An efficient Kalman filter for the identification of low-rank systems

Abstract

System identification problems are very difficult in the scenario of long length impulse responses, raising challenges in terms of convergence, complexity, and accuracy of the solution. However, we can take advantage of the characteristics of the impulse response, in order to improve the overall performance. In this context, a recently introduced approach exploits a Kronecker product decomposition of the impulse response in tandem with low-rank approximations. Also, a recursive least-squares (RLS) algorithm was developed based on this idea, showing appealing results for the identification of low-rank systems, like typical echo paths. In this short communication, we propose a Kalman filter tailored for the identification of such low-rank systems. Simulations performed in the context of echo cancellation indicate that the proposed algorithm outperforms the regular Kalman filter, but also its RLS-based counterpart.