A Sampling based method for linear parameter estimation from correlated noisy measurements

Abstract

We address the problem of linear parameter estimation in discrete time state space models in the presence of serially correlated error in variables. The common way to solve parameter estimation problem is least squares (LS) methods. LS method is not considered to be effective when both dependent and independent variables are contaminated by noise. Total Least Squares (TLS) has been introduced as the method for parameter estimation in the case of noisy response and predictor variables. However, TLS solution is not optimal when number of data is limited and noise is correlated. Constrained TLS is a variant of TLS that considers correlation of noise in the data as additional constraints. We introduced a novel method based on a stochastic sampling method to solve estimation problem from correlated noisy measurements, and we compared it with the existing methods through in silico examples. Our method demonstrates significant improvement over other common estimation algorithms, LS, TLS and Constrained TLS under the different amount of correlated noise and data points. It has the potential to be the valuable tool for the difficult real life problems, such as, biological systems where data is limited and noisy.