The Codex of Business Writing Software for Real-World Solutions 2.pptx
WE2.TO9.4.ppt
1. Meta-optimization of the Extended Kalman filter’s parameters for improved feature extraction on hyper-temporal images. B.P. Salmon 1,2* , W. Kleynhans 1,2 , F. van den Bergh 2 , J.C. Olivier 1 , W.J. Marais 3 and K.J. Wessels 2 1. Department of Electrical Engineering, University of Pretoria, South Africa 2. Remote Sensing Research Unit, Meraka, CSIR, South Africa 3. Space Science and Engineering Center, University of Wisconsin-Madison, Wisconsin, USA * Presenting author
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3. Problem Statement Reliable surveying of land cover and transformation 0.77% 8.11% 5.13% 2.12% 1.71% 0.87% 3.23% 3.11% 2.56% - Change 10,450,000 2008 10,531,300 2009 9,665,841 2007 9,193,800 2006 9,002,534 2005 8,851,455 2004 8,775,200 2003 8,499,900 2002 8,243,719 2001 8,038,200 2000 Estimated Population Year
4. Time Series Analysis MODIS Band 1 MODIS Band 2 Band 2 Separation Band 1 Separation Band 2 Separation Band 1 Separation Band 2 Vegetation Band 1 Vegetation Band 2 Settlement Band 1 Settlement
5. Objective Time series can be modulated with a triply modulated cosine function [1]. [1] W. Kleynhans et. al , 'Improving land cover class separation using an extended Kalman filter on MODIS NDVI time-series data', IEEE Geoscience and Remote Sensing Letters, vol. 6, no. 4. April 2010
6. Objective Parameters of a triply modulated cosine can be used to distinguish between several different land cover classes. Parameters derived using a EKF framework has been proven as a feasible solution. Introduce a meta-optimization approach for setting the parameters of a Extended Kalman filter to rapidly estimate better features for a triply modulated cosine function.
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9. Modelling the time series Unstable parameter Unstable parameter Unstable parameter Mean Amplitude Phase
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11. Tuneable parameters Observation noise covariance matrix Process covariance matrix Initial estimates of state vector Tunable parameters Where j denotes the epoch number
12. What do we want? Mean Amplitude Phase Absolute Error Tunable parameters
13. Creating extreme conditions Absolute Error Tunable parameters Set Capture a probability density function (PDF) for each time increment k using all the pixels and if ideal will be denoted by
14. Creating extreme conditions Tunable parameters Mean Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by
15. Creating extreme conditions Tunable parameters Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by Amplitude
16. Creating extreme conditions Tunable parameters Set Capture a probability density function (PDF) for each time Increment k using all the pixels and if ideal will be denoted by Phase
27. Questions? Expansion of irrigation Commercial forestry Mining Informal settlements Alien tree removal
Editor's Notes
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
www.merka.org.za It is proposed that the NDVI time series be modeled as a triply modulated cosine function in the form: … . To estimate the mean, alpha and phase parameters for each time step k, and extended kalman filter framework was formulated. The EKF statevector was specified as x sub k , the process model specifies the evolution of the state vecor from time step k-1 to k through a possible non-linear function v, in our current formulation, because of the relatively slow variation of state paramters, the state vector at time k to be equal to x sub (k-1). The observation model relates the the state vector to an output.
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