MUltiple SIgnal Classification (MUSIC) is an algorithm used for frequency estimation

Frequency estimation

Frequency estimation is the process of estimating the complex frequency components of a signal in the presence of noise. The most common methods involve identifying the noise subspace to extract these components...

 and emitter location.

MUSIC algorithm

In many practical signal processing problems, the objective is to estimate from measurements a set of constant parameters upon which the received signals depend. There have been several approaches to such problems including the so-called maximum likelihood (ML) method of Capon (1969) and Burg's maximum entropy (ME) method. Although often successful and widely used, these methods have certain fundamental limitations (especially bias and sensitivity in parameter estimates), largely because they use an incorrect model (e.g., AR rather than special ARMA) of the measurements. Pisarenko (1973) was one of the first to exploit the structure of the data model, doing so in the context of estimation of parameters of cisoids in additive noise using a covariance approach. Schmidt (1977), while working at ESL (now part of Northrop Grumman) and independently Bienvenu (1979) currently accepted high-resolution algorithms, MUSIC was the most promising and a leading candidate for further study and actual hardware implementation. However, although the performance advantages of MUSIC are substantial, they are achieved at a cost in computation (searching over parameter space) and storage (of array calibration data).

Application to frequency estimation

MUSIC estimates the frequency content of a signal or autocorrelation matrix

Autocorrelation

Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...

 using an eigenspace method. This method assumes that a signal, , consists of complex exponentials in the presence of Gaussian white noise. Given an autocorrelation matrix, , if the eigenvalues are sorted in decreasing order, the eigenvectors corresponding to the largest eigenvalues span the signal subspace. Note that for , MUSIC is identical to Pisarenko's method

Pisarenko harmonic decomposition

Pisarenko harmonic decomposition, also referred to as Pisarenko's method, is a method of frequency estimation . This method assumes that a signal, x, consists of p complex exponentials in the presence of white noise...

. The general idea is to use averaging to improve the performance of the Pisarenko estimator.

The frequency estimation function for MUSIC is


where are the noise eigenvectors and