Bayesian Transfer Filter In The Presence Of Dual Rate Measurements

In practical engineering applications,the system state is often a hidden variable or provided by observed values that are affected by noise.In order to accurately estimate these states,state estimation algorithms are often used to reduce the impact of noise.Practical engineering systems considering safety and stability usually contain multiple sensors,and due to differences in the sampling rate and quantization accuracy of sensors,the wear and signal transmission during the production process,and the temperature,humidity,and electromagnetic interference in the environment,there are differences in the sampling rate.Therefore,multi-rate sampling is more common in practical environments.In addition,multiple sensors in the system may also have differences in the observed values of the same variable.After multiple observed values are provided to the filter for processing,the resulting multiple estimated values will also have differences.Transfer learning is a method that uses knowledge obtained from related tasks and transfers it to the target domain task to improve the learning effect of the target domain task.It has been widely used in multiple fields.By using the characteristics of transfer learning,the transfer problem between multiple rate filters can be considered,ultimately improving the estimation effect in the target domain.This paper is based on Bayesian theory and introduces the strategy of transfer learning.We study the transfer problem of Bayesian filters among multirate observed information,time-delayed multi-rate observed information,and slow-rate observed information in multiple source domains.The main research work is summarized as follows:(1)For the problem of multi-rate measurements,the Bayesian mechanism is adopted,and source domain filters and target domain filters are designed based on different rates of observation information.In the case where slow-rate measurement values are available,the estimation of the source domain filter is updated,and the prediction of the source domain on observation information is transferred to the target domain filter in the form of a distribution at the next moment to solve the transfer problem.Through numerical simulation and verification of actual industrial processes,the proposed algorithm has better estimation performance.(2)For the problem of multi-rate measurements with time delay,the Bayesian theory and transfer learning idea are also used to transfer the "knowledge" of the source domain to the target domain filter in the form of a distribution.However,due to the time delay of the observation information in the source domain,some changes were made to the design of its filter,and the timing of the transfer was adjusted.After the transfer is completed,the observation information of the target domain filter is used again to recalculate and obtain the estimation of the current moment.Considering continuingly to improve the accuracy of the target domain estimation,a smoother is introduced after each transfer to smooth the estimates between the two transfer times.Through a numerical simulation and evaluation of a distillation tower model,the proposed algorithm and its smoothing algorithm can estimate the system state well.(3)For the problem of slow-rate measurements simultaneously existing in multiple source domains,multiple source domain filters are designed based on considering their multi-source features.When all source domain filters have obtained the observation values and updated their own estimated states,multiple estimated results are used to predict the current target domain observation value distribution.Based on the size of their covariance matrices,corresponding weights are obtained to fuse multiple estimated values to achieve a better estimation effect.Through a numerical simulation and evaluation of a distillation tower model,the proposed algorithm can effectively estimate the system state.