Determination of data matrix dimensions for subspace-based parameter estimation algorithms

This paper provides an analytical solution to the problem of determining the data matrix dimensions when a subspace-based algorithm is used to estimate parameters from a noisy signal. A unified expression of mean squared errors (MSEs) of signal parameter estimates is given first in terms of singular values and singular vectors. This expression is then generalized so that the MSEs are a function of physical parameters such as the data length, the signal frequency spacing, and the number of rows of the data matrix formed for the use of a subspace-based algorithm. When all the physical parameters except the data matrix dimensions are fixed, the mean squared errors of the signal parameter estimate are a function of the data matrix dimension. The optimal matrix dimensions, which correspond to the minima of the error function, can then be determined. Examples using synthetic data are included to demonstrate the significance of the results.