Modified quasi-OBE algorithm with improved numerical properties

The quasi-OBE (QOBE) algorithm is a set-membership adaptive filtering algorithm based on the principles of optimal bounding ellipsoid (OBE) processing. This algorithm can provide enhanced convergence and tracking performance as well as reduced average computational complexity in comparison with the more traditional adaptive filtering algorithms such as the recursive leastsquares (RLS) algorithm. In this paper, we show that the QOBE algorithm is prone to numerical instability due to the unbounded growth/decay of its internal variables. To tackle this problem, we develop a new set-membership adaptive filtering algorithm by transforming QOBE’s internal variables into a new set of internal variables. The new algorithm, called modified quasi-OBE (MQOBE), can be viewed as an exponentially-weighted RLS algorithm with a time-varying forgetting factor, which is optimized at each iteration by imposing a bounded-magnitude constraint on the a posteriori filter output error. The proposed algorithm delivers the same convergence and tracking performance as the QOBE algorithm but with enhanced numerical properties. We demonstrate the improved numerical behavior of the proposed algorithm by simulation examples for a MIMO channel estimation problem.