Unbiased Finite Impulse Response Filter Research Articles

A Performance of AFIRO among Asynchronous Iteration Strategy Metaheuristic Algorithms

Asynchronous Finite Impulse Response Optimizer (AFIRO) is a metaheuristic algorithm that has been developed as a population-based solution with an asynchronous update mechanism. AFIRO is inspired by the Ultimate Unbiased Finite Impulse Response filter framework. AFIRO works with a group of agents where each agent performs the iteration update asynchronously. In the original paper, AFIRO was compared with the Particle Swarm Optimisation algorithm, Genetic Algorithm, and Grey Wolf Optimizer. Although AFIRO shows a better performance, the comparison seems unfair since the iteration strategy of AFIRO is different from those compared algorithms. Hence, this article further investigates the potential of AFIRO against three existent metaheuristic algorithms with the same iteration strategy, namely Asynchronous PSO (A-PSO), Asynchronous Gravitational Search Algorithm (A-GSA), and Asynchronous Simulated Kalman Filter (A-SKF). The CEC2014 test suite was applied to evaluate the performance, where the results revealed that AFIRO leads 18 out of 30 functions. The Holm post hoc showed that AFIRO performs significantly better than A-SKF and A-GSA while having the same performance as A- PSO. Moreover, the Friedman test disclosed that AFIRO has the highest ranking than A-PSO, A-SKF, and A-GSA. Therefore, it can be concluded that AFIRO performs well in the same iteration strategy category.

H∞‐FIR filtering of disturbed systems using LMI under measurement and initial errors

SummaryFinite impulse response (FIR) filtering is known to be more robust than Kalman filtering. In this article, we derive a discrete convolution‐based ‐FIR observer for disturbed systems under measurement and initial errors. The gain for the ‐FIR observer is obtained numerically by solving a linear matrix inequality (LMI). Since the LMI has a term that is quadratic with respect to the filter gain, we modify and constrain LMI by introducing an additional variable and proving a theorem. It is shown numerically and experimentally that for disturbed systems operating under measurement and initial errors, the developed ‐FIR observer surpasses the optimal FIR and Kalman filters in accuracy and has almost the same robustness as a robust unbiased FIR filter.

Moving Vehicle Tracking under Measurement Uncertainties, Multi-step Random Delays, and Packet Dropouts

The unbiased finite impulse response (UFIR) filter, Kalman filter (KF), and game theory <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> filter are developed for vehicle tracking in wireless sensor networks (WSNs) with multi-step random delays and multiple dropouts. The problem with data delays is solved for given delay probabilities by converting a model with delays to another without delays. The dropouts are detected at the receiver by a data sensor, and lost data are compensated for by prediction. The filters developed are experimentally tested for accuracy and robustness using the Global Positioning System-based vehicle tracking database, where the measured coordinates are transmitted over WSN with delays. It is shown that the UFIR filter is the most robust to uncertain delays and the KF is the most accurate when the delay probabilities are known exactly. The game theory <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> filter is the most accurate under ideal conditions and prone to divergency otherwise.

Estimation of States Under Colored Measurement Noise (CMN) Using UFIR and Kalman Filters Modified

The estimate process of a moving target trajectory is a well-known problem, where the main objective is to improve the estimation of object position. During the tracking are presented errors or variations between the true position and the estimated. In this paper, we treat such variations as a Gauss-Markov colored measurement noise (CMN). The estimation process is performed in predict and update, where the prediction indicates the next position of the bounding box, and the update is a correction step, which includes the new measurement of the tracking model and helps to improve the estimation. Looking for this improvement we use Kalman and Unbiased Finite Impulse Response filters in the standard version and modified for CMN to demonstrate the filter with the best performance. To test the most robust filter we use a high coloredness factor. The tests were carried out with simulated data (ideal and no ideal conditions) and with benchmark data (no ideal conditions). The UFIR modified for the CMN algorithm showed favorable results with high precision and low RMSE in the object tracking process with benchmark data and under no ideal conditions. While KF CMN showed better results under ideal conditions.

