Unknown Noise Statistics Research Articles

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.

Adaptive probability hypothesis density filter for multi-target tracking with unknown measurement noise statistics

Under the Gaussian noise assumption, the probability hypothesis density (PHD) filter represents a promising tool for tracking a group of moving targets with a time-varying number. However, inaccurate prior statistics of the random noise will degrade the performance of the PHD filter in many practical applications. This paper presents an adaptive Gaussian mixture PHD (AGM-PHD) filter for the multi-target tracking (MTT) problem in the scenario where both the mean and covariance of measurement noise sequences are unknown. The conventional PHD filters are extended to jointly estimate both the multi-target state and the aforementioned measurement noise statistics. In particular, the Normal-inverse-Wishart and Gaussian distributions are first integrated to represent the joint posterior intensity by transforming the measurement model into a new formulation. Then, the updating rule for the hyperparameters of the model is derived in closed form based on variational Bayesian (VB) approximation and Bayesian conjugate prior heuristics. Finally, the dynamic system state and the noise statistics are updated sequentially in an iterative manner. Simulations results with both constant velocity and constant turn model demonstrate that the AGM-PHD filter achieves comparable performance as the ideal PHD filter with true measurement noise statistics.

Learning-Based Signal Detection for MIMO Systems With Unknown Noise Statistics

This paper aims to devise a generalized maximum likelihood (ML) estimator to robustly detect signals with unknown noise statistics in multiple-input multiple-output (MIMO) systems. In practice, there is little or even no statistical knowledge on the system noise, which in many cases is non-Gaussian, impulsive and not analyzable. Existing detection methods have mainly focused on specific noise models, which are not robust enough with unknown noise statistics. To tackle this issue, we propose a novel ML detection framework to effectively recover the desired signal. Our framework is a fully probabilistic one that can efficiently approximate the unknown noise distribution through a normalizing flow. Importantly, this framework is driven by an unsupervised learning approach, where only the noise samples are required. To reduce the computational complexity, we further present a low-complexity version of the framework, by utilizing an initial estimation to reduce the search space. Simulation results show that our framework outperforms other existing algorithms in terms of bit error rate (BER) in non-analytical noise environments, while it can reach the ML performance bound in analytical noise environments.

BBR-S: A Low-Latency BBR Modification for Fast-Varying Connections

The new possibilities offered by 5G and beyond networks have led to a change in the focus of congestion control from capacity maximization for web browsing and file transfer to latency-sensitive interactive and real-time services, and consequently to a renaissance of research on the subject, whose most well-known result is Google's Bottleneck Bandwidth and Round-trip propagation time (BBR) algorithm. BBR's promise is to operate at the optimal working point of a connection, with the minimum Round Trip Time (RTT) and full capacity utilization, striking the balance between resource use efficiency and latency performance. However, while it provides significant performance improvements over legacy mechanisms such as Cubic, it can significantly overestimate the capacity of fast-varying mobile connections, leading to unreliable service and large potential swings in the RTT. Our BBR-S algorithm replaces the max filter that causes this overestimation issue with an Adaptive Tobit Kalman Filter (ATKF), an innovation on the Kalman filter that can deal with unknown noise statistics and saturated measurements, achieving a 40% reduction in the average RTT over BBR, which increases to 60% when considering worst-case latency, while maintaining over 95% of the throughput in 4G and 5G networks.

AGMC-Based Robust Cubature Kalman Filter for SINS/GNSS Integrated Navigation System With Unknown Noise Statistics

A new robust cubature Kalman filter is proposed using adaptive generalized maximum correntropy (AGMC) criterion rather than the conventional MMSE criterion in this paper. In the proposed method, the adaptive generalized maximum correntropy (AGMC) criterion is firstly constructed from an adaptive forgetting correntropy based cost function, which is rather robust with respect to the process uncertainty and non-Gaussian noise. On this basis, a new robust cubature Kalman filter is further derived, where the predicted state vector and received measurements are processed simultaneously based on the regression form derived via the statistical linearization approach. An adaptive forgetting scheme is then proposed in combination with the AGMC-CKF to update the parameters of the AGMC adaptively in real time. Taking advantage of the AGMC, the unknown noise statistics caused by the process uncertainty and non-Gaussian noise can be effectively suppressed. Simulations and car-mounted experiments demonstrate that the proposed filter is superior in terms of estimation accuracy and robustness as compared with the related state-of-art methods.

