Abstract
Measurements are often provided in the presence of noise and uncertainties that require optimal filters to estimate processes with highest accuracy. The ultimate iterative unbiased finite impulse response (UFIR) filtering algorithm presented in this paper is more robust in real world than the Kalman filter. It completely ignores the noise statistics and initial values while demonstrating better accuracy under the mismodeling and temporary uncertainties and lower sensitivity to errors in the noise statistics.
Highlights
Optimal estimation of system state is often required when measurements are provided in the presence of noise
We introduce the ultimate iterative unbiased finite impulse response (UFIR) filtering algorithm suitable for immediate use
Unbiased finite impulse response (FIR) filtering introduced in this article is another opportunity to provide fast near optimal estimation beyond the Kalman filter (KF)
Summary
Optimal estimation of system state is often required when measurements are provided in the presence of noise. If the process and its measurement are both linear and noise is white Gaussian, the Kalman filter (KF) is recognized to be the best estimator. Among different kinds of FIR filters developed during decades, the unbiased FIR (UFIR) filter is most robust This filter [32,28] appears as a solution to the unbiasedness constraint [24] or as a special case of the optimal FIR (OFIR) filter [30] when the model is noiseless. Advantages of the iterative UFIR algorithm go along with the requirements of the optimal horizon of Nopt points which is applied to minimize the mean square error (MSE). We introduce the ultimate iterative UFIR filtering algorithm suitable for immediate use
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