Continuous‐time optimal unbiased FIR filter for input‐delayed systems

ABSTRACTMost existing finite impulse response (FIR) filters are restricted to models without delays. This paper proposes an continuous‐time optimal unbiased FIR filter for input‐delayed systems (CTOUFFID). A new integral transformation relation was introduced to derive the FIR filter. By applying this relation, the CTOUFFID problem is represented as an optimal control problem with zero terminal state. The filter gain function is obtained by solving two coupled matrix differential equations using initial conditions. The paper also offers discussion on the horizon size and a few special cases. The main benefit of the proposed solution is that it provides the maximum likelihood estimate with no requirements for the initial values. Finally, an application with the ‐404 turbofan engine model is presented to demonstrate the highly robust nature of the proposed FIR filer against incomplete noise information and unspecified model uncertainties.

Comparison of the Kalman Filter and the Unbiased FIR Filter for Network Systems with Multiples Output Delays and Lost Data

In this article, a comparison of the UFIR and Kalman filter to estimate a tracking vehicle system variables is developed considering two possible observation output models. The time stamp approach and the predictive compensation are used to analyze the problem from multiple perturbations, which produces random delayed data and losses during transmissions. For the estimation, a transformation model and a decorrelation covariance matrices are developed with the aim of assure optimal conditions and minimizing the estimation error. Finally, several real situations, miss modeling, uncertain noise covariances, and uncertain probabilities are proposed to demonstrate the effectiveness and robustness of the filter proposed.

Uncertain disturbed systems: Robust H2‐OUFIR filtering under measurement errors

SummaryThis article considers uncertain disturbed systems represented under initial and measurement errors in linear discrete‐time state‐space. A novel bias‐constrained a posteriori optimal unbiased finite impulse response (OUFIR) state observer is derived, in which the requirements of the initial state is removed by embedding the unbiasedness constraint. A suboptimal bias‐constrained ‐FIR filtering algorithms using linear matrix inequality is also obtained. Based on an example of uncertain system and error matrices, it is shown that the ‐OUFIR state observer offers a better tradeoff between the accuracy and robustness than the OFIR filter, maximum likelihood FIR filter, and Kalman filter. It loses in robustness to the unbiased FIR filter, but provides a better accuracy. The performance of the proposed filter is verified experimentally based on daily glucose measurements in diabetic persons with timing jitter.

Effect of sampling time jitter on robust [formula omitted] filtering estimates

In discrete-time processes, the sampling time jitter occurs naturally due to various unavoidable reasons, which make the model uncertain. Therefore, robust state estimators should be used. To find out if it is rational to design such estimators or if we can simply ignore the time jitter, in this paper we investigate its effect on the robust H2 optimal finite impulse response (OFIR) filter in a comparison with the OFIR filter. As benchmarks, we also use the maximum likelihood FIR, unbiased FIR, and Kalman filters. The robust batch H2-OFIR filter is developed for timing jitter under disturbances, initial errors, and measurement errors. For Gaussian errors, its iterative algorithm is designed using modified Kalman recursions. Numerical investigations and applications to blood sugar monitoring in diabetic patients with daily timing jitter have shown that the robust H2-OFIR filter improves the accuracy of the OFIR filter by the factor of less than the fractional time jitter. That is, for large fractional timing jitter of 10% the improvement would be less than 10% that is small. Otherwise, it is worth using robust estimators.

Frobenius Norm-Based Unbiased Finite Impulse Response Fusion Filtering for Wireless Sensor Networks

This article presents a new approach to designing the Frobenius norm-based weighted unbiased finite impulse response (FIR) fusion filter for wireless sensor networks. The weighted Frobenius norm is employed as a cost function to design a local unbiased FIR filter. The design problem is converted into a constrained optimization problem subject to an equality constraint. The Lagrange multiplier method is used to derive the local FIR filter gain. An alternative Frobenius norm is introduced to determine weights for the local unbiased FIR filters in the design of a global fusion FIR filter. The developed FIR fusion filter is demonstrated to have higher robustness against uncertainties than Kalman filter-based methods, such as the optimal fusion Kalman filter, distributed Kalman filter, and distributed weighted Kalman filter, through a numerical example of moving-target tracking employing seven smart sensors and an experiment with temperature and humidity estimation using eight sensors.