An Adaptive Consensus Filter for Distributed State Estimation With Unknown Noise Statistics

An adaptive consensus filter for sensor networks with unknown process and measurement noise statistics is proposed in this letter. The variational Bayes(VB) approach is exploited to get local estimates of unknown noise covariances with prior inverse Wishart distributions. A distributed averaging approach on exponential-class densities is applied for consensus on the natural parameters of the unknown predicted error covariance. Consensus on measurements is performed in parallel and the two consensus outcomes are fused. Simulation results demonstrate the effectiveness of the proposed adaptive consensus filter compared to conventional, non-adaptive, consensus filters.

DeSpeckNet: Generalizing Deep Learning-Based SAR Image Despeckling

Deep learning (DL) has proven to be a suitable approach for despeckling synthetic aperture radar (SAR) images. So far, most DL models are trained to reduce speckle that follows a particular distribution, either using simulated noise or a specific set of real SAR images, limiting the applicability of these methods for real SAR images with unknown noise statistics. In this article, we present a DL method, deSpeckNet, <xref ref-type="fn" rid="fn1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¹</xref> that estimates the speckle noise distribution and the despeckled image simultaneously. Since it does not depend on a specific noise model, deSpeckNet generalizes well across SAR acquisitions in a variety of landcover conditions. We evaluated the performance of deSpeckNet on single polarized Sentinel-1 images acquired in Indonesia, The Democratic Republic of Congo, and The Netherlands, a single polarized ALOS-2/PALSAR-2 image acquired in Japan and an Iceye X2 image acquired in Germany. In all cases, deSpeckNet was able to effectively reduce speckle and restore the images in high quality with respect to the state of the art.

An adaptive variational Bayesian filter for nonlinear multi-sensor systems with unknown noise statistics

An improved adaptive variational Bayesian cubature information fusion algorithm for nonlinear multi-sensor systems with uncertain noise statistics is proposed in this paper. Aiming to estimate uncertain process and measurement noise covariances in nonlinear systems, the variational Bayesian theory is combined with the inverse Wishart distribution. System states and uncertain noise covariances are jointly estimated for nonlinear systems by means of cubature sampling, deriving the variational Bayesian cubature Kalman filter (VBCKF-QR). In addition, a variational Bayesian Cubature Information filter (VBCIF-QR) is proposed, and a distributed information feedback fusion algorithm is also derived for multi-sensor systems with unknown noise statistics. Simulation results demonstrate that the proposed VBCKF-QR/VBCIF-QR outperform conventional cubature Kalman/information filters.

Kalman filter with recursive covariance estimation for protection against system uncertainty

This study is intended to design a novel adaptive Kalman filter (KF) that can solve the filtering problem with unknown noise statistics. The proposed method named as measurement sequence adaptive KF (MSAKF) can adaptively estimate the unknown parameters of noise statistics via the information from measurement sequences. In order to enhance the computational efficiency, algorithm optimisation via recursive covariance estimation is introduced. In addition, stability analysis of the MSAKF is also made under some given conditions. The estimation process is proved to be stable and its filtering results converge to the ones of the ideal KF with exact system parameters. To demonstrate the effectiveness of the MSAKF algorithm, the simulation based on a navigation signal-tracking model is presented, and the results show that the MSAKF algorithm possesses low calculation complexity, fast convergence, high-precision and adaptability in complex application environments.

