Estimation with Applications to Tracking and Navigation Theory Algorithms and Software,9780471416555

Estimation with Applications to Tracking and Navigation Theory Algorithms and Software

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Edition: 1st
ISBN13: 9780471416555
ISBN10: 047141655X
Format: Hardcover
Pub. Date: 2001-06-25
Publisher(s): Wiley-Interscience
List Price: $195.14

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Summary

Expert coverage of the design and implementation of state estimation algorithms for tracking and navigation Estimation with Applications to Tracking and Navigation treats the estimation of various quantities from inherently inaccurate remote observations. It explains state estimator design using a balanced combination of linear systems, probability, and statistics. The authors provide a review of the necessary background mathematical techniques and offer an overview of the basic concepts in estimation. They then provide detailed treatments of all the major issues in estimation with a focus on applying these techniques to real systems. Other features include: * Problems that apply theoretical material to real-world applications * In-depth coverage of the Interacting Multiple Model (IMM) estimator * Companion DynaEst(TM) software for MATLAB(TM) implementation of Kalman filters and IMM estimators * Design guidelines for tracking filters Suitable for graduate engineering students and engineers working in remote sensors and tracking, Estimation with Applications to Tracking and Navigation provides expert coverage of this important area.

Author Biography

YAAKOV BAR-SHALOM, PhD, is Distinguished Professor in the Department of Electrical and Computer Engineering and Director of the Estimation and Signal Processing Lab at the University of Connecticut in Storrs. <BR>

