Implementation of Kalman Filtering with Spiking Neural Networks

Abstract

A Kalman filter can be used to fill space–state reconstruction dynamics based on knowledge of a system and partial measurements. However, its performance relies on accurate modeling of the system dynamics and a proper characterization of the uncertainties, which can be hard to obtain in real-life scenarios. In this work, we explore how the values of a Kalman gain matrix can be estimated by using spiking neural networks through a combination of biologically plausible neuron models with spike-time-dependent plasticity learning algorithms. The performance of proposed neural architecture is verified with simulations of some representative nonlinear systems, which show promising results. This approach traces a path for its implementation in neuromorphic analog hardware that can learn and reconstruct partial and changing dynamics of a system without the massive power consumption that is typically needed in a Von Neumann-based computer architecture.

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“…When v m overpasses certain threshold voltage v th , the neuron emits a spike of amplitude v spk , being δ(t) the Dirac delta function. As described at [9], by solving the differential equation in the time interval it takes to the neuron to v m = v th and considering the frequency definition, a function which relates I ext with the output spiking frequency can be obtained as:…”

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