Adaptive Robust Kalman Filter Research Articles

Performance evaluation of real-time tightly-coupled GNSS PPP/MEMS-based inertial integration using an improved robust adaptive Kalman filter

Abstract Typically, the extended Kalman filter (EKF) is used for tightly-coupled (TC) integration of multi-constellation GNSS PPP and micro-electro-mechanical system (MEMS) inertial navigation system (INS) to provide precise positioning, velocity, and attitude solutions for ground vehicles. However, the obtained solution will generally be affected by both of the GNSS measurement outliers and the inaccurate modeling of the system dynamic. In this paper, an improved robust adaptive Kalman filter (IRKF) is adopted and used to overcome the effect of the measurement outliers and dynamic model errors on the obtained integrated solution. A real-time IRKF-based TC GPS+Galileo PPP/MEMS-based INS integration algorithm is developed to provide precise positioning and attitude solutions. The pre-saved real-time orbit and clock products from the Centre National d’Etudes Spatials (CNES) are used to simulate the real-time scenario. The performance of the real-time IRKF-based TC GNSS PPP/INS integrated system is assessed under open sky environment, and both of simulated partial and complete GNSS outages through two ground vehicular field trials. It is shown that the real-time TC GNSS PPP/INS integration through the IRKF achieves centimeter-level positioning accuracy under open sky environments and decimeter-level positioning accuracy under GNSS outages that range from 10 to 60 seconds. In addition, the use of IRKF improves the positioning accuracy and enhances the convergence of the integrated solution in comparison with the EKF. Furthermore, the IRKF-based integrated system achieves attitude accuracy of 0.052°, 0.048°, and 0.165° for pitch, roll, and azimuth angles, respectively. This represents improvement of 44 %, 48 %, and 36 % for the pitch, roll, and azimuth angles, respectively, in comparison with the EKF-based counterpart.

The robust residual-based adaptive estimation Kalman filter method for strap-down inertial and geomagnetic tightly integrated navigation system.

When noise statistical characteristics of the system are unknown and there are outliers in the measurement information, the filtering accuracy of the strap-down inertial navigation system/geomagnetic navigation system (SINS/GNS) tightly integrated navigation system would decrease, and the filtering may diverge in severe cases. To solve this problem, a robust residual-based adaptive estimation Kalman filter (RRAEKF) method is proposed. In the RRAEKF method, the covariance matching technique is employed to detect whether the system is abnormal or not. When the system is judged to be abnormal, a weighted factor is constructed to identify and weight the wild value in the measurement information, eliminating the influence of the outliers on the filtering accuracy. To further improve the filtering accuracy of the integrated navigation system, a contraction factor is introduced to adaptively adjust the gain matrix of the filter algorithm, obtaining the optimal estimate of the state vector and covariance matrix. Simulation results demonstrate that compared with the standard extended Kalman filter method and residual-based adaptive estimation method, the space position errors of the SINS/GNS tightly integrated navigation system based on the proposed method are improved by 63.37% and 56.93%, respectively, in the case of time-varying noise and the presence of outliers.

GNSS DOPPLER VELOCITY BASED ON ADAPTIVE ROBUST KALMAN FILTERING

Abstract. The main factors affecting the error of Doppler velocity measurement mainly come from the measurement errors of GNSS data, influence of different motion states on GNSS velocity measurement and the noise of different receiver types. To improve the precision of GNSS velocity estimation, an algorithm of adaptive robust Kalman filter based on the PDOP was put forward. PDOP value as well as the number of satellite in each epoch are used as a criterion in the velocity processing. While the PDOP value is greater than the threshold value, which means the observation accuracy is low, then the robust Kalman filter based on IGG – III scheme is introduced. While the PDOP value is between the threshold values, which means the observation precision is normal, adaptive factor could be determined normally, and the single-factor three-stage adaptive model is applied for Kalman filtering. If the above two conditions are not consistent, it indicates that the prediction accuracy of the local epoch satellite is high, and Kalman filtering can be directly used. Through the experiment of shipborne GNSS velocity measurement, it was proved that comparing with conventional least square, the algorithm based on the adaptive robust Kalman filtering can improve the accuracy and stability of the GNSS velocity determination.

