A State-Space Backpropagation Algorithm for Nonlinear Estimation

Abstract

The fact that the knowledge of system model enhances the performance of any estimation algorithm is well known. However, the existing state-space-based algorithms are either linear such as the Kalman Filter and the state-space least mean square algorithms or highly complex in computation such as the Unscented Kalman Filter and the particle filter algorithms. To remedy this situation, we propose a novel state-space version of the most prominent algorithm used with neural networks, namely the backpropagation algorithm by incorporating the knowledge of the state-space model. To stress that this algorithm has a state-space basis, we call it a “State-Space Backpropagation (SSBP)” algorithm. The developed algorithm is then applied and analyzed on various challenging nonlinear estimation problems including the estimation of Remaining Useful Life of a lithium-ion battery and the Phase Permanent Magnet Synchronous Motor. Simulation results show that the performance of the SSBP is comparable to the competitive algorithms but with very reduced computational complexity.