Mat-1.3656 Seminar on
numerical analysis and computational science
Monday, April 7, 2014, room M233 at 14.15, Eirola & Stenberg
Atte Aalto, Aalto?, Department of Mathematics and Systems Analysis
Spatial discretization error in Kalman filtering
It is well known that Kalman filter gives the optimal
solution to the state estimation problem for linear discrete time
systems with Gaussian initial state and Gaussian input and output noise
processes. Kalman filter has also proven to be very robust and so it
has been widely adopted in practical applications. When the system is
infinite dimensional it has to be discretized in order to be able to
numerically compute anything. If the Kalman filter is then applied
directly to the discretized system, the result is not optimal.
In this talk, I will present an optimal one
step state estimator for infinite dimensional systems that takes values
in a finite dimensional subspace of the system's state space ---
consider, for example, a finite element space. In addition, I will
derive a bound for the error caused to the state estimate by the state
space discretization. The results are demonstrated by a simple
numerical example.