Artificial bee colony–based Kalman filter hybridization for three–dimensional position estimation of a quadrotor

Purpose The purpose of this paper is to introduce an artificial bee colony-based Kalman filter algorithm along with an extended objective function to ensure the optimality of the estimator of the quadrotor in the presence of unknown measurement noise statistics. Design/methodology/approach Six degree-of-freedom mathematical model of the quadrotor is derived. Position controller for the quadrotor is designed. Kalman filter-based estimation algorithm is implemented in the sensor feedback loop. Artificial bee colony-based hybrid algorithm is used as an optimization method to handle the unknown noise statistics. Existing objective function is extended with a penalty term. Mathematical proof of the extended objective function is derived. Results of the proposed algorithm is compared with de facto genetic algorithm-based Kalman filter. Findings Artificial bee colony algorithm-based Kalman filter and extended objective function duo are able to optimize the measurement noise covariance matrix with an absolute error as low as 0.001 [m2]. Proposed method and function is capable of reducing the noise from 2 to 0.09 [m] for x-axis, 3.4 to 0.14 [m] for y-axis and 3.7 to 0.2 [m] for z-axis, respectively. Originality/value The motivation behind this paper is to bring a novel optimization-based solution for the estimation problem of the quadrotor when the measurement noise statistics are unknown along with an extended objective function to prevent the infeasible solutions with mathematical convergence analysis.

Artificial evolution based cost-reference particle filter for nonlinear state and parameter estimation in process systems with unknown noise statistics and model parameters

The cost-reference particle filter (CRPF) is a variant of the particle filter (PF). It is simpler, more robust, and more flexible than the standard PF. Particularly, it does not require any statistical information on both state noises and observation noises in its application. However, in order to successfully apply CRPF to the nonlinear state estimation in dynamic process systems, the knowledge of the model parameters should be known a priori. The standard CRPF cannot handle the problem of state and parameter estimation (SPE) with unknown noise statistics and model parameters. To eliminate the above limitation, this paper proposes an evolution algorithm for the SPE in nonlinear dynamic process systems. The algorithm is the combination of the artificial evolution (AE) with CRPF, called AE-CRPF, to estimate the states and the parameters simultaneously. The proposed AE-CRPF is applied to two nonlinear dynamic process systems for practical applications. The results demonstrate the effectiveness and robustness of the proposed method.

Multiple-Step Randomly Delayed Adaptive Robust Filter With Application to INS/VNS Integrated Navigation on Asteroid Missions

This paper develops a novel nonlinear adaptive robust filter called the multiple-step randomly delayed variational Bayesian adaptive high-degree cubature Huber-based filter (MRD-VBAHCHF) for a class of nonlinear stochastic systems whose measurements are randomly delayed by multiple sampling times and corrupted by contaminated Gaussian noise with unknown covariance. First, a system with randomly delayed measurement is modeled in terms of multiple Bernoulli random variables. Then, the multiple-step randomly delayed high-degree cubature Kalman filter (MRD-HCKF) is derived by employing the fifth-degree cubature rule to compute the mean and covariance of the nonlinear equations in the system model. Next, the MRD-HCKF is modified to the MRD-VBAHCHF by incorporating the variational Bayesian theory and Huber technique for estimating the measurement noise covariance online and suppressing the influence of non-Gaussian noise. Consequently, the proposed filter is not only adaptive to unknown measurement noise statistics but also robust to random measurement delays and non-Gaussian noise. Finally, the MRD-VBAHCHF is verified for use in inertial navigation system/visual navigation system (INS/VNS) integrated navigation on asteroid missions, and the results of Monte Carlo simulations demonstrate that the MRD-VBAHCHF outperforms the high-degree cubature Kalman filter (HCKF), the MRD-HCKF and the variational Bayesian adaptive high-degree cubature Huber-based filter (VBAHCHF), thus showing the superiority of the proposed filter.