Table of Contents

Preface xvii
Acronyms xxi
Mathematical Notations xxii
Introduction
1(88)
Background
1(14)
Estimation and Related Areas
1(2)
Applications of Estimation
3(1)
Preview of Estimation/Filtering
4(6)
An Example of State Estimation: Vehicle Collision Avoidance
10(5)
Scope of the Text
15(4)
Objectives
15(1)
Overview and Chapter Prerequisites
16(3)
Brief Review of Linear Algebra and Linear Systems
19(12)
Definitions and Notations
19(1)
Some Linear Algebra Operations
20(1)
Inversion and the Determinant of a Matrix
21(2)
Orthogonal Projection of Vectors
23(1)
The Gradient, Jacobian and Hessian
24(1)
Eigenvalues, Eigenvectors, and Quadratic Forms
25(2)
Continuous-Time Linear Dynamic Systems - Controllability and Observability
27(2)
Discrete-Time Linear Dynamic Systems - Controllability and Observability
29(2)
Brief Review of Probability Theory
31(41)
Events and the Axioms of Probability
31(2)
Random Variables and Probability Density Function
33(2)
Probability Mass Function
35(1)
Mixed Random Variable and Mixed Probability-PDF
36(1)
Expectations and Moments of a Scalar Random Variable
37(1)
Joint PDF of Two Random Variables
38(3)
Independent Events and Independent Random Variables
41(1)
Vector-Valued Random Variables and Their Moments
41(3)
Conditional Probability and PDF
44(1)
The Total Probability Theorem
45(2)
Bayes' Formula
47(3)
Conditional Expectations and Their Smoothing Property
50(1)
Gaussian Random Variables
51(1)
Joint and Conditional Gaussian Random Variables
52(2)
Expected Value of Quadratic and Quartic Forms
54(1)
Mixture Probability Density Functions
55(2)
Chi-Square Distributed Random Variables
57(3)
Weighted Sum of Chi-Square Random Variables
60(1)
Random Processes
61(4)
Random Walk and the Wiener Process
65(1)
Markov Processes
66(3)
Random Sequences, Markov Sequences and Markov Chains
69(1)
The Law of Large Numbers and the Central Limit Theorem
70(2)
Brief Review of Statistics
72(13)
Hypothesis Testing
72(2)
Confidence Regions and Significance
74(5)
Monte Carlo Runs and Comparison of Algorithms
79(3)
Tables of the Chi-Square and Gaussian Distributions
82(3)
Notes and Problems
85(4)
Bibliographical Notes
85(1)
Problems
85(4)
Basic Concepts in Estimation
89(32)
Introduction
89(1)
Outline
89(1)
Basic Concepts - Summary of Objectives
89(1)
The Problem of Parameter Estimation
90(2)
Definitions
90(1)
Models for Estimation of a Parameter
91(1)
Maximum Likelihood and Maximum a Posteriori Estimators
92(6)
Definitions of ML and MAP Estimators
92(1)
MLE vs. MAP Estimator with Gaussian Prior
92(2)
MAP Estimator with One-Sided Exponential Prior
94(1)
MAP Estimator with Diffuse Prior
95(1)
The Sufficient Statistic and the Likelihood Equation
96(2)
Least Squares and Minimum Mean Square Error Estimation
98(3)
Definitions of LS and MMSE Estimators
98(2)
Some LS Estimators
100(1)
MMSE vs. MAP Estimator in Gaussian Noise
100(1)
Unbiased Estimators
101(3)
Definition
101(1)
Unbiasedness of an ML and a MAP Estimator
102(1)
Bias in the ML Estimation of Two Parameters
102(2)
The Variance and MSE of an Estimator
104(4)
Definitions of Estimator Variances
104(1)
Comparison of Variances of an ML and a MAP Estimator
105(1)
The Variances of the Sample Mean and Sample Variance
106(1)
Estimation of the Probability of an Event
107(1)
Consistency and Efficiency of Estimators
108(6)
Consistency
108(1)
The Cramer-Rao Lower Bound and the Fisher Information Matrix
109(1)
Proof of the Cramer-Rao Lower Bound
110(2)
An Example of Efficient Estimator
112(1)
Large Sample Properties of the ML Estimator
113(1)
Summary
114(1)
Summary of Estimators
114(1)
Summary of Estimator Properties
115(1)
Notes and Problems
115(6)
Bibliographical Notes
115(1)
Problems
116(5)
Linear Estimation in Static Systems
121(58)
Introduction
121(1)
Outline
121(1)
Linear Estimation in Static Systems - Summary of Objectives
121(1)
Estimation of Gaussian Random Vectors
122(1)
The Conditional Mean and Covariance for Gaussian Random Vectors
122(1)
Estimation of Gaussian Random Vectors - Summary
123(1)
Linear Minimum Mean Square Error Estimation
123(6)
The Principle of Orthogonality
123(4)
Linear MMSE Estimation for Vector Random Variables
127(2)
Linear MMSE Estimation - Summary
129(1)
Least Squares Estimation
129(17)
The Batch LS Estimation
129(3)
The Recursive LS Estimator
132(3)
Examples and Incorporation of Prior Information
135(2)
Nonlinear LS - An Example