A Novel Dual-Domain Filtering Method to Improve GNSS Performance Based on a Dynamic Model Constructed by TDCP

To overcome the strikes from the tremendous noise of pseudorange and the integer ambiguity of carrier phase observation, we developed a novel dual-domain filtering method that integrates the traditional observation- and an innovative position- domain filtering method. The novel method employed the conventional Hatch's smoother to improve the precision of pseudorange at the observation-domain filtering part. At the position- domain filtering part, the proposed method constructs an accurate dynamical model for KF (Kalman filter) or ARKF (adaptive-robust KF) that relies on the TDCP (time differential carrier phase) velocity measurement technology. To assess the effectiveness of the novel method, we compared it with other methods under various system integration by measured data from IGS (International GNSS Service) MGEX (Multi-GNSS Experiment) and dynamic data collected at CUMT (China University of Mining and Technology). The static numerical experiments obtained from IGS datasets show that the ARKF improves the precision of 60/84 and 55/84 situations' directions compared with the LS method based on OP (original pseudorange) and SP (smoothed pseudorange), respectively, and Hatch's smother improves the precision of all situations' directions. The experiment results prove that both types of observation- and position- domain filtering methods can improve positioning precision. Also, the novel dual-domain filtering improved the precision of 80/84 situations' directions compared with the LS method. Moreover, the dynamic experiment shows that the novel method can improve all of the situations' directions except the N (North) direction provided by KF base on SP under GC and U (Upon) direction provided by LS base on SP under GR. The average of improved accuracy is 0.212m, 0.346m, and 0.588m at the E (East), N, U direction and its corresponding average percentage of improved accuracy is 30.2%, 60.2%, and 26.7%, respectively, which proves the novel dual-domain filtering method provided the best performance among the tested algorithms.

Correlation-Aided Robust Decentralized Dynamic State Estimation of Power Systems With Unknown Control Inputs

This paper proposes a correlation-aided robust adaptive unscented Kalman filter (UKF) for power system decentralized dynamic state estimation with unknown inputs, termed as robust AUKF-UI. The temporal and spatial correlations among the unknown inputs are used to derive a vector auto-regressive (VAR) model in an adaptive manner. This VAR model is further integrated together with state transition and measurement models for joint state and unknown inputs estimation. This allows taking into account the implicit cross-correlations between the states and the unknown inputs. As a result, the rank requirement for unknown input vector estimation is relaxed and the local generator frequency measurement is not required. The temporal correlations of time series innovation vectors, predicted state and input vectors are also leveraged by the robust AUKF-UI to detect, identify and process bad data. Without these correlations, it is very challenging to address bad data with unknown inputs. Simulation results carried out on the IEEE 39-bus system demonstrate that, thanks to the use of hidden system temporal and spatial correlations, the proposed robust AUKF-UI has lower requirement of the number of measurements for dynamic state estimation while achieving better robustness against bad data as compared to the existing UKF methods with unknown inputs.

An Integrated Adaptive Kalman Filter for High-Speed UAVs

In order to solve the problems of filtering divergence and low accuracy in Kalman filter (KF) applications in a high-speed unmanned aerial vehicle (UAV), this paper proposed a new method of integrated robust adaptive Kalman filter: strong adaptive Kalman filter (SAKF). The simulation of two high-dynamic conditions and a practical experiment were designed to verify the new multi-sensor data fusion algorithm. Then the performance of the Sage–Husa adaptive Kalman filter (SHAKF), strong tracking filter (STF), H∞ filter and SAKF were compared. The results of the simulation and practical experiments show that the SAKF can automatically select its filtering process under different conditions, according to an anomaly criterion. SAKF combines the advantages of SHAKF, H∞ filter and STF, and has the characteristics of high accuracy, robustness and good tracking skill. The research has proved that SAKF is more appropriate in high-speed UAV navigation than single filter algorithms.

