Performance Degradation Due to Particle Impoverishment in Particle Filtering

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Particle filtering (PF) has shown its outperforming results compared to that of classical Kalman filtering (KF), particularly for highly nonlinear problems. However, PF may not be universally superior to the extended KF (EKF) although the case (i.e. an example that the EKF outperforms PF) is seldom reported in the literature. Particularly, PF approaches show degraded performance for problems where the state noise is very small or zero. This is because particles become identical within a few iterations, which is so called particle impoverishment (PI) phenomenon; consequently, no matter how many particles are employed, we do not have particle diversity regardless of if the impoverished particle is close to the true state value or not. In this paper, we investigate this PI phenomenon, and show an example problem where a classical KF approach outperforms PF approaches in terms of mean squared error (MSE) criterion. Furthermore, we compare the processing speed of the EKF and PF approaches, and show the better speed performance of classical EKF approaches. Therefore, PF approaches may not be always better option than the classical EKF for nonlinear problems. Specifically, we show the outperforming result of unscented Kalman filter compared to that of PF approaches (which are shown in Fig. 7(c) for processing speed performance, and Fig. 6 for MSE performance in the paper).