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Statistical Sensor Fusion

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Sensor fusion deals with merging information from two or more sensors, where the area of statistical signal processing provides a powerful tool­box to attack both theoretical and practical problems. The objective of this book is to explain state of the art theory and algo­rithms in statistical sensor fusion, covering estimation, detection and non­linear filtering theory with applications to localization, navi­gation and tracking problems. The book starts with a review of the theory on linear ...

Sensor fusion deals with merging information from two or more sensors, where the area of statistical signal processing provides a powerful tool­box to attack both theoretical and practical problems. The objective of this book is to explain state of the art theory and algo­rithms in statistical sensor fusion, covering estimation, detection and non­linear filtering theory with applications to localization, navi­gation and tracking problems. The book starts with a review of the theory on linear and nonlinear estimation, with a focus on sensor network applications. Then, general nonlinear filter theory is surveyed with a particular attention to different variants of the Kalman filter and the particle filter. Complexity and implementation issues are discussed in detail. Simultaneous localization and mapping (SLAM) is used as a challenging application area of high-dimensional nonlinear filtering problems. The book spans the whole range from mathematical foundations pro­vided in extensive appendices, to real-world problems covered in a part surveying standard sensors, motion models and applications in this field. All models and algorithms are available as object-oriented Matlab code with an extensive data file library, and the examples, which are richly used to illustrate the theory, are supplemented by fully reproducible Matlab code.

