New approach to improved detection and tracking performance in track-while-scan radars. Part 2: Detection, track initiation and association

Matrix permanent inequalities for approximating joint assignment matrices in tracking systems

“…A strategy for generating multiple hypotheses within the context of the optimal assignment approach is to identify the k best assignments and take the union of their respective pairings [6,[10][11][12]. The assumption is that pairs in the most likely assignments are most likely to be correct.…”

“…This permits the evaluation of the permanents of the submatrices associated with each of the n 2 elements, as required by Eq. (12), to calculate the joint assignment matrix in Oðn 3 Á 2 n Þ time. This is an improvement over the Oðn 4 Á 2 n Þ scaling obtained by the direct application of Ryser's formula (Eq.…”

“…This is because the factors applied to the various rows and columns cancel in the ratio of permanents in Eq. (12). Therefore, the rows and columns of a matrix can be normalized in any manner before attempting to approximate the joint assignment matrix.…”

“…This is because the goal is to estimate the permanent of a submatrix for every element of the matrix, as required by Eq. (12), to generate an estimate of the joint assignment matrix. If all of the estimates are of the same ''quality'' (i.e., are all too large by approximately the same factor), then some amount of post conditioning could yield good results.…”

An Improved Version of a Multiple Target Tracking Algorithm

“…1 In another of their works, NAGARAJAN and co-authors presented a new approach for calculating probability of each hypothesis. 2 They suggested to utilize information from the signal processor of the radar for improving the tracking process. As a result, in the algorithm of NAGARAJAN 1 the authors consider only two possibilities for any measurement, received at scan k : a) to be originated from one of the tracking targets; or b) to be from a new target.…”