Track-to-Track Association Using Attributes

The problem of track-to-track association (T2TA)– a prerequisite for the fusion of tracks–has been considered initially in the literature for tracks described by kinematic states [1]. More recently, it has been generalized to include additional (continuous valued) feature and (discrete valued) attribute variables which pertain to those tracks.1 These approaches allow the search for the maximum likelihood (ML) or maximum a posteriori (MAP) association. It turns out that, under the Gaussian assumption on the estimation errors–which applies to the kinematic states and, possibly, the features–a simple sufficient statistic exists for the track association hypothesis testing and, consequently, it is easy to find the threshold for the desired Neyman-Pearson test of “common origin” (actually, “same kinematic state”) with a selectable power. However, this does not apply for attributes, which are discrete valued. In this paper the sufficient statistic for the optimal association test in the Neyman-Pearson sense is derived for discrete-valued attribute/classification information and its relationship with the class probability vector is discussed. Feature-aided T2TA was presented in [19, 20, 8]. A comprehensive procedure for incorporation of attributes and their possible dependence on the features was presented in [23, 14, 15] and shown to be amenable to obtain the MAP association of tracks from two sensors using linear programming. A multiple model approach for feature aided tracking (FAT) was presented in [22]. Classification-aided tracking with measurementto-track association via multidimensional assignment (MDA) was discussed in [4]. However, while these approaches provide the ML or MAP association, they do not provide the means to set up a statistical hypothesis test with a desired power. Target features and attributes/classification outputs are in general useful for track-to-track association especially when targets are closely spaced and the association based on the kinematic states only is unreliable. In some cases one deals with sensors that provide target attributes but the associated kinematic information is highly inaccurate. In such a case it is of interest to provide association decisions based on the attributes/classification information alone. This is the major motivation for the present work. The rest of the paper is organized as follows. Section 2 discusses briefly the use of (continuous valued) kinematic and feature variables for track-to-track for association. The modeling and use of (discrete valued) attribute/classification information for track-to-track association is presented in Section 3. The modeling of the