Adaptive Measurement Noise Research Articles

Observability-Constrained Resampling-Free Cubature Kalman Filter for GNSS/INS with Measurement Outliers

Integrating global navigation satellite systems (GNSSs) with inertial navigation systems (INSs) has been widely recognized as an ideal solution for autonomous vehicle navigation. However, GNSSs suffer from disturbances and signal blocking inevitably, making the performance of GNSS/INSs degraded in the occurrence of measurement outliers. It has been proven that the sigma points-based Kalman filter (KF) performs better than an extended KF in cases where large prior uncertainty is present in the state estimation of a GNSS/INS. By modifying the sigma points directly, the resampling-free sigma point update framework (SUF) propagates more information excepting Gaussian moments of prescribed accuracy, based on which the resampling-free cubature Kalman filter (RCKF) was developed in our previous work. In order to enhance the adaptivity and robustness of the RCKF, the resampling-free SUF depending on dynamic prediction residue should be improved by suppressing the time-varying measurement outlier. In this paper, a robust observability-constrained RCKF (ROCRCKF) is proposed based on adaptive measurement noise covariance estimation and outlier detection, where the occurrence of measurement outliers is modelled by the Bernoulli variable and estimated with the state simultaneously. Experiments based on car-mounted GNSS/INSs are performed to verify the effectiveness of the ROCRCKF, and result indicates that the proposed algorithm outperforms the RCKF in the presence of measurement outliers, where the heading error and average root mean square error of the position are reduced from 1.96° and 6.38 m to 0.27° and 5.95 m, respectively. The ROCRCKF is robust against the measurement outliers and time-varying model uncertainty, making it suitable for the real-time implementation of GNSS/INSs in GNSS-challenged environments.

GNSS/accelerometer integrated deformation monitoring algorithm based on sensors adaptive noise modeling

The Global Navigation Satellite System (GNSS) and accelerometer integrated system can obtain more stable and reliable deformation displacement with the full use of the complementary technical characteristics of these two types of sensors. The Kalman Filter (KF) method is often applied to integrate GNSS three-dimensional (3D) coordinates and high-rate accelerometer measurements. The key to obtaining accurate solutions is the reasonable setting of measurement noise and process noise of KF. However, in some complex deformation monitoring scenarios such as landslides, both GNSS and accelerometers are susceptible to interference from factors like vegetation cover and external dynamic disturbance. Traditional adaptive filtering methods is hard to simultaneously and appropriately adjust the two types of noise matrices. To address this problem, an adaptive noise model based on sensors is proposed. The adaptive measurement noise is constructed using the posterior coordinate covariance derived from GNSS-RTK process. The random walk coefficient corresponding to the process noise is estimated online via the standard deviation (STD) of acceleration time-varying information. A series of numerical experiments about simulated three-dimensional (3D) deformation displacement are carried out to validate the proposed algorithm. The results show that: (1) When the GNSS signal is disturbed by complex environment, the adaptive measurement noise model effectively contributes to the accuracy improvement, from decimeter level to centimeter level. (2) In the presence of unstable deformable bodies, the adaptive process noise algorithm significantly suppresses the divergent deformation time series caused by external accelerometer disturbances. (3) Even if suffering the overlying effects of electromagnetic interference and external disturbance, the centimeter-level deformation monitoring accuracy can be achieved by using the joint adaptive measurement and process noise model. The improvement effect is particularly significant in the main deformation direction.

Trajectory PHD Filter for Adaptive Measurement Noise Covariance Based on Variational Bayesian Approximation

In order to solve the problem that the measurement noise covariance may be unknown or change with time in actual multi-target tracking, this paper brings the variational Bayesian approximation method into the trajectory probability hypothesis density (TPHD) filter and proposes a variational Bayesian TPHD (VB-TPHD) filter to obtain measurement noise covariance adaptively. By modeling the unknown covariance as the random matrix that obeys the inverse gamma distribution, VB-TPHD filter minimizes the Kullback–Leibler divergence (KLD) and estimates the sequence of multi-trajectory states with noise covariance matrices simultaneously. We propose the Gaussian mixture VB-TPHD (AGM-VB-TPHD) filter under adaptive newborn intensity for linear Gaussian models and also give the extended Kalman (AEK-VB-TPHD) filter and unscented Kalman (AUK-VB-TPHD) filter in nonlinear Gaussian models. The simulation results prove the effectiveness of the idea that the VB-TPHD filter can form robust and stable trajectory filtering while learning adaptive measurement noise statistics. Compared with the tag-VB-PHD filter, the estimated error of the VB-TPHD filter is greatly reduced, and the estimation of the trajectory number is more accurate.

