Nonlinear Estimation Methods and Applications with Deterministic Sample Points 1st Edition by Shovan Bhaumik, Paresh Date ISBN 1351012347 9781351012355

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ISBN 10: 1351012347 
ISBN 13: 9781351012355
Author: Shovan Bhaumik, Paresh Date

Nonlinear Estimation: Methods and Applications with Deterministic Sample Points focusses on a comprehensive treatment of deterministic sample point filters (also called Gaussian filters) and their variants for nonlinear estimation problems, for which no closed-form solution is available in general. Gaussian filters are becoming popular with the designers due to their ease of implementation and real time execution even on inexpensive or legacy hardware. The main purpose of the book is to educate the reader about a variety of available nonlinear estimation methods so that the reader can choose the right method for a real life problem, adapt or modify it where necessary and implement it. The book can also serve as a core graduate text for a course on state estimation. The book starts from the basic conceptual solution of a nonlinear estimation problem and provides an in depth coverage of (i) various Gaussian filters such as the unscented Kalman filter, cubature and quadrature based filters, Gauss-Hermite filter and their variants and (ii) Gaussian sum filter, in both discrete and continuous-discrete domain. Further, a brief description of filters for randomly delayed measurement and two case-studies are also included. Features: The book covers all the important Gaussian filters, including filters with randomly delayed measurements. Numerical simulation examples with detailed matlab code are provided for most algorithms so that beginners can verify their understanding. Two real world case studies are included: (i) underwater passive target tracking, (ii) ballistic target tracking. The style of writing is suitable for engineers and scientists. The material of the book is presented with the emphasis on key ideas, underlying assumptions, algorithms, and properties. The book combines rigorous mathematical treatment with matlab code, algorithm listings, flow charts and detailed case studies to deepen understanding.

Nonlinear Estimation Methods and Applications with Deterministic Sample Points 1st Table of contents:

1. Introduction
1.1 Nonlinear systems
1.1.1 Continuous time state space model
1.1.2 Discrete time state space model
1.2 Discrete time systems with noises
1.2.1 Solution of discrete time LTI system
1.2.2 States as a Markov process
1.3 Stochastic filtering problem
1.4 Maximum likelihood and maximum a posterori estimate
1.4.1 Maximum likelihood (ML) estimator
1.4.2 Maximum a posteriori (MAP) estimate
1.5 Bayesian framework of filtering
1.5.1 Bayesian statistics
1.5.2 Recursive Bayesian filtering: a conceptual solution
1.6 Particle filter
1.6.1 Importance sampling
1.6.2 Resampling
1.7 Gaussian filter
1.7.1 Propagation of mean and covariance of a linear system
1.7.2 Nonlinear filter with Gaussian approximations
1.8 Performance measure
1.8.1 When truth is known
1.8.2 When truth is unknown
1.9 A few applications
1.9.1 Target tracking
1.9.2 Navigation
1.9.3 Process control
1.9.4 Weather prediction
1.9.5 Estimating state-of-charge (SoC)
1.10 Prerequisites
1.11 Organization of chapters
2. The Kalman filter and the extended Kalman filter
2.1 Linear Gaussian case (the Kalman filter)
2.1.1 Kalman filter: a brief history
2.1.2 Assumptions
2.1.3 Derivation
2.1.4 Properties: convergence and stability
2.1.5 Numerical issues
2.1.6 The information filter
2.1.7 Consistency of state estimators
2.1.8 Simulation example for the Kalman filter
2.1.9 MATLAB®-based filtering exercises
2.2 The extended Kalman filter (EKF)
2.2.1 Simulation example for the EKF
2.3 Important variants of the EKF
2.3.1 The iterated EKF (IEKF)
2.3.2 The second order EKF (SEKF)
2.3.3 Divided difference Kalman filter (DDKF)
2.3.4 MATLAB-based filtering exercises
2.4 Alternative approaches towards nonlinear filtering
2.5 Summary
3. Unscented Kalman filter
3.1 Introduction
3.2 Sigma point generation
3.3 Basic UKF algorithm
3.3.1 Simulation example for the unscented Kalman filter
3.4 Important variants of the UKF
3.4.1 Spherical simplex unscented transformation
3.4.2 Sigma point filter with 4n + 1 points
3.4.3 MATLAB-based filtering exercises
3.5 Summary
4. Filters based on cubature and quadrature points
4.1 Introduction
4.2 Spherical cubature rule of integration
4.3 Gauss-Laguerre rule of integration
4.4 Cubature Kalman filter
4.5 Cubature quadrature Kalman filter
4.5.1 Calculation of cubature quadrature (CQ) points
4.5.2 CQKF algorithm
4.6 Square root cubature quadrature Kalman filter
4.7 High-degree (odd) cubature quadrature Kalman filter
4.7.1 Approach
4.7.2 High-degree cubature rule
4.7.3 High-degree cubature quadrature rule
4.7.4 Calculation of HDCQ points and weights
4.7.5 Illustrations
4.7.6 High-degree cubature quadrature Kalman filter
4.8 Simulation examples
4.8.1 Problem 1
4.8.2 Problem 2
4.9 Summary
5. Gauss-Hermite filter
5.1 Introduction
5.2 Gauss-Hermite rule of integration
5.2.1 Single dimension
5.2.2 Multidimensional integral
5.3 Sparse-grid Gauss-Hermite filter (SGHF)
5.3.1 Smolyak’s rule
5.4 Generation of points using moment matching method
5.5 Simulation examples
5.5.1 Tracking an aircraft
5.6 Multiple sparse-grid Gauss-Hermite filter (MSGHF)
5.6.1 State-space partitioning
5.6.2 Bayesian filtering formulation for multiple approach
5.6.3 Algorithm of MSGHF
5.6.4 Simulation example
5.7 Summary
6. Gaussian sum filters
6.1 Introduction
6.2 Gaussian sum approximation
6.2.1 Theoretical foundation
6.2.2 Implementation
6.2.3 Multidimensional systems
6.3 Gaussian sum filter
6.3.1 Time update
6.3.2 Measurement update
6.4 Adaptive Gaussian sum filtering
6.5 Simulation results
6.5.1 Problem 1: Single dimensional nonlinear system
6.5.2 RADAR target tracking problem
6.5.3 Estimation of harmonics
6.6 Summary
7. Quadrature filters with randomly delayed measurements
7.1 Introduction
7.2 Kalman filter for one step randomly delayed measurements
7.3 Nonlinear filters for one step randomly delayed measurements
7.3.1 Assumptions
7.3.2 Measurement noise estimation
7.3.3 State estimation
7.4 Nonlinear filter for any arbitrary step randomly delayed measurement
7.4.1 Algorithm
7.5 Simulation
7.6 Summary
8. Continuous-discrete filtering
8.1 Introduction
8.2 Continuous time filtering
8.2.1 Continuous filter for a linear Gaussian system
8.2.2 Nonlinear continuous time system
8.2.2.1 The extended Kalman-Bucy filter
8.3 Continuous-discrete filtering
8.3.1 Nonlinear continuous time process model
8.3.2 Discretization of process model using Runge-Kutta method
8.3.3 Discretization using Ito-Taylor expansion of order 1.5
8.3.4 Continuous-discrete filter with deterministic sample points
8.4 Simulation examples
8.4.1 Single dimensional filtering problem
8.4.2 Estimation of harmonics
8.4.3 RADAR target tracking problem
8.5 Summary
9. Case studies
9.1 Introduction
9.2 Bearing only underwater target tracking problem
9.3 Problem formulation
9.3.1 Tracking scenarios
9.4 Shifted Rayleigh filter (SRF)
9.5 Gaussian sum shifted Rayleigh filter (GS-SRF)
9.5.1 Bearing density
9.6 Continuous-discrete shifted Rayleigh filter (CD-SRF)
9.6.1 Time update of CD-SRF
9.7 Simulation results
9.7.1 Filter initialization
9.7.2 Performance criteria
9.7.3 Performance analysis of Gaussian sum filters
9.7.4 Performance analysis of continuous-discrete filters
9.8 Summary
9.9 Tracking of a ballistic target
9.10 Problem formulation
9.10.1 Process model
9.10.1.1 Process model in discrete domain
9.10.1.2 Process model in continuous time domain
9.10.2 Seeker measurement model
9.10.3 Target acceleration model
9.11 Proportional navigation guidance (PNG) law
9.12 Simulation results
9.12.1 Performance of adaptive Gaussian sum filters
9.12.2 Performance of continuous-discrete filters
9.13 Conclusions

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Tags: Shovan Bhaumik, Paresh Date, Nonlinear, Estimation