On-line Bayesian parameter estimation in general non-linear state-space models: A tutorial and new results
On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex multi-dimensional integrals that are not amenable to analytical solution. While basic sequential Monte-Carlo (SMC) or particle filtering (PF) algorithms for simultaneous estimation exist, it is well recognized that there is a need for making these on-line algorithms non-degenerate, fast and applicable to processes with missing measurements. To overcome the deficiencies in traditional algorithms, this work proposes a Bayesian approach to on-line state and parameter estimation. Its extension to handle missing data in real-time is also provided. The simultaneous estimation is performed by filtering an extended vector of states and parameters using an adaptive sequential-importance-resampling (SIR) filter with a kernel density estimation method. The approach uses an on-line optimization algorithm based on Kullback-Leibler (KL) divergence to allow adaptation of the SIR filter for combined state-parameter estimation. An optimal tuning rule to control the width of the kernel and the variance of the artificial noise added to the parameters is also proposed. The approach is illustrated through numerical examples.
Code (0)
등록된 구현이 없습니다.
Tasks
Density Estimationparameter estimationState Space ModelsSimilar Papers 제목 키워드 기반
Bayesian Inference for Consistent Predictions in Overparameterized Nonlinear Regression
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in lin…
Bayesian InferenceLearning TheoryregressionSublinear-Time Approximate MCMC Transitions for Probabilistic Programs
Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such…
parameter estimationProbabilistic ProgrammingState EstimationState Space ModelsSuccessive Linear Approximation VBI for Joint Sparse Signal Recovery and Dynamic Grid Parameters Estimation
For many practical applications in wireless communications, we need to recover a structured sparse signal from a linear observation model with dynamic grid parameters in the sensing matrix. Conventional expectation maxim…
Bayesian Inferencecompressed sensingSafe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Models
We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance param…
Bayesian InferenceGeneralized Approximate Survey Propagation for High-Dimensional Estimation
In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setti…
RetrievalSurveyVocal Bursts Intensity Prediction