Robust Kalman Filter Research Articles

A new robust Kalman filter with measurement loss based on mixing distribution

A new robust Kalman filter (KF) based on mixing distribution is presented to address the filtering issue for a linear system with measurement loss (ML) and heavy-tailed measurement noise (HTMN) in this paper. A new Student’s t-inverse-Wishart-Gamma mixing distribution is derived to more rationally model the HTMN. By employing a discrete Bernoulli random variable (DBRV), the form of measurement likelihood function of double mixing distributions is converted from a weighted sum to an exponential product, and a hierarchical Gaussian state-space model (HGSSM) is therefore established. Finally, the system state, the intermediate random variables (IRVs) of the new STIWG distribution, and the DBRV are simultaneously estimated by utilizing the variational Bayesian (VB) method. Numerical example simulation experiment indicates that the proposed filter in this paper has superior performance than current algorithms in processing ML and HTMN.

An Overdispersed Black-Box Variational Bayesian-Kalman Filter with Inaccurate Noise Second-Order Statistics.

Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a Bayesian robust Kalman filter based on posterior noise statistics (KFPNS) is derived, and the recursive equations of this filter are very similar to that of the classical algorithm. Note that the posterior noise distributions are approximated by overdispersed black-box variational inference (O-BBVI). More precisely, we introduce an overdispersed distribution to push more probability density to the tails of variational distribution and incorporated the idea of importance sampling into two strategies of control variates and Rao–Blackwellization in order to reduce the variance of estimators. As a result, the convergence process will speed up. From the simulations, we can observe that the proposed filter has good performance for the model with uncertain noise. Moreover, we verify the proposed algorithm by using a practical multiple-input multiple-output (MIMO) radar system.

Robust Kalman filter for systems subject to parametric uncertainties

State estimation plays a fundamental role in control systems that rely on the knowledge of the underlying system state, especially when it is not readily available. The Kalman filter is among the most popular techniques in this matter. Nonetheless, one of its well-known shortcomings is the assumption that an exact system model is available. The difficulty in fulfilling this premise justifies the demand for estimation strategies that limit the effect of model uncertainties. In this paper, we propose a robust Kalman filter for uncertain linear discrete-time systems. We assume a general setting in which all matrices of both the system and measurement models are subject to norm-bounded parametric uncertainties. By adopting a purely deterministic viewpoint and applying the penalty function method, we formulate a robust regularized least-squares estimation problem. We further analyze how the penalty parameter influences the estimation performance. The resulting filter is presented both in a symmetric matrix arrangement and as explicit algebraic expressions in a Kalman-like structure that is suitable for online applications. Under reasonable conditions, we show that the steady-state filter is stable and, for quadratically stable systems, guarantees a bounded error variance. With a numerical example, we evaluate the proposed filter and compare its performance with other robust filtering approaches.

Real-time GNSS attitude determination by a direct approach with efficiency and robustness

Estimating attitude directly from multi-antenna carrier phase measurements is known as the direct approach of global navigation satellite system attitude determination. Without the process of resolving baseline vectors in advance, this approach makes full use of raw observations. However, the known baseline constraints would be missing when the least squares method is used in the direct approach, of which the corresponding model contains no baseline parameter. The constraint information is important for real-time ambiguity resolution. Therefore, we propose using an adaptively robust Kalman filter for the direct approach, in which the predicted attitude plays the role of an attitude constraint. An observation model parameterized by the multiplicative quaternion error vector and the integer ambiguities is derived, accompanied with a state model consisting of the quaternion error vector, the ambiguities and the angular rate. Since the state vector contains three different types of parameters, the filter uses an adaptive matrix consisting of different adaptive factors instead of a single factor. The factor of the quaternion error vector is determined by a three-section function containing the ratio value from the ratio-test of ambiguity resolution. The factors of the ambiguities are calculated by the detected cycle slip. The equivalent weight matrix of the filtering can resist the influence of outliers in harsh environment. By the direct approach with the proposed adaptively robust filtering, the accuracy of the float solution and the variance-covariance matrix are significantly improved, and the ambiguity can be efficiently searched and fixed using the standard least-squares ambiguity decorrelation adjustment method. The proposed algorithm is suitable for real-time applications since no time-consuming and complex searching of ambiguity resolution is required. Finally, the efficiency and robustness of the algorithm is validated by a field test.

