System Parameter Estimation Using p-norm Minimization

Real time system parameter estimation from the set of input-outputdata is usually solved by the quadratic norm minimization ofsystem equations errors - known as least squares (LS). Butmeasurement errors are also in the data matrix and so it isnecessary to use a modification known as total least squares (TLS)or mixed LS and TLS.Instead of quadratic norm minimization otherp-norms are used, for 1 <= p <= 2. In the article newmethod is described named Total p-norm and Mixedtotal p-norm which is the analog to TLS and mixed LS and TLSmethod in the quadratic case.The goal of the paper is to develop the method and compare a setof parameter estimations of ARX model where each estimation isobtained by minimizing total p-norm (1<= p <= 2). Totalp-norm and mixed total p-norm approach is used when errors are also in data matrix.