Robust Kalman Filter Research Articles

Monitoring large-area mining subsidence by GNSS based on IGS stations

In order to monitor large-area mining subsidence accurately, a high-precision global navigation satellite system (GNSS) monitoring network was established based on the nearby international GNSS service (IGS) stations taken as reference points. Given the non-linear motions of IGS stations, the robust Kalman filtering (RKF) model was presented to determine the datum of multi-period monitoring network considering the velocity and weekly solution of IGS stations. The theory proposed was applied to monitoring mining subsidence in northern Anhui coal mine in China. According to the case study, the RKF model to establish monitoring datum is better than the prediction method and the weekly solution from IGS analysis centers (ACs), and the corresponding precision of deformation can reach up to millimeter level with 4 h observation. The research provides an efficient and accurate approach for monitoring large-area mining subsidence.

DISCON: Public Transport Dispatching Robust Control

Public transport operation is inherently connected with uncertainty, starting from schedules created for hypothetical operational conditions and demand levels, operational disturbances, dynamic real demand uncertainty and on complex interactions between different lines and transport modes ending. In this context the realisation of the general public transport objective: maintenance in the long-term horizon the guaranteed mobility standards in the city and their surroundings with essential reduction of transport operational negative impacts, calls for Advanced Public Transportation System (APTS) based dedicated approach. In this paper the exploration of Intelligent and Integrated DISpatching CONtrol (DISCON) method capabilities using new available in APTS capabilities was proposed. The uncertainty and stochastic aspects visible in public transport operation create the demand for dedicated intelligent dispatching robust control proposals. The APTS monitoring and surveillance tools and effective communication media make it possible to realize it in “control by opportunity” mode and with dynamic intelligent control feedback. In this paper DISCON robust dispatching real-time control proposals are presented. The first in LQG robust Kalman filter based control perspective and existence of control and state operational constraints. The second one based on cooperation with multi-criteria PIACON traffic control method as multi-criteria individual traffic - public transport integrated approach with compromise solutions represented by so called “reference trajectory”. In the last case the necessary control actions are recognized by real-time detection of the bus arrival to the signalised intersection and evaluation of its measure off-schedule deviations and bus load. Next the dynamic trade-offs with conflicting intersection users demands and service standards are established by PIACON control method and admissible priority control options in terms of so called “reference trajectory” for DISCON control method are proposed. Illustrative practical examples for all new DISCON options are presented.

Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion

A robust Kalman filter scheme is proposed to resist the influence of the outliers in the observations. Two kinds of observation error are studied, i.e., the outliers in the actual observations and the heavy-tailed distribution of the observation noise. Either of the two kinds of errors can seriously degrade the performance of the standard Kalman filter. In the proposed method, a judging index is defined as the square of the Mahalanobis distance from the observation to its prediction. By assuming that the observation is Gaussian distributed with the mean and covariance being the observation prediction and its associate covariance, the judging index should be Chi-square distributed with the dimension of the observation vector as the degree of freedom. Hypothesis test is performed to the actual observation by treating the above Gaussian distribution as the null hypothesis and the judging index as the test statistic. If the null hypothesis should be rejected, it is concluded that outliers exist in the observations. In the presence of outliers scaling factors can be introduced to rescale the covariance of the observation noise or of the innovation vector, both resulting in a decreased filter gain. And the scaling factors can be solved using the Newton’s iterative method or in an analytical manner. The harmful influence of either of the two kinds of errors can be effectively resisted in the proposed method, so robustness can be achieved. Moreover, as the number of iterations needed in the iterative method may be rather large, the analytically calculated scaling factor should be preferred.

Robust weighted fusion Kalman filters for multisensor time-varying systems with uncertain noise variances

This paper addresses the design of robust weighted fusion Kalman filters for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the five robust weighted fusion time-varying Kalman filters are presented based on the worst-case conservative systems with the conservative upper bounds of noise variances. The actual filtering error variances or their traces of each fuser are guaranteed to have a minimal upper bound for all the admissible uncertainties of noise variances. A Lyapunov equation approach is presented to prove the robustness of the robust Kalman filters. The concept of robust accuracy is presented and the robust accuracy relations among the local and fused robust Kalman filters are proved. Specially, the corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization of the local and fused time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.

