Abstract
In this paper, we introduce a new bilinear model in the state space form. The evolution of this model is linear-bilinear in the state of the system. The classical Kalman filter and smoother are not applicable to this model, and therefore, we derive a new Kalman filter and smoother for our model. The new algorithm depends on a special linearization of the second-order term by making use of the best available information about the state of the system. We also derive the expectation maximization (EM) algorithm for the parameter identification of the model. A Monte Carlo simulation is included to illustrate the efficiency of the proposed algorithm. An application in which we fit a bilinear model to wind speed data taken from actual measurements is included. We compare our model with a linear fit to illustrate the superiority of the bilinear model.
| Original language | English |
|---|---|
| Article number | 176 |
| Journal | Advances in Difference Equations |
| Volume | 2012 |
| DOIs | |
| State | Published - 2012 |
Bibliographical note
Funding Information:The first author was supported by Tayyebah University. The second and third authors would like to thank King Fahd University for the excellent research facilities they provide.
Keywords
- EM algorithm
- Kalman filter and smoother
- bilinear state space model
- maximum likelihood estimate
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics