Unknown Noise Statistics Research Articles

Adaptive horizon size moving horizon estimation with unknown noise statistical properties

Abstract Moving horizon estimation (MHE) is an effective technique for state estimation. It formulates state estimation as an optimization problem over a finite time interval and is characterized by inherent robustness, flexibility, and explicit constraint handling capabilities. The horizon size is a crucial parameter influencing the estimation performance of MHE. However, the selection of the horizon size remains an open research question in the field of MHE. In this paper, we propose a novel adaptive horizon size MHE strategy that dynamically adjusts the horizon size based on the value of the objective function. This approach aims to improve the state estimation performance of MHE in real-time applications. Unlike conventional MHE methods that rely on a fixed horizon size, our adaptive strategy enhances robustness against unknown noise statistics by adjusting the horizon size. We analyze the convergence property of the estimation error and provide guidelines for parameter design to ensure optimal performance. The effectiveness and superiority of the proposed method are demonstrated through simulations involving an oscillatory system and a target tracking application under non-stationary noise conditions.

Passive underwater tracking with unknown measurement noise statistics using variational Bayesian approximation

This paper considers a bearings-only tracking problem with unknown measurement noise statistics. It is assumed that the measurement noise follows a Gaussian probability density function where the mean and the covariance of the noise are unknown. Here, an adaptive nonlinear filtering technique is proposed, where the joint distribution of the measurement noise mean and its covariance are considered to follow a normal inverse Wishart (NIW) distribution. Using the variational Bayesian (VB) approximation, joint distribution of the target state, the measurement noise mean and covariance is factorized as the product of their individual probability density function (pdf). Minimizing the Kullback-Leibler divergence (KLD) between the factorized and true joint pdfs, probability distributions of the noise mean, covariance and the target states are evaluated. The estimation of states with the proposed VB based method is compared with the maximum a posteriori (MAP) and the maximum likelihood estimation (MLE) based adaptive filtering. Deterministic sigma points are used to realize the filtering algorithms. The proposed adaptive filter with VB approximation is found to be more accurate compared to their corresponding MAP-MLE based counterparts.

A Robust Interacting Multi-Model Multi-Bernoulli Mixture Filter for Maneuvering Multitarget Tracking under Glint Noise.

In practical radar systems, changes in the target aspect toward the radar will result in glint noise disturbances in the measurement data. The glint noise has heavy-tailed characteristics and cannot be perfectly modeled by the Gaussian distribution widely used in conventional tracking algorithms. In this article, we investigate the challenging problem of tracking a time-varying number of maneuvering targets in the context of glint noise with unknown statistics. By assuming a set of models for the possible motion modes of each single-target hypothesis and leveraging the multivariate Laplace distribution to model measurement noise, we propose a robust interacting multi-model multi-Bernoulli mixture filter based on the variational Bayesian method. Within this filter, the unknown noise statistics are adaptively learned while filtering and the predictive likelihood is approximately calculated by means of the variational lower bound. The effectiveness and superiority of our proposed filter is verified via computer simulations.

Sensing and Deep CNN-Assisted Semi-Blind Detection for Multi-User Massive MIMO Communications

Attaining precise target detection and channel measurements are critical for guiding beamforming optimization and data demodulation in massive multiple-input multiple-output (MIMO) communication systems with hybrid structures, which requires large pilot overhead as well as substantial computational complexity. With benefits from the powerful detection characteristics of MIMO radar, we aim for designing a novel sensing-assisted semi-blind detection scheme in this paper, where both the inherent low-rankness of signal matrix and the essential knowledge about geometric environments are fully exploited under a designated cooperative manner. Specifically, to efficiently recover the channel factorizations via the formulated low-rank matrix completion problem, a low-complexity iterative algorithm stemming from the alternating steepest descent (ASD) method is adopted to obtain the solutions in case of unknown noise statistics. Moreover, we take one step forward by employing the denoising convolutional neural network (DnCNN) to preprocess the received signals due to its favorable performance of handling Gaussian denoising. The overall paradigm of our proposed scheme consists of three stages, namely (1) target parameter sensing, (2) communication signal denoising and (3) semi-blind detection refinement. Simulation results show that significant estimation gains can be achieved by the proposed scheme with reduced training overhead in a variety of system settings.