Enhancing produce safety: State estimation-based robust adaptive control of a produce wash system

The rapid introduction of fresh-cut produce into a produce wash system can dramatically decrease the free chlorine (FC) concentration level in the wash water, resulting in potential widespread cross-contamination throughout the entire wash system. To minimize such contamination, a sufficient level of FC must be maintained in the wash water. This paper presents a state estimation-based robust adaptive sliding mode (RASM) control strategy for the wash system to stabilize the FC concentration level during fresh-cut iceberg lettuce washing. This feedback control law for FC dosing is suggested to provide a sufficient FC injection rate (FCIR) to the wash system in order to compensate for the fall in the FC level and in turn to minimize the Escherichia coli (E. coli) O157:H7 levels on washed lettuce and in the wash water. The proposed controller uses the estimated chemical oxygen demand (COD) and FC concentration as feedback signals while system states are estimated by a hybrid extended Kalman filter (HEKF) and the unknown noise statistics are identified by a noise identification (NI) algorithm. Uniformly ultimately boundedness (UUB) of the FC concentration tracking error in the presence of unmodelled dynamics is proven using the Lyapunov framework and Barbalat’s lemma. The E. coli O157:H7 contamination levels are predicted from the joint estimator and controller properties. Simulation results show that the proposed NI-based HEKF/RASM control methodology achieves FC tracking while the pathogens converge to their predicted levels. The E. coli O157:H7 levels decrease as FC concentration increases and in particular, no E. coli O157:H7 is detected when FC concentration is regulated at 15 mg/L. Two robustness tests are performed to show the performance of the proposed controller in the presence of chlorine actuator failure and system parameter uncertainties. Finally, cross-contamination management is examined in terms of the prevalence and mean pathogen levels of incoming pre-wash lettuce in the context of FC regulation at 15 mg/L.

Short-term forecasting of renewable energy consumption: Augmentation of a modified grey model with a Kalman filter

One of the important global trends in near future is to replace fossil-fuel energy with sustainable energy. The accurate predictions of the renewable energy consumption are seemingly crucial in both national and international levels. In the context of a limited number of historical data, grey prediction system of single variable is one of primary choices for such prediction. Nonetheless, this seems rather sceptical when the dynamics of a system relies on solely one variable. This paper presents a novel approach based on a modification of multivariable grey prediction model whereby the influences of exogenous variables are taken into account. Furthermore, instead of employing the least square method for parameter estimation, states and parameters in our proposed method are sequentially estimated by means of the traditional Kalman filtering. The genetic algorithm is additionally supplemented in the Kalman filter step in order to justify some unknown noise statistics. To validate the effectiveness of the proposed scheme, it is employed to estimate and predict the renewable energy consumption in Thailand along with its associated factors using the data from 1990 to 2015. Compared with the multivariable grey model using the least square method for estimation of model parameters, the results show that the hybrid approach provides a better estimation and prediction performance.

Adaptive filtering-based recursive identification for time-varying Wiener output-error systems with unknown noise statistics

In area of control, model-based robust identification is rare, and studies in presence of unknown noise statistics are especially seldom. The robust estimation problem for time-varying Wiener output-error systems is considered in this paper. An adaptive filtering-based recursive identification scheme is proposed to distinguish nonlinear time-varying characteristics in complex noise environments. Firstly, a virtual equivalent state space model is constructed to achieve adaptive Kalman filtering. In filter design, a weighted noise estimator based on Sage-Husa principle is introduced, and is sensitive to noise changes. Secondly, the state estimates obtained by filters are used to form the unknown intermediate variables in information vectors. Then, a recursive estimation method based on multiple iterations is developed, and the convergence of identification is confirmed by martingale hyperconvergence theorem. Finally, the numerical simulation results verify the theoretical findings.

