Showing papers by "Mani Bhushan published in 2016"

Covariance computation in MHE: A nonlinear regression approach

Abstract: Moving horizon estimation (MHE) has emerged as a popular technique for state estimation of nonlinear dynamical systems. A key parameter in MHE is the arrival cost that links the formulation in the current horizon with the past data. Most approaches available in literature use additional filters, such as extended Kalman filter or unscented Kalman filter to obtain the covariance matrix used in the arrival cost. In this work, we propose conceptually simple, alternate ways for obtaining the covariances of the arrival cost. Our approaches are motivated by parameter estimation in nonlinear regression. We view the MHE problem as a nonlinear regression problem with the states being the unknown parameters of the regression problem. The covariance of these estimated parameters can then be computed based on the Jacobian matrix. We also propose a Monte-Carlo based sampling approach for covariance calculation. This approach avoids Jacobian matrix calculation but is computationally intensive. A third approach utilizing approximate Hessian, based on equivalence between nonlinear regression and maximum likelihood estimation, is also proposed. Thus, the proposed approaches are able to compute the arrival cost without requiring any other external filter implementation. The MHE estimation performances obtained with the arrival cost covariances computed using the proposed approaches are compared with extended Kalman filter (EKF) and EKF based MHE implementation on case studies taken from literature. These comparisons demonstrate the utility of the proposed approaches.

Projection based constrained nonlinear state estimation using Gaussian sum filters

Abstract: Constraint handling is an integral part of any practical state estimation procedure. Most current approaches to constrained state estimation ensure that the point estimate is feasible with respect to the constraints and are based on popular unconstrained approaches such as sampling based approaches such as Unscented Kalman Filter (UKF) [1], which use deterministically chosen set of sigma points. However, UKF is based on an implicit assumption that the conditional state densities at various steps are Gaussian. In a recent work [2], a new filter termed as Unscented Gaussian Sum Filter (UGSF) was proposed that represents the prior density as a Gaussian sum. It was shown, using simulation studies, that the UGSF outperforms UKF thereby demonstrating the advantage of using a non-Gaussian prior. In this work, we propose to extend UGSF to constrained UGSF by incorporation of constraints on the states in the estimation process. In particular, we propose to use Interval Constrained Unscented Transformation (ICUT) [3] and projection algorithm [4] with the UGSF framework. Implementation on the three state isothermal batch reactor case study [5] shows that the proposed constrained UGSF using the projection method outperforms constrained UKF while maintaining the computation effort similar to the constrained UKF version.