A New End-to-End Monitoring Framework for Nonlinear Dynamic Processes With Unknown Noise Statistics

A New End-to-End Monitoring Framework for Nonlinear Dynamic Processes With Unknown Noise Statistics

Localization of underground pipe jacking machinery: A reliable, real-time and robust INS/OD solution

Accurate positioning is important for guidance control in pipeline construction, but traditional approaches fail in GPS-denied environments. This paper addresses the underground localization problem for the pipe jacking machine by presenting an Inertial Navigation System (INS)/ODometry (OD) scheme. It is a loosely coupled navigation system that combines an INS and an OD to provide reliable, real-time, and robust location estimation in an enclosed and restricted space. The combination is achieved by a multi-sensor fusion algorithm to avoid the divergence of standalone INS. Compared with the traditional localization technologies, the advantage of the INS/OD scheme is that there is no performance degradation or service failure despite severe blockage of the thick soil layer due to the selection of dead reckoning-based sensors. Moreover, an Unbiased Finite Impulse Response (UFIR) filter serves as the fusion mechanism to improve the robustness against a prior knowledge of noise, considering unknown and time-varying noise statistics in practice. The INS/OD scheme is verified through a numerical simulation and employed on-site in a real underground sewage pipeline construction project. Despite the construction site being more than 10 meters deep underground, the INS/OD scheme continues to perform reliably and robustly in real-time, significantly benefiting the engineering guidance enterprise.

Cost reference particle filter with multi-probability distribution for nonlinear dynamic systems with unknown noise statistics

The lack of particle diversity is a vital problem in particle filtering for nonlinear dynamic systems with unknown noise statistics. In this paper, cost reference particle filter with multi-probability distribution (CRPF_MPD) is introduced to minimize the effects of the lack of particle diversity and to obtain more realistic state estimations. The core of multi-probability distribution is that two subsets are parallelly initialized and resampled by the processes of cost reference particle filter (CRPF) and are respectively updated with different distributions. Information interaction and particle selection form a set of particles with multi-probability distribution to estimate the more realistic states of systems. CRPF_MPD relies on multi-probability distribution, information interaction and particle selection to have excellent performance. As can be seen from the results of simulations, CRPF_MPDs can enhance the accuracy of state estimation and are more robust to different systems. Thus, CRPF_MPDs are available for dynamic systems with unknown noise statistics.

Modified Strong Tracking Slide Window Variational Adaptive Kalman Filter With Unknown Noise Statistics

The filter performance will be degraded in the measurements with time-varying and unknown noise statistics. To combat the above challenges, a modified strong tracking slide window variational adaptive Kalman filter algorithm is proposed in this article. Firstly, the multiple fading factors are integrated into the proposed algorithm to adjust the error covariance. Next, an improved adaptive slide window method is designed for variational Bayesian Kalman filtering by adaptively adjusting the slide window size and correcting the previous state according to the later state, which improves the estimation accuracy and computational efficiency. Finally, the inverse Wishart distribution is considered for modeling process and measurement noise, and the state vector, as well as noise statistics, are inferred via the variational Bayesian technique without prior noise covariance information. Simulation results demonstrate that the proposed filter algorithm is more robust than existing filters in counteracting measurement and process noise uncertainties.

Improving Treatment of Noise Specification of Kalman Filtering for State Updating of Hydrological Models: Combining the Strengths of the Interacting Multiple Model Method and Cubature Kalman Filter

AbstractFiltering methods have been widely used to improve the forecast performances of hydrological models. Although extensive research has been carried out on filtering methods in the hydrology literature, researchers have not treated the noise statistics of filtering methods in much detail. Wrongly specified noise statistics can lead to degraded state estimates and even filter divergence. A powerful approach for state estimation in the presence of unknown noise statistics is the interacting multiple model method (IMM), which solves the noise specification problem by combining the strengths of multiple filters with different noise statistics. The IMM method has received little to no attention in the hydrologic context. This paper proposes a novel approach (IMM‐CKF) for updating the states of hydrological models in the presence of unknown noise statistics by combining the cubature Kalman filter (CKF) with the IMM. The CKF is a popular nonlinear filter that has received little attention in the hydrology literature. The method is tested using a lumped hydrological model. The results of the synthetic case suggest the IMM‐CKF can yield an accurate estimate for the switch as well as the changed states when there are abrupt changes in the noise statistics of true noises, even if sub‐filter noise statistics are not equal to the real ones. The real case results (a forecast experiment) show that the IMM‐CKF has successfully combined the strengths of different sub‐filters and associated noise statistics. The IMM‐CKF can be useful for hydrological forecasting, especially when useful information about the true noise statistics is unavailable.

