Robust Kalman Filter Algorithm Research Articles

Application of Adaptive Robust Kalman Filter Base on MCC for SINS/GPS Integrated Navigation.

In this paper, an adaptive and robust Kalman filter algorithm based on the maximum correntropy criterion (MCC) is proposed to solve the problem of integrated navigation accuracy reduction, which is caused by the non-Gaussian noise and time-varying noise of GPS measurement in complex environment. Firstly, the Grubbs criterion was used to remove outliers, which are contained in the GPS measurement. Then, a fixed-length sliding window was used to estimate the decay factor adaptively. Based on the fixed-length sliding window method, the time-varying noises, which are considered in integrated navigation system, are addressed. Moreover, a MCC method is used to suppress the non-Gaussian noises, which are generated with external corruption. Finally, the method, which is proposed in this paper, is verified by the designed simulation and field tests. The results show that the influence of the non-Gaussian noise and time-varying noise of the GPS measurement is detected and isolated by the proposed algorithm, effectively. The navigation accuracy and stability are improved.

Robust Filter Method for SINS/DVL/USBL Tight Integrated Navigation System

In order to solve the problem of SINS/DVL/USBL system interference in complex underwater environment. An asynchronous sequential robust filter method is proposed in this paper. The original output azimuth, slant range and altitude of the ultra-short baseline as the measurement information, a compact combination model is established. The problem of large amount of computation caused by the high measurement dimension of multi-sensor information fusion is solved by introducing asynchronous sequential filter technology. Meanwhile, a robust Kalman filter algorithm is proposed, which based on Mahalanobis distance. The outlier detection is designed based on statistical characteristics. Finally, the effectiveness of the method proposed in this paper is verified by simulation and River experiments. The experimental results show that the method proposed in this paper can effectively eliminate outliers and improve the navigation accuracy while reducing the amount of computation.

A modified adaptive Kalman filtering method for maneuvering target tracking of unmanned surface vehicles

The filtering methods are crucial for an unmanned surface vehicle (USV) to realize target tracking. Due to the poor observation caused by the strong vibration during the navigation of the USV, the target tracking accuracy of the traditional filtering method has been significantly degraded. A modified strong tracking-based expended Sage-Husa adaptive robust Kalman filter (MST-ESHARKF) algorithm is proposed to overcome this problem in this paper. In the proposed algorithm, a modified fading factor for the strong tracking Kalman filter is introduced to eliminate disturbance-induced filter divergence. In addition, the adaptive factor of robust Kalman filtering is designed to balance the predicted and observed states dedicated to improving the robustness of the algorithm. Finally, the biased and unbiased estimators for measurement and process noise covariances are merged, and the measurement noise covariance matrix’s interval is constrained, resulting in a simultaneous evaluation of measurement and process noise covariance matrices with improved dependability of the proposed algorithm. The simulation and experiment results show that the proposed MST-ESHARKF outperforms the existing filters in target tracking.

A Polar Robust Kalman Filter Algorithm for DVL-Aided SINSs Based on the Ellipsoidal Earth Model.

Autonomous underwater vehicles (AUVs) play an increasingly essential role in the field of polar ocean exploration, and the Doppler velocity log (DVL)-aided strapdown inertial navigation system (SINS) is widely used for it. Due to the rapid convergence of the meridians, traditional inertial navigation mechanisms fail in the polar region. To tackle this problem, a transverse inertial navigation mechanism based on the earth ellipsoidal model is designed in this paper. Influenced by the harsh environment of the polar regions, unknown and time-varying outlier noise appears in the output of DVL, which makes the performance of the standard Kalman filter degrade. To address this issue, a robust Kalman filter algorithm based on Mahalanobis distance is used to adaptively estimate measurement noise covariance; thus, the Kalman filter gain can be modified to weight the measurement. A trial ship experiment and semi-physical simulation experiment were carried out to verify the effectiveness of the proposed algorithm. The results demonstrate that the proposed algorithm can effectively resist the influence of DVL outliers and improve positioning accuracy.

Radar Target Tracking for Unmanned Surface Vehicle Based on Square Root Sage-Husa Adaptive Robust Kalman Filter.

