State estimation of a supply chain using improved resampling rules for particle filtering

Resampling rules for importance sampling play a critical role in achieving good performance of the particle filters by preventing the sampling procedure from generating degenerated weights for particles, where a single particle abruptly possesses significant amount of normalized weights, and from wasting computational resources by replicating particles proportional to these weights. In this work, we propose two new resampling rules concerning minimized variance and minimized bias, respectively. Then, we revisit a half-with based resampling rule for benchmarking purposes. The proposed rules are derived theoretically and their performances are compared with that of the minimized variance and half width-based resampling rules existing in the literature using a supply chain simulation in terms of their resampling qualities (mean and variance of root mean square errors) and computational efficiencies, where we identify the circumstances that the proposed resampling rules become particularly useful.