The MUSIC algorithm has proven to be an effective means of estimating parameters of multiple incoherent signals. Furthermore, the forward-backward (FB) spatial smoothing technique has been considered the best preprocessing method to decorrelate coherent signals. In this paper, we propose a novel preprocessing technique based upon ideas associated with the FB and adaptive spatial smoothing techniques and report on its superiority in numerical simulations.

It is an important problem in fields of radar, sonar, and so on to estimate parameters of closely spaced multiple signals. The MUSIC algorithm with the forward-backward (FB) spatial smoothing is considered as the most effective technique at present for the problem with coherent signals in a variety of fields. We have applied this in Laser Microvision. Recently, Shimotahira has proposed the Kernel MUSIC algorithm, which is applicable to cases when signal vectors and noise vectors are orthogonal. It also utilizes Gaussian elimination of the covariance matrix instead of eigenvalue analysis to estimate noise vectors. Although the amount of computation by the Kernel MUSIC algorithm became lighter than that of the conventional MUSIC algorithm, the covariance matrix was formed to estimate noise vectors and also all noise vectors were used to analyze the MUSIC eigenspectrum. The heaviest amount of computation in the Kernel MUSIC algorithm exists in the transformation of the covariance matrix and the analysis of the MUSIC eigenspectrum. We propose a more straightforward algorithm to estimate noise vectors without forming a covariance matrix, easier algorithm to analyze the MUSIC eigenspectrum. The superior characteristics will be demonstrated by results of numerical simulation.

We propose the Kernel MUSIC algorithm as an improvement over the conventional MUSIC algorithm. This algorithm is based on the orthogonality between the image and kernel space of an Hermitian mapping constructed from the received data. Spatial smoothing, needed to apply the MUSIC algorithm to coherent signals, is interpreted as constructing procedure of the Hermitian mapping into the subspace spanned by the constituent vectors of the received data. We also propose a new spatial smoothing technique which can remove the redundancy included in the image space of the mapping and discuss that the removal of redundancy is essential for improvement of resolution. By computer simulation, we show advantages of the Kernel MUSIC algorithm over the conventional one, that is, the reduction of processing time and improvement of resolution. Finally, we apply the Kernel MUSIC algorithm to the Laser Microvision, an optical misroscope we are developing, and verify that this algorithm has about two times higher resolution than that of the Fourier transform method.