Robust adaptive unscented Kalman filter for bearings-only tracking in three dimensional case

This paper proposes an improved version of Unscented Kalman Filter (UKF), namely Robust Adaptive UKF (RAUKF), with a special focus on Bearings-Only Target Tracking for three-dimensional case (3DBOT). The automatic tuning of the noise covariance matrices and the robust estimation of the target states form a critical point for the performance of the Kalman-type filtering algorithms, especially in the variable environmental conditions exposed in underwater. The key idea of the proposed filter is to combine robust aspects of UKF and adaption of the process and measurement noise covariance matrices with low computational complexity. The main contribution of this paper is to adjust these matrices by means of the steepest descent algorithm, and the H∞ technique is embedded to achieve superior performance in terms of accuracy and robustness against initial conditions and model uncertainties. Different experiments are performed to evaluate the performance of the proposed algorithm in the 3DBOT problem with a single moving observer. Simulations demonstrate that the proposed filter produce more accurate results with satisfactory computational burden in comparison with other methods.

Improved Pedestrian Dead Reckoning Based on a Robust Adaptive Kalman Filter for Indoor Inertial Location System.

Pedestrian dead reckoning (PDR) systems based on a microelectromechanical-inertial measurement unit (MEMS-IMU) providing advantages of full autonomy and strong anti-jamming performance are becoming a feasible choice for pedestrian indoor positioning. In order to realize the accurate positioning of pedestrians in a closed environment, an improved pedestrian dead reckoning algorithm, mainly including improved step estimation and heading estimation, is proposed in this paper. Firstly, the original signal is preprocessed using the wavelet denoising algorithm. Then, the multi-threshold method is proposed to ameliorate the step estimation algorithm. For heading estimation suffering from accumulated error and outliers, robust adaptive Kalman filter (RAKF) algorithm is proposed in this paper, and combined with complementary filter to improve positioning accuracy. Finally, an experimental platform with inertial sensors as the core is constructed. Experimental results show that positioning error is less than 2.5% of the total distance, which is ideal for accurate positioning of pedestrians in enclosed environment.

Redundant measurement-based second order mutual difference adaptive Kalman filter

Noise distribution plays an essential role in state estimation using Kalman filter. However, statistical characteristics of the noise are often unknown in most practical applications. A second order mutual difference (SOMD) algorithm has been proposed to generate an estimation of the measurement noise covariance matrix R by calculating the autocorrelation of SOMD of redundant measurements, and thus it can avoid coupling with the state estimation error; however, the algorithm cannot be applied directly for a majority of practical systems due to the requirement of redundant measurements. In this paper, the SOMD algorithm is expanded to the system with single measurement by constructing a pseudo measurement. A non-zero estimation bias detection algorithm is presented to address the inconsistency between the mathematical model and the real. A modified robust adaptive Kalman filter (RAKF) is also developed to tackle this inconsistency and improve filtering accuracy by activating adaptive operation properly. The efficacy of the approach is demonstrated via a target tracking problem. Simulation results indicate that the proposed algorithm can reflect the noise properties accurately and outperform several reference algorithms in precision and robustness.

Beidou navigation method based on intelligent computing and extended Kalman filter fusion

Scientific and precise dynamic navigation is the key to improving Beidou positional accuracy of agricultural machinery. Aiming at the gross error of agricultural machinery location. First, the paper deeply explores the principle of Beidou navigation. Second, according to the PVT information (position, velocity and time) solutions of Beidou navigation system, the least square method, Kalman filter method and extended Kalman filter method were studied. Based on their own advantages, algorithms were proposed that combines the differential adaptation and extended Kalman filter. Then, based on the equivalent gain matrix and iterative solution, a robust adaptive Kalman filter model is built to verify its effectiveness in reducing gross errors. At last, the four algorithms were simulated in MATLAB and the simulation results were compared to verify that the newly-proposed method is the optimal solution algorithm. The absolute error remained 5.2 cm, meeting the preciseness limit of the agricultural machinery navigation.

