The document summarizes 6LoWPAN, an open IoT networking protocol specified by the IETF. 6LoWPAN allows IPv6 to be used over low-power wireless personal area networks (LoWPANs) by defining an adaptation layer that compresses IPv6 and UDP headers to accommodate the small packet sizes supported by IEEE 802.15.4 networks. It describes how 6LoWPAN uses header compression techniques like IPHC and NHC to reduce header overhead and enable IPv6 connectivity for constrained IoT devices. The document also provides an overview of the Linux-wpan project, which implements 6LoWPAN and IEEE 802.15.4 support in the Linux kernel.
Introduction to Convolutional Codes
Convolutional Encoder Structure
Convolutional Encoder Representation(Vector, Polynomial, State Diagram and Trellis Representations )
Maximum Likelihood Decoder
Viterbi Algorithm
MATLAB Simulation
Hard and Soft Decisions
Bit Error Rate Tradeoff
Consumed Time Tradeoff
This document discusses IoT data processing. It begins by describing wireless sensor networks and key characteristics of IoT devices. It then discusses topics like in-network processing using techniques like data aggregation and Symbolic Aggregate Approximation (SAX). Publish/subscribe protocols like MQTT are also covered. The document emphasizes the need for efficient and scalable solutions to process the large volumes of data generated by IoT devices with limited resources.
The document summarizes key aspects of the Wireless HART network architecture and security mechanism. It describes:
1) The Wireless HART network architecture includes field devices, routers, adapters, access points, and a gateway connected to a network manager.
2) The basic components of Wireless HART are the gateway, network manager, security manager, field devices, repeaters, and adapters. It supports up to 250 devices.
3) Wireless HART implements 128-bit AES encryption for security, using frequency hopping, encryption keys, and device authentication. The security manager generates and manages encryption keys.
This document introduces channel models and channel capacity. It defines a binary symmetric channel (BSC) as a channel with input and output sets of {0,1} and a crossover probability p that an input bit is flipped. A discrete memoryless channel is characterized by a conditional probability matrix relating discrete inputs to outputs. Channel types include single-input single-output, single-input multiple-output, multiple-input single-output, and multiple-input multiple-output. Channel capacity is the maximum mutual information between input and output, achieved by optimizing the input distribution. Capacity examples include relay channels and multiple access channels. The BSC capacity is 1-H(p) where H(p) is the entropy function
The document discusses the key features and architecture of the Internet of Things (IoT). It describes IoT as connecting physical devices through sensors and software to collect and exchange data over networks. The key features discussed are artificial intelligence, interconnectivity, distributed processing, heterogeneity, interoperability, scalability, security, and dynamic changes. The basic IoT architecture includes sensor networks, gateways, and communication technologies to connect devices. Sensor networks gather data from various sensors, while gateways act as an interface between sensor networks and cloud/application services. Common wireless technologies enabling IoT device connectivity include RFID, WLAN, and short-range wireless protocols.
The document discusses optical network survivability, which refers to a network's ability to continue operating during failures. It outlines existing techniques for survivability, including predesigned protection which reserves backup resources in advance, and restoration which chooses backup resources in real-time. The document also compares approaches like shared path protection, traffic control, hybrid preplanned and real-time allocation, and dual homing. It proposes an algorithm for best-effort fast lightpath routing to improve survivability.
The document summarizes 6LoWPAN, an open IoT networking protocol specified by the IETF. 6LoWPAN allows IPv6 to be used over low-power wireless personal area networks (LoWPANs) by defining an adaptation layer that compresses IPv6 and UDP headers to accommodate the small packet sizes supported by IEEE 802.15.4 networks. It describes how 6LoWPAN uses header compression techniques like IPHC and NHC to reduce header overhead and enable IPv6 connectivity for constrained IoT devices. The document also provides an overview of the Linux-wpan project, which implements 6LoWPAN and IEEE 802.15.4 support in the Linux kernel.
