Performance analysis of music in the presence of modeling errors due to the spatial distributions of sources

Abstract

In this paper, the direction of arrival (DOA) localization of spatially distributed sources impinging on a sensor array is considered. The performance of the well known MUSIC estimator is studied in the presence of model errors due to angular dispersion of sources. Taking into account the coherently distributed source model proposed in [1], we establish closed-form expressions of the DOA estimation error and mean square error (MSE) due to both the model errors and the effects of a finite number of snapshots. The analytical results are validated by numerical simulations and allow to analyze the performance of MUSIC for coherently distributed sources.

Array geometry impact on music in the presence of spatially distributed sources

“…, q. Introducing 9and 10into (8), and keeping only the first order of ∆θ i , the DOA estimation error for source θ i can be expressed as:…”

“…On the other hand, in the scenario of CD sources, the received signal components are delayed and scaled replicas from different points of the same one [6]. For CD sources, the performances of MUSIC with discretely distributed sources and continuously distributed sources have been investigated in [7], and [8], respectively. As expected, due to the angular dispersion the mismatch between the steering vector model of MUSIC and the actual steering vectors of the sources causes estimation errors.…”

“…In our work, we focus on the impact of the array geometry on the performance of the MUSIC estimator with the CD source model, in the presence of errors due to modeling mismatch of source dispersion. Let us first briefly review our work in [8] and [1]. In [8], the point source MUSIC has been extended into CD-MUSIC (coherent source MUSIC), the first order Talyor approximation DOA estimation bias is proposed in the case that the steering vectors in the model and of the actual sources are mismatched.…”

“…Let us first briefly review our work in [8] and [1]. In [8], the point source MUSIC has been extended into CD-MUSIC (coherent source MUSIC), the first order Talyor approximation DOA estimation bias is proposed in the case that the steering vectors in the model and of the actual sources are mismatched. In [1] we make use of the theoretical estimation bias expression in [8], and express the DOA estimation bias as a function of the sensor positions.…”

“…In [8], the point source MUSIC has been extended into CD-MUSIC (coherent source MUSIC), the first order Talyor approximation DOA estimation bias is proposed in the case that the steering vectors in the model and of the actual sources are mismatched. In [1] we make use of the theoretical estimation bias expression in [8], and express the DOA estimation bias as a function of the sensor positions. Impacts of particular array geometries on the estimator performances are studied in the scenario of single source and multiple sources, respectively.…”