Introduction to Optimal Estimation
This book, developed from a set of lecture notes by Professor Kamen, and since expanded and refined by both authors, is an introductory yet comprehensive study of its field. It contains examples that use MATLAB® and many of the problems discussed require the use of MATLAB®. The primary objective is...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
London
Springer London
1999, 1999
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| Edition: | 1st ed. 1999 |
| Series: | Advanced Textbooks in Control and Signal Processing
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 5.5 Derivation of the Kaiman Filter
- 5.6 Summary of Kaiman Filter Equations
- 5.7 Kaiman Filter Properties
- 5.8 The Steady-state Kaiman Filter
- 5.9 The SSKF as an Unbiased Estimator
- 5.10 Summary
- Problems
- 6 Further Development of the Kaiman Filter
- 6.1 The Innovations
- 6.2 Derivation of the Kaiman Filter from the Innovations
- 6.3 Time-varying State Model and Nonstationary Noises
- 6.4 Modeling Errors
- 6.5 Multistep Kaiman Prediction
- 6.6 Kaiman Smoothing
- Problems
- 7 Kaiman Filter Applications
- 7.1 Target Tracking
- 7.2 Colored Process Noise
- 7.3 Correlated Noises
- 7.4 Colored Measurement Noise
- 7.5 Target Tracking with Polar Measurements
- 7.6 System Identification
- Problems
- 8 Nonlinear Estimation
- 8.1 The Extended Kalman Filter
- 8.2 An Alternate Measurement Update
- 8.3 Nonlinear System Identification UsingNeural Networks
- 8.4 Frequency Demodulation
- 8.5 Target Tracking Using the EKF
- 8.6 Multiple Target Tracking
- Problems
- A The State Representation
- A.1 Discrete-Time Case
- A.2 Construction of State Models
- A.3 Dynamical Properties
- A.4 Discretization of Noise Covariance Matrices
- B The z-transform
- B.1 Region of Convergence
- B.2 z-transform Pairs and Properties
- B.3 The Inverse z-transform
- C Stability of the Kaiman Filter
- C.1 Observability
- C.2 Controllability
- C.3 Types of Stability
- C.4 Positive-Definiteness of P(n)
- C.5 An Upper Bound for P(n)
- C.6 A Lower Bound for P(n)
- C.7 A Useful Control Lemma
- C.8 A Kaiman Filter Stability Theorem
- C.9 Bounds for P(n)
- D The Steady-State Kaiman Filter
- D.2 A Stabilizability Lemma
- D.3 Preservation of Ordering
- D.5 Existence and Stability
- E Modeling Errors
- E.1 Inaccurate Initial Conditions
- E.2 Nonlinearities and Neglected States
- References
- 1 Introduction
- 1.1 Signal Estimation
- 1.2 State Estimation
- 1.3 Least Squares Estimation
- Problems
- 2 Random Signals and Systems with Random Inputs
- 2.1 Random Variables
- 2.2 Random Discrete-Time Signals
- 2.3 Discrete-Time Systems with Random Inputs
- Problems
- 3 Optimal Estimation
- 3.1 Formulating the Problem
- 3.2 Maximum Likelihood and Maximum a posteriori Estimation
- 3.3 Minimum Mean-Square Error Estimation
- 3.4 Linear MMSE Estimation
- 3.5 Comparison of Estimation Methods
- Problems
- 4 The Wiener Filter
- 4.1 Linear Time-Invariant MMSE Filters
- 4.2 The FIR Wiener Filter
- 4.3 The Noncausal Wiener Filter
- 4.4 Toward the Causal Wiener Filter
- 4.5 Derivation of the Causal Wiener Filter
- 4.6 Summary of Wiener Filters
- Problems
- 5 Recursive Estimation and the Kaiman Filter
- 5.1 Estimation with Growing Memory
- 5.2 Estimation of a Constant Signal
- 5.3 The Recursive Estimation Problem
- 5.4 The Signal/Measurement Model