A polynomial chaos-based nonlinear Bayesian approach for estimating state and parameter probability distribution functions

Various systems engineering and control applications require the knowledge of the complete probability distribution function (pdf) of system states and parameters. This work presents a nonlinear Bayesian estimation approach that uses the histogram filter algorithm to construct the posterior pdfs of the state variables and uncertain parameters based on histograms of the prior and likelihood pdfs. To address the computational challenges associated with the Bayesian estimation algorithms in obtaining the posterior pdfs, the generalized polynomial chaos framework is used to enable efficient propagation of the time-invariant probabilistic system uncertainties with arbitrary distributions. The proposed estimation approach is demonstrated on a benchmark continuous bioreactor, and its performance and computational requirements are compared to those of a sequential importance resampling particle filter.