Minimum Total Error Entropy Method for Parameter Estimation

In the errors-in-variables (EIV) system/model, both input data and output data are assumed to be contaminated with noise. For the parameter estimation problem of EIV system, the total least squares (TLS) is a classical and widely used method. The TLS method is based on minimizing the squared total error and thus can not sufficiently utilize all possible information from the data when the noise is non-Gaussian. In non-Gaussian cases, the error entropy criterion (EEC) and the EEC-based minimum error entropy (MEE) method have shown their superiority in previous studies. However, the traditional MEE method only considers noise-free input data in the estimation. So it will lead to suboptimal solutions when applied to EIV system. In this work, we present a total error entropy criterion (TEEC) and a corresponding method named minimum total error entropy (MTEE), which additionally considers the existence of noise in input data. Besides, we carry out theoretically the local stability analysis of the proposed method and obtain a bound for the step size to ensure local stability. Simulation results corroborate the effectiveness of the MTEE. It achieves superior performance comparing to the TLS and MEE, when the noise is non-Gaussian.