Conference paper
Efficient Computation of the Continuous-Discrete Extended Kalman Filter Sensitivities Applied to Maximum Likelihood Estimation
Department of Applied Mathematics and Computer Science, Technical University of Denmark1
Scientific Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark2
Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark3
In this paper, we present and compare different methods for computing the likelihood function and its gradient. We consider nonlinear continuous-discrete models described by a system of stochastic differential equations (SDEs) with discrete-time measurements. The problem of maximum likelihood estimation (MLE) is formulated as a nonlinear program (NLP) and it is solved numerically using a gradient-based single shooting algorithm.
The estimates of the mean and its covariance are computed using a continuous-discrete extended Kalman filter (CDEKF). We derive analytical expressions for the gradient of the likelihood function. We discuss some aspects of the implementation of MLE for non-stiff systems. In particular, we present an efficient way of computing the state covariance matrix and its gradient using explicit Runge-Kutta schemes.
We verify our implementation using a numerical example related to type 1 diabetes and demonstrate how to apply it for nonlinear parameter estimation.
| Language: | English |
|---|---|
| Publisher: | IEEE |
| Year: | 2019 |
| Pages: | 6983-6988 |
| Proceedings: | 58th IEEE Conference on Decision and Control |
| ISBN: | 1728113970 , 1728113989 , 1728113997 , 9781728113975 , 9781728113982 and 9781728113999 |
| ISSN: | 25762370 and 07431546 |
| Types: | Conference paper |
| DOI: | 10.1109/cdc40024.2019.9029672 |
| ORCIDs: | Boiroux, Dimitri , Ritschel, Tobias Kasper Skovborg , Poulsen, Niels Kjølstad , Madsen, Henrik and Jørgensen, John Bagterp |
Computational modeling Covariance matrices Kalman filters MLE Maximum likelihood estimation Numerical models Runge-Kutta methods Runge-Kutta schemes Sensitivity Technological innovation continuous-discrete extended Kalman filter continuous-discrete models covariance matrices covariance matrix differential equations discrete-time measurements gradient methods gradient-based single shooting algorithm maximum likelihood estimation nonlinear filters nonlinear parameter estimation nonlinear program nonlinear programming nonstiff systems parameter estimation stochastic differential equations stochastic processes