A novel robust Kalman filter with adaptive estimation of the unknown time-varying latency probability

To better model one-step randomly delayed measurements (ORDM) with unknown time-varying latency probability (UTLP) in linear systems with heavy-tailed measurement noise (HMN), a novel Normal-Gamma-Beta mixture (NGBM) distribution is presented. By introducing a Bernoulli random variable, the probability density function of the proposed NGBM distribution can be reformulated as a Gaussian hierarchical form. Based on this, a novel robust Kalman filter is designed using the variational Bayesian technique. A target tracking simulation verifies the potential of the proposed robust filter, which has higher filtering accuracy than existing cutting-edge filters and can adaptively estimate the UTLP. Furthermore, it is concluded that when HMN and ORDM concurrently exist, the HMN has more influence on the accuracy of the filter than the ORDM.

Constrained fault-tolerant control for hypersonic vehicle subject to actuator failure and with unmeasurable states

In this article, a novel constrained fault-tolerant control (FTC) scheme is proposed to solve the attitude tracking control problem of the hypersonic vehicle (HSV) subject to multiple constraints, actuator faults, and disturbances. The reentry model of HSV with state constraints and the fault model of aerodynamic surface considering surface deflection constraints are constructed firstly. The adaptive robust unscented Kalman filter (ARUKF)-based estimation algorithm is designed, which can quickly estimate state variables, stuck faults, partial loss of effectiveness (PLOE) faults, and disturbances at the same time. By utilising the improved model predictive static programming (MPSP) technique, the complexity of processing multiple constraints and the computation are significantly reduced. Moreover, the closed-loop control system stability of HSV is analysed and the simulation results under two fault cases are given to demonstrate the effectiveness of the presented FTC scheme.

A robust Kalman filter time scale algorithm with data anomaly

Kalman filtering is utilized in many fields because of its capability to separate data from white phase noise. In time and frequency domain, employing Kalman filter is particularly important because of its use in building time scales. The studied time scale algorithms have been usually based on an ensemble of clocks without data anomaly, or the anomaly data is processed in advance to secure the reliability of the data used in Kalman filter algorithm. This increases the amount of computation and affects the real-time performance of the algorithm. In this study a robust Kalman filter is employed to present a method of time scale calculation. It extends a previously published Kalman filter algorithm that is useful for an ensemble of clocks without phase anomalies. In the algorithm, the inflation factor and the optimal adaptive factor are applied to the clock ensemble. The introduced algorithm may be useful for an ensemble of clocks with measurement outliers and phase jumps. The effectiveness of the proposed method can be verified through simulation and experimental analysis. The analysis result shows that the robust Kalman filter algorithm can resist the influence of measurement outliers and phase jumps on time scale performance. So, the accuracy and the stability of time scale can be improved.

Combined adaptive robust Kalman filter algorithm

The precise positioning of dynamic and static objects such as vehicles and pedestrians is a key technology. A global navigation satellite system signal is the primary signal source required to achieve precise positioning, and the optimal estimation method used in precise positioning is Kalman filtering (KF). Standard KF can only achieve optimal estimation results under the conditions that the mathematical model has been determined and the noise characteristics are known. However, when there are measurement outliers and prior noise information deviations, the accuracy of KF cannot be guaranteed. To effectively solve the above problems, a combined adaptive robust Kalman filter (CARKF) algorithm is proposed. First, the influence of measurement outliers on KF accuracy is resisted using the robust Kalman filter method. Then, the influence of an anomalous innovation on its autocorrelation sequence and cross-correlation sequence is resisted by the robust estimator for correlated observations based on the IGGIII method, to ensure the correct estimation of the correlation function sequence of the filtered innovation statistics. Finally, the autocovariance least-squares method is used to eliminate the coupling effect between noise covariances and accurately estimate the unknown noise covariance information. Moreover, an iterative strategy is adopted to eliminate the effect of errors caused by prior noise covariance deviations. The results of the three experiments show that the CARKF method can not only effectively resist the influence of measurement outliers on filtering accuracy and noise covariance valuation but also overcome the influence of errors caused by prior noise deviations and accurately simultaneously estimate two kinds of unknown noise covariance information.

Smart Video Surveillance System Based on Edge Computing.

New processing methods based on artificial intelligence (AI) and deep learning are replacing traditional computer vision algorithms. The more advanced systems can process huge amounts of data in large computing facilities. In contrast, this paper presents a smart video surveillance system executing AI algorithms in low power consumption embedded devices. The computer vision algorithm, typical for surveillance applications, aims to detect, count and track people’s movements in the area. This application requires a distributed smart camera system. The proposed AI application allows detecting people in the surveillance area using a MobileNet-SSD architecture. In addition, using a robust Kalman filter bank, the algorithm can keep track of people in the video also providing people counting information. The detection results are excellent considering the constraints imposed on the process. The selected architecture for the edge node is based on a UpSquared2 device that includes a vision processor unit (VPU) capable of accelerating the AI CNN inference. The results section provides information about the image processing time when multiple video cameras are connected to the same edge node, people detection precision and recall curves, and the energy consumption of the system. The discussion of results shows the usefulness of deploying this smart camera node throughout a distributed surveillance system.

Robust Cascade Vision/Force Control of Industrial Robots Utilizing Continuous Integral Sliding-Mode Control Method

This article presents a robust cascade vision/force approach to control industrial robots interacting with unknown workpieces considering model uncertainties. This cascade structure, consisting of an inner vision loop and an outer force loop, avoids the conflict between the force and vision control in the traditional hybrid methods without decoupling force and vision systems. To apply an advanced image-based visual servoing (IBVS) compensator, some newly modified image features are used that render an invertible image interaction matrix. A practical task-based method is proposed to extract the features corresponding to the desired path in a three-dimensional space. An adaptive robust Kalman filter is adopted for filtering the noise in the force feedback signal. A robust continuous integral sliding-mode control (CISMC) method is developed for both IBVS and force compensators. CISMC exploits the advantages of the modified supertwisting algorithm to reduce the chattering. The stability of the proposed cascade controller is proved. Additionally, a contact detector algorithm is developed to manage the robot's free motion and its interaction with the workpiece. To evaluate the performance of the proposed method, several experimental tests are performed and compared with other well-known methods. The results show the superiority of the proposed approach.

A fast robust Kalman filter for initial alignment of strapdown inertial navigation system

This paper investigates the non-Gaussian initial alignment for the strapdown inertial navigation system (SINS) with main focus on reducing the computational burden, meanwhile, ensuring the robustness of alignment filter. Conventional Kalman filter (KF) is the commonly used alignment filter, which brings a large computational burden during the filtering process, and assumes the statistic characteristics of the system noise is Gaussian in advance. When there are non-Gaussian characteristics in practice, it is difficult to improve the alignment filter speed without sacrificing the filter accuracy. In view of this problem, a fast robust Kalman filter (FRKF) is proposed. The approximated matrix inversion based on Neumann series expansion is used in the update step of the maximum correntropy criterion KF (MCC-KF). The computational complexity of the KF/MCC-KF/FRKF is analyzed, the approximated inversion method requires much less computational cost than the traditional inversion method, such that the FRKF is attractive from a complexity point of view. The alignment results show that the FRKF can obtain the state estimation accuracy as well as MCC-KF, while the computational burden is reduced remarkably.

Robust Kalman Filter-Based Dynamic State Estimation of Natural Gas Pipeline Networks

To obtain the accurate transient states of the big scale natural gas pipeline networks under the bad data and non-zero mean noises conditions, a robust Kalman filter-based dynamic state estimation method is proposed using the linearized gas pipeline transient flow equations in this paper. Firstly, the dynamic state estimation model is built. Since the gas pipeline transient flow equations are less than the states, the boundary conditions are used as supplementary constraints to predict the transient states. To increase the measurement redundancy, the zero mass flow rate constraints at the sink nodes are taken as virtual measurements. Secondly, to ensure the stability under bad data condition, the robust Kalman filter algorithm is proposed by introducing a time-varying scalar matrix to regulate the measurement error variances correctly according to the innovation vector at every time step. At last, the proposed method is applied to a 30-node gas pipeline network in several kinds of measurement conditions. The simulation shows that the proposed robust dynamic state estimation can decrease the effects of bad data and achieve better estimating results.

Improved robust Kalman filter for state model errors in GNSS-PPP/MEMS-IMU double state integrated navigation

The integration of Global Navigation Satellite System (GNSS) with Inertial Navigation Systems (INS) has been actively researched and widely applied as it can provide reliable positioning information continuously. In recent years, Micro Electro Mechanical Systems (MEMS) technology achieves rapid development and Micro Electro Mechanical Systems and Inertial Measurement Unit (MEMS-IMU) has aroused wide concern due to its excellent properties in some cases. However, the observations from MEMS-IMU are easy to be influenced by motion state and location environment because of its manufacturing process. It is not easy to judge whether gross errors are in the state model or the observation model by the widely adopted robust filter based on innovation. In this contribution, we present an improved robust filter with a double state model on the basis of the chi-square distribution of the square of the Mahalanobis distance. The vehicle motion model acts as the external constraint information and can be adopted to construct robust statistic with the results from INS mechanization. And then a robust factor was determined to adjust the observation noise covariance matrix. To evaluate the performance of this method, the simulation test and the field test based on locomotive platform of Nottingham Geospatial Institute (NGI) were carried out. According to the results, in the simulation test, the position improvements are 33%, 30% in the north and east directions; in the real test, the loosely and tightly coupled was adopted and the position accuracy can be improved by about 50–60% in the horizontal direction and the improvement of the pitch and the roll accuracy was lower than the azimuth accuracy due to poor observability and experimental scene which is of the characteristics of small elevation change. Therefore, the proposed robust filter could diminish the effect of the gross error from MEMS-IMU and enhance the integrated system.

A novel robust Kalman filter with unknown non-stationary heavy-tailed noise

In this article, the state estimation with unknown non-stationary heavy-tailed process and measurement noises (HPMN) is considered. The measurement likelihood and the one-step state prediction are modelled as the mixture of two Gaussian (M2G) distributions, respectively. In the proposed M2G, one is a high probability Gaussian distribution with a nominal covariance and the other is a low probability Gaussian distribution with an adaptive large covariance. The adaptive large covariance is formulated as the nominal covariance multiplied by a time varying scale parameter. An indicator is introduced to identify whether it is generated by the nominal covariance or the larger covariance. The unknown nominal covariance is modelled as an inverse Wishart distribution. Using hierarchical priors on the indicator and scale parameter, a robust model is formulated and a variational Bayesian algorithm is developed. Experiments with synthetic data and real intelligent vehicle data show the effectiveness of the proposed filter under unknown non-stationary HPMN.

Event-Triggered Robust Fault Diagnosis Kalman Filter for Stochastic Systems

This paper proposes a new method for robust fault diagnosis based on data-sending management in discrete-time linear stochastic systems. First, a methodology for identifying a subspace independent of disturbances is presented, which significantly attenuates the effects of disturbances. The sufficient conditions are proposed as linear matrix inequalities (LMIs) to guarantee the observability and stability of a new subspace. After that, the recursive robust Kalman filter is extended based on data-sending management. Finally, this Kalman filter is used to design residual signals. Event-triggered and self-triggered hybrid methods are used to decrease the transfer amount of measured data, and at the same time to preserve the fault diagnosis method performance. Simulation results illustrate the capabilities and effectiveness of the proposed design methodology for fault diagnosis in linear stochastic systems with unknown inputs while the data-sending rate decreases significantly.

