Noisy FIR parameter estimation by combining of total least mean squares estimation and least mean squares estimation

Least Squares Estimation

Recursive Least Squares Estimation

We start with estimation of a constant based on several noisy measurements. Suppose we have a resistor but do not know its resistance. So we measure it several times using a cheap (and noisy) multimeter. How do we come up with a good estimate of the resistance based on these noisy measurements? More formally, suppose x = (x1, x2, . . . , xn) T is a constant but unknown vector, and y = (y1, y2, ...

Decomposition Methods for Least Squares Parameter Estimation

In this paper least squares method with matrix decomposition is revisited and a multiple model formulation is proposed The proposed formulation takes advantage of the well established decomposition methods but possesses a multiple model structure which leads to simpler and more exible implementations and produces more infor mation than the original least squares methods Several application exam...

Total Least Squares Estimation of Dynamical Systems

The Total least squares error criterion is considered for estimation problems. Exact necessary conditions for the total error criterion have been derived. Several solution methodologies are presented to solve the modified normal equations obtained from the necessary conditions. A monte-carlo simulation depicting the effect of parameter variations on the coefficients of the resulting characteris...

Nonlinear Least-squares Estimation

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu’s illustrates the use of t...