First-order analysis of the prior-based knowledge MinNorm algorithm

In the context of the direction-of-arrival (DOA) estimation problem, we can sometimes assume the a priori knowledge of M-S DOA among M. Some authors have propose to incorporate this a priori knowledge to better estimate the DOA of interest (ie., the unknown ones). In a previous work, the authors have proposed two prior MinNorm schemes based on oblique projection which allow the integration of this prior-knowledge. In particular, numerical and theoretical expressions of the variances have been derived. In this work, we go further into the analysis already given. We first focus on the asymptotic (large number of sensors) behavior of the standard, the constrained and the prior versions of the MinNorm algorithm and we show that in this case the exploitation of a prior-knowledge is not beneficial. Next, we derive closed-form approximations of the variance of these algorithms in case of two closely-spaced sources for small/moderate number of sensors and we show that the prior-MinNorm algorithms based on oblique projection is much more insensitive to the proximity of the DOA as compared to the standard and the constrained MinNorm algorithms. Finally, these theoretical analysis are checked against computer simulations by means of Monte-Carlo runs.