Towards Predicting the Measurement Noise Covariance with a Transformer and Residual Denoising Autoencoder for GNSS/INS Tightly-Coupled Integrated Navigation

The tightly coupled navigation system is commonly used in UAV products and land vehicles. It adopts the Kalman filter to combine raw satellite observations, including the pseudorange, pseudorange rate and Doppler frequency, with the inertial measurements to achieve high navigational accuracy in GNSS-challenged environments. The accurate estimation of measurement noise covariance can ensure the quick convergence of the Kalman filter and the accuracy of the navigation results. Existing tightly coupled integrated navigation systems employ either constant noise covariance or simple noise covariance updating methods, which cannot accurately reflect the dynamic measurement noises. In this article, we propose an adaptive measurement noise estimation algorithm using a transformer and residual denoising autoencoder (RDAE), which can dynamically estimate the covariance of measurement noise. The residual module is used to solve the gradient degradation problem. The DAE is adopted to learn the essential characteristics from the noisy ephemeris data. By introducing the attention mechanism, the transformer can effectively learn the time and space dependency of long-term ephemeris data, and thus dynamically adjusts the noise covariance with the predicted factors. Extensive experimental results demonstrate that our method can achieve sub-meter positioning accuracy in the outdoor open environment. In a GNSS-degraded environment, our proposed method can still obtain about 3 m positioning accuracy. Another test on a new dataset also confirms that our proposed method has reasonable robustness and adaptability.

An USBL/DR Integrated Underwater Localization Algorithm Considering Variations of Measurement Noise Covariance

Ultrashort baseline (USBL) positioning system is an important part of the integrated navigation for underwater vehicles. The single USBL positioning system has problems such as reduced accuracy of azimuth measurement due to target motion and large impact of small angular variations, especially in the region where the target is close to the conical boundary, that is, the low-elevation region. To improve the positioning accuracy of the USBL-based integrated navigation system, a tightly coupled USBL/Dead Reckoning (DR) integrated localization algorithm that considers the time varying characteristics of the measurement noise was proposed, and the filtering model of the algorithm was designed. The algorithm exploits the mechanism of the azimuth measurement covariance variation of the USBL system, constructs an adaptive measurement noise estimator for the USBL system, and applies it to the integration filtering of USBL/DR data. A nonlinear extended Kalman filtering (EKF) model was used to fuse the USBL positioning and dead reckoning trajectories. A number of simulation tests with different elevation angle settings were performed to compare the performance of the proposed algorithm with that of a conventional EKF for underwater localization. The test results reveal that the proposed algorithm can effectively reduce the positioning error caused by the change in the relative azimuth of the acoustic signal owing the motion of the mother ship and the motion of the underwater vehicle.

In-motion initial alignment method for a laser Doppler velocimeter-aided strapdown inertial navigation system based on an adaptive unscented quaternion H-infinite filter

With its advantages of high velocity measurement accuracy and fast dynamic response, the laser Doppler velocimeter (LDVs) is expected to replace the odometer (OD) in combination with a strapdown inertial navigation system (SINS) to give a higher-precision integrated navigation system. Since a LDV has higher velocity measurement accuracy and data update frequency than an OD and Doppler velocity log, a LDV is used for the first time in this paper to aid a SINS in in-motion alignment. Considering that some approximation is used in the alignment model, the uncertainty noise of the sensors during the motion process and the unknown noise parameters during the filter process, an adaptive unscented quaternion H-infinite estimator (AUSQUHE) is proposed. The proposed AUSQUHE method has high robustness since it combines the advantages of an unscented quaternion estimator and H-infinite filter. The adaptive threshold of the H-infinite filter and the adaptive measurement noise covariance matrix are introduced to make the filter adapt to the changing environment and accelerate the convergence of errors. The performance of the proposed method is verified by a vehicle field test with a normal LDV signal and a vehicle test with the LDV signal disturbed by noise. The results show that the proposed method has higher alignment accuracy, faster convergence speed and stronger robustness than the four other compared methods.

An Adaptive Low-Cost INS/GNSS Tightly-Coupled Integration Architecture Based on Redundant Measurement Noise Covariance Estimation.

The main objective of the introduced study is to design an adaptive Inertial Navigation System/Global Navigation Satellite System (INS/GNSS) tightly-coupled integration system that can provide more reliable navigation solutions by making full use of an adaptive Kalman filter (AKF) and satellite selection algorithm. To achieve this goal, we develop a novel redundant measurement noise covariance estimation (RMNCE) theorem, which adaptively estimates measurement noise properties by analyzing the difference sequences of system measurements. The proposed RMNCE approach is then applied to design both a modified weighted satellite selection algorithm and a type of adaptive unscented Kalman filter (UKF) to improve the performance of the tightly-coupled integration system. In addition, an adaptive measurement noise covariance expanding algorithm is developed to mitigate outliers when facing heavy multipath and other harsh situations. Both semi-physical simulation and field experiments were conducted to evaluate the performance of the proposed architecture and were compared with state-of-the-art algorithms. The results validate that the RMNCE provides a significant improvement in the measurement noise covariance estimation and the proposed architecture can improve the accuracy and reliability of the INS/GNSS tightly-coupled systems. The proposed architecture can effectively limit positioning errors under conditions of poor GNSS measurement quality and outperforms all the compared schemes.

