Recursive Optimal Finite Impulse Response Filter and Its Application to Adaptive Estimation

In this paper, the recursive form of an optimal finite impulse response filter is proposed for discrete time-varying state-space models. The recursive form of the finite impulse response filter is derived by employing finite horizon Kalman filtering with optimally estimated initial conditions. The horizon initial state and its error covariance on the horizon are optimally estimated by using recent finite measurements, in the sense of maximum likelihood estimation, then initiating the finite horizon Kalman filter. The optimality and unbiasedness of the proposed filter are proved by comparison with the conventional optimal finite impulse response filter in batch form. Moreover, an adaptive FIR filter is also proposed by applying the adaptive estimation scheme to the proposed recursive optimal FIR filter as its application. To evaluate the performance of the proposed algorithms, a computer simulation is performed to compare the conventional Kalman filter and adaptive Kalman filters for the gas turbine aircraft engine model

Novel Unbiased Optimal Receding-Horizon Fixed-Lag Smoothers for Linear Discrete Time-Varying Systems

This paper proposes novel unbiased minimum-variance receding-horizon fixed-lag (UMVRHF) smoothers in batch and recursive forms for linear discrete time-varying state space models in order to improve the computational efficiency and the estimation performance of receding-horizon fixed-lag (RHF) smoothers. First, an UMVRHF smoother in batch form is proposed by combining independent receding-horizon local estimators for two separated sub-horizons. The local estimates and their error covariance matrices are obtained based on an optimal receding horizon filter and the smoother in terms of the unbiased minimum variance; they are then optimally combined using Millman’s theorem. Next, the recursive form of the proposed UMVRHF smoother is derived to improve its computational efficiency and extendibility. Additionally, we introduce a method for extending the proposed recursive smoothing algorithm to a posteriori state estimations and propose the Rauch–Tung–Striebel receding-horizon fixed-lag smoother in recursive form. Furthermore, a computational complexity reduction technique that periodically switches the two proposed recursive smoothing algorithms is proposed. The performance and effectiveness of the proposed smoothers are demonstrated by comparing their estimation results with those of previous algorithms for Kalman and receding-horizon fixed-lag smoothers via numerical experiments

Adaptive Fading-Memory Receding-Horizon Filters and Smoother for Linear Discrete Time-Varying Systems

In this paper, an adaptive fading-memory receding-horizon (AFMRH) filter is proposed by combining the receding-horizon structure and the adaptive fading-memory method. In the recent finite horizon, state error covariance is adapted with an adaptive fading factor; then the process noise covariance matrix adaption is realized by adjusting the properties of systems. An AFMRH fixed-lag smoother is also proposed by combining the proposed AFMRH filtering algorithm and a Rauch–Tung–Striebel smoothing algorithm to improve the estimation accuracy. Because the proposed AFMRH filter and smoother are reduced to the optimal receding-horizon (RH) filter and smoother when all measurements have the same weight, the proposed adaptive RH estimators could provide a more general solution than the optimal RH filter and smoother. To reduce the complexity and improve the estimation performance of the proposed RH estimators, an adaptive horizon adjustment method and a switching filtering algorithm based on an adaptive fading factor are also proposed. In particular, the proposed adaptive horizon adjustment method is designed to be computationally efficient, which makes it suitable for online and real-time applications. Through computer simulation, the performance and adaptiveness of the proposed approaches were verified by comparing them with existing fading-memory approaches

Recursive Optimal Finite Impulse Response Filter and Its Application to Adaptive Estimation

In this paper, the recursive form of an optimal finite impulse response filter is proposed for discrete time-varying state-space models. The recursive form of the finite impulse response filter is derived by employing finite horizon Kalman filtering with optimally estimated initial conditions. The horizon initial state and its error covariance on the horizon are optimally estimated by using recent finite measurements, in the sense of maximum likelihood estimation, then initiating the finite horizon Kalman filter. The optimality and unbiasedness of the proposed filter are proved by comparison with the conventional optimal finite impulse response filter in batch form. Moreover, an adaptive FIR filter is also proposed by applying the adaptive estimation scheme to the proposed recursive optimal FIR filter as its application. To evaluate the performance of the proposed algorithms, a computer simulation is performed to compare the conventional Kalman filter and adaptive Kalman filters for the gas turbine aircraft engine model

Least-Mean-Square Receding Horizon Estimation

We propose a least-mean-square (LMS) receding horizon (RH) estimator for state estimation. The proposed LMS RH estimator is obtained from the conditional expectation of the estimated state given a finite number of inputs and outputs over the recent finite horizon. Any a priori state information is not required, and existing artificial constraints for easy derivation are not imposed. For a general stochastic discrete-time state space model with both system and measurement noise, the LMS RH estimator is explicitly represented in a closed form. For numerical reliability, the iterative form is presented with forward and backward computations. It is shown through a numerical example that the proposed LMS RH estimator has better robust performance than conventional Kalman estimators when uncertainties exist.open1111Nsciescopu

On-line Model Parameter Estimations for Time-delay Systems

This paper concerns a problem of on-line model parameter estimations for multiple time-delay systems. In order to estimate unknown model parameters from measured state variables, we propose two schemes using Lyapunov's direct method, called parallel and series-parallel model estimators. It is shown through a numerical example that the proposed parallel and series-parallel model estimators can be effective when sufficiently rich inputs are applied.open1122sciescopu

An automated impedance estimation method in low-voltage distribution network for coordinated voltage regulation

Internode line impedance values are essential information for achieving coordinated voltage regulation with distributed energy devices. However, in a low-voltage distribution system, these values are difficult to acquire, especially when the devices are installed in an ad hoc manner by individual users. This paper proposes a novel method for automated impedance estimation based on practically available parameters at the terminal nodes. The distributed energy devices measure and transmit the terminal parameters to a host device. Then, the host device estimates the line impedances based on its impedance model and the collected parameters. For practical implementation, the proposed method is built under several assumptions. For example, it is assumed that the phases of terminal voltages are not synchronized owing to communication latency. Instead, only the magnitude value is incorporated during the impedance estimation. The proposed method is verified via a simulation that assumes a realistic environment.1185sciescopu