Physics – Data Analysis – Statistics and Probability
Scientific paper
2008-07-10
Physics
Data Analysis, Statistics and Probability
26 pages, 2 figures
Scientific paper
The continuous-discrete filtering problem requires the solution of a partial differential equation known as the Fokker-Planck-Kolmogorov forward equation (FPKfe). In this paper, it is pointed out that for a state model with an affine, linear drift and state-independent diffusion matrix the fundamental solution can be obtained using only linear algebra techniques. In particular, no differential equations need to be solved. Furthermore, there are no restrictions on the size of the time step size, or on the measurement model. Also discussed are important computational aspects that are crucial for potential real-time implementation for higher-dimensional problems. The solution is universal in the sense that the initial distribution may be arbitrary.
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