9 represents the result of the proposed tracking
algorithm for clip in31 2, which contains 6 targets. Using
the proposed PMHT + IMM approach, mean error in po-
sition is depicted in Table 1. Table 1(a) compares the results
obtained using PMHT with only CA (CA-PMHT) and only
SMM (SMM-PMHT) algorithms, that is, approach proposed
[14] for batch mode length set to 1, for different trajectories
in different infrared image clips. We have also tested the pro-
posed algorithm to track multiple-point target in image clips
with different clutter levels. For all trajectories, filters are ini-
tialized using positions of the targets in the first two frames.
For example, 0.02% clutter level in an image frame represents
0.02% number of pixels of the total pixels in an image to be
noisy. “Traj.” indicates trajectory number in an image clip. In
Table 1, PMHT + IMM represents combined mean error in a
position.
For clips ir49 and ir50 in Table 1(a), mean error in po-
sition using SMM-PMHT approach [14] is less compared to
that of using PMHT + IMM approach. Such a result is ex-
pected if only one particular model represents the trajectory
quite accurately. For clips ir44 and ir50 in Table 1(a) and ir44,
ir49, and ir50 in Table 1(b) with different clutter level, only
PMHT + IMM method is able to track both trajectories si-
multaneously. Therefore, in a scenario where there is no a
priori information available about the model for a trajectory,
we advocate that the most preferred approach is PMHT +
IMM.
Results of the investigations reported [25, 26] indi-
cate that the performance of homothetic (multiple model)
Table 1: Mean Prediction Error in Position.
(a) Without clutter
Traj. CA-PMHT SMM-PMHT PMHT + IMM
ir44
1 1.9650 Fails 1.8523
2 3.4995 Fails 3.3542
ir49
1 4.9959 1.9257 3.2662
2 5.1730 2.1353 3.0113
ir50
1 Fails 2.3164 3.0710
2 5.7795 2.1093 3.1088
(b) With clutter
Traj. PMHT + IMM
ir44
— 0.02% 0.03%
1 2.2849 2.6126
2 Fails Fails
ir49
— 0.02% 0.03%
1 3.4328 3.7474
2 3.1441 5.2833
ir50
— 0.02% 0.03%
1 3.3201 3.3174
2 3.6560 3.7897
8. 8 EURASIP Journal on Image and Video Processing
Trajectory
Predicted trajectory
True traj.
1
2
Figure 6: Target trajectories for ir49 clip with clutter level 0.02% at frame number 49.
Trajectory
Predicted
traj.
True
traj.
2
1
Figure 7: Target trajectories for ir50 clip with clutter level 0.03% at frame number 44.
0 5 10 15 20 25 30 35 40 45
Frame number
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Model
probability
Model probability for target 1
CA filter
Maneuver filter
(a)
0 5 10 15 20 25 30 35 40 45
Frame number
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Model
probability
Model probability for target 2
CA filter
Maneuver filter
(b)
Figure 8: Model probability (ir50 clip with clutter level 0.03%).
Trajectory
Predicted
traj.
True
traj.
4
5
6
Trajectory
2
1
3
Figure 9: Target Trajectories for in31 2 clip at frame number 79.
9. Mukesh A. Zaveri et al. 9
PMHT is better than the version of IMM-PMHT discussed
[25, 26]. Therefore, we have also experimented using ho-
mothetic (multiple model) PMHT [25, 26] for batch mode
length set to 1. From the results of our investigation, it is ob-
served that by using maneuvering models based on different
process noise covariance values only, it is difficult to track
multiple arbitrary trajectories. These results are depicted in
Figures 10 and 11 for clip n16. In the first case, we used
two constant acceleration models with different noise covari-
ance values, and it fails to track all the targets simultaneously
(Figure 10). Whereas in the second case, we used two Singer’s
models with different noise covariance values and again it
fails to track all the targets in the clip. But our proposed ap-
proach, namely, PMHT + IMM, is able to track all the targets
successfully which are depicted in Figure 12. From the results
of this investigation, a reasonable conclusion is that it is not
sufficient to model maneuver as a change in the process noise
alone, and that improved performance can be obtained on
inclusion of the change in target’s motion model.
In order to demonstrate the efficacy of our proposed al-
gorithm, we have experimented with a large number of tar-
gets, that is, 40 targets in a clip. Figure 13 represents the
tracking results for one such clip, namely, ip24 clip. From
Figure 13, it is clear that our proposed algorithm is also ef-
fective in tracking all the targets successfully in a dense envi-
ronment, that is, in the presence of a large number of targets.
It is also important to note that the parameters for the track-
ing filters are set to the same value as those set for the clips
with few targets. These parameters are process noise vari-
ance, observation noise variance and validation gate of size
28 × 28, and so forth. It is obvious that with such a large
validation gate and a large number of targets, the data as-
sociation problem is very crucial and needs an efficient al-
gorithm. The proposed algorithm performs data association
successfully with this set of values. We have performed ex-
haustive empirical study for a large number of clips with 40
targets. Due to space limitation, it is not possible to include
them in the manuscript. We also performed Monte Carlo
simulations with a different set of trajectory sets to evaluate
the performance of the proposed PMHT + IMM algorithm.
