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Tiivistelmä v
List of Abbreviations vi
List of Symbols vii
1 Introduction 1
2 Kalman Filtering 4
2.1 Standard Kalman Filter 4
2.2 Extended Kalman Filter 8
2.3 Handling of Clutter--g- s -Gate and PDA 10
2.3.1 Validation of Measurements 11
2.3.2 Probabilistic Data Association 12
2.4 Multisensor Kalman Filtering 14
2.4.1 Parallel Update 14
2.4.2 Sequential Update 18
3 Modelling of Target Dynamics 20
3.1 Targets Moving at Nearly Constant Velocity 20
3.1.1 Discretized Process Noise 21
3.1.2 Discrete-time Model 22
3.2 Modelling Maneuvers as Coloured Process Noise 23
3.2.1 Singer Acceleration Model in Three Dimensions 25
3.3 Modelling Maneuvers as Random Bias 27
3.4 Tracking Stationary Targets 28
3.4.1 Simple Model for Stationary Targets 28
3.4.2 Test for Velocity Estimates 29
4 Interacting Multiple Model Algorithm 31
4.1 Outline of IMM Algorithm 32
4.2 Multisensor IMM 35
4.3 Mixing of State Vectors 37
5 Two-Stage Kalman Estimator 40
5.1 Two-Stage Estimator for Bias 40
5.2 Two-Stage Estimator for Tracking Maneuvering Targets 42
5.2.1 Maneuver Detector 43
5.2.2 Initialisation of the Acceleration Filter 44
5.2.3 Selecting the Process Noise 45
5.2.4 Adaptation of the Algorithm to Multisensor Passive Tracking 45
6 Interacting Acceleration Compensation 49
6.1 Outline of IAC Algorithm 49
6.2 Multisensor IAC Algorithm 51
7 Performance Evaluation 54
7.1 Simulation Scenario 54
7.1.1 Targets 55
7.1.2 Sensors 56
7.2 Tracking Configuration 58
7.2.1 General Tracking Parameters 58
7.2.2 Parameters for the Tracking Algorithms 59
7.3 Simulation Results 62
7.3.1 Position and Velocity Errors 63
7.3.2 Stationary Target Models 65
7.3.3 Maneuver Detection 66
7.3.4 Filter Consistency 68
7.3.5 Data Association 69
8 Summary 71
References 73
Appendix A: Derivation of the IMM Algorithm 76
A.1 The Initial Mixed Estimate 76
A.2 Model Likelihoods and the Final Estimate 79
A.3 Covariance Estimate 81
Appendix B: Tracking Performance 82
B.1 RMSE Errors of Position and Velocity 82
B.2 Normalized Errors 87
B.3 Data Association 90