A new perturbation analysis for signal enumeration in rotational invariance techniques

Roland Badeau (1) , Bertrand David (1) , Gael Richard (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information

The ESPRIT algorithm is a subspace-based high resolution method used in source localization and spectral analysis, which provides very accurate estimates of the signal parameters. However, the underlying theory assumes a known model order, which is usually not the case in many applications. In particular, it is well known that under-evaluating the model order biases the estimation. In this paper, we analyze the perturbation induced by an erroneous model order, and we present an error bound for the estimated parameters. Based on this theoretical framework, we propose a new method for selecting an appropriate modeling order, which consists in minimizing the error bound. This approach is applied to both synthetic and musical signals and its performance is compared to that of existing methods, such as the Information Theoretic Criteria.

Keywords: ESPRIT; Rotational invariance; Model order selection; Signal enumeration; Perturbation theory

Domains: Physics [physics]; Mechanics [physics]; Acoustics [physics.class-ph]; Engineering Sciences [physics]; Acoustics [physics.class-ph]

Roland Badeau, Bertrand David, Gael Richard. A new perturbation analysis for signal enumeration in rotational invariance techniques. IEEE Transactions on Signal Processing, 2006, 54 (2), pp.450-458. ⟨10.1109/TSP.2005.861899⟩. ⟨hal-00479779⟩