Neural Learning of Kalman Filtering, Kalman Control, and System Identification

Kalman filtering and control methods have been important in engineering since they were introduced in 1960. Recent theoretical work on principles that may describe core computations of cerebral cortex has focussed on the possible role of Kalman filtering and its nonlinear extensions, and of Bayesian inference more generally. However, no neural network (NN) method for learning either the optimal Kalman filter or the optimal Kalman control matrix (for nonstationary control problems) has to my knowledge been described.

Here we show that Kalman estimation (including filtering and prediction) and control, and system identification, can be fully implemented within an NN whose only input is a stream of noisy measurement data. The operation of the fully-integrated algorithm is illustrated by a numerical example. The resulting network is a multilayer recurrent NN that may be useful for engineering applications, and that also bears certain resemblances to the putative ‘local circuit’ of mammalian cerebral cortex.

By: Ralph Linsker

Published in: RC24742 in 2009


This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.


Questions about this service can be mailed to .