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Acknowledgments | |

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Acronyms | |

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List of algorithms | |

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Introduction | |

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Introductory Material | |

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Linear systems theory | |

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Matrix algebra and matrix calculus | |

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Matrix algebra | |

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The matrix inversion lemma | |

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Matrix calculus | |

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The history of matrices | |

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Linear systems | |

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Nonlinear systems | |

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Discretization | |

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Simulation | |

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Rectangular integration | |

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Trapezoidal integration | |

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Runge-Kutta integration | |

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Stability | |

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Continuous-time systems | |

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Discrete-time systems | |

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Controllability and observability | |

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Controllability | |

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Observability | |

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Stabilizability and detectability | |

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Summary | |

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Problems | |

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Probability theory | |

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Probability | |

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Random variables | |

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Transformations of random variables | |

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Multiple random variables | |

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Statistical independence | |

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Multivariate statistics | |

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Stochastic Processes | |

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White noise and colored noise | |

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Simulating correlated noise | |

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Summary | |

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Problems | |

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Least squares estimation | |

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Estimation of a constant | |

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Weighted least squares estimation | |

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Recursive least squares estimation | |

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Alternate estimator forms | |

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Curve fitting | |

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Wiener filtering | |

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Parametric filter optimization | |

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General filter optimization | |

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Noncausal filter optimization | |

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Causal filter optimization | |

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Comparison | |

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Summary | |

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Problems | |

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Propagation of states and covariances | |

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Discrete-time systems | |

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Sampled-data systems | |

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Continuous-time systems | |

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Summary | |

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Problems | |

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The Kalman Filter | |

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The discrete-time Kalman filter | |

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Derivation of the discrete-time Kalman filter | |

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Kalman filter properties | |

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One-step Kalman filter equations | |

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Alternate propagation of covariance | |

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Multiple state systems | |

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Scalar systems | |

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Divergence issues | |

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Summary | |

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Problems | |

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Alternate Kalman filter formulations | |

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Sequential Kalman filtering | |

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Information filtering | |

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Square root filtering | |

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Condition number | |

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The square root time-update equation | |

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Potter's square root measurement-update equation | |

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Square root measurement update via triangularization | |

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Algorithms for orthogonal transformations | |

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U-D filtering | |

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U-D filtering: The measurement-update equation | |

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U-D filtering: The time-update equation | |

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Summary | |

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Problems | |

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Kalman filter generalizations | |

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Correlated process and measurement noise | |

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Colored process and measurement noise | |

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Colored process noise | |

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Colored measurement noise: State augmentation | |

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Colored measurement noise: Measurement differencing | |

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Steady-state filtering | |

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[alpha]-[beta] filtering | |

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[alpha]-[beta]-[gamma] filtering | |

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A Hamiltonian approach to steady-state filtering | |

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Kalman filtering with fading memory | |

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Constrained Kalman filtering | |

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Model reduction | |

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Perfect measurements | |

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Projection approaches | |

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A pdf truncation approach | |

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Summary | |

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Problems | |

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The continuous-time Kalman filter | |

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Discrete-time and continuous-time white noise | |

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Process noise | |

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Measurement noise | |

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Discretized simulation of noisy continuous-time systems | |

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Derivation of the continuous-time Kalman filter | |

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Alternate solutions to the Riccati equation | |

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The transition matrix approach | |

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The Chandrasekhar algorithm | |

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The square root filter | |

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Generalizations of the continuous-time filter | |

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Correlated process and measurement noise | |

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Colored measurement noise | |

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The steady-state continuous-time Kalman filter | |

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The algebraic Riccati equation | |

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The Wiener filter is a Kalman filter | |

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Duality | |

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Summary | |

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Problems | |

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Optimal smoothing | |

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An alternate form for the Kalman filter | |

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Fixed-point smoothing | |

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Estimation improvement due to smoothing | |

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Smoothing constant states | |

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Fixed-lag smoothing | |

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Fixed-interval smoothing | |

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Forward-backward smoothing | |

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RTS smoothing | |

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Summary | |

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Problems | |

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Additional topics in Kalman filtering | |

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Verifying Kalman filter performance | |

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Multiple-model estimation | |

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Reduced-order Kalman filtering | |

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Anderson's approach to reduced-order filtering | |

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The reduced-order Schmidt-Kalman filter | |

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Robust Kalman filtering | |

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Delayed measurements and synchronization errors | |

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A statistical derivation of the Kalman filter | |

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Kalman filtering with delayed measurements | |

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Summary | |

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Problems | |

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The H[subscript infinity] Filter | |

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The H[subscript infinity] filter | |

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Introduction | |

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An alternate form for the Kalman filter | |

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Kalman filter limitations | |

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Constrained optimization | |

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Static constrained optimization | |

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Inequality constraints | |

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Dynamic constrained optimization | |

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A game theory approach to H[subscript infinity] filtering | |

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Stationarity with respect to x[subscript 0] and w[subscript k] | |

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Stationarity with respect to x and y | |

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A comparison of the Kalman and H[subscript infinity] filters | |

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Steady-state H[subscript infinity] filtering | |

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The transfer function bound of the H[subscript infinity] filter | |

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The continuous-time H[subscript infinity] filter | |

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Transfer function approaches | |

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Summary | |

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Problems | |

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Additional topics in H[subscript infinity] filtering | |

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Mixed Kalman/H[subscript infinity] filtering | |

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Robust Kalman/H[subscript infinity] filtering | |

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Constrained H[subscript infinity] filtering | |

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Summary | |

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Problems | |

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Nonlinear Filters | |

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Nonlinear Kalman filtering | |

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The linearized Kalman filter | |

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The extended Kalman filter | |

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The continuous-time extended Kalman filter | |

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The hybrid extended Kalman filter | |

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The discrete-time extended Kalman filter | |

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Higher-order approaches | |

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The iterated extended Kalman filter | |

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The second-order extended Kalman filter | |

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Other approaches | |

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Parameter estimation | |

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Summary | |

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Problems | |

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The unscented Kalman filter | |

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Means and covariances of nonlinear transformations | |

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The mean of a nonlinear transformation | |

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The covariance of a nonlinear transformation | |

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Unscented transformations | |

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Mean approximation | |

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Covariance approximation | |

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Unscented Kalman filtering | |

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Other unscented transformations | |

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General unscented transformations | |

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The simplex unscented transformation | |

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The spherical unscented transformation | |

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Summary | |

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Problems | |

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The particle filter | |

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Bayesian state estimation | |

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Particle filtering | |

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Implementation issues | |

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Sample impoverishment | |

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Particle filtering combined with other filters | |

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Summary | |

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Problems | |

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Historical perspectives | |

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Other books on Kalman filtering | |

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State estimation and the meaning of life | |

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References | |

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Index | |