This chapter covers the Kalman filter and its variants. Kalman filter is the optimal Bayesian filter in the sense of minimizing the mean‐square estimation error for linear systems with Gaussian noise. Algorithms that extend the applicability of the Kalman filter to nonlinear systems either use power series to approximate the nonlinear functions in the state‐space model or use numerical methods to approximate the corresponding probability distributions. While the extended Kalman filter and the divided‐difference filter belong to the former category of algorithms, the unscented Kalman filter and the cubature Kalman filter belong to the latter. Information filter and extended information filter provide alternative formulations of the Kalman filter and the extended Kalman filter by recursively updating the inverse of the estimation error covariance matrix. Using a mixture of Gaussians to approximate the posterior, the Gaussian‐sum filter extends the applicability of the Kalman filter to non‐Gaussian systems. In the Kalman filter algorithm, the corrective term is reminiscent of the proportional controller. The generalized proportional‐integral‐derivative (PID) filter uses a more sophisticated corrective term inspired by the PID controller. Finally, a number of applications of Kalman filtering algorithms are reviewed including information fusion, augmented reality, urban traffic network, cybersecurity of power systems, incidence of influenza, and COVID‐19 pandemic.
Kalman Filter
Nonlinear Filters ; 49-70
2022-04-12
22 pages
Article/Chapter (Book)
Electronic Resource
English
Wiley | 2019
|Wiley | 2022
|Wiley | 2000
|Wiley | 2000
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