Robust adaptive unscented Kalman filter and its application in initial alignment for body frame velocity aided strapdown inertial navigation system.

In the in-motion alignment of a strapdown inertial navigation system (SINS), the unscented Kalman filter (UKF) is usually used to solve non-linear problems. The measurement noise covariance R has a direct influence on the filtering results of the alignment of the SINS. The measurement noise is assumed to follow Gaussian distribution with a constant covariance R . However, these assumptions are often not realistic, neither the Gaussianity nor the constant covariance. This will degrade the performance of the UKF. To solve this problem, this paper proposes a novel adaptive robust UKF (NARUKF). In the NARUKF, a sliding window is used in estimating the covariance R in real-time. The NARUKF is divided into three main steps, the first step is to use the Mahalanobis distance algorithm to robustify the UKF. The second step is to use the projection statistics algorithm to reweight the abnormal stored innovations. Finally, the covariance R is adaptively estimated. The simulation and experimental results for the problem of the body frame velocity aided SINS in-motion alignment under heavier-tail distribution and/or outlier conditions demonstrate the superiority of the proposed method over the traditional ones.

An Optimal Radial Basis Function Neural Network Enhanced Adaptive Robust Kalman Filter for GNSS/INS Integrated Systems in Complex Urban Areas.

Inertial Navigation System (INS) is often combined with Global Navigation Satellite System (GNSS) to increase the positioning accuracy and continuity. In complex urban environments, GNSS/INS integrated systems suffer not only from dynamical model errors but also GNSS observation gross errors. However, it is hard to distinguish dynamical model errors from observation gross errors because the observation residuals are affected by both of them in a loosely-coupled integrated navigation system. In this research, an optimal Radial Basis Function (RBF) neural network-enhanced adaptive robust Kalman filter (KF) method is proposed to isolate and mitigate the influence of the two types of errors. In the proposed method, firstly a test statistic based on Mahalanobis distance is treated as judging index to achieve fault detection. Then, an optimal RBF neural network strategy is trained on-line by the optimality principle. The network’s output will bring benefits in recognizing the above two kinds of filtering fault and the system is able to choose a robust or adaptive Kalman filtering method autonomously. A field vehicle test in urban areas with a low-cost GNSS/INS integrated system indicates that two types of errors simulated in complex urban areas have been detected, distinguished and eliminated with the proposed scheme, success rate reached up to 92%. In particular, we also find that the novel neural network strategy can improve the overall position accuracy during GNSS signal short-term outages.

New Vehicle Positioning Method Based on RMINS/KC and Robust Adaptive KF

Aiming at the characteristics of vehicle positioning, a new vehicle positioning method based on the rotation modulation (RM) technology, kinematic constraint (KC), and the robust adaptive Kalman filter (RAKF) is proposed. On the one hand, on the basis of RM inertial navigation system and KC, this method achieves the whitening of colored measurement noise by improving the measurement equation; on the other hand, the RAKF algorithm is used to suppress the influence of the dynamic model error and observation anomaly on the estimation of the state parameters. Finally, the proposed new method is applied to the practical vehicle positioning system. Compared with the results of KF or MEMS-RMINS, the maximum position error of the proposed method by using RAKF is less than that of the KF algorithm or MEMS-RMINS, and the positioning accuracy is improved by 26.7% than that of the KF algorithm and only 21.87% of the MEMS-RMINS. At the same time, when the system has the observation anomaly, this method can also ensure the positioning accuracy of the system. The experimental results show that the new method can effectively suppress the influence of the system model error and observation anomaly to improve the vehicle positioning accuracy.

