Nonlinear state and parameter estimation of spatially distributed systems

✍ Scribed by Sawo F.

• Publisher: Univer. Karlsruhe
• Year: 2009
• Tongue: English
• Leaves: 178
• Category: Library

✦ Synopsis

In this book two probabilistic model-based estimators are introduced that allow the reconstruction and identification of space-time continuous physical systems. The Sliced Gaussian Mixture Filter (SGMF) exploits linear substructures in mixed linear/nonlinear systems, and thus is well-suited for identifying various model parameters. The Covariance Bounds Filter (CBF) allows the efficient estimation of widely distributed systems in a decentralized fashion.

✦ Table of Contents

Table of Contents......Page 13
Conventions, Notations, and Glossary......Page 17
1 Introduction......Page 25
1.1 Prospective Sensor Network Applications......Page 26
1.2 Mathematical Description of Dynamic Systems......Page 27
1.3 Problem Formulation and Contributions......Page 31
1.4 Thesis Organization......Page 34
2 Reconstruction and Interpolation of Space-Time Continuous Systems......Page 37
2.1 Related Work......Page 38
2.2 Overview of the Reconstruction Process and Considered System......Page 40
2.3 Conversion of Space-Time Continuous Systems......Page 43
2.3.1 Spatial/temporal Discretization Methods......Page 45
2.3.2 Spatial Decomposition of System Description......Page 47
2.3.3 Spatial Decomposition of Sytem Input and Process Noise......Page 50
2.3.4 Selection of Shape Functions......Page 52
2.3.5 Derivation of the Space-Time Discrete System Model......Page 54
2.4 Derivation of the Measurement Model......Page 57
2.5.1 Prediction Step......Page 60
2.5.2 Measurement Step (Filtering)......Page 61
2.5.3 Conversion into Continuous Space......Page 62
2.6 Simulation Results......Page 64
2.6.1 Simulated Case Study 1: Precise System Description......Page 65
2.6.2 Simulated Case Study 2: Incorrect Process Parameters......Page 67
2.6.3 Simulated Case Study 3: Effect of Sensor Locations......Page 71
2.7 Summary and Discussion......Page 72
3.1 Related Work......Page 75
3.2 Overview of the Sliced Gaussian Mixture Filter (SGMF)......Page 78
3.3 Density Representation......Page 79
3.4.1 Prediction Step......Page 81
3.4.2 Combined Measurement/Prediction Step......Page 84
3.5 Reapproximation Step......Page 86
3.6 Simulation Results......Page 90
3.7 Summary and Discussion......Page 91
4 Parameter Identification of Space-Time Continuous Systems......Page 93
4.1 State Augmentation of the System Description......Page 94
4.2 Overview and Considered Space-Time Continuous System......Page 96
4.3 Application 1: Identification of Process Parameters......Page 98
4.4 Application 2: Node Localization based on Local Observations......Page 101
4.4.1 Key Idea of the Proposed Passive Localization Method......Page 103
4.4.2 Identification/Calibration Stage......Page 104
4.4.3 Localization Stage......Page 106
4.4.4 Tracking of Movable Sensor Nodes......Page 107
4.4.5 Simulation Results......Page 108
4.5 Application 3: Source and Leakage Localization......Page 112
4.6 Summary and Discussion......Page 116
5 Decentralized State Reconstruction of Space-Time Continuous Systems......Page 119
5.1 Related Work......Page 120
5.2 Conversion and Decomposition of the System Description......Page 122
5.3 Decomposition of Probability Density Functions......Page 125
5.4.1 Completely Unknown Correlation......Page 127
5.4.2 Arbitrary Correlation Constraints......Page 128
5.5 Process of the Decentralized State Reconstruction......Page 135
5.5.1 Decentralized prediction step......Page 136
5.5.2 Local measurement step......Page 138
5.6 Simulation Results......Page 139
5.7 Summary and Discussion......Page 140
6.1 Parameterized Joint Densities with Gaussian Marginals......Page 143
6.2 Gaussian Mixture Marginals......Page 146
6.3 Processing of Parameterized Joint Densities......Page 150
6.4 Summary and Discussion......Page 153
7 Conclusion and Future Research......Page 155
List of Figures......Page 158
List of Examples......Page 161