1 What are Bayesian filtering and smoothing? 1
1.1 Applications of Bayesian filtering and smoothing 1
1.2 Origins of Bayesian filtering and smoothing 7
1.3 Optimal filtering and smoothing as Bayesian inference 8
1.4 Algorithms for Bayesian filtering and smoothing 12
1.5 Parameter estimation 14
1.6 Exercises 15
2 Bayesian inference 17
2.1 Philosophy of Bayesian inference 17
2.2 Connection to maximum likelihood estimation 17
2.3 The building blocks of Bayesian models 19
2.4 Bayesian point estimates 20
2.5 Numerical methods 22
2.6 Exercises 24
3 Batch and recursive Bayesian estimation 27
3.1 Batch linear regression 27
3.2 Recursive linear regression 30
3.3 Batch versus recursive estimation 31
3.4 Drift model for linear regression 34
3.5 State space model for linear regression with drift 36
3.6 Examples of state space models 39
3.7 Exercises 46
4 Bayesian filtering equations and exact solutions 51
4.1 Probabilistic state space models 51
4.2 Bayesian filtering equations 54
4.3 Kalman filter 56
5 Extended and unscented Kalman filtering 64
5.1 Taylor series expansions 64
5.2 Extended Kalman filter 69
5.3 Statistical linearization 75
5.4 Statistically linearized filter 77
5.5 Unscented transform 81
5.6 Unscented Kalman filter 86
5.7 Exercises 92
6 General Gaussian filtering 96
6.1 Gaussian moment matching 96
6.2 Gaussian filter 97
6.3 Gauss–Hermite integration 99
6.4 Gauss–Hermite Kalman filter 103
6.5 Spherical cubature integration 106
6.6 Cubature Kalman filter 110
6.7 Exercises 114
7 Particle filtering 116
7.1 Monte Carlo approximations in Bayesian inference 116
7.2 Importance sampling 117
7.3 Sequential importance sampling 120
7.4 Sequential importance resampling 123
7.5 Rao–Blackwellized particle filter 129
7.6 Exercises 132
8 Bayesian smoothing equations and exact solutions 134
8.1 Bayesian smoothing equations 134
8.2 Rauch–Tung–Striebel smoother 135
8.3 Two-filter smoothing 139
8.4 Exercises 142
9 Extended and unscented smoothing 144
9.1 Extended Rauch–Tung–Striebel smoother 144
9.2 Statistically linearized Rauch–Tung–Striebel smoother 146
9.3 Unscented Rauch–Tung–Striebel smoother 148
9.4 Exercises 152
10 General Gaussian smoothing 154
10.1 General Gaussian Rauch–Tung–Striebel smoother 154
10.2 Gauss–Hermite Rauch–Tung–Striebel smoother 155

个人觉得这本书还不错