Six Object Tracking Algorithms: A Comparative Study

Objectives: To compare five different objects tracking algorithms performance wise with the proposed algorithm and to find out the best one among them for tracking of an object in occlusion and Background clutter condition i.e. when background contains target features. Methods/Analysis: In the proposed algorithm, the object’s position is obtained by Mean Shift tracking and then the prediction of object’s position is done through Kalman Filter. The Proposed method has Kalman Filter which consists of an adaptive system matrix and adaptive process error covariance and measurement error covariance matrices respectively. Adaptive system matrix of Kalman Filter is getting updated online depending on the quality of observation by Mean Shift algorithm and adaptive process and measurement noise covariance matrices are getting updated according to the variation in Bhattacharya Coefficient respectively. Findings: Proposed algorithm has a maximum value (0.2177 and 0.4821) of tracking efficiency metric i.e. Bhattacharya Coefficient in both video dataset among all the algorithms and it is taking less execution time (0.002761 sec and 0.005431 sec) than other Kalman filter based tracking algorithms. Applications/Improvements: Proposed algorithm is able to track the target in occlusion and background variation condition with more efficiency and less execution time than rest of the algorithms.

Autonomous navigation for lunar satellite using X‐ray pulsars with measurement faults

X-ray pulsar-based navigation (XNAV) is a navigation method using celestial X-ray source observations for spacecraft orbit determination. However, if the measurements are not reliable due to any kind of malfunction, the performance of XNAV may result in considerable errors and even divergence. In this study, a new algorithm called robust extended Kalman filter (REKF) is proposed for the lunar satellite autonomous navigation system, which is robust against measurement malfunctions. First, the satellite dynamic model applied perturbations is derived under the J2 perturbation of the Moon. The pulse time-of-arrival (TOA) is used to build the observation model. Second, the performance of XNAV system is discussed by analysing the transformation error of TOA, system observability and controllability. Then, an adaptive measurement noise scale factor (AMNSF) is designed by using the innovation sequence in REKF. Meanwhile, the gain matrix is modified by adding the AMNSF to reduce the influence of malfunction and enhance the robustness of XNAV system. Finally, the simulation results show the proposed navigation scheme is valid and feasible, and it is appropriate for lunar satellite autonomous navigation.

Extended Kalman Filter for Real Time Indoor Localization by Fusing WiFi and Smartphone Inertial Sensors

Indoor localization systems using WiFi received signal strength (RSS) or pedestrian dead reckoning (PDR) both have their limitations, such as the RSS fluctuation and the accumulative error of PDR. To exploit their complementary strengths, most existing approaches fuse both systems by a particle filter. However, the particle filter is unsuitable for real time localization on resource-limited smartphones, since it is rather time-consuming and computationally expensive. On the other hand, the light computation fusion approaches including Kalman filter and its variants are inapplicable, since an explicit RSS-location measurement equation and the related noise statistics are unavailable. This paper proposes a novel data fusion framework by using an extended Kalman filter (EKF) to integrate WiFi localization with PDR. To make EKF applicable, we develop a measurement model based on kernel density estimation, which enables accurate WiFi localization and adaptive measurement noise statistics estimation. For the PDR system, we design another EKF based on quaternions for heading estimation by fusing gyroscopes and accelerometers. Experimental results show that the proposed EKF based data fusion approach achieves significant localization accuracy improvement over using WiFi localization or PDR systems alone. Compared with a particle filter, the proposed approach achieves comparable localization accuracy, while it incurs much less computational complexity.

An adaptive filter method for spacecraft using gravity assist

Celestial navigation (CeleNav) has been successfully used during gravity assist (GA) flyby for orbit determination in many deep space missions. Due to spacecraft attitude errors, ephemeris errors, the camera center-finding bias, and the frequency of the images before and after the GA flyby, the statistics of measurement noise cannot be accurately determined, and yet have time-varying characteristics, which may introduce large estimation error and even cause filter divergence. In this paper, an unscented Kalman filter (UKF) with adaptive measurement noise covariance, called ARUKF, is proposed to deal with this problem. ARUKF scales the measurement noise covariance according to the changes in innovation and residual sequences. Simulations demonstrate that ARUKF is robust to the inaccurate initial measurement noise covariance matrix and time-varying measurement noise. The impact factors in the ARUKF are also investigated.