RLS adaptive filter with inequality constraints

In practical implementations of estimation algorithms, designers usually have information about the range in which the unknown variables must lie, either due to physical constraints (such as power always being nonnegative) or due to hardware constraints (such as in implementations using fixedpoint arithmetic). In this paper we propose a fast (that is, whose complexity grows linearly with the filter length) version of the dichotomous coordinate descent recursive least-squares adaptive filter which can incorporate constraints on the variables. The constraints can be in the form of lower and upper bounds on each entry of the filter, or norm bounds. We compare the proposed algorithm with the recently proposed normalized non-negative least mean squares (LMS) and projected-gradient normalized LMS filters, which also include inequality constraints in the variables.