Title :
Conditional moment generating functions for integrals and stochastic integrals
Author :
Charalambous, Charalambos D. ; Elliott, Robert J. ; Krishnamurthy, Vikram
Author_Institution :
Dept. of Electr. Eng., McGill Univ., Montreal, Que., Canada
Abstract :
We present two methods for computing filtered estimates for moments of integrals and stochastic integrals of continuous-time nonlinear systems. The first method utilizes recursive stochastic partial differential equations. The second method utilizes conditional moment generating functions. For the case of Gaussian systems the recursive computations involve integrations with respect to Gaussian densities, while the moment generating functions involve differentiations of parameter dependent ordinary stochastic differential equations. The second method is applied in the expectation maximization algorithm
Keywords :
Kalman filters; continuous time systems; filtering theory; integral equations; matrix algebra; nonlinear control systems; partial differential equations; state estimation; stochastic processes; Gaussian densities; Gaussian systems; conditional moment generating functions; continuous-time nonlinear systems; expectation maximization algorithm; parameter dependent ordinary stochastic differential equations; recursive stochastic partial differential equations; stochastic integrals; Covariance matrix; Differential equations; Filtering theory; Integral equations; Nonlinear equations; Nonlinear systems; Stochastic processes; Stochastic systems; Testing; Vectors;
Conference_Titel :
Decision and Control, 1997., Proceedings of the 36th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
0-7803-4187-2
DOI :
10.1109/CDC.1997.652479
