A Tensor Approach to Model Order Selection of Multiple Sinusoids

Abstract

The letter presents a covariance tensor based estimator that can effectively provide the model order for multiple sinusoids in noise. For moderate to high signal-to-noise ratios the estimator works effectively even for short length observations. Unlike the conventional methods that use a covariance matrix, the proposed estimator makes use of a three-way covariance tensor formed from the one-dimensional data. Estimate of the model order has been determined by processing the incremental Frobenius norms of the leading principal subtensors of the core tensor obtained via higher order singular value decomposition. Simulations under additive white Gaussian noise show that the new estimator offers significant improvements over conventional methods such as multiple signal classification (MUSIC), estimation of signal parameters via rotational invariance technique+maximum a posteriori, and entropy-based MUSIC. The improvement is particularly notable at larger orders or when frequency separation is small.