Sparse tensors and discrete-time nonlinear filtering

In many applications it is desired that discrete-discrete filtering problem can be solved in a reliable and computationally efficient manner. In particular, the signal and measurement models often include nonlinearity and/or non-Gaussian characteristics. In this paper, it is pointed out that this can be done efficiently by noting two key observations. Firstly, the bulk of the computations associated with the ldquopredictionrdquo step can be done off-line. The second key point is that the transition probability tensor and the conditional probability density are effectively sparse and so can be efficiently stored and manipulated using sparse tensors. These ideas are crucial for efficiently solving the higher dimensional filtering problems. The resulting technique, termed sparse grid filtering, is demonstrated by some examples, where it is shown that it works very well.