A Covariance Adaptive Student's t Based Kalman Filter

TL;DR

This paper introduces a covariance adaptive Student's t based Kalman filter (TGKF) that improves estimation accuracy in Gaussian noise environments by using a Gaussian mixture model to adaptively optimize the covariance matrix.

Contribution

It proposes a novel covariance adaptive Student's t Kalman filter using GMM to overcome confidence level limitations in Gaussian noise.

Findings

Enhanced accuracy in Gaussian noise conditions

Breakthrough in confidence level adjustment limits

Validated improved performance through experiments

Abstract

In the classical Kalman filter(KF), the estimated state is a linear combination of the one-step predicted state and measurement state, their confidence level change when the prediction mean square error matrix and covariance matrix of measurement noise vary. The existing student's t based Kalman filter(TKF) works similarly to the way KF works, they both work well with impulse noise, but when it comes to Gaussian noise, TKF encounters an adjustment limit of the confidence level, this can lead to inaccuracies in such situations. This brief optimizes TKF by using the Gaussian mixture model(GMM), which generates a reasonable covariance matrix from the measurement noise to replace the one used in the existing algorithm and breaks the adjustment limit of the confidence level. At the end of the brief, the performance of the covariance adaptive student's t based Kalman filter(TGKF) is verified.