Parallel Implementation of the Extended Square-Root Covariance Filter for Tracking Applications
IEEE Transactions on Parallel and Distributed Systems
Maximum likelihood estimation via the extended covariance and combined square-root filters
Mathematics and Computers in Simulation
On scalarized calculation of the likelihood function in array square-root filtering algorithms
Automation and Remote Control
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Theoretical and applied aspects are considered for development of numerically stable adaptive methods of the parametric identification of linear discrete stochastic systems in the space of states. The unknown system parameters to be estimated can enter into any matrices specifying a system and into initial conditions. The class of gradient methods is first suggested, which is developed on the basis of orthogonal square-root implementations of the discrete Kalman filter with the use of the technology of sequential data processing. It is shown that the algorithms of the given type can be effectively used to solve ill-conditioned problems of parametric identification. A test example is drawn. The practical significance of the suggested class of methods is illustrated by an example of the solution for one of the financial mathematics problems -- the identification of a multidimensional model of stochastic volatility.