An efficient implementation of square root filtering : error analysis, complexity and simulations on flight-path reconstruction

In this paper we first develop a new kind of numerical implementation of the so-called "square root filters" used for Kalman filtering. The method is based on the choice of an initial state transformation which "condensed" the model. This preliminary transformation can be done without loss of numerical precision and leads to substantial savings in computing time for the subsequent implementation of the filter. The new filter implementation is also compared with the conventional Kalman filter (KF). For this purpose a detailed analysis is done of the propagation of computational errors in the recursive algorithms. In a second part we use this method for implementing an efficient on-line flight-path reconstruction technique based on a two-step method. The above method is shown to be particularly suited for this problem, even though the model here is inherently time varying.