137(8)
LS Estimation - Summary
145(1)
Polynomial Fitting
146(8)
Fitting a First-Order Polynomial to Noisy Measurements
146(3)
Fitting a General Polynomial to a Set of Noisy Measurements
149(3)
Mapping of the Estimates to an Arbitrary Time
152(2)
Polynomial Fitting - Summary
154(1)
Goodness-of-Fit and Statistical Significance of Parameter Estimates
154(7)
Hypothesis Testing Formulation of the Problem
154(2)
The Fitting Error in a Least Squares Estimation Problem
156(3)
A Polynomial Fitting Example
159(2)
Order Selection in Polynomial Fitting - Summary
161(1)
Use of LS for a Nonlinear Problem: Bearings-Only Target Motion Analysis
161(11)
The Problem
161(1)
Observability of the Target Parameter in Passive Localization
162(1)
The Likelihood Function for Target Parameter Estimation
163(1)
The Fisher Information Matrix for the Target Parameter
164(3)
The Goodness-of-Fit Test
167(1)
Testing for Efficiency with Monte Carlo Runs
168(1)
A Localization Example
169(1)
Passive Localization - Summary
169(3)
Notes, Problems and a Project
172(7)
Bibliographical Notes
172(1)
Problems
172(4)
Project: An Interactive Program for Bearings-Only Target Localization
176(3)
Linear Dynamic Systems with Random Inputs
179(20)
Introduction
179(1)
Outline
179(1)
Linear Stochastic Systems - Summary of Objectives
179(1)
Continuous-Time Linear Stochastic Dynamic Systems
180(7)
The Continuous-Time State-Space Model
180(1)
Solution of the Continuous-Time State Equation
181(2)
The State as a Markov Process
183(1)
Propagation of the State's Mean and Covariance
184(1)
Frequency Domain Approach
185(2)
Discrete-Time Linear Stochastic Dynamic Systems
187(8)
The Discrete-Time State-Space Model
187(2)
Solution of the Discrete-Time State Equation
189(1)
The State as a Markov Process
190(1)
Propagation of the State's Mean and Covariance
191(1)
Frequency Domain Approach
192(3)
Summary
195(1)
Summary of State Space Representation
195(1)
Summary of Prewhitening
195(1)
Notes and Problems
196(3)
Bibliographical Notes
196(1)
Problems
196(3)
State Estimation in Discrete-Time Linear Dynamic Systems
199(68)
Introduction
199(1)
Outline
199(1)
Discrete-Time Linear Estimation - Summary of Objectives
199(1)
Linear Estimation in Dynamic Systems - the Kalman Filter
200(18)
The Dynamic Estimation Problem
200(2)
Dynamic Estimation as a Recursive Static Estimation
202(2)
Derivation of the Dynamic Estimation Algorithm
204(3)
Overview of the Kalman Filter Algorithm
207(4)
The Matrix Riccati Equation
211(2)
Properties of the Innovations and the Likelihood Function of the System Model
213(1)
The Innovations Representation
214(1)
Some Orthogonality Properties
215(1)
The Kalman Filter - Summary
215(3)
Example of a Filter
218(14)
The Model
218(1)
Results for a Kalman Filter
219(1)
A Step-by-Step Demonstration of DynaEstTM
219(13)
Consistency of State Estimators
232(13)
The Problem of Filter Consistency
232(2)
Definition and the Statistical Tests for Filter Consistency
234(3)
Examples of Filter Consistency Testing
237(6)
Absolute Errors
243(1)
Filter Consistency - Summary
244(1)
Initialization of State Estimators
245(3)
Initialization and Consistency
245(1)
Initialization in Simulations
246(1)
A Practical Implementation in Tracking
247(1)
Filter Initialization - Summary
248(1)
Sensitivity
248(13)
Model Mismatch
249(5)
Reduced-Order Filters
254(2)
Suboptimal Gains
256(1)
Examples of Modeling Errors and Filter Approximations
256(5)
Notes and Problems
261(6)
Bibliographical Notes
261(1)
Problems
261(4)
Computer Applications
265(2)
Estimation for Kinematic Models
267(34)
Introduction
267(1)
Outline
267(1)
Kinematic Models - Summary of Objectives
267(1)
Discretized Continuous-Time Kinematic Models
268(4)
The Kinematic Models
268(1)
Continuous White Noise Acceleration Model
269(1)
Continuous Wiener Process Acceleration Model
270(2)
Direct Discrete-Time Kinematic Models
272(4)
Introduction
272(1)
Discrete White Noise Acceleration Model
273(1)
Discrete Wiener Process Acceleration Model
274(1)
Kinematic Models - Summary
275(1)
Explicit Filters for Noiseless Kinematic Models
276(1)
LS Estimation for Noiseless Kinematic Models
276(1)
The KF for Noiseless Kinematic Models
276(1)
Steady-State Filters for Noisy Kinematic Models
277(17)
The Problem
277(1)
Derivation Methodology for the Alpha-Beta Filter
278(2)
The Alpha-Beta Filter for the DWNA Model
280(6)
The Alpha-Beta Filter for the Discretized CWNA Model
