Orthogonal estimation algorithm

This paper introduces a new algorithm for nonlinear parameter estimation. It is valid for a memoryless nonlinearity where the output is a nonlinear function of the input. A set of orthogonal basis functions is defined that allow independent estimation of the nonlinear parameters. The nonlinearity is estimated as a linear combination of the basis functions. A curious feature about this algorithm is that it uses only additions and multiplications but no divisions. The algorithm uses the probability density function statistics of the input to formulate the orthogonal basis functions. The method is shown to be convergent and stable in the large. It compares favorably with the LMS estimator in terms of accuracy and computational complexity. Simulations are included that show that this algorithm can estimate polynomial and transcendental nonlinearities accurately