Estimation with applications to tracking and navigation /
by Yaakov Bar-Shalom, Xiao-Rong Li, Thiagalingam Kirubarajan.
- 1 online resource (xxiii, 558 pages) : illustrations
"A Wiley-Interscience publication."
Includes bibliographical references and index.
Background -- Scope of the Text -- Brief Review of Linear Algebra and Linear Systems -- Brief Review of Probability Theory -- Brief Review of Statistics -- Basic Concepts in Estimation -- The Problem of Parameter Estimation -- Maximum Likelihood and Maximum a Posteriori Estimators -- Least Squares and Minimum Mean Square Error Estimation -- Unbiased Estimators -- The Variation and MSE of an Estimator -- Linear Estimation in Static Systems -- Estimation of Gaussian Random Vectors -- Linear Minimum Mean Square Error Estimation -- Least Squares Estimation -- Polynomial Fitting -- Goodness-of-Fit and Statistical Significance of Parameter Estimates -- Use of LS for a Nonlinear Problem: Bearings-Only Target Motion Analysis -- Linear Dynamic Systems with Random Inputs -- Continuous-Time Linear Stochastic Dynamic Systems -- Discrete-Time Linear Stochastic Dynamic Systems -- State Estimation in Discrete-Time Linear Dynamic Systems -- Linear Estimation in Dynamic Systems: The Kalman Filter -- Example of a Filter -- Consistency of State Estimators -- Initialization of State Estimators -- Sensitivity -- Estimation for Kinematic Models -- Discretized Continuous-Time Kinematic Models -- Direct Discrete-Time Kinematic Models -- Explicit Filters for Noiseless Kinematic Models -- Steady-State Filters for Noisy Kinematic Models -- Computation Aspects of Estimation -- The Information Filter -- Sequential Processing of Measurements -- Square-Root Filtering -- Extensions of Discrete-Time Linear Estimation -- Autocorrelated Process Noise -- Cross-Correlated Measurement and Process Noise -- Autocorrelated Measurement Noise -- Prediction -- Smoothing -- Continuous-Time Linear State Estimation -- The Continuous-Time Linear State Estimation Filter -- Prediction and the Continuous-Discrete Filter -- Duality of Estimation and Control -- The Wiener-Hopf Problem -- State Estimation for Nonlinear Dynamic Systems -- Estimation in Nonlinear Stochastic Systems -- The Extended Kalman Filter -- Error Compensation in Linearized Filters -- Some Error Reduction Methods -- Maximum a Posteriori Trajectory Estimation via Dynamic Programming -- Nonlinear Continuous-Discrete Filter -- Adaptive Estimation and Maneuvering Targets -- Adjustable Level Process Noise -- Input Estimation -- The Variable State Dimension Approach -- A Comparison of Adaptive Estimation Methods for Maneuvering Targets -- The Multiple Model Approach -- Design of an IMM Estimator for ATC Tracking -- When Is an IMM Estimator Needed? -- Use of EKF for Simultaneous State and Parameter Estimation -- Introduction to Navigation Applications -- Complementary Filtering for Navigation -- Inertial Navigation Systems -- Models for Inertial Navigation Systems -- The Global Positioning System (GPS) -- GPS Positioning -- The Accuracy of GPS Positioning -- State-Space Models for GPS -- Example: GPS Navigation with IMM Estimator -- Integrated Navigation.
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.