Kalman Filter With Dynamical Setting of Optimal Process Noise Covariance

Abstract

We propose a dynamical way to set the process error covariance matrix (Q) for a constant velocity (CV) model Kalman filter. We are able to achieve the best possible solution for the estimated state, in the sense of forecast error, while significantly reducing the convergence time at no significant computational cost. No assumptions regarding the statistical nature of the observed process are made and no prior knowledge of the system is required. To achieve this, we adopt a recently proposed performance index for the Kalman filter, we map the best Q for an ample range of model deviations (accelerations) and dynamically set the best possible Q for the CV filter by identifying the average acceleration of the measured signal online. We demonstrate our scheme ability by filtering simulated trajectories with low, medium, and high signal-to-noise ratios. We also track a real erratic target and compare our filter prediction with the best possible a posteriori CV filter.