UFIR State Estimator for Network Systems with Two-Step Delayed and Lost Data

Wireless communication over networks often produces issues associated with delayed and missing data. In this paper, we consider one-step and two-step delays. The state space model is transformed to have no delay with new system and observation matrices. To mitigate the effect, we develop the unbiased finite impulse response (UFIR) filter, Kalman filter (KF), and game theory H∞ filter for Bernoulli-distributed delays with possible packet dropouts. A comparative study of the filters developed is provided under the uncertain noise and transmission probability. Numerical simulation is conducted employing a GPSbased tracking network system. A better performance of the UFIR filter is demonstrated experimentally

Distributed UFIR Filtering with Applications to Environmental Monitoring

Environmental monitoring requires an analysis of large and reliable amount of data collected through node stations distributed over a very wide area. Equipment used in such stations are often expensive that limits the amount of sensing stations to be deployed. The technology known as Wireless Sensor Networks (WNS) is a viable option to deliver low-cost sensor information. However, unpredictable issues such as interference from electromagnetic sources, damaged and unstable sensors and the landscape itself may cause the network to suffer from unstable links as well as missing and corrupted data. Therefore robust estimators are required to mitigate such effects. In this sense,the unbiased finite impulse response (UFIR) filter is used as a robust estimator for applications over WSN, especially when the process statistics are unknown. In this paper, we investigate the robustness of the distributed UFIR (dUFIR) filter with optimal consensus on estimates against missing and incorrect data. The dUFIR algorithm is tested in two different scenarios of very unstable WSN using real data. It is shown that the dUFIR filteris more suitable for real life applications requiring the robustness against missing and corrupted measurements under the unknown noise statistics.

Three-Wheeled Omnidirectional Robot Localization in RFID-Tag Environments using UFIR Filtering

This paper describes a way to improve the indoor navigation of mobile robots using radio frequency identification (RFID) technology. A net of RFID tags is deployed in the navigation space. A measurement system measures distances from the tags to the robot with in the presence of the firstorder Markov-Gauss colored measurement noise (CMN) and is combined with a digital gyroscope to measure the robot heading. To increase the localization accuracy, the Kalman filter (KF) and unbiased finite impulse response (UFIR) modified for CMN are used. It is shown that the navigation system developed is more accurate than the basic one employing the standard KF and UFIR filter

Unbiased FIR, Kalman, and game theory [formula omitted] filtering under bernoulli distributed random delays and packet dropouts

It is known that due to uncertain delays and missing data wireless sensor networks (WSNs) may incur a significant loss in performance. In this work, we solve the problem in discrete-time state-space by developing the unbiased finite impulse response (UFIR) filter, Kalman filter (KF), and game theory H∞ filter for systems with randomly delayed data and packet dropouts. The binary Bernoulli distribution is adopted for WSN channels to model the arrival data with supposedly known delay-time probability. The effectiveness of the UFIR filter, KF, and H∞ filter is compared experimentally in terms of accuracy and robustness employing the GPS-measured vehicle coordinates transmitted with latency over WSN.

Distributed UFIR Filtering with Applications to Environmental Monitoring

Environmental monitoring requires an analysis of large and reliable amount of data collected through node stations distributed over a very wide area. Equipments used in such stations are often expensive that limits the amount of sensing stations to be deployed. The technology known as Wireless Sensor Networks (WNS) is a viable option to deliver low-cost sensor information. However, electromagnetic interference, damaged sensors, and the landscape itself often cause the network to suffer from faulty links as well as missing and corrupted data. Therefore robust estimators are required to mitigate such effects. In this sense, the unbiased finite impulse response (UFIR) filter is used as a robust estimator for applications over WSN, especially when the process statistics are unknown. In this paper, we investigate the robustness of the distributed UFIR (dUFIR) filter with optimal consensus on estimates against missing and incorrect data. The dUFIR algorithm is tested in two different scenarios of very unstable WSN using real data. It is shown that the dUFIR filter is more suitable for real life applications requiring the robustness against missing and corrupted measurements under the unknown noise statistics.

