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.

Determining possible avenues of approach using ANTS

Threat assessment is an important part of level 3 data fusion. Here we study a subproblem of this, worst-case risk assessment. Inspired by agent-based models used for simulation of trail formation for urban planning, we use ant colony optimization (ANTS) to determine possible avenues of approach for the enemy, given a situation picture. One way of determining such avenues would be to calculate the ``potential field'' caused by placing sources at possible goals for the enemy. This requires postulating a functional form for the potential, and also takes long time. Here we instead seek a method for quickly obtaining an effective potential. ANTS, which has previously been used to obtain approximate solutions to various optimization problems, is well suited for this. The output of our method describes possible avenues of approach for the enemy, i.e, areas where we should be prepared for attack. (The algorithm can also be run ``reversed'' to instead get areas of opportunity for our forces to exploit.) Using real geographical data, we found that our method gives a fast and reliable way of determining such avenues. Our method can be used in a computer-based command and control system to replace the first step of human intelligence analysis.

Multi-target particle filtering for the probability hypothesis density

When tracking a large number of targets, it is often computationally expensive to represent the full joint distribution over target states. In cases where the targets move independently, each target can instead be tracked with a separate filter. However, this leads to a model-data association problem. Another approach to solve the problem with computational complexity is to track only the first moment of the joint distribution, the probability hypothesis density (PHD). The integral of this distribution over any area S is the expected number of targets within S. Since no record of object identity is kept, the model-data association problem is avoided. The contribution of this paper is a particle filter implementation of the PHD filter mentioned above. This PHD particle filter is applied to tracking of multiple vehicles in terrain, a non-linear tracking problem. Experiments show that the filter can track a changing number of vehicles robustly, achieving near-real-time performance.