Estimating state probability distributions from noisy and corrupted data

The method of recursive state density estimation (RSDE) is developed for determining the probability distribution of the states of a system from measurements that contain both random noise and gross errors. The technique is based on the expectation maximization algorithm and is iterative in nature. Similar to EM, at each iteration the likelihood of the distribution estimated by the RSDE algorithm is guaranteed to increase, thus arriving at the most likely distribution of the true states, given the measurement data set and the algorithm initial conditions. Convergence of the algorithm to the correct solution, for a simple case where an analytical answer can be derived for comparison, is shown. Two chemical process examples that have more complex distributions are also shown. Once the probability distribution of the states has been determined, many monitoring and statistical process and quality control functions can be performed using the more accurate distributions of the process states, avoiding corruption of the distribution due to faulty measurements.