Pixel-size effects on the probability of detection and on measurement extraction accuracy (the position measurement noise variance) for point sources in the focal plane (FP) of an optical sensor are analyzed from a general target tracking perspective. The analysis uses the point spread function of the optical sensor, which causes distant targets | point sources | to appear as a spatially extended pattern in the FP. Measurement extraction, both via Maximum Likelihood Estimation (MLE) and pixel detection centroiding is examined. The impact of pixel size, target strength (SNR) and target motion uncertainty (“maneuvering index") on tracking accuracy are quantified theoretically and verified by simulations.
Proc. SPIE. 5913, Signal and Data Processing of Small Targets 2005
KEYWORDS: Target detection, Radar, Signal to noise ratio, Statistical analysis, Detection and tracking algorithms, Particles, Monte Carlo methods, Signal processing, Particle filters, Filtering (signal processing)
The ultimate goal of this paper is to track two closely spaced and unresolved targets using monopulse radar measurements, the quality of such tracking being a determinant of successful detection of target spawn. It explores statistical estimation techniques based on the maximum likelihood criterion and Gibbs sampling, and addresses concerns about the accuracy of the measurements delivered thereby. In particular, the Gibbs approach can deliver <i>joint</i> measurements (and the associated covariances) from both targets, and it is therefore natural to consider a joint filter. The ideas are compared; and amongst the various strategies discussed, a particle filter that operates <i>directly on the monopulse measurements</i> is especially promising.
With high resolution radars, realistic objects should be considered as extended rather than point targets. If several closely-spaced targets fall within the same radar beam and between adjacent matched filter samples in range, the full monopulse information from all of these samples can and should be used for estimation, both of angle and of range (with the range to sub-bin accuracy). To detect and localize multiple unresolved extended targets, we establish a model for monopulse radar returns from extended objects, and use a maximum likelihood estimator to localize the targets. Rissanen's minimum description length (MDL) will be used to decide the number of existing extended objects. We compare the new extended target monopulse processing scheme with previously developed point target monopulse techniques to show the improvement in terms of the estimation of target locations, the detection of the number of existing targets, and the tracking performance with a multiple hypothesis tracker (MHT) using the output from the proposed extended target monopulse processor.
This paper considers the optimal resolution cell (pixel) size in detection and tracking IR targets. Using refined resolution can help localizing the position of the targets precisely. However, along with a smaller resolution cell the signal power in each resolution cell becomes lower, because a point target is recorded as a blur according to the point spread function (PSF). Meanwhile, since the noise power is proportional to the area of the pixel, the noise is also lower. On the other hand, using coarse resolution (which is the result of opting for a high signal power in the resolution cell) renders less accurate target position estimates together with higher noise power. That is, as the pixel size changes there is a trade-off in terms of detection performance versus estimation accuracy. We submit that the only defensible way to rationalize this is from system level concerns: what is best for tracking? We will first look at the initial state estimation of a constant velocity target. Relationships between the Cramer-Rao lower bound for the initial state estimation and the resolution cell size will be established. Then, from a general target tracking perspective, the pixel-size effects on the probability of detection and the target location centroiding accuracy will be analyzed.
Here we discuss intervisibility - the existence of an unobstructed line of sight (LOS) between two points - accounting for the vertical and horizontal errors in the estimated locations of both points as well as elevation errors in the database of terrain that could obstruct the LOS between these points. The errors are first simply
treated as a "white" noise sequence: we assume no correlation between the intervisibility at two different times, and only the probability of the intervisibility event is in this case developed. This is useful; but perhaps of greater concern is whether or not a target remains visible long enough and/or often enough that something can
be done about it. Consequently we present a second treatment in which the errors are stochastic processes of given and width, and both the probability density function of the intervisible time and the average number of intervisible intervals over a certain time period interval are developed.
Previously, in a sequence of papers, there has been considerable analysis of the effects of waveforms on tracking; but these have always assumed that measurements both of range and of range-rate are deliverable. Many radar systems use what may be termed “conventional” processing, in which measurements only of range are available, and for which range-rate information must be inferred. Thus, in this paper, results are extended to that case. As an example result, we show that to allow for the bias to the observed range measurement via a linear function of the range-rate results in a considerable loss versus what would be possible with more accurate accounting.