Robustness of the coherently distributed MUSIC algorithm to the imperfect knowledge of the spatial distribution of the sources

Abstract

The MUltiple SIgnal Classification (MUSIC) estimator has been widely studied for a long time for its high resolution capabilities in the domain of the directional of arrival (DOA) estimation, with the sources assumed to be point. However, when the actual sources are spatially distributed with angular dispersion, the performance of the conventional MUSIC is degraded. This paper deals with the sensitivity of MUSIC to modeling error due to coherently distributed (CD) sources. A performance analysis of an extended MUSIC taking into account a generalized steering vector based on a CD source model (CD-MUSIC) is first studied. We establish closed-form expressions of the DOA estimation bias and mean square error due to both the model error and the effects of a finite number of snapshots. The aim of this paper is also to determine when the point source assumption is acceptable for standard MUSIC. The analytical results are validated by numerical simulations and discussed in different configurations.

DOA Tracking of Two-Dimensional Coherent Distribution Source Based on Fast Approximated Power Iteration

“…(1) Initialize W(0) and L(0) (2) Update snapshot data X(t) and obtain the signal subspace W(t) at time t by the FAPI algorithm described in Table 1 (3) Divide the subspace into K/2 groups of W 1 2ς−1 , W 2 2ς−1 , and W 1 2ς (4) Calculate the nominal elevation from the eigenvalue obtained by eigendecomposition using equation (30) and calculate the azimuth angle using equations (31) and (32) (5) Obtained the mean value by equations (33) and (34) as the estimated elevation and azimuth It can be seen from table that the computational complexity required for each iteration of signal subspace updating is O (MKq), which is a very low value. After the signal subspace is obtained, the complexity of DOA estimation mainly lies in the eigendecomposition of R Z , which is O[(MK) 3 ], and calculate a pseudoinverse of W 1 2ζ−1 , which is O[(MK) 3 ].…”

“…Considering the targets are static, scholars have presented different algorithms to model and solve DOA estimation of distributed sources under diverse arrays [19][20][21][22][23][24][25][26][27][28][29][30]. Nevertheless, in the background of a moving target, the DOAs of distributed sources are time-varying.…”

Parameter Estimation for Two-Dimensional Incoherently Distributed Source with Double Cross Arrays

“…Considering CD sources, scholars have presented estimators in [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ]. For 1D ID distributed sources, scholars have proposed various parameter estimation algorithms, mainly including subspace algorithms such as DSPE [ 1 ] and DSPARE [ 4 ], covariance matching estimation techniques [ 26 , 27 , 28 ], maximum likelihood estimation algorithms [ 29 , 30 , 31 , 32 ] and beamforming algorithms [ 33 , 34 , 35 ].…”

DOA Estimation of Two-Dimensional Coherently Distributed Sources Based on Spatial Smoothing of Uniform Rectangular Arrays

“…Supposing that signals from different CD sources are coherent, sample covariance matrices are rank deficient. us, subspace-based algorithms [1,2,[12][13][14][15][16][17][18][19] and ESPRIT class algorithms [20][21][22][23] which are based on eigendecomposition of sample covariance matrices cannot be applied for DOA estimation. PM class algorithms [24][25][26][27] based on linear operation of full rank sample covariance matrices are no longer applicable too.…”

“…In [1,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], CD sources have been regarded as uncorrelated with each other; estimators cannot be applied for CD sources which are correlated. In [24], CD sources correlated with each other are discussed while sources are supposed to be 1D case.…”