Maximum likelihood estimation using square root information filters

The maximum likelihood parameter estimation algorithm is known to provide optimal estimates for linear time-invariant dynamic systems. However, the algorithm is computationally expensive and requires evaluations of the gradient of a log likelihood function and the Fisher information matrix. By using the square-root information filter, a numerically reliable algorithm to compute the required gradient and the Fisher information matrix is developed. The algorithm is a significant improvement over the methods based on the conventional Kalman filter. The square-root information filter relies on the use of orthogonal transformations that are well known for numerical reliability. This algorithm can be extended to real-time system identification and adaptive control.<
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