Introduction to Convolutional Codes
Convolutional Encoder Structure
Convolutional Encoder Representation(Vector, Polynomial, State Diagram and Trellis Representations )
Maximum Likelihood Decoder
Viterbi Algorithm
MATLAB Simulation
Hard and Soft Decisions
Bit Error Rate Tradeoff
Consumed Time Tradeoff
This document discusses IoT data processing. It begins by describing wireless sensor networks and key characteristics of IoT devices. It then discusses topics like in-network processing using techniques like data aggregation and Symbolic Aggregate Approximation (SAX). Publish/subscribe protocols like MQTT are also covered. The document emphasizes the need for efficient and scalable solutions to process the large volumes of data generated by IoT devices with limited resources.
The document summarizes key aspects of the Wireless HART network architecture and security mechanism. It describes:
1) The Wireless HART network architecture includes field devices, routers, adapters, access points, and a gateway connected to a network manager.
2) The basic components of Wireless HART are the gateway, network manager, security manager, field devices, repeaters, and adapters. It supports up to 250 devices.
3) Wireless HART implements 128-bit AES encryption for security, using frequency hopping, encryption keys, and device authentication. The security manager generates and manages encryption keys.
This document introduces channel models and channel capacity. It defines a binary symmetric channel (BSC) as a channel with input and output sets of {0,1} and a crossover probability p that an input bit is flipped. A discrete memoryless channel is characterized by a conditional probability matrix relating discrete inputs to outputs. Channel types include single-input single-output, single-input multiple-output, multiple-input single-output, and multiple-input multiple-output. Channel capacity is the maximum mutual information between input and output, achieved by optimizing the input distribution. Capacity examples include relay channels and multiple access channels. The BSC capacity is 1-H(p) where H(p) is the entropy function
The document discusses the key features and architecture of the Internet of Things (IoT). It describes IoT as connecting physical devices through sensors and software to collect and exchange data over networks. The key features discussed are artificial intelligence, interconnectivity, distributed processing, heterogeneity, interoperability, scalability, security, and dynamic changes. The basic IoT architecture includes sensor networks, gateways, and communication technologies to connect devices. Sensor networks gather data from various sensors, while gateways act as an interface between sensor networks and cloud/application services. Common wireless technologies enabling IoT device connectivity include RFID, WLAN, and short-range wireless protocols.
The document discusses optical network survivability, which refers to a network's ability to continue operating during failures. It outlines existing techniques for survivability, including predesigned protection which reserves backup resources in advance, and restoration which chooses backup resources in real-time. The document also compares approaches like shared path protection, traffic control, hybrid preplanned and real-time allocation, and dual homing. It proposes an algorithm for best-effort fast lightpath routing to improve survivability.
The document summarizes key concepts from the first chapter of a book on IoT. It defines IoT, outlines its characteristics and components. These include the physical design of IoT devices and their logical design involving identification, sensing, communication and management. It also describes various communication models and levels of IoT systems from single to multiple interconnected devices with local and cloud-based storage, analysis and applications.
This study guide is intended to provide those pursuing the CCNA certification with a framework of what concepts need to be studied. This is not a comprehensive document containing all the secrets of the CCNP nor is it a “braindump” of questions and answers.
I sincerely hope that this document provides some assistance and clarity in your studies.
The document discusses WTLS (Wireless Transport Layer Security), which provides security for wireless communication through cell phones. WTLS is needed to securely enable e-commerce, online banking, and other internet activities via cell phones. It functions similarly to TLS/SSL by providing data integrity, privacy, authentication, and protection against denial-of-service attacks. WTLS specifications include full and abbreviated handshaking protocols to securely establish connections, as well as alert, cipher specification, and record protocols to protect the transmission of data.
Python programming concepts for the Internet of things applications development. This PPT contains details about classes, list , tuples, dictionaries, packages like HTTPLib,SMTPLib, etc
6LoWPAN allows the use of IPv6 over low-power wireless networks. It compresses IPv6 packet headers to accommodate the small packet sizes of low-power wireless standards like 802.15.4. 6LoWPAN finds applications in home automation, healthcare, industrial automation, and environmental monitoring. It defines adaptations for addressing, forwarding, routing, header compression, and security to enable IPv6 connectivity over low-power wireless networks. Implementations of 6LoWPAN exist in open-source operating systems like Contiki and TinyOS, as well as commercial solutions.
Zigbee is a wireless networking technology used for low-power, low data rate applications. It operates in the industrial, scientific and medical radio bands between 868-915MHz and 2.4GHz. Zigbee devices include low-power digital radios, sensors and controls that allow for wireless monitoring and control applications. Zigbee uses mesh networking which allows many devices to interconnect to extend wireless range and connectivity. Its low power consumption allows longer life with smaller batteries. Common applications include wireless lighting, HVAC and security systems.
The eye diagram is a visualization technique used to evaluate the quality of a received digital signal. It reveals the impact of intersymbol interference and noise by showing the variation in sample values and jitter sensitivity of the sampling instant. The eye diagram is created by overlapping traces of symbols and the open part represents the safe sampling region. It allows estimating the bit error rate, with a larger eye opening corresponding to a lower bit error rate.
Internet of Things -Indoor Environmental Monitoring And Control Systemsalim lakade
This document describes an IOT-based indoor environment monitoring and control system. It discusses:
1) The system architecture uses various sensors to monitor indoor conditions and send data to a Raspberry Pi controller over I2C or serial ports.
2) The Raspberry Pi executes instructions to control hardware devices and interact with a server based on sensor readings.
3) The system was tested by monitoring temperature and detecting fires. It showed advantages like remote control, automatic adjustment, and scalability. Future work could expand functions and improve the interface and hardware/software.
OSPF is an intra-domain routing protocol that uses a link-state algorithm to calculate the shortest path to destinations within an autonomous system. It divides an autonomous system into areas to limit routing updates and allows for route summarization between areas. OSPF uses hello packets to discover neighbors, database description packets to exchange routing information, link-state request packets to request updates, and link-state acknowledgment packets to acknowledge receipt of updates.
The document provides an overview of adaptive filters. It discusses that adaptive filters are digital filters that have self-adjusting characteristics to changes in input signals. They have two main components: a digital filter with adjustable coefficients and an adaptive algorithm. Common adaptive algorithms are LMS and RLS. Adaptive filters are used for applications like noise cancellation, system identification, channel equalization, and signal prediction. The key aspects of adaptive filter theory and algorithms like LMS, RLS, Wiener filters are also covered.
The document discusses geo-cast routing protocols, which deliver data packets to nodes within a specified geographic region. It describes two categories of geo-cast protocols: data-transmission oriented protocols, which focus on transmitting information from source to geographic region, and routing creation oriented protocols, which aim to reduce flooding overhead while maintaining delivery accuracy. Specific protocols discussed include Location-Based Multicast, Geo-GRID, Geo-TORA, and mesh-based geo-cast routing. The document concludes by noting open issues like scalability, applications, addressing, and security for geo-cast routing over mobile ad hoc networks.
Understanding GPS & NMEA Messages and Algo to extract Information from NMEA.Robo India
This article is about learning Global Positioning system.
In order to understand GPS, we need to communication protocol of GPS. GPS communicates in NMEA messages.
This document describes NMEA messages and algorithm to extract data.
We welcome all of your queries and views. We are found at-
website- http://roboindia.com
mail-info@roboindia.com
constrained application protocol(CoAP) is a specialized web transfer protocol for use with constrained networks in internet of things and constrained devices such as microcontrollers.
The document discusses the Internet of Things (IoT). It describes the key elements of an IoT architecture as including connected devices that generate data, an aggregator device that acts as an internet gateway, a cloud service that logically aggregates devices for users, communication protocols, an access system for users, and security. It also lists several application areas for IoT, such as agriculture, automotive, construction, health, and more. Example use cases are automated tractors, self-driving cars, smart buildings, wearables, and predictive maintenance.
The document describes the iCore project which aims to develop an open cognitive framework for empowering the Internet of Things. It discusses:
- The project details including partners, duration, budget.
- The iCore concept of virtual and composite virtual objects to represent real and digital objects.
- The technical challenges of addressing interoperability, reusability, reliability and energy efficiency.
- The technical approach including cognitive mechanisms, semantic descriptions and context awareness.
- The work organization split into clusters for technology, implementation, use case definition and management.
- Potential application domains and example use cases like smart cities, transport, homes and businesses.
