CS versus MAP and MMOSPA for multi-target radar AOAs

Abstract

We expand upon existing the literature regarding using Minimum Mean Optimal Sub-Pattern Assignment error (MMOSPA) estimates in multitarget tracking to apply it to angular superresolution of closely-space targets, noting its advantages in comparison to Maximum a Posteriori (MAP) and Minimum Mean Squared Error (MMSE) estimation. MMOSPA estimators sacrifice target labeling, but in doing so they can (often) avoid coalescence of estimates of closely-spaced objects. A compressive sensing solution, which is a form of MAP estimation, is also considered and is solved via a brute force search, which, contrary to popular belief, is computationally feasible when the number of targets is low, having execution times on the order of tens of milliseconds for two targets on a linear array. 8 We shall note the identities for complex vectors that ∂ ∂b * a H b = 0 and ∂ ∂b * b H a = a. The gradient vector of a complex function, J, is simply ∇ b J = 2 ∂ ∂b * J. 9 Note that A H Q −1 A is real and that (XY) H = Y H X H .

Constrained Multi-Sensor Control Using a Multi-Target MSE Bound and a δ-GLMB Filter

“…As a result, for the various state estimate and permutation in , although the value of the integration may change, the MSE lower bound on the unbiased estimate of is always the same as . Furthermore, it can be known from the references [ 44 , 45 , 46 , 47 , 48 , 49 , 50 ] that the integration on the left-hand side of the inequality (A15) will achieve the minimum value and so, be closest to the lower bound if the unbiased estimator in (A15) is a Minimum Mean OSPA (MMOSPA) estimator. Substituting (A15) into (A14) and then (A13), we get Since both of and are clearly independent of the , (A16) can be reduced to Finally, (32)–(34) can easily be obtained from (A17).…”

“…Substituting (A15) into (A14) and then (A13), we get Since both of and are clearly independent of the , (A16) can be reduced to Finally, (32)–(34) can easily be obtained from (A17). One more important thing to be explained in detail is the relationship between the proposed bound of Theorem 1 and the Minimum Mean OSPA (MMOSPA) presented in [ 44 , 45 , 46 , 47 , 48 , 49 , 50 ]: It can be known from the references [ 44 , 45 , 46 , 47 , 48 , 49 , 50 ] that the proposed OSPA-based multi-target MSE defined in (14) of this paper is actually the Mean OSPA (MOSPA) in [ 44 , 45 , 46 , 47 , 48 , 49 , 50 ]. The MOSPA achieves the minimum value when the estimator is a MMOSPA estimator.…”