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New look at the Student's t-based Kalman filter from maximum a posterior perspective

New look at the Student's t-based Kalman filter from maximum a posterior perspective

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In this study, the newly derived Student's t -based Kalman filter (STKF) is re-derived from Bayesian maximum a posterior perspective for linear systems with heavy-tailed measurement noises. This re-derivation reveals that the STKF is an M-estimator with Cauchy function as the robust cost function. The presented re-derivation can also be used as the unified procedure to derive robust Kalman-type filters by assuming the likelihood probability density function to be elliptical distributions.

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