Incremental Activation Detection for Real-Time fMRI Series Using Robust Kalman Filter

Real-time functional magnetic resonance imaging (rt-fMRI) is a technique that enables us to observe human brain activations in real time. However, some unexpected noises that emerged in fMRI data collecting, such as acute swallowing, head moving and human manipulations, will cause much confusion and unrobustness for the activation analysis. In this paper, a new activation detection method for rt-fMRI data is proposed based on robust Kalman filter. The idea is to add a variation to the extended kalman filter to handle the additional sparse measurement noise and a sparse noise term to the measurement update step. Hence, the robust Kalman filter is designed to improve the robustness for the outliers and can be computed separately for each voxel. The algorithm can compute activation maps on each scan within a repetition time, which meets the requirement for real-time analysis. Experimental results show that this new algorithm can bring out high performance in robustness and in real-time activation detection.

Fast Algorithm of Robust Kalman Filter via l1 Regression by a Closed Form Solution

Robust Kalman filter (RKF) via l1 regression is a linear filter for non-Gaussian measurement noise, and it can be formulated as a l1 optimization problem. Generally, the optimization problem cannot be solved analytically, and some numerical iterative methods are needed. This paper proposes a closed form solution of RKF via l1 regression by an approximation of its optimal solution and it gives a fast algorithm. The approximated solution can be calculated by upper and lower bounds of the optimal solution. Moreover, a bound of an estimation error of the approximated solution can be analyzed. Some numerical simulations demonstrate the effectiveness of the proposed algorithm.

外れ値環境下におけるロバストSelf-tuning Controller

In this paper, we propose a robust self-tuning controller (STC) under outliers. A parameter update law of a conventional STC consists of a recursive least squares estimation, and the estimation is given by a solution of a minimization problem of estimated errors. In the proposed method, we estimate parameters and outliers explicitly by addition of a l1 regression to the minimization problem like a robust Kalman filter via l1 regression, and the estimated outliers are removed from measurement outputs in the controller. We also analyze control performances of the proposed method under outliers, and it is shown theoretically that performances in the proposed method with outliers are nearly equal to ones in the normal STC without outliers. Numerical simulation, in which a controlled object is a non-minimum phase system, demonstrates effectiveness of the proposed method.

Robust Adaptive Filter for Small Satellite Attitude Estimation Based on Magnetometer and Gyro

Based on magnetometer and gyro measurement, a sequential scheme is proposed to determine the orbit and attitude of small satellite simultaneously. In order to reduce the impact of orbital errors on attitude estimation, a robust adaptive Kalman filter is developed. It uses a scale factor and an adaptive factor, which are constructed by Huber function and innovation sequence, respectively, to adjust the covariance matrix of system state and observational noise, change the weights of predicted and measured parameters, get suitable Kalman filter gain and approximate optimal filtering results. Numerical simulations are carried out and the proposed filter is approved to be robust for the noise disturbance and parameter uncertainty and can provide higher accuracy attitude estimation.

Finite-Horizon Robust Kalman Filter for Uncertain Attitude Estimation System with Star Sensor Measurement Delays

This paper addresses the robust Kalman filtering problem for uncertain attitude estimation system with star sensor measurement delays. Combined with the misalignment errors and scale factor errors of gyros in the process model and the misalignment errors of star sensors in the measurement model, the uncertain attitude estimation model can be established, which indicates that uncertainties not only appear in the state and output matrices but also affect the statistic of the process noise. Meanwhile, the phenomenon of star sensor measurement delays is described by introducing Bernoulli random variables with different delay characteristics. The aim of the addressed attitude estimation problem is to design a filter such that, in the presence of model uncertainties and star sensors delays for the attitude estimation system, the optimized filter parameters can be obtained to minimize the upper bound on the estimation error covariance. Therefore, a finite-horizon robust Kalman filter is proposed to cope with this question. Compared with traditional attitude estimation algorithms, the designed robust filter takes into account the effects of star sensor measurement delays and model uncertainties. Simulation results illustrate the effectiveness of the developed robust filter.

Hierarchical fusion robust Kalman filter for clustering sensor network time‐varying systems with uncertain noise variances

SUMMARYFor the clustering time‐varying sensor network systems with uncertain noise variances, according to the minimax robust estimation principle, based on the worst‐case conservative system with conservative upper bounds of noise variances, applying the optimal Kalman filtering, the two‐level hierarchical fusion time‐varying robust Kalman filter is presented, where the first‐level fusers consist of the local decentralized robust fusers for the clusters, and the second‐level fuser is a global decentralized robust fuser for the cluster heads. It can reduce the communication load and save energy resources of sensors. Its robustness is proved by the proposed Lyapunov equation method. The concept of robust accuracy is presented, and the robust accuracy relations of the local, decentralized, and centralized fused robust Kalman filters are proved. Specially, the corresponding steady‐state robust local and fused Kalman filters are also presented, and the convergence in a realization between the time‐varying and steady‐state robust Kalman filters is proved by the dynamic error system analysis method. A simulation example shows correctness and effectiveness. Copyright © 2013 John Wiley & Sons, Ltd.

