An unbiased finite impulse response (FIR) filter is proposed to estimate the time-interval error (TIE) K-degree polynomial model of a local clock in Global Positioning System (GPS)-based timekeeping in the presence of noise that is not obligatory Gaussian. Generic coefficients for the unbiased FIRs are derived. The low-degree FIRs and noise power gains are given. An estimation algorithm is proposed and examined for the TIE measurements of a crystal clock in the presence of the uniformly distributed sawtooth noise induced by the multichannel GPS timing receiver. Based upon this algorithm, we show that the unbiased FIR estimates are consistent with the reference (rubidium) measurements and fit them better than the standard Kalman filter

This paper provides a comparative analysis for robustness of the Kalman filter (KF), H _∞ filter derived using the game theory, and unbiased finite impulse response (UFIR) filter, which ignores the noise statistics and initial values. A comparison is provided for Gaussian models by studying the effects of errors and disturbing factors on the bias correction gain. It is shown that the rule of thumb of optimal filtering in terms of accuracy, UFIR <; H _∞ = KF, typically does not hold in the realworld implying errors in the noise statistics, mismodeling, temporary uncertainties, and difficulties in filter tuning to optimal mode. Under such conditions, the filters are related to each other as KF ≤ H _∞ <; UFIR. A justification of this statement is provided analytically and confirmed by simulations and experimentally based on two-state polynomial and harmonic models.

Accurate indoor localization information of the quadrotor plays an important role in many Internet of Things applications. To improve the estimation accuracy and robustness, a fix-lag extended finite impulse response smoother (FEFIRS) algorithm is proposed for fusing the inertial navigation system (INS) and ultra wide band (UWB) data tightly, which employs distance between the UWB reference nodes and a blind node measured by the INS and UWB. The FEFIRS algorithm consists of an extended unbiased finite impulse response (EFIR) filter and a fix-lag unbiased FIR (UFIR) smoother. The EFIR filter is employed to improve the robustness, and the fix-lag UFIR smoother is capable of improving the accuracy. Based on extensive test investigations employing real data, the proposed FEFIRS has a higher accuracy and robustness than the Kalman-based solutions in tightly integrated INS/UWB-based indoor quadrotor localization.

An unbiased finite impulse response (UFIR) filtering algorithm is designed in the discrete-time state-space for industrial processes with unknown measurement data covariance. By assuming an inverse-Wishart distribution, the data noise covariance is recursively estimated using the variational Bayesian (VB) approach. The optimal averaging horizon length Nopt is estimated in real time by incorporating the estimated data noise covariance into the full-horizon UFIR filter and specifying Nopt at a point, where the estimation error covariance reaches a minimum. The proposed VB-UFIR algorithm is applied to a quadrupled water tank system and moving target tracking. It is demonstrated that the VB-UFIR filter self-estimates Nopt more accurately than known solutions. Furthermore, the VB-UFIR filter is not prone to divergence and produces more stable and more reliable estimates than the VB-Kalman filter.

In this paper, an iterative finite impulse response (FIR) filter is proposed for discrete time-varying state-space models, with the purpose of a new initialization strategy for the iterative FIR structure as well as consideration of possible unexpected state dynamics in a finite horizon. A compensation variable that satisfies the Gaussian property is introduced into the state equation, and its probability density function (pdf) is estimated analytically together with the pdf of state variable using the variational Bayesian inference technique. Different from the existing methods, the proposed filter exploits the FIR structure from the perspective of pdf propagation, which provides a new efficient way to use the iterative FIR filtering structure without any particular initialization scheme. Moreover, the effects of uncertainties (caused by initialization and/or possible un-modeled state dynamics) on the filtering output are loosened adaptively. Two examples of applications demonstrate that the proposed algorithm can not only provide optimal estimates when the model used perfectly matches the measurements, but can also exhibit better robustness than the Kalman filter, optimal FIR filter, maximum likelihood FIR filter, and some commonly used robust and/or adaptive Kalman filters when the underlying process suffers from unpredicted uncertainties.