A State-Space Backpropagation Algorithm for Nonlinear Estimation

  • Hasan A. BjailiEmail author
  • Muhammad Moinuddin
  • Ali M. Rushdi


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.


State space Neural network Estimation Backpropagation Prognostics 



Funding was provided by Deanship of Scientic Research, King Abdulaziz University.


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Authors and Affiliations

  1. 1.Department of Electrical and Computer Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Center of Excellence in Intelligent Engineering Systems (CEIES)King Abdulaziz UniversityJeddahSaudi Arabia

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