Robust Kalman filtering for small satellite attitude estimation in the presence of measurement faults

In normal working conditions it is possible to achieve sufficient attitude estimation accuracy for a satellite using regular Kalman filter algorithm. On the other hand, when there is a fault in the measurements, the Kalman filter fails in providing the required accuracy and may even collapse over time. In this paper, a Robust Kalman filtering method is proposed for the attitude estimation problem. By using the proposed method both the Extended Kalman Filter and Unscented Kalman Filter are modified and the new algorithms, which are robust against measurement malfunctions, are called Robust Extended Kalman Filter and Robust Unscented Kalman Filter, respectively. A multiple scale factor based adaptation scheme is preferred for adapting the filters so only the data of the faulty sensor is scaled and any unnecessary information loss is prevented. The proposed algorithms are demonstrated for attitude estimation of a small satellite and performances of these two robust Kalman filters are compared in case of different measurement faults. The application of the algorithm is discussed for small satellite missions where the attitude accuracy depends on a limited number of measurements.

Covariance Intersection Fusion Robust Time-Varying Kalman Filter for Two-Sensor System with Uncertain Noise Variances

This paper investigates the problem of designing covariance intersection fusion robust time-varying Kalman filter for two-sensor time-varying system with uncertain noise variances. Using the minimax robust estimation principle, the local and covariance intersection (CI) fusion robust time-varying Kalman filters are presented based on the worst-case conservative system with the conservative upper bounds of noise variances. Their robustness is proved based on the proposed Lyapunov equation, and the robust accuracy of time-varying CI fuser is higher than that of each local robust time-varying Kalman filter. A two-sensor tracking system simulation verifies the robustness and robust accuracy relations.

Robust Kalman Filtering Cooperated Elman Neural Network Learning for Vision-Sensing-Based Robotic Manipulation with Global Stability

In this paper, a global-state-space visual servoing scheme is proposed for uncalibrated model-independent robotic manipulation. The scheme is based on robust Kalman filtering (KF), in conjunction with Elman neural network (ENN) learning techniques. The global map relationship between the vision space and the robotic workspace is learned using an ENN. This learned mapping is shown to be an approximate estimate of the Jacobian in global space. In the testing phase, the desired Jacobian is arrived at using a robust KF to improve the ENN learning result so as to achieve robotic precise convergence of the desired pose. Meanwhile, the ENN weights are updated (re-trained) using a new input-output data pair vector (obtained from the KF cycle) to ensure robot global stability manipulation. Thus, our method, without requiring either camera or model parameters, avoids the corrupted performances caused by camera calibration and modeling errors. To demonstrate the proposed scheme's performance, various simulation and experimental results have been presented using a six-degree-of-freedom robotic manipulator with eye-in-hand configurations.

Adaptive robust Kalman filter for relative navigation using global position system

An adaptive robust Kalman filter algorithm is derived to account for both process noise and measurement noise uncertainty. The adaptive algorithm estimates process noise covariance based on the recursive minimisation of the difference between residual covariance matrix given by the filter and that calculated from time-averaging of the residual sequence generated by the filter at each time step. A recursive algorithm is proposed based on both Massachusetts Institute of Technology (MIT) rule and typical non-linear extended Kalman filter equations for minimising the difference. The measurement update using a robust technique to minimise a criterion function originated from Huber filter. The proposed adaptive robust Kalman filter has been successfully implemented in relative navigation using global position system for spacecraft formation flying in low earth orbit, with real-orbit perturbations and non-Gaussian random measurement errors. The numerical simulation results indicate that the proposed adaptive robust filter can provide better relative navigation performance in terms of accuracy and robustness as compared with previous filter algorithms.

