Adaptive Robust Kalman Filter Research Articles

A novel robust adaptive Kalman filter with application to urban vehicle integrated navigation systems

This study addresses the formidable challenge presented by non-Gaussian, time-varying, heavy-tailed process noise in integrated vehicle navigation systems. While robust adaptive filtering methods exist, their efficacy is constrained, and certain algorithms exhibit suboptimal usability due to an excess of a priori parameters. We deduce an adaptive robust Kalman filter, characterizing process noise with a Student's t distribution and measurement noise adhering to a Gaussian distribution. To enhance robustness against unknown or varying noise statistics, our method simultaneously estimates the scale matrix, degrees of freedom parameters, state vector, and measurement noise covariance through the expectation–maximization (EM) algorithm and Bayesian variational inference theory. Rigorous simulations and empirical experiments validate its superior accuracy and stability, requiring minimal a priori parameter information. Vehicle-based experiments further demonstrate positioning error below 2.78 m, velocity error below 0.34 m/s, and heading error less than 1.28° after achieving a steady state. This approach exhibits significant potential for advancing the precision and reliability of vehicle navigation systems.

Research on indoor positioning system algorithm based on UWB technology

Ultra wideband (UWB) indoor positioning technology is attracting significant attention in the present realm of indoor wireless positioning technology due to its numerous advantages, including low energy consumption, exceptional wireless transmission rates, remarkable resolution, and powerful anti-interference capabilities.This paper applies the time of arrival (TOA) location technique, derived from the research on UWB location method, to calculate the distance between the base station and the tag using the signal flight time. By incorporating the bilateral two-way ranging algorithm, the system has been fine-tuned to lower the precision demands on the hardware.A novel positioning algorithm is introduced, utilizing both C-Taylor and adaptive robust Kalman filter, which is based on the Time of Arrival (TOA) method. This algorithm aims to address the limitations of Chan and Taylor algorithms and minimize the non-line-of-sight (NLOS) error. This algorithm has excellent theoretical research value and practical application value.

Robust adaptive Kalman filter for structural performance assessment

SummaryStructural performance assessment is a critical stage in the health monitoring for the maintenance and risk management of engineering structures, in which the interstory drift is a key indicator. In this paper, a robust adaptive Kalman filter is proposed for an interstory drift estimation problem to show the health condition of steel structures in the case that the statistics or internal dynamics describing the signals and measurements are not known precisely. More precisely, we build an adaptive current Jerk model (ACJM) where the model parameters are updated in each time step to presuppose the statistics characterization of the steel dynamic, while the unknown measurement noise covariance is adapted based on a fixed‐lag innovation with respect to measurements. Moreover, a robust adaptive Kalman filter is designed for the modelling uncertainties in each time increment by solving a minimax game: one player tries to select an “actual” model far from the proposed ACJM with an exponential decay tolerance, while its “hostile” player, namely, the optimum filter, is designed by minimizing the estimation error according to the selected “actual” model. Finally, some simulation and experimental results show the effectiveness of the proposed algorithm.

Research on Robust Adaptive RTK Positioning of Low-Cost Smart Terminals.

The performance of low-cost smart terminals is limited by the performance of their low-cost Global Navigation Satellite System (GNSS) hardware and chips, as well as by the impact of complex urban environments, which affect the positioning accuracy and stability of GNSS services. To this end, this paper proposes a robust adaptive Kalman filter for different environments that can be applied after data preprocessing. Based on the Kalman filter algorithm, a robust estimation approach is introduced into real-time kinematic (RTK) positioning to make judgments on the abnormal observation values of low-cost smart terminals, which amplifies the variance and covariance of the outlier observation equation, and reduces the impact of outliers on positioning performance. The Institute of Geodesy and Geophysics III (IGG III) function is used for regulation purposes, where prior information is modified and refreshed using the equivalent weight matrix and adaptive factors, thus reducing the impact of system model errors on system state estimation results. In addition, a robust factor is defined to adjust positioning deviation weighting between the pre- and post-test robust estimates. The experimental results show that after robust RTK positioning in the static experiments, the overall improvement in positioning accuracies of the Xiaomi 8, Huawei P40, Huawei mate40, and low-cost M8 receiver reached 29.6%, 31.3%, 32.1%, and 30.7%, respectively. Similarly, after applying the proposed robust method in the dynamic experiments, the overall positioning accuracies of the Xiaomi 8, Huawei P40, Huawei mate40, and the low-cost M8 receiver improved by 28.3%, 32.9%, 35.4%, and 26.2%, respectively. The experimental results reveal that an excellent positioning effect of a smartphone is positively correlated with robust RTK positioning performance. However, it is worth noting that when the positioning accuracy reaches a high level, such as the positioning results achieved using low-cost receivers, the robustness performance shows a relatively decreasing trend. This finding suggests that under the condition of high positioning accuracy, the sensitivity of specific positioning equipment to interference sources may increase, resulting in a decline in the effect of robust RTK positioning.

