STATE ESTIMATION OF A SCALAR DYNAMIC PRECIPITATION MODEL FROM TIME-AGGREGATE OBSERVATIONS

Developed is an exact, recursive, state estimator for linear, scalar systems whose observables are time integrals, over an interval DELTA t, of linear functions of the state. In general, implementation of the estimator results in excessive computations. The computationally inexpensive, ordinary Kalman filter with inflated observation error variance is used to approximate the developed estimator in terms of prediction accuracy. Comparison of the exact estimator and of the Kalman filter, using precipitation data of various aggregation intervals DELTA t and a scalar dynamic precipitation model, shows that the Kalman filter develops prediction bias as DELTA t increases.