Tracking small targets, such as missile warheads, from a remote distance is a difficult task since the targets are “points” which are similar to sensor’s noise points. As a result, traditional tracking algorithms only use the information contained in point measurement, such as the position information and intensity information, as characteristics to identify targets from noise points. But in fact, as a result of the diffusion of photon, any small target is not a point in the focal plane array and it occupies an area which is larger than one sensor cell. So, if we can take the geometry characteristic into account as a new dimension of information, it will be of helpful in distinguishing targets from noise points. In this paper, we use a novel method named sparse representation (SR) to depict the geometry information of target intensity and define it as the SR information of target. Modeling the intensity spread and solving its SR coefficients, the SR information is represented by establishing its likelihood function. Further, the SR information likelihood is incorporated in the conventional Probability Hypothesis Density (PHD) filter algorithm with point measurement. To illustrate the different performances of algorithm with or without the SR information, the detection capability and estimation error have been compared through simulation. Results demonstrate the proposed method has higher estimation accuracy and probability of detecting target than the conventional algorithm without the SR information.
Track-before-detect (TBD) based target detection involves a hypothesis test of merit functions which measure each track as a possible target track. Its accuracy depends on the precision of the distribution of merit functions, which determines the threshold for a test. Generally, merit functions are regarded Gaussian, and on this basis the distribution is estimated, which is true for most methods such as the multiple hypothesis tracking (MHT). However, merit functions for some other methods such as the dynamic programming algorithm (DPA) are non-Guassian and cross-correlated. Since existing methods cannot reasonably measure the correlation, the exact distribution can hardly be estimated. If merit functions are assumed Guassian and independent, the error between an actual distribution and its approximation may occasionally over 30 percent, and is divergent by propagation. Hence, in this paper, we propose a novel estimation of distribution method based on Copulas, by which the distribution can be estimated precisely, where the error is less than 1 percent without propagation. Moreover, the estimation merely depends on the form of merit functions and the structure of a tracking algorithm, and is invariant to measurements. Thus, the distribution can be estimated in advance, greatly reducing the demand for real-time calculation of distribution functions.