In-Motion Filter-QUEST Alignment for Strapdown Inertial Navigation Systems

By analyzing the error models of the measured vectors of the gravitational apparent motion, an in-motion filter-QUEST alignment method only with the inertial measurement unit is presented in this paper. The contribution of the proposed method lies in constructing the in-motion model of the measured vectors of the gravitational apparent motion and developing the extracted method to reconstruct the measured vectors. Furthermore, the relationship between the noise characteristic and the moving state of the vehicle is analyzed in detail. Different from the several current techniques, the presented method can be carried out without any other external additional equipment, when the vehicle is in-motion. With the designed real-time wavelet denoising (RWD) method, the high-frequency noises of the measured vectors are filtered. Based on the constructed parameter recognition model of the measured vectors, a robust adaptive Kalman filter is devised to estimate the optimal parameters, which are used to calculate the reconstructed observation vectors. Moreover, the gross outliers, which are contained in the filtered vectors of the RWD, are eliminated effectively. The simulation and the field trial results demonstrate that the presented method is applicable to the in-motion initial alignment, and it can serve as a nice initial alignment method in the follow-on fine alignment process and navigation process.

Adaptive Robust Unscented Kalman Filter via Fading Factor and Maximum Correntropy Criterion.

In most practical applications, the tracking process needs to update the data constantly. However, outliers may occur frequently in the process of sensors’ data collection and sending, which affects the performance of the system state estimate. In order to suppress the impact of observation outliers in the process of target tracking, a novel filtering algorithm, namely a robust adaptive unscented Kalman filter, is proposed. The cost function of the proposed filtering algorithm is derived based on fading factor and maximum correntropy criterion. In this paper, the derivations of cost function and fading factor are given in detail, which enables the proposed algorithm to be robust. Finally, the simulation results show that the presented algorithm has good performance, and it improves the robustness of a general unscented Kalman filter and solves the problem of outliers in system.

Robust Adaptive Cubature Kalman Filter and Its Application to Ultra-Tightly Coupled SINS/GPS Navigation System.

In this paper, we propose a robust adaptive cubature Kalman filter (CKF) to deal with the problem of an inaccurately known system model and noise statistics. In order to overcome the kinematic model error, we introduce an adaptive factor to adjust the covariance matrix of state prediction, and process the influence introduced by dynamic disturbance error. Aiming at overcoming the abnormality error, we propose the robust estimation theory to adjust the CKF algorithm online. The proposed adaptive CKF can detect the degree of gross error and subsequently process it, so the influence produced by the abnormality error can be solved. The paper also studies a typical application system for the proposed method, which is the ultra-tightly coupled navigation system of a hypersonic vehicle. Highly dynamical scene experimental results show that the proposed method can effectively process errors aroused by the abnormality data and inaccurate model, and has better tracking performance than UKF and CKF tracking methods. Simultaneously, the proposed method is superior to the tracing method based on a single-modulating loop in the tracking performance. Thus, the stable and high-precision tracking for GPS satellite signals are preferably achieved and the applicability of the system is promoted under the circumstance of high dynamics and weak signals. The effectiveness of the proposed method is verified by a highly dynamical scene experiment.

Robust adaptive filter for shipborne kinematic positioning and velocity determination during the Baltic Sea experiment

Information on trajectory and attitude is essential for analyzing gravimetric data collected on kinematic platforms. Usually, a Kalman filter is used to obtain high-accuracy positional and velocity information. However, this can be affected by measurement outliers and by state disturbances that occur frequently under a fast-changing environment. To overcome these problems, a robust adaptive Kalman filtering algorithm is applied for state estimates, which introduces an equivalent weight to resist measurement outliers and an optimal adaptive factor to balance the contributions of the kinematic model information and the measurements. In addition to the conventional robust estimator, an improved Current Statistical (CS) model is proposed. The improved CS model adopts a variance adaptive learning algorithm, and it can perform self-adaptation of acceleration variance with the innovation information; thus, it can overcome the shortcoming of lower tracking accuracy and avoid setting the maximum acceleration. Following a gravimetry campaign on the Baltic Sea, it is shown in theory and in practice that the robust adaptive Kalman filter is not only simple in its calculation but also more reliable in controlling the colored observation noise and kinematic state disturbance compared with the classical Kalman filter. The improved CS model performs best, especially when analyzing the positioning errors at the turns due to the target maneuvering. Compared to the CS model, the RMS values of the positional estimates derived from the improved CS model decrease by almost 30% in the horizontal direction, and no significant improvement in the vertical direction is found.

