| |
| |
| Acknowledgments | |
| |
| |
| Acronyms | |
| |
| |
| List of algorithms | |
| |
| |
| Introduction | |
| |
| |
| |
| Introductory Material | |
| |
| |
| |
| Linear systems theory | |
| |
| |
| |
| Matrix algebra and matrix calculus | |
| |
| |
| |
| Matrix algebra | |
| |
| |
| |
| The matrix inversion lemma | |
| |
| |
| |
| Matrix calculus | |
| |
| |
| |
| The history of matrices | |
| |
| |
| |
| Linear systems | |
| |
| |
| |
| Nonlinear systems | |
| |
| |
| |
| Discretization | |
| |
| |
| |
| Simulation | |
| |
| |
| |
| Rectangular integration | |
| |
| |
| |
| Trapezoidal integration | |
| |
| |
| |
| Runge-Kutta integration | |
| |
| |
| |
| Stability | |
| |
| |
| |
| Continuous-time systems | |
| |
| |
| |
| Discrete-time systems | |
| |
| |
| |
| Controllability and observability | |
| |
| |
| |
| Controllability | |
| |
| |
| |
| Observability | |
| |
| |
| |
| Stabilizability and detectability | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Probability theory | |
| |
| |
| |
| Probability | |
| |
| |
| |
| Random variables | |
| |
| |
| |
| Transformations of random variables | |
| |
| |
| |
| Multiple random variables | |
| |
| |
| |
| Statistical independence | |
| |
| |
| |
| Multivariate statistics | |
| |
| |
| |
| Stochastic Processes | |
| |
| |
| |
| White noise and colored noise | |
| |
| |
| |
| Simulating correlated noise | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Least squares estimation | |
| |
| |
| |
| Estimation of a constant | |
| |
| |
| |
| Weighted least squares estimation | |
| |
| |
| |
| Recursive least squares estimation | |
| |
| |
| |
| Alternate estimator forms | |
| |
| |
| |
| Curve fitting | |
| |
| |
| |
| Wiener filtering | |
| |
| |
| |
| Parametric filter optimization | |
| |
| |
| |
| General filter optimization | |
| |
| |
| |
| Noncausal filter optimization | |
| |
| |
| |
| Causal filter optimization | |
| |
| |
| |
| Comparison | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Propagation of states and covariances | |
| |
| |
| |
| Discrete-time systems | |
| |
| |
| |
| Sampled-data systems | |
| |
| |
| |
| Continuous-time systems | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| The Kalman Filter | |
| |
| |
| |
| The discrete-time Kalman filter | |
| |
| |
| |
| Derivation of the discrete-time Kalman filter | |
| |
| |
| |
| Kalman filter properties | |
| |
| |
| |
| One-step Kalman filter equations | |
| |
| |
| |
| Alternate propagation of covariance | |
| |
| |
| |
| Multiple state systems | |
| |
| |
| |
| Scalar systems | |
| |
| |
| |
| Divergence issues | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Alternate Kalman filter formulations | |
| |
| |
| |
| Sequential Kalman filtering | |
| |
| |
| |
| Information filtering | |
| |
| |
| |
| Square root filtering | |
| |
| |
| |
| Condition number | |
| |
| |
| |
| The square root time-update equation | |
| |
| |
| |
| Potter's square root measurement-update equation | |
| |
| |
| |
| Square root measurement update via triangularization | |
| |
| |
| |
| Algorithms for orthogonal transformations | |
| |
| |
| |
| U-D filtering | |
| |
| |
| |
| U-D filtering: The measurement-update equation | |
| |
| |
| |
| U-D filtering: The time-update equation | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Kalman filter generalizations | |
| |
| |
| |
| Correlated process and measurement noise | |
| |
| |
| |
| Colored process and measurement noise | |
| |
| |
| |
| Colored process noise | |
| |
| |
| |
| Colored measurement noise: State augmentation | |
| |
| |
| |
| Colored measurement noise: Measurement differencing | |
| |
| |
| |
| Steady-state filtering | |
| |
| |
| |
| [alpha]-[beta] filtering | |
| |
| |
| |
| [alpha]-[beta]-[gamma] filtering | |
| |
| |
| |
| A Hamiltonian approach to steady-state filtering | |
| |
| |
| |
| Kalman filtering with fading memory | |
| |
| |
| |
| Constrained Kalman filtering | |
| |
| |
| |
| Model reduction | |
| |
| |
| |
| Perfect measurements | |
| |
| |
| |
| Projection approaches | |
| |
| |
| |
| A pdf truncation approach | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| The continuous-time Kalman filter | |
| |
| |
| |
| Discrete-time and continuous-time white noise | |
| |
| |
| |
| Process noise | |
| |
| |
| |
| Measurement noise | |
| |
| |
| |
| Discretized simulation of noisy continuous-time systems | |
| |
| |
| |
| Derivation of the continuous-time Kalman filter | |
| |
| |
| |
| Alternate solutions to the Riccati equation | |
| |
| |
| |
| The transition matrix approach | |
| |
| |
| |