- Engagement of an external stakeholders group
This document discusses communications network requirements for substation automation. It describes how utilities are adopting IP and Ethernet-based intelligent electronic devices (IEDs) to improve grid performance and efficiency. This requires new communications network infrastructures within substations and between substations and control centers to handle increased traffic. The document outlines architectures that segment intra-substation and wide area network communications according to standards like IEC 61850. It also provides an example case study of a smart substation project in France where Nokia is implementing digital substations for grid improvements.
The Sky X technology transparently enhances performance for users on a satellite network. It increases web performance by 3 times and file transfer speeds by 10 to 100 times by overcoming limitations of TCP protocols over satellite connections. The Sky X gateway replaces TCP with the Xpress Transport Protocol for the satellite link, improving throughput while remaining transparent to users and compatible with internet infrastructure. The Sky X system maximizes available bandwidth and is well-suited for satellite communication and remote network access.
The document describes a module called fft_16 that implements a 16 point fast Fourier transform (FFT). It takes in input signals x0 to x15 and parameters w0 to w7. It performs the FFT in 3 stages using butterfly operations defined in submodules bfly1 to bfly4. The results y0 to y15 are output based on a select signal.
This document discusses data link layer protocols. It covers topics such as framing, flow control, error control, protocols for noisy and noiseless channels, and HDLC. Specific protocols discussed include stop-and-wait, go-back-N ARQ, and selective repeat ARQ. Examples are provided to illustrate how these protocols handle frame transmission and retransmission in different scenarios.
The document summarizes key concepts from the first chapter of a book on IoT. It defines IoT, outlines its characteristics and components. These include the physical design of IoT devices and their logical design involving identification, sensing, communication and management. It also describes various communication models and levels of IoT systems from single to multiple interconnected devices with local and cloud-based storage, analysis and applications.
This study guide is intended to provide those pursuing the CCNA certification with a framework of what concepts need to be studied. This is not a comprehensive document containing all the secrets of the CCNP nor is it a “braindump” of questions and answers.
I sincerely hope that this document provides some assistance and clarity in your studies.
The document discusses WTLS (Wireless Transport Layer Security), which provides security for wireless communication through cell phones. WTLS is needed to securely enable e-commerce, online banking, and other internet activities via cell phones. It functions similarly to TLS/SSL by providing data integrity, privacy, authentication, and protection against denial-of-service attacks. WTLS specifications include full and abbreviated handshaking protocols to securely establish connections, as well as alert, cipher specification, and record protocols to protect the transmission of data.
Python programming concepts for the Internet of things applications development. This PPT contains details about classes, list , tuples, dictionaries, packages like HTTPLib,SMTPLib, etc
6LoWPAN allows the use of IPv6 over low-power wireless networks. It compresses IPv6 packet headers to accommodate the small packet sizes of low-power wireless standards like 802.15.4. 6LoWPAN finds applications in home automation, healthcare, industrial automation, and environmental monitoring. It defines adaptations for addressing, forwarding, routing, header compression, and security to enable IPv6 connectivity over low-power wireless networks. Implementations of 6LoWPAN exist in open-source operating systems like Contiki and TinyOS, as well as commercial solutions.
Zigbee is a wireless networking technology used for low-power, low data rate applications. It operates in the industrial, scientific and medical radio bands between 868-915MHz and 2.4GHz. Zigbee devices include low-power digital radios, sensors and controls that allow for wireless monitoring and control applications. Zigbee uses mesh networking which allows many devices to interconnect to extend wireless range and connectivity. Its low power consumption allows longer life with smaller batteries. Common applications include wireless lighting, HVAC and security systems.
The eye diagram is a visualization technique used to evaluate the quality of a received digital signal. It reveals the impact of intersymbol interference and noise by showing the variation in sample values and jitter sensitivity of the sampling instant. The eye diagram is created by overlapping traces of symbols and the open part represents the safe sampling region. It allows estimating the bit error rate, with a larger eye opening corresponding to a lower bit error rate.
Internet of Things -Indoor Environmental Monitoring And Control Systemsalim lakade
This document describes an IOT-based indoor environment monitoring and control system. It discusses:
1) The system architecture uses various sensors to monitor indoor conditions and send data to a Raspberry Pi controller over I2C or serial ports.