Heading Estimation for Pedestrian Dead Reckoning Based on Robust Adaptive Kalman Filtering.

Pedestrian dead reckoning (PDR) using smart phone-embedded micro-electro-mechanical system (MEMS) sensors plays a key role in ubiquitous localization indoors and outdoors. However, as a relative localization method, it suffers from the problem of error accumulation which prevents it from long term independent running. Heading estimation error is one of the main location error sources, and therefore, in order to improve the location tracking performance of the PDR method in complex environments, an approach based on robust adaptive Kalman filtering (RAKF) for estimating accurate headings is proposed. In our approach, outputs from gyroscope, accelerometer, and magnetometer sensors are fused using the solution of Kalman filtering (KF) that the heading measurements derived from accelerations and magnetic field data are used to correct the states integrated from angular rates. In order to identify and control measurement outliers, a maximum likelihood-type estimator (M-estimator)-based model is used. Moreover, an adaptive factor is applied to resist the negative effects of state model disturbances. Extensive experiments under static and dynamic conditions were conducted in indoor environments. The experimental results demonstrate the proposed approach provides more accurate heading estimates and supports more robust and dynamic adaptive location tracking, compared with methods based on conventional KF.

A Novel Grid SINS/DVL Integrated Navigation Algorithm for Marine Application.

Integrated navigation algorithms under the grid frame have been proposed based on the Kalman filter (KF) to solve the problem of navigation in some special regions. However, in the existing study of grid strapdown inertial navigation system (SINS)/Doppler velocity log (DVL) integrated navigation algorithms, the Earth models of the filter dynamic model and the SINS mechanization are not unified. Besides, traditional integrated systems with the KF based correction scheme are susceptible to measurement errors, which would decrease the accuracy and robustness of the system. In this paper, an adaptive robust Kalman filter (ARKF) based hybrid-correction grid SINS/DVL integrated navigation algorithm is designed with the unified reference ellipsoid Earth model to improve the navigation accuracy in middle-high latitude regions for marine application. Firstly, to unify the Earth models, the mechanization of grid SINS is introduced and the error equations are derived based on the same reference ellipsoid Earth model. Then, a more accurate grid SINS/DVL filter model is designed according to the new error equations. Finally, a hybrid-correction scheme based on the ARKF is proposed to resist the effect of measurement errors. Simulation and experiment results show that, compared with the traditional algorithms, the proposed navigation algorithm can effectively improve the navigation performance in middle-high latitude regions by the unified Earth models and the ARKF based hybrid-correction scheme.

Image-aided platform orientation determination with a GNSS/low-cost IMU system using robust-adaptive Kalman filter

The availability of miniaturized sensors with enhanced capabilities, new methods for image processing, and easy access to small and low-weight airborne platforms for data acquisition, including unmanned vehicles, opens new possibilities for geodetic navigation applications and developing new developments in sensor fusion. In this context, the development of efficient methods, based on low-cost sensors, to extract precise georeferenced information from digital cameras is of utmost interest. We present a method to improve the performance of the integration of GNSS/low-cost IMU by exploiting the orientation changes retrieved from digital images. In this work, a robust-adaptive Kalman filter is also introduced to further improve the performance of the method deployed. The adaptive factor and the robust factor accomplished are determined by innovation information and the threshold value of orientation changes between consecutive images. Results from airborne tests used to assess the performance of the method are presented. The results show that using a non-metric camera, the Euler angle estimation accuracy of the GNSS/low-cost IMU integration can be improved to be close to 0.5 degree and an additional improvement, which can reach 59%, can be achieved after using the robust-adaptive Kalman filter.