| The Chandrasekhar algorithm | |
| |
| |
| |
| The square root filter | |
| |
| |
| |
| Generalizations of the continuous-time filter | |
| |
| |
| |
| Correlated process and measurement noise | |
| |
| |
| |
| Colored measurement noise | |
| |
| |
| |
| The steady-state continuous-time Kalman filter | |
| |
| |
| |
| The algebraic Riccati equation | |
| |
| |
| |
| The Wiener filter is a Kalman filter | |
| |
| |
| |
| Duality | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Optimal smoothing | |
| |
| |
| |
| An alternate form for the Kalman filter | |
| |
| |
| |
| Fixed-point smoothing | |
| |
| |
| |
| Estimation improvement due to smoothing | |
| |
| |
| |
| Smoothing constant states | |
| |
| |
| |
| Fixed-lag smoothing | |
| |
| |
| |
| Fixed-interval smoothing | |
| |
| |
| |
| Forward-backward smoothing | |
| |
| |
| |
| RTS smoothing | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Additional topics in Kalman filtering | |
| |
| |
| |
| Verifying Kalman filter performance | |
| |
| |
| |
| Multiple-model estimation | |
| |
| |
| |
| Reduced-order Kalman filtering | |
| |
| |
| |
| Anderson's approach to reduced-order filtering | |
| |
| |
| |
| The reduced-order Schmidt-Kalman filter | |
| |
| |
| |
| Robust Kalman filtering | |
| |
| |
| |
| Delayed measurements and synchronization errors | |
| |
| |
| |
| A statistical derivation of the Kalman filter | |
| |
| |
| |
| Kalman filtering with delayed measurements | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| The H[subscript infinity] Filter | |
| |
| |
| |
| The H[subscript infinity] filter | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| An alternate form for the Kalman filter | |
| |
| |
| |
| Kalman filter limitations | |
| |
| |
| |
| Constrained optimization | |
| |
| |
| |
| Static constrained optimization | |
| |
| |
| |
| Inequality constraints | |
| |
| |
| |
| Dynamic constrained optimization | |
| |
| |
| |
| A game theory approach to H[subscript infinity] filtering | |
| |
| |
| |
| Stationarity with respect to x[subscript 0] and w[subscript k] | |
| |
| |
| |
| Stationarity with respect to x and y | |
| |
| |
| |
| A comparison of the Kalman and H[subscript infinity] filters | |
| |
| |
| |
| Steady-state H[subscript infinity] filtering | |
| |
| |
| |
| The transfer function bound of the H[subscript infinity] filter | |
| |
| |
| |
| The continuous-time H[subscript infinity] filter | |
| |
| |
| |
| Transfer function approaches | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Additional topics in H[subscript infinity] filtering | |
| |
| |
| |
| Mixed Kalman/H[subscript infinity] filtering | |
| |
| |
| |
| Robust Kalman/H[subscript infinity] filtering | |
| |
| |
| |
| Constrained H[subscript infinity] filtering | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Nonlinear Filters | |
| |
| |
| |
| Nonlinear Kalman filtering | |
| |
| |
| |
| The linearized Kalman filter | |
| |
| |
| |
| The extended Kalman filter | |
| |
| |
| |
| The continuous-time extended Kalman filter | |
| |
| |
| |
| The hybrid extended Kalman filter | |
| |
| |
| |
| The discrete-time extended Kalman filter | |
| |
| |
| |
| Higher-order approaches | |
| |
| |
| |
| The iterated extended Kalman filter | |
| |
| |
| |
| The second-order extended Kalman filter | |
| |
| |
| |
| Other approaches | |
| |
| |
| |
| Parameter estimation | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| The unscented Kalman filter | |
| |
| |
| |
| Means and covariances of nonlinear transformations | |
| |
| |
| |
| The mean of a nonlinear transformation | |
| |
| |
| |
| The covariance of a nonlinear transformation | |
| |
| |
| |
| Unscented transformations | |
| |
| |
| |
| Mean approximation | |
| |
| |
| |
| Covariance approximation | |
| |
| |
| |
| Unscented Kalman filtering | |
| |
| |
| |
| Other unscented transformations | |
| |
| |
| |
| General unscented transformations | |
| |
| |
| |
| The simplex unscented transformation | |
| |
| |
| |
| The spherical unscented transformation | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| The particle filter | |
| |
| |
| |
| Bayesian state estimation | |
| |
| |
| |
| Particle filtering | |
| |
| |
| |
| Implementation issues | |
| |
| |
| |
| Sample impoverishment | |
| |
| |
| |
| Particle filtering combined with other filters | |
| |
| |
| |
| Summary | |
| |
| |
| Problems | |
| |
| |
| |
| Historical perspectives | |
| |
| |
| |
| Other books on Kalman filtering | |
| |
| |
| |
| State estimation and the meaning of life | |
| |
| |
| References | |
| |
| |
| Index | |