Effects of unknown covariances in the state estimation fusion equation

This paper explores the effect of unknown covariances on the track association and fusion algorithms. For legacy sensors that produce tracks without covariance information, a priori covariances are often used. In other network scenarios quantized covariances are used. These a priori or quantized covariances can be different from the actual underlying sensor uncertainty. In a typical fusion process these covariances are used for gating and in state estimation equations. The question addressed in this paper is how to predict and quantify the likelihood of the fused solution being better or worse given unknown uncertainty in the underlying sensor. This paper evaluates the probability of corruption for the fusion of two sensors, where one sensor has a fixed, known variance, and the other sensor has an equal or larger, known variance. Next, the paper evaluates when one sensor has a fixed, known variance and the other sensor has an equal or larger, unknown variance. Analytical and numerical calculations were developed to predict the percent improvement and likelihood of corruption for one-dimensional sensors. Numerical results were also obtained using Monte Carlo simulations to study the effect of the unknown uncertainties for two dimensional sensors for various covariance configurations. The paper also explores the effects of quantized variances. The results demonstrate the degradation of the fusion performance when the covariances used for one of the sensors does not match reality.