Dynamic information such as the position and velocity of the target detected by marine radar is frequently susceptible to external measurement white noise generated by the oscillations of an unmanned surface vehicle (USV) and target. Although the Sage–Husa adaptive Kalman filter (SHAKF) has been applied to the target tracking field, the precision and stability of SHAKF remain to be improved. In this paper, a square root Sage–Husa adaptive robust Kalman filter (SR-SHARKF) algorithm together with the constant jerk model is proposed, which can not only solve the problem of filtering divergence triggered by numerical rounding errors, inaccurate system mathematics, and noise statistical models, but also improve the filtering accuracy. First, a novel square root decomposition method is proposed in the SR-SHARKF algorithm for decomposing the covariance matrix of SHAKF to assure its non-negative definiteness. After that, a three-segment approach is adopted to balance the observed and predicted states by evaluating the adaptive scale factor. Finally, the unbiased and the biased noise estimators are integrated while the interval scope of the measurement noise is constrained to jointly evaluate the measurement and observation noise for better adaptability and reliability. Simulation and experimental results demonstrate the effectiveness of the proposed algorithm in eliminating white noise triggered by the USV and target oscillations.

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.

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.

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.

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.

Two-Stage Kalman Filter for Fault Tolerant Estimation of Wind Speed and UAV Flight Parameters

Abstract In this study, an estimation algorithm based on a two-stage Kalman filter (TSKF) was developed for wind speed and Unmanned Aerial Vehicle (UAV) motion parameters. In the first stage, the wind speed estimation algorithm is used with the help of the Global Positioning System (GPS) and dynamic pressure measurements. Extended Kalman Filter (EKF) is applied to the system. The state vector is composed of the wind speed components and the pitot scale factor. In the second stage, in order to estimate the state parameters of the UAV, GPS, and Inertial Measurement Unit (IMU) measurements are considered in a Linear Kalman filter. The second stage filter uses the first stage EKF estimates of the wind speed values. Between these two stages, a sensor fault detection algorithm is placed. The sensor fault detection algorithm is based on the first stage EKF innovation process. After detecting the fault on the sensor measurements, the state parameters of the UAV are estimated via robust Kalman filter (RKF) against sensor faults. The robust Kalman filter algorithm, which brings the fault tolerance feature to the filter, secures accurate estimation results in case of a faulty measurement without affecting the remaining good estimation characteristics. In simulations, noise increment and bias type of sensor faults are considered.

A robust total Kalman filter algorithm with numerical evaluation

In this study, the observation model of Kalman Filter (KF) is extended to an errors-in-variables (EIV) model because the observations may exist in the design matrix of the observation model. Then, a robust total least squares method (RTLS) is introduced into the KF, and a robust total Kalman filter (RTKF) algorithm is derived. The RTKF is a simple, flexible and effective algorithm. It is simple because its computational formulae are similar to the computational formulae of a standard KF; it is flexible because it can be used in a wide range of applications; it is effective because the influence of outliers on estimated results is weakened. Finally, the simulated example of the indoor location and the empirical example of pseudorange differential positioning are used to demonstrate the performance of the RTKF algorithm. The results prove the validity, robustness, and reliability of the RTKF in dealing with the outliers that exist in both observation vector and design matrix of the EIV model. Furthermore, the results of the empirical example show that the RTKF improves the precision of a pseudorange differential positioning compared with KF and robust Kalman filter (RKF) algorithms regardless the observation model has outliers or not in this empirical example.

Distributed Robust Kalman Filtering with Unknown and Noisy Parameters in Sensor Networks

This paper investigates the distributed filtering for discrete-time-invariant systems in sensor networks where each sensor’s measuring system may not be observable, and each sensor can just obtain partial system parameters with unknown coefficients which are modeled by Gaussian white noises. A fully distributed robust Kalman filtering algorithm consisting of two parts is proposed. One is a consensus Kalman filter to estimate the system parameters. It is proved that the mean square estimation errors for the system parameters converge to zero if and only if, for any one system parameter, its accessible node subset is globally reachable. The other is a consensus robust Kalman filter to estimate the system state based on the system matrix estimations and covariances. It is proved that the mean square estimation error of each sensor is upper-bounded by the trace of its covariance. An explicit sufficient stability condition of the algorithm is further provided. A numerical simulation is given to illustrate the results.