A Static Reduced-Order Multiple-Model Adaptive Estimator for Noise Identification

A reduced-order multiple-model (MM) estimator for noise identification in dynamic stochastic systems is developed. The unknown noise statistics are assumed to be static. While a standard static MM estimator does not grow exponentially over time, its computational complexity grows exponentially with the number of modes. The proposed algorithm reduces the computational complexity of MM estimation from exponential to polynomial by constructing a significantly smaller set of mode models which are updated every time step. It is assumed that the constructed mode models do not change significantly between time steps, which in turn holds if the smoothness of the mode probabilities is guaranteed. It is shown that in the case where there is “enough” statistical distinction between the noise modes, the proposed reduced-order MM estimator converges to the standard MM estimator. The proposed reduced-order MM estimator is evaluated using Monte Carlo simulations, showing that it performs nearly similar to the standard MM estimator with a fraction of its complexity. The numerical example shows less than a 2% increase in the root mean-squared errors (RMSEs) of the reduced-order MM estimator from the standard one, while the reduction in the number of filters in the reduced-order MM estimator is 300%. To further validate the proposed filter, experimental results are presented of an unmanned aerial vehicle (UAV) navigating with terrestrial signals of opportunity. Opportunistic navigation serves a relevant application for MM-based estimation, as system parameters, namely the statistics of the clock error dynamics of opportunistic sources, are unknown and must be adaptively estimated. The experimental results show a UAV navigating for more than 5 minutes over a trajectory of more than 3 km, achieving a final position error of 6.21 m obtained using the standard MM estimator versus a final position error of 6.25 m obtained using the proposed reduced-order MM estimator. A standard extended Kalman filter (EKF) was implemented for comparative analysis, showing a final error of 40.03 m. In the experiments, the reduced-order MM estimator was implemented with 16 filters, while the standard MM was implemented with 256 filters.

Distributed variational Bayesian adaptive filtering for randomly delayed measurements and unknown noise statistics in multi-sensor networked systems

To deal with randomly delayed measurements and unknown noise statistics in multi-sensor networked systems, a distributed variational Bayesian adaptive cubature Kalman filtering algorithm (DVB_ACKF) is presented in this paper. To compensate for the effects induced by randomly delayed measurements, a refined measurement reorganization method is designed via a two-stage estimation strategy. Specifically, we first estimate the time delay step. The measurements are then rearranged based on the estimated results from the first stage. Then, a novel noise estimator with the sliding-window and variational Bayesian method is developed to estimate the mean and covariance of the unknown noise. The network topology attribute and measurement accuracy have been combined to eliminate the distributed fusion error. The tuning parameter and forgetting factor as well as their bounds are analyzed. Furthermore, numerical simulations are carried out to verify the superior performance of the developed algorithm.

A variational Bayesian inference technique for model updating of structural systems with unknown noise statistics

Dynamic models of structural and mechanical systems can be updated to match the measured data through a Bayesian inference process. However, the performance of classical (non-adaptive) Bayesian model updating approaches decreases significantly when the pre-assumed statistical characteristics of the model prediction error are violated. To overcome this issue, this paper presents an adaptive recursive variational Bayesian approach to estimate the statistical characteristics of the prediction error jointly with the unknown model parameters. This approach improves the accuracy and robustness of model updating by including the estimation of model prediction error. The performance of this approach is demonstrated using numerically simulated data obtained from a structural frame with material non-linearity under earthquake excitation. Results show that in the presence of non-stationary noise/error, the non-adaptive approach fails to estimate unknown model parameters, whereas the proposed approach can accurately estimate them.

Data-compatibility Analysis Based on Expectation-Maximization Algorithm with Unknown Noise Statistics

In this paper, data-compatibility analysis (DCA) problem is investigated with both the measurement noise and input noise considered. The expectation-maximization (EM) algorithm is exploited to deal with the unknown noise statistics. Motivated by the fact that although there exists an excellent EM based estimator for dynamic systems, it cannot be used in the context of DCA due to the presence of non-additive input noises, a generalized EM based estimator is developed to reconstruct the flight path, as well as to estimate the sensor model parameters. Making full use of the special dependencies among the state components and the fact that the associated dynamic system has an affine nonlinear structure, the generalized estimator retains many advantages of the existing EM based one, such as the simple optimization process for the unknowns. Experimental results show that it can give more accurate results than the classical output error method and the existing EM based one in the case of high input noise.

Adaptive fractional‐order unscented Kalman filter with unknown noise statistics

SummaryThis article deals with state estimation of complex nonlinear discrete fractional‐order systems with unknown noise statistics by means of an adaptive fractional‐order Unscented Kalman filter (AFUKF). Firstly, in order to alleviate the communication burden of fractional‐order Unscented Kalman filter, short‐term memory effect is utilized to decide an appropriate memory length. Then aiming at the problem of filtering divergence and accuracy degradation caused by unknown statistical characteristics of noise, based on the maximum a posterior (MAP) principle, a noise statistical estimator is introduced to estimate and correct the statistical characteristics of noise in real‐time. Finally, the unbiasedness of the proposed algorithm is analyzed to verify that the estimated mean and covariance of noise are unbiased. The effectiveness and accuracy of AFUKF are demonstrated via simulation experiments.