Design of Robust and Non-Fragile Kalman Filter with Polytopic Uncertainties: PLMI Approach

In this paper, we describe the synthesis of robust and non-fragile Kalman filter design for a class of uncertain linear system with polytopic uncertainties and filter gain variations. The sufficient condition of filter existence, the design method of robust non-fragile filter, and the measure of non-fragility in filter are presented via LMIs(Linear Matrix Inequality) technique. And the obtained sufficient condition can be represented as PLMIs(Parameterized Linear Matrix Inequalities) that is, coefficients of LMIs are functions of a parameter confined to a compact set. Since PLMIs generate infinite LMIs, we use relaxation technique, find a finite solution for robust non-fragile filter, and show that the resulting filter guarantees the asymptotic stability with parameter uncertainties and filter fragility. Finally, a numerical example is shown to validate the proposed design method.

Robust Kalman tracking and smoothing with propagating and non-propagating outliers

A common situation in filtering where classical Kalman filtering does not perform particularly well is tracking in the presence of propagating outliers. This calls for robustness understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods. Based on optimality results for distributional-robust Kalman filtering from Ruckdeschel (Ansätze zur Robustifizierung des Kalman-Filters, vol 64, 2001; Optimally (distributional-)robust Kalman filtering, arXiv: 1004.3393, 2010a), we propose new robust recursive filters and smoothers designed for this purpose as well as specialized versions for non-propagating outliers. We apply these procedures in the context of a GPS problem arising in the car industry. To better understand these filters, we study their behavior at stylized outlier patterns (for which they are not designed) and compare them to other approaches for the tracking problem. Finally, in a simulation study we discuss efficiency of our procedures in comparison to competitors.

Simultaneous Air Fraction and Low-Pressure EGR Mass Flow Rate Estimation for Diesel Engines

This paper describes a low-pressure exhaust gas recirculation (LP-EGR) mass flow rate estimation method and a robust air mass fraction observer for a Diesel engine with dual-loop EGR system. Both observers operate simultaneously eliminating the need for pressure measurement upstream the LP-EGR valve. A sliding mode observer is designed to estimate the LP-EGR mass flow rate using the standard sensors available in commercial Diesel engines. A robust linear parameter varying Kalman filter is designed for the air mass fraction estimation. The convergence and robustness of the observers are ensured by means of Lyapunov stability and a linear matrix inequality (LMI) framework for the sliding mode observer and robust Kalman filter, respectively. The observers are evaluated with a Motor Vehicle Emission Group (NMVEG) cycle using an engine model validated on an experimental benchmark as a reference.

Research on robust Kalman filter based on depth-weighted

After the analysis of cumulative effect on filter results of gross errors,a new robust filter under the Kalman framework is proposed by improving the weighted mode of the innovation with the depth-weighted algorithm.For the introduction of the calculation of data depth and weighted coefficients,the filter can straightforwardly adjust the contribution of the observations to the filter states without any gross error detections.The depth-weighted step can be viewed as an extension of the optimal criterion(the minimum mean square error,MMSE) in the Kalman filter,By utilizing of the relativity of different observations as well as the relativity between the observations and the states,the new filter can effectively release the disadvantage effect on the filter results of gross errors.Based on the robustness analysis,the feasibility and the efficiency of the new filter are validated by numerical examples finally.

Robust Real-Time Model Predictive Control for Torsional Vibration System

In this paper, explicit, robust Model Predictive Control (MPC) is proposed for the control of a two-mass system in order to achieve not only good tracking performance and load-change effect rejection, but also low torsional vibration, when the measurement noise contains outliers. The control structure presented in this paper is based fundamentally on the combination of explicit MPC and region detection via a self-optimizing variable. In addition, the well-known Kalman filter is replaced by the robust Kalman filter to deal with the outlier signals. The effectiveness of the proposed method is compared with a PID-based control.

A Robust Kalman Algorithm to Facilitate Human-Computer Interaction for People with Cerebral Palsy, Using a New Interface Based on Inertial Sensors

This work aims to create an advanced human-computer interface called ENLAZA for people with cerebral palsy (CP). Although there are computer-access solutions for disabled people in general, there are few evidences from motor disabled community (e.g., CP) using these alternative interfaces. The proposed interface is based on inertial sensors in order to characterize involuntary motion in terms of time, frequency and range of motion. This characterization is used to design a filtering technique that reduces the effect of involuntary motion on person-computer interaction. This paper presents a robust Kalman filter (RKF) design to facilitate fine motor control based on the previous characterization. The filter increases mouse pointer directivity and the target acquisition time is reduced by a factor of ten. The interface is validated with CP users who were unable to control the computer using other interfaces. The interface ENLAZA and the RKF enabled them to use the computer.