System Parameter Estimation Using Total P -norm Minimization

Real time system parameter estimation from the set of input-output data is usually solved by the quadratic norm minimization of system equations errors known as least squares (LS). But measurement errors are also in the data matrix and so it is necessary to use a modification known as total least squares (TLS) or mixed LS and TLS. Instead of quadratic norm minimization other p-norms are used, for 1 ≤ p ≤ 2. In the article new method is described named Total p-norm and Mixed total p-norm which is the analog to TLS and mixed LS and TLS method in the quadratic case. The goal of the paper is to develop the method and to compare a set of parameter estimations of ARX model where each estimation is obtained by minimizing total p-norm (1 ≤ p ≤ 2). Total p-norm and mixed total p-norm approach is used when errors are also in data matrix. If the measurement of the system output is damaged by some outliers described method gives better results than standard TLS or mixed LS and TLS approach. Copyright c ©2005 IFAC