Comparing Multi-Target Trackers on Different Force Unit Levels

Consider the problem of tracking a set of moving targets. Apart from the tracking result, it is often important to know where the tracking fails, either to steer sensors to that part of the state-space, or to inform a human operator about the status and quality of the obtained information. An intuitive quality measure is the correlation between two tracking results based on uncorrelated observations. In the case of Bayesian trackers such a correlation measure could be the Kullback-Leibler difference. We focus on a scenario with a large number of military units moving in some terrain. The units are observed by several types of sensors and "meta-sensors" with force aggregation capabilities. The sensors register units of different size. Two separate multi-target probability hypothesis density (PHD) particle filters are used to track some type of units (e.g., companies) and their sub-units (e.g., platoons), respectively, based on observations of units of those sizes. Each observation is used in one filter only. Although the state-space may well be the same in both filters, the posterior PHD distributions are not directly comparable -- one unit might correspond to three or four spatially distributed sub-units. Therefore, we introduce a mapping function between distributions for different unit size, based on doctrine knowledge of unit configuration. The mapped distributions can now be compared -- locally or globally -- using some measure, which gives the correlation between two PHD distributions in a bounded volume of the state-space. To locate areas where the tracking fails, a discretized quality map of the state-space can be generated by applying the measure locally to different parts of the space.