A Novel Particle Filter Algorithm:
Markov Jump-Adjusted Particle Filter (MJAPF)
In this project, a novel Particle Filter algorithm known as the Markov Jump-Adjusted Particle Filter (MJAPF) algorithm is presented. The goal of this modification on the Particle Filter algorithm is to make this state and parameter estimation technique more robust to multi-modal systems such as dynamic systems that are fault-prone, meaning that the system is susceptible to operating in more than one mode which could include nominal and different faulty modes. MJAPF has been proven to be more reliable than the standard Particle Filter in estimating the dynamic states of such systems. The implementation presented in the GitHub repository is a dual-state estimator script.
Figure 1 illustrates the effectivity of the MJAPF algorithm in estimating the state of a system with time-variant dynamics and multiple operating modes. It can be seen that the MJAPF algorithm decidedly surpasses the performance of a standard Particle Filter in such systems.
Figure 1. Comparison between a sample RW motor’s signals obtained under the following conditions: (a) As received from the noisy sensor (b) The real RW’s signal with process noise but without the measurement noise, (c) As filtered by MJAPF with 2000 particles, (d) As filtered by a standard Particle Filter with 2000 particles, and (e) The signal's different operating modes.
The main idea behind the MJAPF is that the particles are drawn from dynamics that include the faulty modes. In other words, each particle follows a trajectory that is susceptible to transitioning to any of the available operating modes at any time-step in a randomized manner. In this way, after each iteration, the likely particle trajectories are resampled to focus computation power on the most likely regions of the state-space dynamics.
The contents of this study have been published here. For more information regarding this study and to view the complete topic outline, results, and discussions, please consult the following work:
Hedayati, M.; Rahimi, A. A hybrid framework for real-time satellite fault diagnosis using Markov jump-adjusted models and 1D sliding window Residual Networks. Acta Astronautica, from Elsevier BV, Volume 228, pp. 1066-1087.