A suboptimal estimation algorithm with probabilistic editing for false measurements with applications to target tracking with wake phenomena

Abstract
The purpose of this paper is to describe a suboptimal technique called probabilistic edit, which can be used for state variable estimation in conjunction with Kalman filtering techniques when the underlying noisy measurement process can contain false measurements, i.e., measuremernts containing no information about the state variables at certain random periods of time. The basic probabilistic edit algorithm is modified to accommodate real-time considerations and is incorporated into a seven-state extended kalman filter which: 1) tracks ballistic reentry vehicles, and 2) estimates their ballistic coefficient. In estimation problems of this kind, the radar measurements of the reentry vehicle's position are corrupted due to contamination of the hard body return with that of the wake. Consequently, a degradation in the performance of the basic tuned extended Kalman filter occurs. Thus, measurements that appear (in a probabillstic sense) to be highly contaminated by wake are modeled as false measurements. The paper includes a discussion of the effect of wake, a description of the basic tracking algoritim, and modifications of the basic tracking algorithm to compensate for the wake-corrupted measurements. Finally, the performance of three distinct algorithm, 1) unmodified ballistic tracking filter, 2) modified ballistic tracking filter using a chi-square test to reject bad measurements, and 3) modified ballistic tracking filter using the probabilistic edit algorithm, using actual data will be presented. The comparison of the three algorithms is conducted using several distinct experiments which differ markedly in the percentage of measurements containing significant wake-corrupted data. The results indicate that the probabilistic edit algorithm can provide improved estimation of the ballistic coefficient with minimal additional real-time computational requirements.

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