Performance Analysis of Subspace-Based Parameter Estimation Algorithms
Progress rept. 1 Jan-30 Jun 1990,
RHODE ISLAND UNIV KINGSTON DEPT OF ELECTRICAL ENGINEERING
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We have developed new perturbation formulas for signal and orthogonal subspaces which are estimated from a noisy data matrix. These formulas are 1 based on a finite amount of data 2 derived under the assumption of high signal-to-noise ratio and 3 applicable to arrays of arbitrary geometry, and they provide a common foundation for all our analyses. We have analyzed a number of array processing algorithms which we classify as follows 1 Signal subspace algorithms ESPRIT, State-space realization including TAM, and Matrix Pencil, 2 Orthogonal subspace algorithms MUSIC and Min-Norm. We have developed analytical variance formulas for the case in which estimates are obtained by searching for the extrema of a function used with arbitrary array geometry, as well as the case in which estimates are obtained by rooting a polynomial or finding the eigenvalues of a matrix used with a uniform line array geometry. In addition, we have developed improvements to a state-space algorithm for frequency-wavenumber 2-D estimation. We give a procedure to pair individual frequency and wavenumber estimates, and we also show how a 2-D forward-backward data matrix can be used to improve the performance of the state-space approach.
- Electrical and Electronic Equipment