ARCI Track Performance Bounds

This report outlines the analytical procedures for bounding the performance of the ACF track functions. The open-loop bearing, time-delay, and frequency interpolation algorithms are rigorously analyzed by developing a probabilistic description for the coarse estimation errors as a function of the input signal-to-noise ratio and the interpolation parameters for both an energy detector (full-aperture) and cross-correlator (split-aperture) frontend. Error bounds for the closed-loop tracker are determined by analogy with an extended Kalman filter and are examined under both linear and nonlinear track assumptions. The linear conditional track error is determined over a small neighborhood that includes the true track. It is valid for reasonably high signal-to-noise ratios where the interpolation bias is negligible. The nonlinear track error is valid at lower signal-to-noise ratios and is based on exploiting the Markov property of the track estimates. For general nonstationary track problems, track error estimates are developed numerically through solution of the Fokker-Planck equation. A closed-form analytic solution is developed for the case of a stationary long observation time track assumption. In both cases, the average track loss times are determined. Although several general examples are included in this report, specific system performance bounds are classified and, therefore, are not discussed here.