【本書は、非線形フィルタについて解説した英語書籍です】

This book covers a broad range of filter theories, algorithms, and numerical examples. The representative linear and nonlinear filters such as the Kalman filter, the steady-state Kalman filter, the H infinity filter, the extended Kalman filter, the Gaussian sum filter, the statistically linearized Kalman filter, the unscented Kalman filter, the Gaussian filter, the cubature Kalman filter are first visited. Then, the non-Gaussian filters such as the ensemble Kalman filter and the particle filters based on the sequential Bayesian filter and the sequential importance resampling are described, together with their recent advances. Moreover, the information matrix in the nonlinear filtering, the nonlinear smoother based on the Markov Chain Monte Carlo, the continuous-discrete filters, factorized filters, and nonlinear filters based on stochastic approximation method are detailed.



1 Review of the Kalman Filter and Related Filters

2 Information Matrix in Nonlinear Filtering

3 Extended Kalman Filter and Gaussian Sum Filter

4 Statistically Linearized Kalman Filter

5 The Unscented Kalman Filter

6 General Gaussian Filters and Applications

7 The Ensemble Kalman Filter

8 Particle Filter

9 Nonlinear Smoother with Markov Chain Monte Carlo

10 Continuous-Discrete Filters

11 Factorized Filters

12 Nonlinear Filters Based on Stochastic Approximation Method