Spooky effect in optimal OSPA estimation and how GOSPA solves it

--In this paper, we show the spooky effect at a distance that arises in optimal estimation of multiple targets with the optimal sub-pattern assignment (OSPA) metric. This effect refers to the fact that if we have several independent potential targets at distant locations, a change in the probability of existence of one of them can completely change the optimal estimation of the rest of the potential targets. As opposed to OSPA, the generalised OSPA (GOSPA) metric ( α 2) penalises localisation errors for properly detected targets, false targets and missed targets. As a consequence, optimal GOSPA estimation aims to lower the number of false and missed targets, as well as the localisation error for properly detected targets, and avoids the spooky effect. Multiple target estimation is an inherent part of many applications such as surveillance, self-driving vehicles, and air-traffic control [1]-[3]. The special characteristic of multiple target estimation is that it requires the estimation of the number of targets, which is unknown, as well as their states. In a Bayesian paradigm, given some noisy observations of a random variable of interest, all information about this variable is contained in its posterior probability density function [4]. Given the posterior and a cost function, optimal estimation is performed by minimising the expected value of this cost function with respect to the posterior [5], [6]. For example, for random vectors of fixed dimensionality, if the cost function is the square error, the optimal estimator, which is referred to as the minimum mean square error estimator, is the posterior mean.