| Processing the signals received on an array of sensors for the purpose of locating a source is important enough to have been treated under many well-known, special case assumptions. Mathematically, they represent forms of spectral estimation.; The general problem considers sensors with arbitrary locations and directional characteristics (gain/phase/polarization) in an arbitrary additive noise/interference environment.; The signal subspace approach is developed to provide a vector space framework which is general, yet well-suited for practical "real-world" implementations. Signal subspaces are "reachable" vector subspaces which directly connect observed data vectors with the geometric scenario of emitter positions from which they arose.; This thesis develops the signal subspace approach paying special attention to the multiple emitter aspect of this problem as well as to the additive noise/interference characterization. A solution is derived for the general problem which provides (asymptotically) unbiased estimates of (1) number of emitters present; (2) emitter locations; (3) strengths, polarizations, cross-correlations; (4) noise/interference strength.; The MUltiple SIgnal Characterization (MUSIC) algorithm utilizes the signal subspace approach and the geometry of the complex M dimensional vector space C('M). The signal subspace is defined as the K dimensional subspace of C('M) reachable by the received data if K signals are present. Also, the array is completely characterized in C('M) by the array manifold which can be highly nonlinear. Then the solution to the multiple emitter location problem is seen to be the intersection of the signal subspace (obtainable, for example, from received data via eigenstructure analysis) and the array manifold (obtained, perhaps, via array calibration).; Special cases include interferometry (i.e. using uniform collinear arrays), monopulse radar (i.e. using arrays of essentially colocated elements with different directional responses) and time series frequency analysis (estimation of pole location) for data with additive noise.; The MUSIC solution is shown to provide a least squares fit to data and, if the noise is Gaussian, it also represents a maximum likelihood and a maximum entropy estimator. Under practical conditions it is shown to achieve the Cramer-Rao accuracy bound for multiple signals. Examples and comparisons with other maximum likelihood and maximum entropy methods are included. For example, MUSIC is shown to outperform Capon's and Burg's methods in additive noise. Cramer-Rao accuracy limits are derived. An example of the use of MUSIC on time series to estimate multiple frequencies is included. |
