Matrix-Valued Measures and Wishart Statistics for Target Tracking Applications

Ensuring sufficiently accurate models is crucial in target tracking systems. If the assumed models deviate too much from the truth, the tracking performance might be severely degraded. While the models are usually defined using multivariate conditions, the measures used to validate them are most often scalar-valued. In this paper, we propose matrix-valued measures for both offline and online assessment of target tracking systems. Recent results from Wishart statistics, and approximations thereof, are adapted and it is shown how these can be incorporated to infer statistical properties for the eigenvalues of the proposed measures. In addition, we relate these results to the statistics of the baseline measures. Finally, the applicability of the proposed measures are demonstrated using two important problems in target tracking: (i) distributed track fusion design; and (ii) filter model mismatch detection.