UWB positioning algorithm and accuracy evaluation for different indoor scenes

ABSTRACT UWB indoor positioning is a research hotspot, but there are few literatures systematically describing different positioning algorithms for different scenes. Therefore, several positioning algorithms are proposed for different indoor scenes. Firstly, for the sensing positioning scenes, a sensing positioning algorithm is proposed. Secondly, for the straight and narrow scenes, a two anchors robust positioning algorithm based on high pass filter is proposed. Experimental results show that this algorithm has better positioning accuracy and robustness than the traditional algorithm. Then, for ordinary indoor scenes, a robust indoor positioning model is proposed based on robust Kalman filter and total LS, which considers the coordinate error of UWB anchors. The positioning accuracy is 0.093m, which is about 29.54% higher than that of the traditional LS algorithm. Finally, for indoor scenes with map information, a map aided indoor positioning algorithm is proposed based on two UWB anchors. This algorithm can effectively improve the reliability and reduce the cost of UWB indoor positioning system, which average positioning accuracy is 0.238m. The biggest innovation of this paper lies in the systematic description of multi-scene positioning algorithm and the realisation of indoor positioning based on double anchors.

Robust Kalman filter for Tuberculosis Incidence Time Series Forecasting

Abstract Governments must detect and treat people with tuberculosis, also prevent the uninfected community. In this sense, must promote the study of algorithms for the prediction of the epidemic trend. This paper addresses the forecasting of tuberculosis cases in Bogota, considering health surveillance system data from 2007-2020. Forecasts are obtained using the Kalman Filter and the Robust Kalman Filter. Results show better performance using the robust filter for six-week tuberculosis cases prediction.

Robust Attitude Estimation Using IMU-Only Measurements

This article proposes two novel covariance-tuning methods to form a robust Kalman filter (RKF) algorithm for attitude (i.e., roll and pitch) estimation using the measurements of only an inertial measurement unit (IMU). KF-based and complementary filtering (CF)-based approaches are the two common methods for solving the attitude estimation problem. Efficiency and optimality of the KF-based attitude filters are correlated with appropriate tuning of the covariance matrices. Manual tuning process is a difficult and time-consuming task. Specifically, the IMU-only attitude estimation filters are prone to the external accelerations unless their covariances are adapted to gain robustness. The proposed algorithms provide an adaptive method for tuning the measurement noise covariance such that they can accurately estimate the attitude in the two axes. The first method relies on a single tuning factor, whereas the second one tunes the covariance with different (multiple) factors for each measurement axis. The proposed methodologies are tested and compared with other existing filtering algorithms in the literature under different dynamical conditions and using real-world experimental datasets in order to validate their effectiveness. Results show that highly dynamic scenarios, especially the multiple tuning factor strategy, can increase the attitude estimation accuracy more than two-times compared to the competitive algorithms.

Distributed Design of Robust Kalman Filters Over Corrupted Channels

We study distributed filtering for a class of uncertain systems over corrupted communication channels. We propose a distributed robust Kalman filter with stochastic gains, through which upper bounds of the conditional mean square estimation errors are calculated online. We present a robust collective observability condition, under which the mean square error of the distributed filter is proved to be uniformly upper bounded if the network is strongly connected. For better performance, we modify the filer by introducing a switching fusion scheme based on a sliding window. It provides a smaller upper bound of the conditional mean square error. Numerical simulations are provided to validate the theoretical results and show that the filter scales to large networks.

An Improved Robust Kalman Filter for SINS/DVL Tightly Integrated Navigation System

Aiming at the problem of outliers in Doppler velocity log (DVL) beam measurements, for strapdown inertial navigation system (SINS)/Doppler velocity log (DVL) tightly coupled system, an improved robust Kalman filter (KF) algorithm is proposed, which can handle the measurement noise variance of each DVL beam individually. First, the multidimensional measurement equation is decomposed into several 1-D measurement equations, i.e., different DVL beam measurements are assumed to be obtained by different sensors. Second, the statistical similarity measure (SSM) is introduced to quantify the similarity between two random vectors. And a new cost function based on SSM is constructed for the dynamic system containing one state equation and multiple measurement equations. To optimize this cost function, the iterative procedures to update the posterior state is derived based on the Gauss-Newton iteration algorithm. Both the simulation and lake trial illustrate the superiority and effectiveness of the proposed algorithm. It is shown that in the case of partial DVL beams with outliers, the proposed algorithm can avoid the loss of normal measurement information and thus improve estimation accuracy.