Maximum likelihood estimation via the extended covariance and combined square-root filters

The method of maximum likelihood is a general method for parameter estimation and is often used in system identification. To implement it, it is necessary to maximize the likelihood function, which is usually done using the gradient approach. It involves the computation of the likelihood gradient with respect to unknown system parameters. For linear stochastic system models this leads to the implementation of the Kalman filter, which is known to be numerically unstable. The aim of this work is to present new efficient algorithms for likelihood gradient evaluation. They are more reliable in practice and improve robustness of computations against roundoff errors. All algorithms are derived in measurement and time updates form. The comparison with the conventional Kalman filter approach and results of numerical experiments are given.