A new class of nonlinearly constrained linear estimator

The problem of model parameter estimation subject to a simple class of nonlinear constraints in the time domain is addressed. The model parameters correspond to tap-delay filter weights and are used to approximate, within the constraints, a desired signal in the mean-square sense. The class of nonlinear constraints consists of convex quadratic functions with one-dimensional null space. This class, which includes the variance of the weight vector, allows the constrained optimization problem to be carried out by two successive unconstrained optimization algorithms implemented in multidimensional and unidimensional spaces. When the least-mean-squares (LMS) technique is used in both spaces, it is shown that the overall convergence time is not influenced by the constraint, i.e. it is primarily determined by the constraint-free LMS algorithm in the multidimensional space