Robust Extended Kalman Filters
The extended Kalman filter arises by linearizing the signal model about the current state estimate and using the linear Kalman filter to predict the next estimate. This attempts to produce a locally optimal filter, however, it is not necessarily stable because the solutions of the underlying Riccati equation are not guaranteed to be positive definite. One way of improving performance is the faux algebraic Riccati technique which trades off optimality for stability. The familiar structure of the extended Kalman filter is retained but stability is achieved by selecting a positive definite solution to a faux algebraic Riccati equation for the gain design.
Another way of improving extended Kalman filter performance is to employ the H-infinity results from robust control. Robust filters are obtained by adding a positive definite term to the design Riccati equation. The additional term is parametrized by a scalar which the designer may tweak to achieve a trade-off between mean-square-error and peak error performance criteria.
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