MHE Based State and Parameter Estimation for Systems subjected to Non-Gaussian Disturbances Devyani Varshney * Sachin C. Patwardhan * Mani Bhushan * Lorenz T. Biegler ** * Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India (e-mail: sachinp@iitb.ac.in) ** Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, USA (e-mail:biegler@cmu.edu) Abstract: Moving horizon estimation (MHE) is a popular state estimation technique, partic- ularly due to its similarity with model predictive control. The probabilistic formulation of the conventional MHE is developed under the simplifying assumption that state disturbances and measurement noise densities are Gaussian. However, many systems of interest are subjected to uncertainties that have non-Gaussian densities. In current work, we formally extend an existing probabilistic Bayesian formulation of MHE [Varshney et al., 2019] to simultaneous state and parameter estimation for systems subjected to non-Gaussian uncertainties in the state dynamics and measurement model. The efficacy of the proposed MHE has been demonstrated by conducting stochastic simulation studies on a system subjected to non-Gaussian densities. Analysis of simulation results reveals that the estimation performance of the proposed MHE formulation is superior to estimation performances of the conventional Bayesian estimators that can handle non-Gaussian densities and employ the random walk model for parameter variations. Keywords: Moving horizon estimation, Bayesian estimation, State and parameter estimation, Non-Gaussian disturbances 1. INTRODUCTION Nonlinear state estimation is a prerequisite for advanced process control and fault diagnosis tasks. Nonlinear state estimation techniques combine predictions from uncertain system dynamics and noisy measurements to obtain un- known states and parameters. Bayesian state estimation techniques provide a way to optimally combine the in- formation available in the presence of such uncertainties. Sequential Bayesian techniques such as extended Kalman filter (EKF), unscented Kalman filter (UKF), etc. have become very popular due to the ease of their implementa- tion. However, all the existing methods rely on simplifying assumptions about the probability distributions of the underlying variables to obtain a tractable optimization problem. A popular assumption in these techniques is that uncertainties are modeled as Gaussian [Patwardhan et al., 2012]. Such assumptions could be largely incorrect. This has been shown by posterior probability density function (pdf ) of concentration for a CSTR system in Chen et al. [2004]. These approximations may be more violated when constraints are present on the variables which force their probability to be zero for certain regions [Robertson et al., 1996]. However, such assumptions, even though largely incorrect, have been applied in most of the estimation techniques for simplifications irrespective of the original problem. Estimation problems involving non-Gaussian densities have been recently solved using sampling based methods such as particle filters (PF) [Arulampalam et al., 2002] or ensemble Kalman filter (EnKF). An alternative approach to sequential Bayesian approaches, which has become pop- ular over the last decade, is moving horizon approach [Lopez-Negrete et al., 2011]. Moving horizon estimation (MHE) approach formulates the estimation problem as a constrained optimization problem over a moving window framework similar to the model predictive control strategy. Also, the similarity with MPC formulation makes it rela- tively easy to maintain when implemented in combination with MPC. Further, as MHE is posed as an optimization problem, state or disturbance constraints can be easily added to the problem. Another advantage of the approach is that it provides filtered as well as smoothed estimates of states simultaneously within the same window. However, conventional MHE approaches have either been formulated in deterministic settings as weighted least squares problem or in probabilistic settings for Gaussian disturbances only [Rao, 2000]. MHE for systems subjected to non-Gaussian densities has been recently explored by Varshney et al. [2019]. However, approaches discussed so far only handle state estimation problems and unknown parameters are not considered in the problem statement. Many parameters/inputs used in the nonlinear model are seldom known accurately. Significant mismatch between their actual values and the values assumed in the model can severely degrade estimation performance. Towards this end, general practice for parameter estimation is to assume models about the dynamic variation of the parameters Preprints of the 21st IFAC World Congress (Virtual) Berlin, Germany, July 12-17, 2020 Copyright lies with the authors 6018