A data association algorithm for the robust confidence ellipsoid filter

In this paper, we propose an algorithm to deal with the data association problem of the robust confidence ellipsoid filter. First, at every time instant, for each target, we need to get a validation gate based on the confidence ellipsoid of the previous time instant. Herein, the validation gate is the minimum volume ellipsoid which guarantees that the true measurement of the target at the current time instant must be contained within it. To obtain the validation gate, an optimization problem is derived from the uncertain dynamic system and it is further converted into a semidefinite programming problem. Then, we make use of the measurements in the validation gate (candidate measurements) and the confidence ellipsoid of the previous time instant to gain the confidence ellipsoid of the current time instant. Similar to the process of obtaining the validation gate, the confidence ellipsoid is obtained by solving a semidefinite programming problem. The ellipsoid has the minimum volume and simultaneously, ensures that the true state vector is contained in it. Next, we propose a strategy to deal with the case where there is no measurement in the validation gate (missing measurement). Last, the numerical examples show the verifications of the proposed algorithm.