Stochastic Estimation for Two-State Linear Dynamic Systems With Additive Cauchy Noises


An economical recursive state estimator is developed for two-state linear systems driven by Cauchy distributed process and measurement noises. For a general vector-state system, the estimator is based on recursively propagating the characteristic perform of the conditional probability density operate (cpdf), where the amount of terms in the add that expresses this characteristic operate grows with each measurement update. Both the conditional mean and therefore the conditional error variance are functions of the measurement history. For systems with 2 states, the proposed estimator reduces substantially the amount of terms needed to precise the characteristic operate of the cpdf by benefiting from relationships not yet developed in the general vector-state case. Additional, by employing a mounted sliding window of the most recent measurements, the improved potency of the proposed 2-state estimator permits an accurate approximation for real-time computation. During this way, the computational complexity of each measurement update eventually becomes constant, and an arbitrary number of measurements can be processed. The numerical performance of the Cauchy estimator in each Cauchy and Gaussian simulations was demonstrated and compared to the Kalman Filter.

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