Particle Filter With Unknown Statistics to Estimate Liquid Level in the Silicon Single-Crystal Growth

In the process of silicon single-crystal growth, the detection of melt level is an important step to ensure that the grown silicon single crystal is of high quality. Since there exist many mechanical motions, chemical interactions, thermal convection, and so on, it is extremely difficult to obtain the noise statistics of the liquid-level data. To attain a high-accuracy detection of liquid level with unknown noise statistics, we present an extended set-membership-based particle filter (PF). The key points are as follows. We construct a nonlinear state-space model for liquid-level detection system based on the kinematic principle and laser triangulation measurement principle and cast the detection problem of the liquid level into a state estimation problem. Based on this model, we use the extended set-membership estimation theory to generate an ellipsoid set that contains the true value of the liquid-level state. To overcome the difficulty of drawing particles under the case of unknown statistics noise, we draw particles from a Gaussian distribution in the obtained ellipsoidal set. In order to resample particles when the measurement noise statistic is unknown, we introduce a cost function to obtain the weights of the particles, and the ultimate estimation of liquid level is calculated by the weighted particles after the resampling procedure. Comparing with the extended Kalman PF (EPF) and the cost-reference PF (CRPF), the proposed algorithm has higher estimation accuracy. Some simulation and experiment results are presented to illustrate the effectiveness of the proposed method.

Consensus-based cubature information filtering for sensor networks with incomplete measurements

Consensus-based distributed filtering is an effective technique for state estimation or data fusion over sensor networks. However, nonlinearity of systems as well as network-induced incomplete information problems are the main obstacles on the way. In this paper, we deal with the distributed filtering of nonlinear systems over sensor networks with incomplete measurements. A perception of credibility evaluation on nodes’ estimations is presented, followed by a novel credibility weight design method. The weights are redistributed by nodes’ estimations in a normal fashion at each time step. The convergence of data fusion with the weights is proved. Further the credibility weight method is integrated into the general consensus-based cubature information filtering algorithm to handle various incomplete measurement problems. Numerical experiments, in the case of unknown noise statistics, measurement interference and measurement missing, demonstrate the effectiveness and robustness of the proposed algorithm.

Robust dynamic state estimation of power systems with model uncertainties based on adaptive unscented filter

This study considers the dynamic state estimation of power systems with model uncertainties that might be caused by the unknown noise statistics or unpredicted changes to the model parameters. To deal with these issues, an innovation-based estimator that is able to dynamically revise the statistics of system and measurement noise is proposed firstly. Then, based on the H ∞ criteria for bounding the adverse influences on the estimation error of model uncertainties and unscented transform technique, an adaptive strategy is developed to adjust the estimation error covariance matrix under various conditions. Finally, by incorporating the proposed approaches and H ∞ filter theory, a novel adaptive unscented H ∞ filter is established to realise dynamic state estimation of power system against model uncertainties. Extensive simulation results obtained from the IEEE-39 bus test system are presented to illustrate the effectiveness and robustness of the proposed method.

Development of a Robust UFIR Filter with Consensus on Estimates for Missing Data and unknown noise statistics over WSNs

Wireless sensor networks (WSN) are often deployed in harsh environments, where electromagnetic interference, damaged sensors, or the landscape itself cause the network to suffer from faulty links and missing data. In this paper, we develop an unbiased finite impulse response (UFIR) filtering algorithm for optimal consensus on estimates in distributed WSN. Simulations are provided assuming two possible scenarios with missing data. The results show that the distributed UFIR filter is more robust than the distributed Kalman filter against missing data.

Robust Cubature Kalman Filter for Dynamic State Estimation of Synchronous Machines Under Unknown Measurement Noise Statistics

Kalman-type filtering techniques including cubature Kalman filter (CKF) does not work well in non-Gaussian environments, especially in the presence of outliers. To solve this problem, Huber's M-estimation based robust CKF (RCKF) is proposed for synchronous machines by combining the Huber's M-estimation theory with the classical CKF, which is capable of coping with the deterioration in performance and discretization of tracking curves when measurement noise statistics deviatefrom the prior noise statistics. The proposed RCKF algorithm has good adaptability to unknown measurement noise statistics characteristics including non-Gaussian measurement noise and outliers. The simulation results on the WSCC 3-machine 9-bus system and New England 16-machine 68-bus system verify the effectiveness of the proposed method and its advantage over the classical CKF.