Rational subspace estimation using adaptive lossless filters

Rational models have been studied as a tractable attempt to account for frequency dependencies using a finite parameter description. In this context, the following problem is addressed: Given time-domain measurements, estimate rational orthonormal spanning vectors for the signal and noise subspaces. It is shown that the problem can be rephrased as adapting a lossless transfer matrix so as to maximize the power split between two sets of output bins. An efficient and numerically robust adaptive filtering algorithm is derived for lossless multivariable lattice filters, and the system can be programmed in real time using CORDIC processors. The adaptive filter equations are consistent with the proper subspace identification if the subspace filter satisfies a sufficient order condition. In under-modeled scenarios the stable stationary points are characterized by a minimized Rayleigh quotient which leads to good subspace fits. The proposed adaptive filter makes real-time rational subspace estimation an accessible alternative to computationally expensive offline techniques