UFIR Filtering Under Uncertain One-Step Delayed and Missing Data

This paper develops the unbiased finite impulse response (UFIR) filter for wireless sensor network (WSN) systems whose measurements are affected by random delays and packet dropout due to inescapable failures in the transmission and sensors. The Bernoulli distribution is used to model delays in arrived measurement data with known transmission probability. The effectiveness of the UFIR filter is compared experimentally to the KF and game theory recursive H1 filter in terms of accuracy and robustness employing the GPS-measured vehicle coordinates transmitted with latency over WSN.

Backward optimal FIR filtering and recursive forms for discrete LTV processes

Backward filtering is a useful tool to compute initial values in finite horizon signal processing. To make it optimally, a backward a posteriori optimal finite impulse response (B-OFIR) state estimator (filter) is proposed for discrete time-varying linear processes. The B-OFIR filter is derived in a discrete convolution-based batch form and represented with a fast iterative algorithm using recursions. The performance of the B-OFIR filter is compared to the forward OFIR filter (F-OFIR), KF, and unbiased FIR filter (UFIR). Simulations conducted based on a two-state tracking model and one degree-of-freedom torsion load system show that the B-OFIR filter is statistically equivalent to the F-OFIR filter, but operates with noise samples ordered back in time and therefore produces a bit different estimates.

Multipass Optimal FIR Filtering for Processes With Unknown Initial States and Temporary Mismatches

In this article, the multipass optimal finite impulse response (OFIR) filtering approach is developed for industrial processes with unknown initial conditions under temporary model mismatches. The forward and backward OFIR filters are derived in batch and fast iterative forms using recursions. The double-pass OFIR (DOFIR) filter supported by the unbiased FIR (UFIR) filter and triple-pass OFIR (TOFIR) filter starting with some initial values are designed and extensively investigated using simulations and experimental data. It is shown that the DOFIR and TOFIR filters are able to essentially improve the performance close to the initial values and are more robust against temporary model mismatches than the Kalman, OFIR, and UFIR filters.

Optimal FIR Filter for Discrete-Time LTV Systems and Fast Iterative Algorithm

An a posteriori optimal finite impulse response (OFIR) filter is proposed for linear time-varying systems. The OFIR filter is derived in a discrete convolution-based batch form and represented with a computationally efficient iterative algorithm using recursions. A comparison of the OFIR filter, Kalman filter (KF), and unbiased FIR (UFIR) filter performances is provided using an experimental example of object tracking. It is shown that responding to temporary uncertainties the OFIR filter produces shorter transients and a bit smaller excursions than the KF and smaller excursions than the UFIR filter.

Self-Tuning Unbiased Finite Impulse Response Filtering Algorithm for Processes With Unknown Measurement Noise Covariance

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 N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> is estimated in real time by incorporating the estimated data noise covariance into the full-horizon UFIR filter and specifying N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> 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 N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> 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.

State estimation in pairwise Markov models with improved robustness using unbiased FIR filtering

We propose a novel estimation procedure for linear time-varying pairwise Markov models (PMM), that is robust to system parameter uncertainties occurring in real-world applications. In order to cope with mismodeling errors and ignorance of noise/initial state statistics, we solve a finite-horizon state estimation problem. The resulting unbiased finite impulse response filter for PMMs (PMM-UFIR) is first derived in batch form and then converted to a recursive Kalman-like form for the sake of complexity reduction. Closed forms for the error covariance matrix of the state estimate are also provided for analytical performance assessment.Numerical results illustrate the effectiveness of the proposed estimation method over Gaussian processes, by showing that the PMM-UFIR is nearly as accurate as (resp. more robust than) optimal filtering under perfect (resp. uncertain) system parameters after tuning the horizon size.