Robust Estimators for Linear Dynamic Systems Based on Additive Cauchy Uncertainty
A new class of implementable real-time vector-state estimators for linear dynamic systems based on additive heavy-tailed Cauchy process and measurement noises is discussed. The estimation methodology for a vector-state, linear dynamic system with additive Cauchy noises was addressed by developing a recursion for the analytic measurement update and propagation of the character function of the unnormalized conditional probability density function (ucpdf) of the state given the measurement history. Other than the Kalman filter, the current estimation paradigm that is based on the light-tailed Gaussian pdf, this Cauchy estimator stands alone in being the only other estimator for linear multi-variable systems, which has an analytic recursive structure. The Cauchy estimator resolves efficiently uncertainties due to an impulse in the measurement or process noises. In fact, in contrast to the Kalman filter, the conditional probability density function for the Cauchy system is not always unimodal. The currently available results for estimator entail significant numerical complexities due to the rich analytic form of the character function of the ucpdf, which produces a sum of terms that grows at each measurement update. Implementable real-time vector-state estimators are determined by using approximations that are consistent with the fundamental structure of the algorithm.
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