2) The Raspberry Pi executes instructions to control hardware devices and interact with a server based on sensor readings.
3) The system was tested by monitoring temperature and detecting fires. It showed advantages like remote control, automatic adjustment, and scalability. Future work could expand functions and improve the interface and hardware/software.
OSPF is an intra-domain routing protocol that uses a link-state algorithm to calculate the shortest path to destinations within an autonomous system. It divides an autonomous system into areas to limit routing updates and allows for route summarization between areas. OSPF uses hello packets to discover neighbors, database description packets to exchange routing information, link-state request packets to request updates, and link-state acknowledgment packets to acknowledge receipt of updates.
The document provides an overview of adaptive filters. It discusses that adaptive filters are digital filters that have self-adjusting characteristics to changes in input signals. They have two main components: a digital filter with adjustable coefficients and an adaptive algorithm. Common adaptive algorithms are LMS and RLS. Adaptive filters are used for applications like noise cancellation, system identification, channel equalization, and signal prediction. The key aspects of adaptive filter theory and algorithms like LMS, RLS, Wiener filters are also covered.
The document discusses geo-cast routing protocols, which deliver data packets to nodes within a specified geographic region. It describes two categories of geo-cast protocols: data-transmission oriented protocols, which focus on transmitting information from source to geographic region, and routing creation oriented protocols, which aim to reduce flooding overhead while maintaining delivery accuracy. Specific protocols discussed include Location-Based Multicast, Geo-GRID, Geo-TORA, and mesh-based geo-cast routing. The document concludes by noting open issues like scalability, applications, addressing, and security for geo-cast routing over mobile ad hoc networks.
Understanding GPS & NMEA Messages and Algo to extract Information from NMEA.Robo India
This article is about learning Global Positioning system.
In order to understand GPS, we need to communication protocol of GPS. GPS communicates in NMEA messages.
This document describes NMEA messages and algorithm to extract data.
We welcome all of your queries and views. We are found at-
website- http://roboindia.com
mail-info@roboindia.com
constrained application protocol(CoAP) is a specialized web transfer protocol for use with constrained networks in internet of things and constrained devices such as microcontrollers.
The document discusses the Internet of Things (IoT). It describes the key elements of an IoT architecture as including connected devices that generate data, an aggregator device that acts as an internet gateway, a cloud service that logically aggregates devices for users, communication protocols, an access system for users, and security. It also lists several application areas for IoT, such as agriculture, automotive, construction, health, and more. Example use cases are automated tractors, self-driving cars, smart buildings, wearables, and predictive maintenance.
The document describes the iCore project which aims to develop an open cognitive framework for empowering the Internet of Things. It discusses:
- The project details including partners, duration, budget.
- The iCore concept of virtual and composite virtual objects to represent real and digital objects.
- The technical challenges of addressing interoperability, reusability, reliability and energy efficiency.
- The technical approach including cognitive mechanisms, semantic descriptions and context awareness.
- The work organization split into clusters for technology, implementation, use case definition and management.
- Potential application domains and example use cases like smart cities, transport, homes and businesses.
- Engagement of an external stakeholders group
This document discusses communications network requirements for substation automation. It describes how utilities are adopting IP and Ethernet-based intelligent electronic devices (IEDs) to improve grid performance and efficiency. This requires new communications network infrastructures within substations and between substations and control centers to handle increased traffic. The document outlines architectures that segment intra-substation and wide area network communications according to standards like IEC 61850. It also provides an example case study of a smart substation project in France where Nokia is implementing digital substations for grid improvements.
The Sky X technology transparently enhances performance for users on a satellite network. It increases web performance by 3 times and file transfer speeds by 10 to 100 times by overcoming limitations of TCP protocols over satellite connections. The Sky X gateway replaces TCP with the Xpress Transport Protocol for the satellite link, improving throughput while remaining transparent to users and compatible with internet infrastructure. The Sky X system maximizes available bandwidth and is well-suited for satellite communication and remote network access.
The document describes a module called fft_16 that implements a 16 point fast Fourier transform (FFT). It takes in input signals x0 to x15 and parameters w0 to w7. It performs the FFT in 3 stages using butterfly operations defined in submodules bfly1 to bfly4. The results y0 to y15 are output based on a select signal.
