State Estimation in Large-scale Open Channel Networks Using Sequential Monte Carlo Methods: Optimal Sampling Importance Resampling and Implicit Particle Filters

This article investigates the performance of Monte Carlo-based estimation methods for estimation of flow state in large-scale open channel networks. After constructing a state space model of the flow based on the Saint-Venant equations, we implement the optimal sampling importance resampling filter to perform state estimation in a case in which measurements are available at every time step. Considering a case in which measurements become available intermittently, a random-map implementation of the implicit particle filter is applied to estimate the state trajectory in the interval between the measurements. Finally, some heuristics are proposed, which are shown to improve the estimation results and lower the computational cost. In the first heuristics, considering the case in which measurements are available at every time step, we apply the implicit particle filter over time intervals of a desired size while incorporating all the available measurements over the corresponding time interval. As a second heuristic method, we introduce a maximum a posteriori (MAP) method, which does not require sampling. It will be seen, through implementation, that the MAP method provides more accurate results in the case of our application while having a smaller computational cost. All estimation methods are tested on a network of 19 tidally forced subchannels and 1 reservoir, Clifton Court Forebay, in Sacramento-San Joaquin Delta in California, and numerical results are presented.