An improved Sage-Husa variational robust adaptive kalman filter with uncertain noise covariances

An improved Sage-Husa variational robust adaptive kalman filter with uncertain noise covariances

An improved Sage-Husa variational robust adaptive kalman filter with uncertain noise covariances

An improved Sage-Husa variational robust adaptive kalman filter with uncertain noise covariances

Data-Driven Model Predictive Control for Uncalibrated Visual Servoing

This paper addresses the image-based visual servoing (IBVS) control problem with an uncalibrated camera, unknown dynamics, and constraints. A novel data-driven uncalibrated IBVS (UIBVS) strategy is proposed, incorporated with the Koopman-based model predictive control (KMPC) algorithm and the adaptive robust Kalman filter (ARKF). First, to alleviate the need for calibration of the camera’s intrinsic and extrinsic parameters, the ARKF with an adaptive factor is utilized to estimate the image Jacobian matrix online, thereby eliminating the laborious camera calibration procedures and improving robustness against camera disturbances. Then, a data-driven MPC strategy is proposed, wherein the unknown nonlinear dynamic model is learned using the Koopman operator theory, resulting in a linear Koopman prediction model. Only input–output data are used to construct the prediction model, and hence, the proposed approach is robust against model uncertainties. Furthermore, with a symmetric quadratic cost function, the proposed approach solves the quadratic programming problem online, and visibility constraints as well as joint torque constraints are taken into account. As a result, the proposed KMPC scheme can be implemented in real time, and the UIBVS performance degradation which arises from the control torque constraints can be avoided. Simulations and comparisons for a 2-DOF robotic manipulator demonstrate the feasibility of the proposed approach. Simulation results further validate that the computation time of the proposed approach is comparable to the one of kinematic-based methods.

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

This paper proposes a novel robust adaptive filter that combines smooth variable structure filter and extended Kalman filter for the spacecraft attitude estimation with model uncertainty originating from gyro drift, parameter error, and installation error. The proposed filter employs the extended Kalman filter based on quaternion and fuses an adaptive factor and smooth variable structure filter to improve robustness to the model uncertainty and noise. To improve the robustness of the extended Kalman filter, an adaptive factor that tunes the predicted covariance matrix is utilized to design the attitude estimation strategy. Moreover, to further decrease the impact of the suddenly rapid maneuvering and improve its robust effect of model uncertainty induced by dynamic error, gyro drift, and so on, a smooth variable structure estimation strategy founded on sliding mode theory is derived and utilized for the satellite attitude estimation. Thereby, a novel filtering algorithm is proposed by incorporating an adaptive factor and a smooth variable structure estimation strategy. Simulation results indicate that our proposed algorithm delivers exceptional robustness and achieves high precision and accuracy in satellite attitude estimation compared with the traditional extended Kalman filter.

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.