On robust constrained Kalman filter for dynamic errors-in-variables model

A robust Kalman filter algorithm is proposed to solve nonlinear errors-in-variables dynamic problems in the presence of outliers. This algorithm is robust constrained integrated total Kalman filter (RCITKF). The method iteratively reweights the predicted solution when the observable quantities are contaminated by gross errors (outliers). It can impose the quadratic constrains which may appear in some problems. Moreover, the RCITKF algorithm can consider the neglected random unknowns of the functional model of the dynamic problem which gives an added advantage over the previous Kalman filters. In two geodetic applications, the efficiency of these algorithms is demonstrated in contrast to the extended Kalman filter (EKF) and unscented Kalman filter (UKF) algorithms.

A MIMU/GPS/magnetometer integrated alignment method based on sequential robust estimation

For a micro-electro-mechanical system inertial measurement unit (MEMS-IMU), Global Positioning System (GPS) and magnetometer integrated navigation system, the procedure of initial alignment is a necessity. However, both magnetometer and GPS receiver are susceptible to external complex environment. Outliers in the observations of the two devices are inevitable. In order to reduce the influence of the outliers and improve the initial alignment accuracy, a sequential robust Kalman filter (SRKF) algorithm based on the square dimension of the innovation vector is proposed. The proposed SRKF algorithm can reasonably decrease the contribution of outlier affected elements of the observation vector in an element-wise way. Robust factor, used to suppress the influence of outliers, is constructed according to the Mahalanobis distance and the Chi-square distribution significance level. The results of different simulations and field tests all indicate the feasibility and the effectiveness of the proposed method.

Robust Kalman Filter Based Estimation of AUV Dynamics in the Presence Of Sensor Faults

Abstract This article is basically focused on application of the Robust Kalman Filter (RKF) algorithm to the estimation of high speed an autonomous underwater vehicle (AUV) dynamics. In the normal operation conditions of AUV, conventional Kalman filter gives sufficiently good estimation results. However, if the measurements are not reliable because of any kind of malfunction in the estimation system, Kalman Filter (KF) gives inaccurate results and diverges by time. This study, introduces Robust Kalman Filter algorithm with the filter gain correction for the case of measurement malfunctions. By the use of defined variables named as measurement noise scale factor, the faulty measurements are taken into the consideration with a small weight and the estimations are corrected without affecting the characteristic of the accurate ones. In the presented RUKF, the filter gain correction is performed only in the case of malfunctions in the measurement system and in all other cases procedure is run optimally with regular KF.

Fault tolerant estimation of electro-mechanical actuator parameters via robust EKF

A robust extended Kalman filter (REKF) algorithm for the fault tolerant estimation of parameters of electro-mechanical actuator (EMA) in the presence of measurement faults is proposed. The proposed REKF is based on the evaluation of the posterior probability of the normal operation of the system, given for the current measurement. This probability is proposed to calculate via the posterior probability density of the normalised innovation sequence at the current estimation step. As a result, faults in the estimation system are corrected by the system, without affecting the good estimation behaviour. The developed REKF algorithm is applied for the parameter identification process of an EMA. The performance of the proposed filter is tested for the different types of measurement faults. The single actuator sensor faults are considered. The proposed REKF algorithm is tested for different measurement malfunction scenarios; continuous bias at measurements, measurement noise increment, instantaneous abnormal measurements and fault of zero output.

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.

Robust unscented Kalman filtering for nonlinear uncertain systems

AbstractA derivative‐free robust Kalman filter algorithm is proposed for nonlinear uncertain systems. The unscented transform (UT) is adopted instead of the linearization technique to obtain the solution of the H∞ filter Riccati equation. A robust unscented Kalman filter (RUKF) is derived to guarantee an optimized upper bound on the estimation error covariance despite the model uncertainties and the approximation error of the UT. The proposed algorithm is applied to a satellite attitude determination system. Simulation results show that the RUKF is more effective than the unscented Kalman filter (UKF) in cases where alignment errors are present. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

RKF‐based fault tolerant integrated INS/radar altimeter

In this study, the integrated navigation system, consisting of radio and inertial navigation system (INS) altimeters, is presented. INS and the radio altimeter have different benefits and drawbacks. The integration is achieved by using an indirect Kalman filter. Hereby, the error models of the navigators are used by the Kalman filter to estimate vertical channel parameters of the navigation system. In the open loop system, INS is the main source of information, and radio altimeter provides discrete aiding data to support the estimations. At the next step of the study, in case of abrupt faults, the performance of the integrated system is examined. The optimal Kalman filter reacts with abnormal estimates to this situation as expected. To recover such a possible malfunctioning, the robust Kalman filter algorithm is suggested.