286(3)
The Alpha-Beta-Gamma Filter for the DWPA Model
289(3)
A System Design Example for Sampling Rate Selection
292(1)
Alpha-Beta and Alpha-Beta-Gamma Filters - Summary
293(1)
Notes and Problems
294(7)
Bibliographical Notes
294(1)
Problems
295(6)
Computational Aspects of Estimation
301(18)
Introduction
301(2)
Implementation of Linear Estimation
301(1)
Outline
302(1)
Computational Aspects - Summary of Objectives
303(1)
The Information Filter
303(5)
Recursions for the Information Matrices
303(3)
Overview of the Information Filter Algorithm
306(1)
Recursion for the Information Filter State
307(1)
Sequential Processing of Measurements
308(3)
Block vs. Sequential Processing
308(1)
The Sequential Processing Algorithm
309(2)
Square-Root Filtering
311(6)
The Steps in Square-Root Filtering
311(1)
The LDL' Factorization
312(1)
The Predicted State Covariance
312(2)
The Filter Gain and the Updated State Covariance
314(1)
Overview of the Square-Root Sequential Scalar Update Algorithm
315(1)
The Gram-Schmidt Orthogonalization Procedure
315(2)
Notes and Problems
317(2)
Bibliographical Notes
317(1)
Problems
317(2)
Extensions of Discrete-Time Linear Estimation
319(22)
Introduction
319(1)
Outline
319(1)
Extensions of Estimation - Summary of Objectives
319(1)
Autocorrelated Process Noise
320(4)
The Autocorrelated Process Noise Problem
320(1)
An Exponentially Autocorrelated Noise
321(1)
The Augmented State Equations
322(2)
Estimation with Autocorrelated Process Noise - Summary
324(1)
Cross-Correlated Measurement and Process Noise
324(3)
Cross-Correlation at the Same Time
324(2)
Cross-Correlation One Time Step Apart
326(1)
State Estimation with Decorrelated Noise Sequences - Summary
327(1)
Autocorrelated Measurement Noise
327(3)
Whitening of the Measurement Noise
327(2)
The Estimation Algorithm with the Whitened Measurement Noise
329(1)
Autocorrelated Measurement Noise - Summary
330(1)
Prediction
330(3)
Types of Prediction
330(1)
The Algorithms for the Different Types of Prediction
330(2)
Prediction - Summary
332(1)
Smoothing
333(5)
Types of Smoothing
333(1)
Fixed-Interval Smoothing
334(3)
Overview of Smoothing
337(1)
Smoothing - Summary
338(1)
Notes and Problems
338(3)
Bibliographical Notes
338(1)
Problems
338(3)
Continuous-Time Linear State Estimation
341(30)
Introduction
341(1)
Outline
341(1)
Continuous-Time Estimation - Summary of Objectives
341(1)
The Continuous-Time Linear State Estimation Filter
342(13)
The Continuous-Time Estimation Problem
342(1)
Connection Between Continuous - and Discrete-Time Representations and Their Noise Statistics
343(2)
The Continuous-Time Filter Equations
345(2)
The Continuous-Time Innovation
347(2)
Asymptotic Properties of the Continuous-Time Riccati Equation
349(2)
Examples of Continuous-Time Filters
351(2)
Overview of the Kalman-Bucy Filter
353(1)
Continuous-Time State Estimation - Summary
354(1)
Prediction and The Continuous-Discrete Filter
355(3)
Prediction of the Mean and Covariance
355(1)
The Various Types of Prediction
356(1)
The Continuous-Discrete Filter
357(1)
Duality of Estimation and Control
358(4)
The Two Problems
358(1)
The Solutions to the Estimation and the Control Problems
359(1)
Properties of the Solutions
360(2)
The Wiener-Hopf Problem
362(4)
Formulation of the Problem
362(1)
The Wiener-Hopf Equation
362(4)
Notes and Problems
366(5)
Bibliographical Notes
366(1)
Problems
367(4)
State Estimation For Nonlinear Dynamic Systems
371(50)
Introduction
371(1)
Outline
371(1)
Nonlinear Estimation - Summary of Objectives
371(1)
Estimation in Nonlinear Stochastic Systems
372(9)
The Model
372(1)
The Optimal Estimator
373(1)
Proof of the Recursion of the Conditional Density of the State
374(2)
Example of Linear vs. Nonlinear Estimation of a Parameter
376(3)
Estimation in Nonlinear Systems with Additive Noise
379(2)
Optimal Nonlinear Estimation - Summary
381(1)
The Extended Kalman Filter
381(14)
Approximation of the Nonlinear Estimation Problem
381(2)
Derivation of the EKF
383(2)
Overview of the EKF Algorithm
385(2)
An Example: Tracking with an Angle-Only Sensor
387(7)
The EKF - Summary
394(1)
Error Compensation in Linearized Filters
395(9)
Some Heuristic Methods
395(1)
An Example of Use of the Fudge Factor
396(1)
An Example of Debiasing: Conversion from Polar to Cartesian
397(5)
Error Compensation in Linearized Filters - Summary
402(2)
Some Error Reduction Methods
404(3)
