Ultimate iterative UFIR filtering algorithm (original) (raw)

A Generalized Algorithm for Nonlinear State Estimation Using Extended UFIR Filtering

The unbiased finite impulse response (UFIR) filter provides better accuracy when the noise statistics are not fully known. Based on the UFIR approach, a generalized algorithm is developed for extended UFIR (EFIR) filtering of nonlinear models in discrete time state space. As well as the UFIR filter, the EFIR filter completely ignore the noise statistics and requires an optimal averaging horizon of Nopt points. The optimal horizon can be determined via measurements with much smaller efforts and cost than for the noise statistics. These properties of EFIR filtering are distinctive advantages against the extended Kalman filter (EKF). Extensive simulations confirm that the proposed iterative EFIR filtering algorithm is more successful in accuracy and more robust than EKF under the unknown noise statistics and model uncertainties.

A Fusion Kalman Filter and UFIR Estimator Using the Influence Function Method

IEEE/CAA Journal of Automatica Sinica, 2022

In this paper, the Kalman filter (KF) and the unbiased finite impulse response (UFIR) filter are fused in the discrete-time state-space to improve robustness against uncertainties. To avoid the problem where fusion filters may give up some advantages of UFIR filters by fusing based on noise statistics, we attempt to find a way to fuse without using noise statistics. The fusion filtering algorithm is derived using the influence function that provides a quantified measure for disturbances on the resulting filtering outputs and is termed as an influence finite impulse response (IFIR) filter. The main advantage of the proposed method is that the noise statistics of process noise and measurement noise are no longer required in the fusion process, showing that a critical feature of the UFIR filter is inherited. One numerical example and a practice-oriented case are given to illustrate the effectiveness of the proposed method. It is shown that the IFIR filter has adaptive performance and can automatically switch from the Kalman estimate to the UFIR estimates according to operating conditions. Moreover, the proposed method can reduce the effects of optimal horizon length on the UFIR estimate and can give the state estimates of best accuracy among all the compared methods.

On the Iterative Computation of Error Matrix in Unbiased FIR Filtering

It is proved that the iterative computation form for the mean square error (MSE) matrix of the batch unbiased finite impulse response (UFIR) filter exactly equals to that of the iterative UFIR filter form, unlike what was previously thought. Based on the iterative MSE matrix form, we suggest two strategies for defining the optimal horizon length for the UFIR filter. The results are verified using the two-state polynomial and harmonic models. Index Terms—Unbiased FIR filter, mean square error, iterative algorithm, optimal horizon, state-space.

Iterative algorithms for unbiased state estimation in discrete time

The 21st European Signal Processing Conference, 2013

Various iterative unbiased finite impulse response (UFIR) algorithms are proposed for filtering, smoothing, and prediction of discrete-time state-space models in white Gaussian noise. The distinctive property of UFIR algorithms is that noise statistics are completely ignored. Instead, an optimal window size is required for optimal performance. Under real-world operating conditions with uncertainties, non-Gaussian noise, and unknown noise statistics, the UFIR estimator generally demonstrates better robustness than the Kalman filter, even with suboptimal window size.

Blind Robust Estimation with Missing Data for Smart Sensors Using UFIR Filtering

—Smart sensors are often designed to operate under harsh industrial conditions with incomplete information about noise and missing data. Therefore, signal processing algorithms are required to be unbiased, robust, predictive, and desirably blind. In this paper, we propose a novel blind iterative unbiased finite impulse response (UFIR) filtering algorithm, which fits these requirements as a more robust alternative to the Kalman filter (KF). The trade-off in robustness between the UFIR filter and KF is learned analytically. The predictive UFIR algorithm is developed to operate in control loops under temporary missing data. Experimental verification is given for carbon monoxide concentration and temperature measurements required to monitor urban and industrial environments. High accuracy and precision of the predictive UFIR estimator are demonstrated in a short time and on a long baseline.

Iterative algorithms for unbiased FIR state estimation in discrete time

10th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), 2013

Various iterative unbiased finite impulse response (UFIR) algorithms are discussed for filtering, smoothing, and prediction of discrete-time state-space models in white Gaussian noise. The distinctive property of UFIR algorithms is that noise statistics are completely ignored. Instead, an optimal window size is required for optimal performance. Under real-world operating conditions with uncertainties, non-Gaussian noise, and unknown noise statistics, the UFIR estimator generally demonstrates better robustness than the Kalman filter, even with suboptimal window size.

Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

2012

Abstract The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators.