|
A number of applications require the precise tracking or position estimation of an object that is unresolved in the system optics. This paper evaluates the performance of several interpolation algorithms designed to make these estimates to subpixel accuracy. The tracking sensor examined was a scanning linear array of infrared detectors which were assumed to be background limited. The optics blur spot was assumed gaussian. The relative change in performance with changes in the array configuration was investigated. The detector size and physical spacing were varied parametrically, but with realistic fabrication constraints, to obtain the optimum configuration. The sources of error considered to affect the performance were the systematic algorithm bias, the random noise, and the post-calibration residual detector responsivity nonuniform-ities. The systematic algorithm error or bias was calculated and its rms value over an array pitch was used as one measure of estimation error. The random noise in the signal was propagated by variance analysis into another source of estimation error. Finally, the residual nonuniformities in the detector responsivities after calibration were propagated by variance analysis into an rms spread in the algorithm error, and provide a third source of error. The interpolation algorithms investigated were the odd N point centroids (N = 3, 5, 7, 9) and the three and five-point quadratic curve fits. A simple coarse search routine of peak signal detection was assumed to determine the origin. The optimum performance of a two-row staggered linear array with square detectors and realistic fabrication constraints (P ≥ L/2) occurs for detector lengths (L) slightly less than 1/3 the blur spot size, as defined by 2.44 λ/D where A is the spectral wavelength and D is the optics aperture. The 3 point centroid performs best as a function of signal-to-noise (SNR), but requires a systematic correction of the algorithm bias. The higher N-point centroids quickly degraded in SNR performance but had negligible algorithm error. The quadratic curve fits were worse in SNR performance than the three-point centroid (except for larger, nonoptimized detector sizes) and still required a correction algorithm. The analysis was confirmed with Monte Carlo simulations. An experimental infrared tracking focal plane was purchased and used in a tracker simulation. The tracker error data, taken as a function of SNR confirmed closely the analysis for all signal-to-noise ratios above four. The track error follows the predicted SNR-1 behavior until limited at high SNR to a constant that corresponds to the algorithm bias error in the absence of correction or to the nonuniformity error if a correction routine is included. With the three point algorithms, an experimental accuracy to smaller than 1/100th a detector (<1/250th a blur spot) was obtained at high signal-to-noise ratios.
|