This document discusses data link layer protocols. It covers topics such as framing, flow control, error control, protocols for noisy and noiseless channels, and HDLC. Specific protocols discussed include stop-and-wait, go-back-N ARQ, and selective repeat ARQ. Examples are provided to illustrate how these protocols handle frame transmission and retransmission in different scenarios.
Fast fading, Slow fading and Multipath effect in wireless communicationsPei-Che Chang
Fast fading, Slow fading and multipath effect in wireless communications
QPSK in AWGN channel
QPSK in AWGN + Rayleigh fading channel
using GNU Octave simulation
8. 鲁道夫·卡尔曼(Rudolf Emil Kalman, 1930年5
月-),匈牙利数学家,1930年出生于匈牙利
首都布达佩斯 1953 1954年于麻省理工学院首都布达佩斯。1953-1954年于麻省理工学院
分别获得电机工程学士及硕士学位。1957年于
哥伦比亚大学获得博士学位 曾任职于斯坦福哥伦比亚大学获得博士学位。曾任职于斯坦福
大学,佛罗里达大学,瑞士苏黎世联邦理工学
院院
Kalman filter invented in 1960 by R. E. Kalman
17. Kalman滤波器的产生,是为了摆脱那些对没有
任何物理意义的观测数据本身进行的信号处理,
通过分析系统属性,建立精确的系统数学模型,
模型来辅 测 从 提高对系统 估计精用模型来辅助预测,从而提高对系统的估计精
度。Kalman正是一种连接(或者说融合)系统
模型和观测数据的纽带 有机的结合了两者的模型和观测数据的纽带。有机的结合了两者的
优势。
The Kalman filter uses a system's dynamics model (i e physical The Kalman filter uses a system s dynamics model (i.e., physical
laws of motion), known control inputs to that system, and
measurements (such as from sensors) to form an estimate of the
system's varying quantities (its state) that is better than thesystem s varying quantities (its state) that is better than the
estimate obtained by using any one measurement alone. As such,
it is a common sensor fusion algorithm.
22. 事 定义:在给定一定的“信息”之后,发生某事
件的概率。
数学表达:假设已知信息是z,事件为x
( | ), zP x z x 事件空间, 条件空间
例子1:投硬币
假设“信息”z:此次投的不是正面(1)
( | ),
息 是
例子2:掷骰子
( 1| ) 0, ( 0 | ) 100P x z P x z
例子2:掷骰子
假设“信息”z:此次掷的不是1
( 1| ) 0, ( 2,3,4,5,6 | ) 1/ 5P x z P x z
23. 期望:
方差:
( ) ( ) , ( ) i iE x xf x dx E x x P
2
([ ( )] )E X E X
协方差: (( ( ))( ( )))E X E X Y E Y
( ( ) ( ) ( ) ( ))E XY XE Y YE X E X E Y
( ) ( ( )) ( ( )) ( ( ) ( ))E XY E XE Y E YE X E E X E Y
( ) ( ) ( ) ( ) ( ) ( ) ( )E XY E X E Y E Y E X E X E Y ( ) ( ) ( ) ( ) ( ) ( ) ( )E XY E X E Y E Y E X E X E Y
( ) ( ) ( )E XY E X E Y
24. 态 系统方程(状态方程):
1 1 1k k k kx Ax Bu w
举例1:自由落体物体速度为 ,信号采集频率
为100Hz,该系统状态方程为
kx
举例2:匀速运动小车,速度为c(m/s),设位移
1 1/100k k kx x g w
举 车 度为 ( ) 位移
为 ,位移采集频率为1Hz,该系统状态方程
为
kx
1 1k k kx x c w
25. 测量方程:
k k kz Hx v
举例1:自由落体物体速度为 ,传感器为风力
测速计,该系统测量方程为