Fifty simulations are performed for a given set of trajectories.
The process noise covariance and observation noise covari-
ance are set to 0.2 and 2.0, respectively, for trajectory gener-
ation. The number of clutter is assumed to be Poisson dis-
tributed. The size of clutter window is 10 × 10 around the
actual observed target position. The average number of clut-
ter that falls inside the clutter window is set to 1.
For one of the trajectory sets, the details are as follows.
The trajectory set consists of three trajectories. (a) The first
is a constant acceleration trajectory with initial position, ve-
locity, and acceleration set to (70, 70), (20, 3), and (0.5, 0.5),
and it exists for 22 frames. (b) The second trajectory is gener-
ated using constant velocity model and exists for 30 frames.
The initial X-Y position and velocity are set to (70, 200) and
(20, -3). (c) The third trajectory is of “MIX” type and exists
for 70 frames. The initial position and velocity are set to (30,
30) and (10, 1). The target travels with constant velocity from
frame 1 to frame 15. It takes three turns: (i) 15◦
per second
from frame 16 to frame 27, (ii) −15◦
per second from frame
36 to 47, and (iii) 12◦
per second from frame 58 to frame 68.
Then, the target has acceleration of (0.02, 0.02) in X-Y. The
true trajectory plot is shown in Figure 14. The prediction and
estimation error plot for the third trajectory (MIX type) are
depicted in Figures 16 and 15.
To test the bias of the state estimate, we follow the statisti-
cal method described in [41]. For this, an estimation error for
each component of the state vector is tested individually. Un-
der the hypothesis that the state estimation is unbiased, and
assuming that the error is normally distributed each compo-
nent, indexed by subscript j, is also normally distributed:
e(j) =
Φ
j
t|t ∼ N
0, P
j j
t|t
, (35)
where
Φ
j
t|t is an estimation error in jth component of the
state vector. Each component of the state error is divided
by its standard deviation which makes it (under ideal con-
ditions) N (0, 1), which is also evident from Figure 15.
5. CONCLUSION
Results of our investigation clearly demonstrate the effec-
tiveness of combining PMHT with IMM for the tracking of
multiple single-pixel maneuvering targets in sequences of in-
frared images in a dense cluttered environment. We also con-
clude that modeling maneuver as a change in targets’ motion
model could provide enhanced performance compared to
modeling it as an increase in the level of process noise. From
the simulation results, it is also concluded that the developed
method combining PMHT and IMM, with the inclusion of
IMM based on only two filters, namely, CA and SMM, per-
forms very well in the application discussed in this paper.
The proposed algorithm uses the centroid of observations for
state update and prediction. It avoids implicit observation to
track assignment and hence there is no ambiguity about the
origin of an observation, thereby resolving data association
problem. Moreover, the proposed approach is able to track
an arbitrary trajectory by incorporating multiple target dy-
namic models, in the presence of the dense clutter without
using any a priori information about the target dynamics.
APPENDIX
Optimal estimate for
Φ
(p+1)
t can be obtained using (17):
Φ
(p+1)
t = arg max
(Φt;Πt)
Q
O |
O(p)
+ log p
Φt; Πt
|
Φt−1
(A.1)
by taking derivative of Q(O |
O(p)) and log p((Φt; Πt) |
Φt−1) with respect to π(s) and Φ(s), s = 1, ..., Nt and equat-
ing to zero. Targets are assumed to be independent of each
other. The first term in (17) is obtained from E-step using
10. 10 EURASIP Journal on Image and Video Processing
Tracking failure
Figure 10: n16 clip: tracking with two CA models based on different process noise covariance values [25, 26].
Tracking
failure
Figure 11: n16 clip: tracking with two SMM models based on different process noise covariance values [25, 26].
Successful
tracking
Figure 12: n16 clip: tracking with our proposed PMHT + IMM approach.
(15). The maximization of Q(O |
O(p)) with respect to π(s)
results into (20). Maximization with respect to Φ(s) leads to
∇Φ(s)Q(O |
O(p)
)
=
Nt
s=1
∇Φ(s)
No
j=1
log p
yt(j) | Φt(s)
zt(s, j)
= 0,
(A.2)
where p(yt(j) | Φt(s)) is assumed to be Gaussian and written
as
p
yt(j) | Φt(s)
=
1
√
2π|R|
exp −
yt(j)−h
Φt(s)
T
R−1
yt(j)−h
Φt(s)
,
(A.3)
where R is observation noise covariance matrix. Then, (A.2)
can be written as
Nt
s=1
∇Φ(s)
No
j=1
log
1
√
2π | R |
− yt(j)−h
Φt(s)
T
R−1
yt(j)−h
Φt(s)
zt(s, j)
=
Nt
s=1
∇Φ(s)
No
j=1
− yt(j)
−h
Φt(s)
T
R−1
yt(j)−h
Φt(s)
zt(s, j)
=0.
