A particle filter to reconstruct a free-surface flow from a depth camera

We investigate the combined use of a kinect depth sensor and of a stochastic data assimilation (DA) method to recover free-surface flows. More specifically, we use a weighted ensemble Kalman filter method to reconstruct the complete state of free-surface flows from a sequence of depth images only. This particle filter accounts for model and observations errors. This DA scheme is enhanced with the use of two observations instead of one classically. We evaluate the developed approach on two numerical test cases: a collapse of a water column as a toy-example and a flow in an suddenly expanding flume as a more realistic flow. The robustness of the method to depth data errors and also to initial and inflow conditions is considered. We illustrate the interest of using two observations instead of one observation into the correction step, especially for unknown inflow boundary conditions. Then, the performance of the Kinect sensor in capturing the temporal sequences of depth observations is investigated. Finally, the efficiency of the algorithm is qualified for a wave in a real rectangular flat bottomed tank. It is shown that for basic initial conditions, the particle filter rapidly and remarkably reconstructs the velocity and height of the free surface flow based on noisy measurements of the elevation alone.