Distributed least-squares estimation applied to GNSS networks

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, ...

Distributed Incremental Least Mean-Square for Parameter Estimation using Heterogeneous Adaptive Networks in Unreliable Measurements

Adaptive networks include a set of nodes with adaptation and learning abilities for modeling various types of self-organized and complex activities encountered in the real world. This paper presents the effect of heterogeneously distributed incremental LMS algorithm with ideal links on the quality of unknown parameter estimation. In heterogeneous adaptive networks, a fraction of the nodes, defi...

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...

Empirical Distributions in Least Squares Estimation for Distributed Parameter Systems

We consider the estimation of error distributions in least squares identiication of distributed parameter systems. Asymptotic properties of approximate error sequences are developed. In particular, we examine consistency and asymptotic normality of empirical estimates of the error distribution. The consistency obtained is analogous to the Glivenko-Cantelli theorem. For asymptotic normality, we ...