kx
举例2:匀速运动小车,传感器选用GPS传感器,
k k kz x v
举 车 传 选 传
该系统测量方程为tx
1k k kx x v
26. 随机变量 和 分别代表过程噪声和测量噪声,
它们是独立不相关且正太分布的白噪声。
kw kv
它们是独立不相关且正太分布的白噪声。
其中Q和R分别是过程噪声和测量噪声的协方差
( ) (0, ), ( ) (0, ).p w N Q p v N R
其中Q和R分别是过程噪声和测量噪声的协方差
矩阵。
完整的Kalman滤波器表达式:完整的Kalman滤波器表达式:
1 1 1k k k kx Ax Bu w ( ) (0, )p w N Q
k k kz Hx v ( ) (0, )p v N R
小提示:在实际的系统中,A,B,H,Q和R可能在系统运行过程
中会发生变化
比如:惯导数据比如:惯导数据
27. 贝叶斯原理。
( | ) ( )
( | )k kP x z
( | ) ( )
( | )
( )
k k k
k k
k
p z x p x
P x z
p z
( | ) ( )
1
1
( | ) ( | )
( | )
k k k k
k k
p z x p x z
p z z
1
1
( , | ) ( )
( , )
k k k k
k k
p z z x p x
p z z
( | ) ( | ) ( )1 1
1 1
( | , ) ( | ) ( )
( | ) ( )
k k k k k k
k k k
p z z x p z x p x
p z z p z
1 1 1
1 1
( | , ) ( | ) ( ) ( )
( | ) ( ) ( )
k k k k k k k
k k k k
p z z x p x z p z p x
p z z p z p x
1
1
( | ) ( | )
( | )
k k k k
k k
p z x p x z
p z z
(1)
1( | )k kp
28. 贝叶斯原理。 ( | )k kP x z
1
1
( | ) ( | )
( | )
k k k k
k k
p z x p x z
p z z
状态方程
X(k)=AX(k-1)
29. 贝叶斯原理。 X(k) ( | )k kP x z
1
1
( | ) ( | )
( | )
k k k k
k k
p z x p x z
p z z
状态方程
X(k)=AX(k-1)
1 1( | ) ( , )k k kP x x N Ax Q 1 1( | ) ( , )k k k Q
30. 贝叶斯原理。 X(k) ( | )k kP x z
1
1
( | ) ( | )
( | )
k k k k
k k
p z x p x z
p z z
状态方程
X(k)=AX(k-1)
测量方程
Z(k)=HX(k)
1 1( | ) ( , )k k kP x x N Ax Q 1 1( | ) ( , )k k k Q
31. 贝叶斯原理。 X(k) ( | )k kP x z
1
1
( | ) ( | )
( | )
k k k k
k k
p z x p x z
p z z
测量方程
Z(k)=HX(k)
状态方程
X(k)=AX(k-1)
X(k)
1 1( | ) ( , )k k kP x x N Ax Q ( | ) ( , )k k kP z x N Hx R(2) (3)1 1( | ) ( , )k k k Q ( | ) ( , )k k k
1 1 1( | ) ( | )k k k kP x x P x z dx 1( | )k kP x z
( )
(4)
32. 假设 是给定上一步给出 的先验状态估计。
假设 是给定了当前测量值 的后验状态估计
ˆ n
kx
1kx
ˆ n
假设 是给定了当前测量值 的后验状态估计。
我们定义先验和后验估计误差为:
ˆ n
kx kz
ˆk k ke x x
ˆe x x
(5)
(6)
那么,先验估计误差的协方差矩阵为:
k k ke x x (6)
那 计 阵
( )T
k k kP E e e
(7)
后验估计误差的协方差矩阵为:
T (8)( )T
k k kP E e e (8)
39. M b k P S 1979 S h i M d l E i i d Maybeck, Peter S. 1979. Stochastic Models, Estimation, and
Control, Volume 1, Academic Press, Inc.
Brown, R. G. and P. Y. C. Hwang. 1992. Introduction to Random
Signals and Applied Kalman Filtering, Second Edition, John Wiley
& Sons, Inc.
Grewal, Mohinder S., and Angus P. Andrews (1993). Kalman, , g ( )
Filtering Theory and Practice. Upper Saddle River, NJ USA,
Prentice Hall.
Greg Welch and Gary Bishop. An Introduction to the Kalman Greg Welch and Gary Bishop. An Introduction to the Kalman
Filter