Description
Acknowledgments. Acronyms. List of algorithms. Introduction. PART I INTRODUCTORY MATERIAL. 1 Linear systems theory. 1.1 Matrix algebra and matrix calculus. 1.2 Linear systems. 1.3 Nonlinear systems. 1.4 Discretization. 1.5 Simulation. 1.6 Stability. 1.7 Controllability and observability. 1.8 Summary. Problems. Probability theory. 2.1 Probability. 2.2 Random variables. 2.3 Transformations of random variables. 2.4 Multiple random variables. 2.5 Stochastic Processes. 2.6 White noise and colored noise. 2.7 Simulating correlated noise. 2.8 Summary. Problems. 3 Least squares estimation. 3.1 Estimation of a constant. 3.2 Weighted least squares estimation. 3.3 Recursive least squares estimation. 3.4 Wiener filtering. 3.5 Summary. Problems. 4 Propagation of states and covariances. 4.1 Discretetime systems. 4.2 Sampled-data systems. 4.3 Continuous-time systems. 4.4 Summary. Problems. PART II THE KALMAN FILTER. 5 The discrete-time Kalman filter. 5.1 Derivation of the discrete-time Kalman filter. 5.2 Kalman filter properties. 5.3 One-step Kalman filter equations. 5.4 Alternate propagation of covariance. 5.5 Divergence issues. 5.6 Summary. Problems. 6 Alternate Kalman filter formulations. 6.1 Sequential Kalman filtering. 6.2 Information filtering. 6.3 Square root filtering. 6.4 U-D filtering. 6.5 Summary. Problems. 7 Kalman filter generalizations. 7.1 Correlated process and measurement noise. 7.2 Colored process and measurement noise. 7.3 Steady-state filtering. 7.4 Kalman filtering with fading memory. 7.5 Constrained Kalman filtering. 7.6 Summary. Problems. 8 The continuous-time Kalman filter. 8.1 Discrete-time and continuous-time white noise. 8.2 Derivation of the continuous-time Kalman filter. 8.3 Alternate solutions to the Riccati equation. 8.4 Generalizations of the continuous-time filter. 8.5 The steady-state continuous-time Kalman filter 8.6 Summary. Problems. 9 Optimal smoothing. 9.1 An alternate form for the Kalman filter. 9.2 Fixed-point smoothing. 9.3 Fixed-lag smoothing. 9.4 Fixed-interval smoothing. 9.5 Summary. Problems. 10 Additional topics in Kalman filtering. 10.1 Verifying Kalman filter performance. 10.2 Multiple-model estimation. 10.3 Reduced-order Kalman filtering. 10.4 Robust Kalman filtering. 10.5 Delayed measurements and synchronization errors. 10.6 Summary. Problems. PART I l l THE H, FILTER. 11 The H, filter. 11.1 Introduction. 11.2 Constrained optimization. 11.3 A game theory approach to H, filtering. 11.4 The continuous-time H, filter. 11.5 Transfer function approaches. 11.6 Summary. Problems. 12 Additional topics in H, filtering. 12.1 Mixed KalmanIH, filtering. 12.2 Robust Kalman/H, filtering. 12.3 Constrained H, filtering. 12.4 Summary. Problems. PART IV NONLINEAR FILTERS. 13 Nonlinear Kalman filtering. 13.1 The linearized Kalman filter. 13.2 The extended Kalman filter. 13.3 Higher-order approaches. 13.4 Parameter estimation. 13.5 Summary. Problems. 14 The unscented Kalman filter. 14.1 Means and covariances of nonlinear transformations. 14.2 Unscented transformations. 14.3 Unscented Kalman filtering. 14.4 Other unscented transformations. 14.5 Summary. Problems. 15 The particle filter. 15.1 Bayesian state estimation. 15.2 Particle filtering. 15.3 Implementation issues. 15.4 Summary. Problems. Appendix A: Historical perspectives. Appendix B: Other books on Kalman filtering. Appendix C: State estimation and the meaning of life. References. Index.
