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
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