Coal mine personnel positioning algorithm based on improved adaptive unscented Kalman filter with wireless channel fading and unknown noise statistics

This paper is concerned with the problem of personnel localization in the complex coal mine environment with wireless channel fading and unknown noise statistics. Considering the random channel fading caused by signal fluctuation and transmission fault, an improved adaptive unscented Kalman filter (IAUKF) algorithm is proposed. The mean and error covariances of noise are estimated adaptively by adopting the improved Sage–Husa noise estimation method. In order to save energy and improve energy utilization, the multi-sensor clustering is performed to divide the spatial distribution of sensors into multiple clusters. The sensors in the same cluster can communicate with each other to maintain the consistency of estimation. The simulation results show that the IAUKF algorithm is better than extended Kalman filter (EKF), unscented Kalman filter (UKF), and improved unscented Kalman filter (IUKF) algorithms.

A Student's T-Based Measurement Uncertainty Filter for SINS/USBL Tightly Integration Navigation System

In order to suppress the impact of some error factors of the existing strap-down inertial navigation system and ultra-short base line (SINS/USBL) position matching loosely integration approach on positioning accuracy, a tightly integration strategy is creatively proposed and designed relying on the derived state error equation and measurement equation, the relative measurement information are directly used as the observation information. The error factors such as attitude error and installation error are considered in the filtering model to avoid the influences on the matching position, and the filter algorithm can be also effectively designed according to the sensor parameters of USBL, which can improve the integration positioning accuracy. Meanwhile, in order to address the decreased positioning performance caused by the measurement uncertainty, a Student's t-based Kalman filter with adaptiveness and robustness is reorganized and derived for the proposed SINS/USBL tightly integration strategy, the adaptiveness can be obtained by estimating the unknown measurement noise statistics using variational Bayesian (VB) approximation, and the robustness can be achieved by dealing with the measurement outliers based on the Student's t distribution. Finally, the feasibility and the superiority of the proposed strategy are evidenced both through the simulations and the field tests in the river.

The MAPWE-Boosted AEKF with Recursive-Against-Iteration Noise Statistic for Feature-Based SLAM Algorithm

The unknown noise statistic might degrade the Filter performance or even lead to filter divergence. Accordingly, to enhance the classical EKF to approximate the recursive process and measurement noise statistic, based on Maximum A Posteriori creation and Weighted Exponent (WE) as the divergence suppression method, abbreviated as MAPWE, an adaptive EKF is proposed through this paper. Moreover, the existence of simplification during estimating noise statistics under MAP creation might also degrade its quality. Thus, the suboptimal MAP solution was also estimated based on Weighted Exponent. Indeed, the time-varying noise statistic under this process seems strongly accurate. But the complexity of the measurement covariance might also diverge from its positive definite characteristic. Thus, aiming to prevent this condition, the additional divergence suppression method was also involved in correcting the error state covariance in the smoothing step. This improvement is then used as SLAM algorithm for a mobile robot. Comparing to the conventional methods, it is better in term of RMSE for the estimated path and estimated map.

A new adaptive Kalman filter for navigation systems of carrier-based aircraft

The features of carrier-based aircraft’s navigation systems during the approach and landing phases are investigated. A new adaptive Kalman filter with unknown state noise statistics is proposed to improve the accuracy of the INS/GNSS integrated navigation system. The adaptive filtering algorithm aims to estimate and adapt the unknown state noise covariance Q in high dynamic conditions, when the measurement noise covariance R is assumed to be known empirically in advance. The new adaptive Kalman filter based on the innovation sequence and pseudo-measurement vector approach makes it more effective to estimateandadapt Q. The simulation results and semi-physical experiments show that the application of the proposed adaptive Kalman filter can guarantee a higher estimation accuracy of the state variables.

State of Charge Estimation of Lithium-Ion Battery Based on Improved Adaptive Unscented Kalman Filter

State of charge (SOC) of the lithium-ion battery is an important parameter of the battery management system (BMS), which plays an important role in the safe operation of electric vehicles. When existing unknown or inaccurate noise statistics of the system, the traditional unscented Kalman filter (UKF) may fail to estimate SOC due to the non-positive error covariance of the state vector, and the SOC estimation accuracy is not high. Therefore, an improved adaptive unscented Kalman filter (IAUKF) algorithm is proposed to solve this problem. The IAUKF is composed of the improved unscented Kalman filter (IUKF) that is able to suppress the non-positive definiteness of error covariance and Sage–Husa adaptive filter. The IAUKF can improve the SOC estimation stability and can improve the SOC estimation accuracy by estimating and correcting the system noise statistics adaptively. The IAUKF is verified under the federal urban driving schedule test, and the SOC estimation results are compared with IUKF and UKF. The experimental results show that the IAUKF has higher estimation accuracy and stability, which verifies the effectiveness of the proposed method.

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.