A Pearson-Type VII Distribution With Adaptive Parameters Selection-Based Interacting Multiple Model Kalman Filter

Existing robust filters under generalized non-stationary noises conditions are difficult to choose suitable prior parameters, this brief proposed a Pearson-type VII distribution with adaptive parameters selection based interacting multiple model (IMM) Kalman filter (IMM-PVIIKF). In the model conditional filtering process, both the one-step prediction and the measurement likelihood are modeled as Pearson-type VII distributions. They are decomposed into Gaussian-Gamma Hierarchies (GGH), which are then matched to the time-varying heavy-tailed properties of the noises by pre-selecting the sets of shape and rate parameters and the variational Bayesian (VB) technique. Finally, a new model probability update method for filter under non-Gaussian conditions is derived. Simulation results show that the filter proposed in this brief has better robustness and adaptability to generalized non-stationary noises than the existing filters.

Automated summary

This paper proposes an adaptive parameter selection of Pearson VII distribution based on interacting multiple model (IMM) Kalman filter (IMM-PVIIKF). Both the one-step prediction and the measurement likelihood in the model conditional filtering process are modeled as Pearson VII distributions. They are decomposed into Gaussian-Gamma Hierarchies (GGH) and matched to the time-varying heavy-tailed properties of the noises. A new model probability update method for filters under non-Gaussian conditions is derived. Simulation results show that the proposed filter has better robustness and adaptability to generalized non-stationary noises than existing filters.