Table of Contents

Preface
1 Introduction

1.1 Sensor Networks
1.2 Inertial Navigation
1.3 Situational Awareness
1.4 Statistical Approaches
1.5 Software Support
1.6 Outline of the Book

Part I Fusion in the Static Case

2 Linear Models

2.1 Introduction
2.2 Least Squares Approaches
2.3 Fusion
2.4 The Maximum Likelihood Approach
2.5 Cramér-Rao Lower Bound
2.6 Summary

3 Nonlinear models

3.1 Introduction
3.2 Nonlinear Least Squares
3.3 Linearizing the Measurement Equation
3.4 Inversion of the Measurement Equation
3.5 A General Approximation Strategy
3.6 Conditionally Linear Models
3.7 Implicit Measurement Equation
3.8 Summary

4 Sensor Networks

4.1 Typical Observation Models
4.2 Target Localization
4.3 NLS and SLS Solutions
4.4 Dedicated Least Squares Solutions
4.5 Extended Estimation Problems
4.6 Summary

5 Detection and Classification Problems

5.1 Detection
5.2 Classification
5.3 Association
5.4 Summary

Part II Fusion in the Dynamic Case

6 Filter Theory

6.1 Introduction
6.2 The Fusion-Diffusion Approach to Filtering
6.3 The Classical Approach to Nonlinear Filtering
6.4 Grid Based Methods
6.5 Nonlinear Filtering Bounds
6.6 Summary

7 The Kalman Filter

7.1 Kalman Filter Algorithms
7.2 Practical Issues
7.3 Computational Aspects
7.4 Smoothing
7.5 Square Root Implementation
7.6 Filter Monitoring
7.7 Examples
7.8 Summary

8. The Extended and Unscented Kalman Filters

8.1 DARE-based Extended Kalman Filter
8.2 Riccati-Free EKF and UKF
8.3 Target Tracking Examples
8.4 Summary

9 The Particle Filter

9.1 Introduction
9.2 Recapitulation of Nonlinear Filtering
9.3 The Particle Filter
9.4 Tuning
9.5 Choice of Proposal Distribution
9.6 Theoretical Performance
9.7 Complexity Bottlenecks
9.8 Marginalized Particle Filter Theory
9.9 Particle Filter Code Examples
9.10 Summary

10 Kalman Filter Banks

10.1 General Solution
10.2 On-Line Algorithms
10.3 Off-Line Algorithms
10.4 Summary

11 Simultaneous Localization and Mapping

11.1 Introduction
11.2 Kalman Filter Approach
11.3 The FastSLAM Algorithm
11.4 Marginalized FastSLAM
11.5 Summary

Part III Practice

12 Modeling

12.1 Discretizing Linear Models
12.2 Discretizing Nonlinear Models
12.3 Discretizing State Noise
12.4 Linearization Error and Choice of State Coordinates
12.5 Sensor Noise Modeling
12.6 Choice of Sampling Interval
12.7 Calibration of Dynamical Systems
12.8 Summary

13 Motion Models

13.1 Translational Kinematics
13.2 Rotational Kinematics
13.3 Rigid-Body Kinematics
13.4 Constrained Kinematic Models
13.5 Odometric Models
13.6 Vehicle Models
13.7 Aircraft Dynamics
13.8 Underwater Vehicle Dynamics
13.9 Summary

14 Sensors and Sensor Near Processing

14.1 Ranging Sensors
14.2 Physical Sensors
14.3 Wheel Speed Sensors
14.4 Wireless Network Measurements
14.5 Summary

15 Filter and Model Validation

15.1 Parametric Uncertainty
15.2 Ground Truth Data
15.3 Sensor Calibration Issues
15.4 Summary

16 Applications

16.1 Sensor Networks
16.2 Kalman Filtering
16.3 Particle Filter Positioning Applications

Appendices

A Statistics Theory

A.1 Selected Distributions
A.2 Conjugate Priors
A.3 Nonlinear Transformations

B Sampling Theory

B.1 Generating Samples from Uniform Distribution
B.2 Accept-Reject Sampling
B.3 Bootstrap
B.4 Resampling
B.5 Stochastic Integration by Importance Sampling
B.6 Markov Chain Monte Carlo
B.7 Gibbs Sampling

C Estimation Theory

C.1 Basic Concepts
C.2 Cramér-Rao Lower Bound
C.3 Sufficient Statistics
C.4 Rao-Blackman-Lehmann-Scheffe's Theorem
C.5 Maximum Likelihood Estimation
C.6 The Method of Moments
C.7 Bayesian Methods
C.8 Recursive Bayesian Estimation

D Detection Theory

D.1 Notation
D.2 The Likelihood Ratio Test
D.3 Detection of Known Mean in Gaussian Noise
D.4 Eliminating Unknown Parameters
D.5 Nuisance Parameters
D.6 Bayesian Extensions
D.7 Linear Model

E Least Squares Theory

E.1 Derivation of Least Squares Algorithms
E.2 Matrix Notation and QR Factorizations
E.3 Comparing On-Line and Off-Line Expressions
E.4 Asymptotic Expressions
E.5 Derivation of Marginal Densities

Index