M<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e466" altimg="si2.svg"><mml:msup><mml:mrow /><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>-spectral estimation: A relative entropy approach

Abstract This paper deals with M 2 -signals, namely multivariate (or vector-valued) signals defined over a multidimensional domain. In particular, we propose an optimization technique to solve the covariance extension problem for stationary random vector fields. The Itakura–Saito distance is employed as criterion select solution among spectra satisfying finite number of moment constraints. order avoid technicalities that may happen on boundary feasible set, deal discrete version where integrals are approximated by Riemann sums. spectrum also discrete, which occurs naturally when underlying field periodic. We show exists, unique and depends smoothly data. Therefore, have well-posed whose can be tuned in smooth manner. Finally, applied our theory target parameter estimation integrated system automotive modules. Simulation results spectral estimator has promising performance.