Target tracking sensors and algorithms are usually evaluated using Monte Carlo simulations covering a large
parameter space. We show a tracker for which the evaluation can be greatly simplified. We apply it to the one
dimensional crossing track problem (e.g. ground target tracking in a dense target environment, where targets are
confined to a road), and estimate the probability that measurements and tracks are incorrectly associated. If only
position is measured, we find the probability of a misassociation is a very simple analytic function of the relevant
parameters: measurement standard deviation, measurement interval, target density, and target acceleration. For
normally distributed target velocities, the average time between misassociations also has a simple form. We
suggest roll-up metrics for tracking sensors and tracking problems.
Steady-state performance of a tracking filter is traditionally evaluated immediately after a track update. However,
there is commonly a further delay (e.g., processing and communications latency) before the tracks can actually
be used. We analyze the accuracy of extrapolated target tracks for four tracking filters: Kalman filter with the
Singer maneuver model and worst-case correlation time, with piecewise constant white acceleration, and with
continuous white acceleration, and the reduced state filter proposed by Mookerjee and Reifler.<sup>1, 2</sup>
Performance evaluation of a tracking filter is significantly simplified by appropriate normalization. For the
Kalman filter with the Singer maneuver model, the steady-state RMS error immediately after an update depends
on only two dimensionless parameters.<sup>3</sup> By assuming a worst case value of target acceleration correlation time,
we reduce this to a single parameter without significantly changing the filter performance (within a few percent
for air tracking).<sup>4</sup>
With this simplification, we find for all four filters that the RMS errors for the extrapolated state are functions
of only two dimensionless parameters. We provide simple analytic approximations in each case.
The unscented transformation is extended to use extra test points beyond the minimum necessary to determine the second moments of a multivariate normal distribution. The additional test points can improve the estimated mean and variance of the transformed distribution when the transforming function of its derivatives have discontinuities.