(A.4)
11. Mukesh A. Zaveri et al. 11
Figure 13: ip24 clip: tracking with our proposed PMHT + IMM
approach.
Trajectory
3
1 2
Figure 14: True trajectory plot for Monte Carlo simulation.
Let exponent
yt(j) − h
Φt(s)
T
R−1
yt(j) − h
Φt(s)
= f
Φt
= f
φ1
t , ..., φM
t
,
(A.5)
where Φt(s) is combined state vector of a target s. Each model
is also assumed to be independent of the other models and
hence state vector due to each model φm
t (s) is also indepen-
dent of the other state vectors. For optimal estimate, deriva-
tive of a function f (Φt(s)) = f (φ1
t , ..., φM
t ) with respect to
Φt leads to a derivative with respect to each φm
t (1 ≤ m ≤ M)
due to independence assumption of each model and it results
into an estimate of
φm
t (s), which can be obtained by solving
φ
m(p+1)
t (s) = argmin
φm
t
yc
t − h
φm
t
T
Rc(−1)
t yc
t − h
φm
t
,
(A.6)
where yc
t and Rc
t are effective observation and effective obser-
vation covariance matrix, respectively, as described in (23)
and (24). Equation (A.6) represents approximated solution
to the exact solution which may be messy due to the term
wt(s, j).
MAP estimate of
Φ
(p+1)
t can be obtained using a priori in-
formation about state, that is, the second term in (17). Using
an independence assumption for each target, a second term
log p((Φt; Πt) |
Φt−1) in (17) can be written as in (19):
log p
Φt; Πt
|
Φt−1
=
Nt
s=1
log p
Φ0(s)
+ log p
Φt(s) |
Φt−1(s)
.
(A.7)
Assumption of each model being independent of the other
assumptions leads to
log p
Φt; Πt
|
Φt−1
=
Nt
s=1
log
M
m=1
pφm
φ0(s)
+log
M
m=1
pφm
φt(s) |
φt−1(s)
=
Nt
s=1
M
m=1
pφm
φ0(s)
+
M
m=1
pφm
φt(s) |
φt−1(s)
,
(A.8)
where pφm (φ0(s)) represents PDF of model m for target s at
time t = 0. Each φm(t) is also assumed to be Gaussian dis-
tributed and written as
pφm
φt |
φt−1
=
1
√
2π|Pt|t−1|
exp −
φt −
φt|t−1
T
P−1
t|t−1
φt −
φt|t−1
.
(A.9)
With an independence assumption for each model and tak-
ing a derivative of the term log p(Φt(s) |
Φt−1(s)) with re-
spect to Φt(s), it is written as
∇Φt(s) log p
Φt(s) |
Φt−1(s)
= ∇Φt(s)
Nt
s=1
log
M
m=1
pφm
φt(s) |
φt−1(s)
= ∇Φt(s)
−
Nt
s=1
M
m=1
φm
t (s) −
φm
t|t−1(s)
T
× P(−1)m
t|t−1 (s)
φm
t (s) −
φm
t|t−1(s)
= −
Nt
s=1
M
m=1
∇φm
t (s)
φm
t (s) −
φm
t|t−1(s)
T
× P(−1)m
t|t−1 (s)
φm
t (s) −
φm
t|t−1(s)
.
(A.10)
Now,
Φt is estimated using (A.4) and (A.10), that is, maxi-
mization of (17) with respect to Φt(s) results into MAP esti-
mate of a state for model m, φm
t (s), and can be obtained by
φ
(p+1)
t = argmin
φt
φ −
φt|t−1
T
P−1
t|t−1
φ −
φt|t−1
+ yc
t − h
φt
T
Rc(−1)
yc
t − h
φt
(A.11)
which can be solved using Kalman filtering.
12. 12 EURASIP Journal on Image and Video Processing
20 40 60
Frame
−3
−2
−1
0
1
X
position
(a)
20 40 60
Frame
−2
−1
0
1
2
X
velocity
(b)
20 40 60
Frame
−1
−0.5
0
0.5
1
X
acceleration
(c)
20 40 60
Frame
−3
−2
−1
0
1
Y
position
(d)
20 40 60
Frame
−3
−2
−1
0
1
2
Y
velocity
(e)
20 40 60
Frame
−1
−0.5
0
0.5
1
Y
acceleration
(f)
Figure 15: Estimation error plot for all state parameters.
20 40 60
Frame
−3
−2
−1
0
1
2
3
X
position
(a)
20 40 60
Frame
−4
−2
0
2
4
X
velocity
(b)
20 40 60
Frame
−1
−0.5
0
0.5
1
Y
acceleration
(c)
20 40 60
Frame
−4
−3
−2
−1
0
1
2
3
Y
position
(d)
20 40 60
Frame
−4
−2
0
2
4
Y
velocity
(e)
20 40 60
Frame
−1
−0.5
0
0.5
1
Y
acceleration
(f)
Figure 16: Prediction error plot for all state parameters.
13. Mukesh A. Zaveri et al. 13
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