Parameter Estimation Of A Class Of Soft Sensor Model Based On Unscented Kalman Filter

There are lots of development on soft senor in recent years,and modeling is the key work for soft sensor technology.This paper mainly studies parameter estimation for a class of soft sensor model under different working conditions.Firstly,the parameter estimation models of single-rate and dual-rate soft sensor are presented respectively after analyzing their structures and characteristics.In addition,the performance evaluation indexes,relative error,mean square error and posterior CRLB(p CRLB),which is the lower bound of nonlinear filter in the sense of mean square error,are introduced.The p CRLB recursions for the time-variant and time-invariant parameter estimation model are given.Secondly,the parameter estimation for dual-rate model under variable and steady working conditions is studied.The mean and covariance modification UKF algorithm(MCM-UKF)is proposed to estimate the time-variant parameters under variable working conditions.The stability of MCM-UKF is analyzed by Lyapunov Theorem,and the existence and verifiability of stability conditions are discussed.The estimation accuracy of MCM-UKF is verified by comparing with p CRLB in simulations.UKF is used to estimate the time-invariant parameters under steady working conditions,and UKF are closer to the posterior CRLB than slow convergence EKF in simulations.Finally,the parameter estimation for single-rate model under variable and steady working conditions is studied.For single-rate model,the KF or mean and covariance modification KF algorithm(MCM-KF)proposed in the paper can be used to estimate time-invariant or time-variant parameters after some transformations.However,the functional relationship of the transformations requires the transformed variables to satisfy some limitations.The model parameters cannot be obtained by the transformations if the limitations are not satisfied,and the nonlinear filter directly estimates the model parameters without such limitations.The MCM-KF and the commonly used covariance modification KF algorithm(CM-KF)are compared in the simulation of time-variant parameter estimations.The UKF algorithm is used for estimating the time-invariant parameters when the limitation of transformation is not satisfied in simulations,and the performance is improved by adding virtual noise to increase the adaptability of the model.