    • xi
      Preface
      • 1
        1
        Introduction
        • 1.1
          3
          Sensor Networks
        • 1.2
          6
          Inertial Navigation
        • 1.3
          7
          Situational Awareness
        • 1.4
          10
          Statistical Approaches
        • 1.5
          12
          Software Support
        • 1.6
          14
          Outline of the Book
  • 19
    Part I Fusion in the Static Case
      • 2
        21
        Linear Models
        • 2.1
          22
          Introduction
        • 2.2
          23
          Least Squares Approaches
        • 2.3
          29
          Fusion
        • 2.4
          36
          The Maximum Likelihood Approach
        • 2.5
          39
          Cramér-Rao Lower Bound
        • 2.6
          41
          Summary
      • 3
        45
        Nonlinear models
        • 3.1
          46
          Introduction
        • 3.2
          47
          Nonlinear Least Squares
        • 3.3
          52
          Linearizing the Measurement Equation
        • 3.4
          57
          Inversion of the Measurement Equation
        • 3.5
          65
          A General Approximation Strategy
        • 3.6
          65
          Conditionally Linear Models
        • 3.7
          68
          Implicit Measurement Equation
        • 3.8
          70
          Summary
      • 4
        73
        Sensor Networks
        • 4.1
          74
          Typical Observation Models
        • 4.2
          76
          Target Localization
        • 4.3
          83
          NLS and SLS Solutions
        • 4.4
          89
          Dedicated Least Squares Solutions
        • 4.5
          92
          Extended Estimation Problems
        • 4.6
          97
          Summary
      • 5
        101
        Detection and Classification Problems
        • 5.1
          101
          Detection
        • 5.2
          111
          Classification
        • 5.3
          117
          Association
        • 5.4
          121
          Summary
  • 123
    Part II Fusion in the Dynamic Case
      • 6
        125
        Filter Theory
        • 6.1
          126
          Introduction
        • 6.2
          129
          The Fusion-Diffusion Approach to Filtering
        • 6.3
          131
          The Classical Approach to Nonlinear Filtering
        • 6.4
          140
          Grid Based Methods
        • 6.5
          143
          Nonlinear Filtering Bounds
        • 6.6
          149
          Summary
      • 7
        153
        The Kalman Filter
        • 7.1
          154
          Kalman Filter Algorithms
        • 7.2
          162
          Practical Issues
        • 7.3
          168
          Computational Aspects
        • 7.4
          175
          Smoothing
        • 7.5
          181
          Square Root Implementation
        • 7.6
          186
          Filter Monitoring
        • 7.7
          188
          Examples
        • 7.8
          192
          Summary
      • 8
        195
        The Extended and Unscented Kalman Filters
        • 8.1
          197
          DARE-based Extended Kalman Filter
        • 8.2
          201
          Riccati-Free EKF and UKF
        • 8.3
          205
          Target Tracking Examples
        • 8.4
          208
          Summary
      • 9
        211
        The Particle Filter
        • 9.1
          212
          Introduction
        • 9.2
          214
          Recapitulation of Nonlinear Filtering
        • 9.3
          218
          The Particle Filter
        • 9.4
          224
          Tuning
        • 9.5
          226
          Choice of Proposal Distribution
        • 9.6
          233
          Theoretical Performance
        • 9.7
          236
          Complexity Bottlenecks
        • 9.8
          239
          Marginalized Particle Filter Theory
        • 9.9
          250
          Particle Filter Code Examples
        • 9.10
          258
          Summary
      • 10
        261
        Kalman Filter Banks
        • 10.1
          262
          General Solution
        • 10.2
          264
          On-Line Algorithms
        • 10.3
          272
          Off-Line Algorithms
        • 10.4
          276
          Summary
      • 11
        279
        Simultaneous Localization and Mapping
        • 11.1
          280
          Introduction
        • 11.2
          288
          Kalman Filter Approach
        • 11.3
          302
          The FastSLAM Algorithm
        • 11.4
          306
          Marginalized FastSLAM
        • 11.5
          310
          Summary
  • 313
    Part III Practice
      • 12
        315
        Modeling
        • 12.1
          316
          Discretizing Linear Models
        • 12.2
          318
          Discretizing Nonlinear Models
        • 12.3
          321
          Discretizing State Noise
        • 12.4
          323
          Linearization Error and Choice of State Coordinates
        • 12.5
          326
          Sensor Noise Modeling
        • 12.6
          330
          Choice of Sampling Interval
        • 12.7
          333
          Calibration of Dynamical Systems
        • 12.8
          340
          Summary
      • 13
        343
        Motion Models
        • 13.1
          344
          Translational Kinematics
        • 13.2
          346
          Rotational Kinematics
        • 13.3
          351
          Rigid-Body Kinematics
        • 13.4
          352
          Constrained Kinematic Models
        • 13.5
          356
          Odometric Models
        • 13.6
          358
          Vehicle Models
        • 13.7
          362
          Aircraft Dynamics
        • 13.8
          364
          Underwater Vehicle Dynamics
        • 13.9
          369
          Summary
      • 14
        373
        Sensors and Sensor Near Processing
        • 14.1
          373
          Ranging Sensors
        • 14.2
          384
          Physical Sensors
        • 14.3
          387
          Wheel Speed Sensors
        • 14.4
          402
          Wireless Network Measurements
        • 14.5
          410
          Summary
      • 15
        413
        Filter and Model Validation
        • 15.1
          413
          Parametric Uncertainty
        • 15.2
          416
          Ground Truth Data
        • 15.3
          422
          Sensor Calibration Issues
        • 15.4
          424
          Summary
      • 16
        427
        Applications
        • 16.1
          427
          Sensor Networks
        • 16.2
          431
          Kalman Filtering
        • 16.3
          439
          Particle Filter Positioning Applications
    • 453
      Appendices
      • 455
        A Statistics Theory
        • 455
          A1 Selected Distributions
        • 457
          A2 Conjugate Priors
        • 457
          A3 Nonlinear Transformations
      • 471
        B Sampling Theory
        • 471
          B1 Generating Samples from Uniform Distribution
        • 472
          B2 Accept-Reject Sampling
        • 475
          B3 Bootstrap
        • 475
          B4 Resampling
        • 476
          B5 Stochastic Integration by Importance Sampling
        • 479
          B6 Markov Chain Monte Carlo
        • 480
          B7 Gibbs Sampling
      • 483
        C Estimation Theory
        • 483
          C1 Basic Concepts
        • 484
          C2 Cramér-Rao Lower Bound
        • 488
          C3 Sufficient Statistics
        • 490
          C4 Rao-Blackman-Lehmann-Scheffe's Theorem
        • 490
          C5 Maximum Likelihood Estimation
        • 491
          C6 The Method of Moments
        • 492
          C7 Bayesian Methods
        • 495
          C8 Recursive Bayesian Estimation
      • 497
        D Detection Theory
        • 497
          D1 Notation
        • 498
          D2 The Likelihood Ratio Test
        • 499
          D3 Detection of Known Mean in Gaussian Noise
        • 503
          D4 Eliminating Unknown Parameters
        • 504
          D5 Nuisance Parameters
        • 506
          D6 Bayesian Extensions
        • 507
          D7 Linear Model
      • 509
        E Least Squares Theory
        • 509
          E1 Derivation of Least Squares Algorithms
        • 512
          E2 Matrix Notation and QR Factorizations
        • 513
          E3 Comparing On-Line and Off-Line Expressions
        • 518
          E4 Asymptotic Expressions
        • 519
          E5 Derivation of Marginal Densities
    • 538
      Index

Information

Författare:
Fredrik Gustafsson
Språk:
Engelska
ISBN:
9789144127248
Utgivningsår:
2010
Revisionsår:
2018
Artikelnummer:
33373-03
Upplaga:
Tredje
Sidantal:
554

Författare

Fredrik Gustafsson

Fredrik Gustafsson is professor at the Department of Electrical Engineering at Linköping University.

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