Sam Pimentel, Trinity Western University
Data assimilation with filtering methods that use Kullback-Leibler distance
Abstract: In this paper we will present two filtering algorithms that minimize a cost function of weighted Kullback-Leibler (cross entropy) distance rather than the standard Euclidean distance. Because Kullback-Leibler distance is non-symmetric two filtering methods emerge, the EM (expectation maximization) filter and the SMART filter (simultaneous multiplicative algebraic reconstruction technique). These filters were originally developed to solve an ill-posed inverse problem that arises in reconstructing a time-varying medical image. The algorithms hold potential for data assimilation applications in geophysical fluid problems where we are also interested in time-varying variables of large-scale systems. These new methods have advantages over traditional methods, such as the Kalman filter, in that they do not involve matrix-matrix multiplication or matrix inversion and thus are computationally more efficient. We introduce the EM and SMART filter as a solution to the data assimilation problem and implement these methods on a few simple data assimilation applications. Results are compared with those from more standard approaches. We will highlight the advantages and disadvantages of the EM and SMART filters and demonstrate the potential benefits of the algorithms for geophysical data assimilation applications.