Computing the gradient of the auxiliary quality functional in the parametric identification problem for stochastic systems

We consider an application of the auxiliary quality functional (AQF) method for identifying the parameters of a linear dynamical system in case when the filtering is done with a square root covariance filter. We construct a new algorithm for computing the gradient of the auxiliary quality functional. The advantages of this algorithm are that it is stable to computer rounding errors and does not require the user to write down the ‘differentiated’ Kalman filter in the standard form for every unknown system parameter. All values necessary to compute the values of the AQF gradient are computed in terms of the square root covariance filter with orthogonal transformations.