A modified federated Student’s t-based variational adaptive Kalman filter for multi-sensor information fusion

To overcome the problem of poor performance of multi-sensor fusion algorithm in linear systems with time-varying noise and outliers, a modified federated Student’s t-based variational robust adaptive Kalman filter (MFSTVRAKF) is proposed in this article. In this algorithm, an improved Student’s t-based variational robust adaptive Kalman filter (ISTVRAKF) is developed for adaptively mitigating the effects of time-varying noise and outliers of each local sensor, which improves the estimation accuracy of the algorithm. It reorganizes and derives a simplified variational filter to approximate the prior distribution of the measurement noise covariance via the Student’s t distribution to eliminate outliers. Subsequently, an adaptive factor is introduced into ISTVRAKF for adjusting the weights of prediction and measurement to further exclude outliers. Moreover, a modified adaptive information sharing factor is devised to adjust the multi-sensor fusion weights in accordance with the performance of local filter, which improves the fusion accuracy of the MFSTVRAKF algorithm. Simulations exhibit that the proposed algorithm is capable of resisting the effects of time-varying noise and outliers and achieving higher accuracy compared to other filtering algorithms and fusion algorithms.

Vehicle state estimation using a maximum likelihood based robust adaptive extended kalman filter considering unknown white Gaussian process and measurement noise signal

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

State estimation of radar tracking system using a robust adaptive unscented Kalman filter

State estimation of radar tracking system using a robust adaptive unscented Kalman filter

Adaptive unscented Kalman filter for neuronal state and parameter estimation.

Data assimilation techniques for state and parameter estimation are frequently applied in the context of computational neuroscience. In this work, we show how an adaptive variant of the unscented Kalman filter (UKF) performs on the tracking of a conductance-based neuron model. Unlike standard recursive filter implementations, the robust adaptive unscented Kalman filter (RAUKF) jointly estimates the states and parameters of the neuronal model while adjusting noise covariance matrices online based on innovation and residual information. We benchmark the adaptive filter's performance against existing nonlinear Kalman filters and explore the sensitivity of the filter parameters to the system being modelled. To evaluate the robustness of the proposed solution, we simulate practical settings that challenge tracking performance, such as a model mismatch and measurement faults. Compared to standard variants of the Kalman filter the adaptive variant implemented here is more accurate and robust to faults.

UWB Localization Based on Improved Robust Adaptive Cubature Kalman Filter.

Aiming at the problems of Non-Line-of-Sight (NLOS) observation errors and inaccurate kinematic model in ultra-wideband (UWB) systems, this paper proposed an improved robust adaptive cubature Kalman filter (IRACKF). Robust and adaptive filtering can weaken the influence of observed outliers and kinematic model errors on filtering, respectively. However, their application conditions are different, and improper use may reduce positioning accuracy. Therefore, this paper designed a sliding window recognition scheme based on polynomial fitting, which can process the observation data in real-time to identify error types. Simulation and experimental results indicate that compared to the robust CKF, adaptive CKF, and robust adaptive CKF, the IRACKF algorithm reduces the position error by 38.0%, 45.1%, and 25.3%, respectively. The proposed IRACKF algorithm significantly improves the positioning accuracy and stability of the UWB system.

Augmented Underwater Acoustic Navigation with Systematic Error Modeling Based on Seafloor Datum Network

Underwater acoustic navigation technology is an important approach to achieving high precision ocean navigation. One of the critical issues of the technology is to correct systematic errors, which are related to time delays and time-varying sound speed errors. In this study, we propose an augmented underwater acoustic navigation with systematic error model based on seafloor datum network. The proposed algorithm first selects data sets of piece-wise systematic error modeling by extracting the main periodic term of systematic errors based on the Fourier transform. Before that, the wavelet transform is used for denoising to better extract the main periodic term. Then the systematic error correction model is constructed by using the polynomial fitting method. After that, an augmented observation equation of underwater acoustic navigation with systematic error correction is constructed. Finally, an adaptive robust Kalman filter is developed for underwater acoustic navigation. The proposed algorithm is verified by an experiment in the South China Sea. The three-dimensional root mean square values of underwater acoustic navigation are 1.010 and 1.502 m in the operating range of 2.7 and 8.7 km. The results demonstrate that the proposed algorithm can efficiently reduce the influence of systematic error, thus improving underwater acoustic navigation accuracy.