Improved State Prediction
404(1)
The Iterated Extended Kalman Filter
404(3)
Some Error Reduction Methods - Summary
407(1)
Maximum a Posteriori Trajectory Estimation Via Dynamic Programming
407(2)
The Approach
407(1)
The Dynamic Programming for Trajectory Estimation
408(1)
Nonlinear Continuous-Discrete Filter
409(5)
The Model
409(1)
The Fokker-Planck Equation
410(3)
Example
413(1)
Notes, Problems and a Project
414(7)
Bibliographical Notes
414(1)
Problems
414(5)
Project - Nonlinear Filtering with Angle-Only Measurements
419(2)
Adaptive Estimation and Maneuvering Targets
421(70)
Introduction
421(3)
Adaptive Estimation - Outline
421(2)
Adaptive Estimation - Summary of Objectives
423(1)
Adjustable Level Process Noise
424(3)
Continuous Noise Level Adjustment
424(1)
Process Noise with Several Discrete Levels
424(2)
Adjustable Level Process Noise - Summary
426(1)
Input Estimation
427(4)
The Model
427(1)
The Innovations as a Linear Measurement of the Unknown Input
428(1)
Estimation of the Unknown Input
429(1)
Correction of the State Estimate
430(1)
Input Estimation - Summary
431(1)
The Variable State Dimension Approach
431(4)
The Approach
431(1)
The Maneuver Detection and Model Switching
432(1)
Initialization of the Augmented Model
433(1)
VSD Approach - Summary
434(1)
A Comparison of Adaptive Estimation Methods for Maneuvering Targets
435(6)
The Problem
435(1)
The White Noise Model with Two Levels
436(1)
The IE and VSD Methods
436(2)
Statistical Test for Comparison of the IE and VSD Methods
438(2)
Comparison of Several Algorithms - Summary
440(1)
The Multiple Model Approach
441(25)
Formulation of the Approach
441(1)
The Static Multiple Model Estimator
441(3)
The Dynamic Multiple Model Estimator
444(3)
The GPB1 Multiple Model Estimator for Switching Models
447(2)
The GPB2 Multiple Model Estimator for Switching Models
449(4)
The Interacting Multiple Model Estimator
453(4)
An Example with the IMM Estimator
457(3)
Use of DynaEst™ to Design an IMM Estimator
460(5)
The Multiple Model Approach - Summary
465(1)
Design of an IMM Estimator for ATC Tracking
466(10)
ATC Motion Models
466(2)
The EKF for the Coordinated Tum Model
468(2)
Selection of Models and Parameters
470(1)
The ATC Scenario
471(1)
Results and Discussion
472(4)
When is an IMM Estimator Needed?
476(5)
Kalman Filter vs. IMM Estimator
477(4)
Use of EKF for Simultaneous State and Parameter Estimation
481(3)
Augmentation of the State
481(1)
An Example of Use of the EKF for Parameter Estimation
482(2)
EKF for Parameter Estimation - Summary
484(1)
Notes, Problems, and Term Project
484(7)
Bibliographical Notes
484(1)
Problems
485(3)
Term Project - IMM Estimator for Air Traffic Control
488(3)
Introduction to Navigation Applications
491(46)
Introduction
491(1)
Navigation Applications - Outline
491(1)
Navigation Applications - Summary of Objectives
492(1)
Complementary Filtering for Navigation
492(3)
The Operation of Complementary Filtering
492(1)
The Implementation of Complementary Filtering
493(2)
Inertial Navigation Systems
495(1)
Models For Inertial Navigation Systems
496(5)
State Models
496(1)
Sensor Error Models
496(1)
Single-Axis Models
497(2)
Three-Axis Models
499(1)
Coordinate Transformation
500(1)
The Global Positioning System (GPS)
501(1)
The GPS Segments
502(1)
GPS Satellite Constellation
502(1)
GPS Positioning
502(5)
The GPS Principle
502(1)
The GPS Signals
503(3)
The GPS Observables
506(1)
The Accuracy of GPS Positioning
507(4)
Dilution of Precision
507(2)
GPS Positioning Accuracy
509(2)
State-Space Models for GPS
511(4)
Models for Receiver Clock State
511(1)
Dynamic Models
512(1)
Linearized Measurement Model
512(1)
A Model for Exponentially Autocorrelated Noise
513(2)
Coordinate Transformation
515(1)
Example: GPS Navigation With IMM Estimator
515(8)
Generation of Satellite Trajectories
516(1)
Generation of Trajectories and Pseudorange Measurements
517(1)
State-Space Models
518(2)
Simulation Results and Discussion
520(3)
Do We Need and IMM Estimator for GPS?
523(1)
Integrated Navigation
523(7)
Integration by Complementary Filtering
524(1)
Example
525(2)
Integration by Centralized Estimation Fusion
527(1)
Integration by Distributed Estimation Fusion
528(2)
Notes and Problems
530(7)
Bibliographical Notes
530(1)
Problems
530(3)
Term Project - Extended Kalman Filter for GPS
533(4)
Bibliography 537(10)
Index 547

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