Robust sequential adaptive Kalman filter algorithm for ultrashort baseline underwater acoustic positioning

Affected by dynamic changes in the complex marine environment, ultrashort baseline (USBL) systems may exhibit continuous gross errors in underwater target positioning, resulting in the distortion of the target coordinates. To effectively detect and eliminate continuous gross errors in USBL underwater acoustic positioning, a robust sequential adaptive Kalman filter (RSAKF) algorithm is proposed in this paper. The RSAKF algorithm employs sequential filtering to decompose all measurement updates into multiple submeasurement updates and uses the fading memory weighted average method to estimate the one-step prediction mean square error of the metrics for each submeasurement update. Then, the RSAKF algorithm adopts an adaptive correction method of submeasurement noise variance, which eliminates the influence of continuous gross errors through a more targeted adaptive correction of each submeasurement noise variance. The effectiveness of the algorithm was quantitatively analyzed using a USBL positioning simulation experiment, and the results showed that the continuous gross errors rejection rate of the RSAKF algorithm reached 84.12%. The point error of the RSAKF algorithm is improved by 62.65%, 46.76%, 36.09%, and 26.48% compared with the Kalman filter (KF), KF based on Huber, KF based on Institute of Geodesy and Geophysics, and the maximum correntropy KF, respectively. The USBL positioning remotely operated vehicle experiment was conducted in the South China Sea, and the results showed that the RSAKF has the best filtering accuracy. Simulation and actual measurement experiments verified that the RSAKF algorithm can effectively eliminate the influence of continuous gross errors.

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.

Improving the performance of GNSS precise point positioning by developed robust adaptive Kalman filter

Global Navigation Satellite Systems (GNSS) Precise Point Positioning (PPP) is a great precision positioning method based on GNSS. PPP based on multi-constellation GNSS uses the extended Kalman filter (EKF). Inappropriately, the measurement outliers and the system's dynamic model might produce mistakes in the positioning accuracy acquired using this method. An adaptive robust Kalman filter (RKF) was recently developed in order to alleviate these errors. In addition, the preceding variance is sometimes used to determine the weights of different categories of observations, which has an effect on PPP performance. A novel developed robust adaptive filtering (DRKF) has been developed to provide better placement results. For the equivalent weight matrix to be generated, an equivalent weight model that is statistically robust by the chi-square test for classification is constructed in this technique. According to prior Kalman filter models employing International GNSS Service (IGS) final clock and orbit products, the performance of GNSS PPP using the DRKF is confirmed in contrast to those produced using the current model. DRKF surpasses traditional robust adaptive filters in terms of positioning accuracy, convergence time, and PPP sturdiness according to the results of this study. In comparison to RKF, DRKF improves the positioning solution by 201 mm with 119.10 %, 77 mm with 164.86 %, and 160 mm with 211.74 % in the east, north, and up (ENZ) directions, respectively. It is recommended to use the newly developed robust adaptive Kalman filter in kinematic mode, especially in urban areas, due to the noticeable improvement in position accuracy.

Robust adaptive cubature Kalman filter for tracking manoeuvring target by wireless sensor network under noisy environment

Robust adaptive cubature Kalman filter for tracking manoeuvring target by wireless sensor network under noisy environment

Integrated navigation system (INS/auxiliary sensor) based on adaptive robust Kalman filter with partial measurements

Inertial navigation system (INS) is the most common positioning system in the underwater vehicle due to the limitations of penetration of the global navigation system. Amendment of INS cumulative error is made possible using data of auxiliary sensors such as Doppler velocity log (DVL). Due to the environmental conditions of the seabed, access to full DVL beams is impractical. Moreover, the statistical characteristics of measuring noise are unknown. These dramatically reduce the performance of the navigation system. Therefore, a loosely coupled (LC) approach is used to fuse partial DVL measurements in this study. This approach benefits from a virtual beam containing the velocity obtained in the last INS step instead of inaccessible DVL beams. To deal with the unknown statistical characteristics of the measurement and the limitations of access to DVL beams, an adaptive robust Kalman filter (ARKF) based on the Huber cost function is proposed. The performance of the proposed integrated navigation system for a remotely operated vehicle is investigated in the presence of observation noise and outliers. Results show that the proposed ARKF is robust against vigorous maneuvers, improves the estimation accuracy effectively, and can effectively reject measurement outliers.