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The robust and high-precision estimation of position and attitude information using a combined global navigation satellite system/inertial navigation system (GNSS/INS) model is essential to a wide range of applications in intelligent driving and smart transportation. GNSS systems are susceptible to inaccuracies and signal interruptions in occluded environments, which lead to unreliable parameter estimations in GNSS/INS based on filter models. To address this issue, in this paper, a GNSS/INS combination model based on factor graph optimization (FGO) is investigated and the robustness of this optimization model is evaluated in comparison to the traditional extended Kalman filter (EKF) model and robust Kalman filter (RKF) model. In this paper, both high- and low-accuracy GNSS/INS combination data are used and the two sets of urban scene data are collected using high- and low-precision consumer-grade inertial guidance systems and an in-vehicle setup. The experimental results demonstrate that the position, velocity, and attitude estimates obtained using the GNSS/INS and the FGO model are superior to those obtained using the traditional EKF and robust EKF methods. In the simulated scenarios involving gross interference and GNSS signal loss, the FGO model achieves optimal results. The maximum improvement rates of the position, velocity, and attitude estimates are 81.1%, 73.8%, and 75.1% compared to the EKF method and 79.8%, 72.1%, and 57.1% compared to the RKF method, respectively. [ABSTRACT FROM AUTHOR]

Multi-source heterogeneous information fusion based on the Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS)/odometer is an important technical means to solve the problem of navigation and positioning in complex environments. The measurement noise of the GNSS/INS/odometer integrated navigation system is complex and non-stationary; it approximates a Gaussian distribution in an open-sky environment, and it has heavy-tailed properties in the GNSS challenging environment. This work models the measurement noise and one-step prediction as the Gaussian and Student's t mixture distribution to adjust to different scenarios. The mixture distribution is formulated as the hierarchical Gaussian form by introducing Bernoulli random variables, and the corresponding hierarchical Gaussian state-space model is constructed. Then, the mixing probability of Gaussian and Student's t distributions could adjust adaptively according to the real-time kinematic solution state. Based on the novel distribution, a robust variational Bayesian Kalman filter is proposed. Finally, two vehicle test cases conducted in GNSS-friendly and challenging environments demonstrate that the proposed robust Kalman filter with the Gaussian–Student's t mixture distribution can better model heavy-tailed non-Gaussian noise. In challenging environments, the proposed algorithm has position root mean square (RMS) errors of 0.80 m, 0.62 m, and 0.65 m in the north, east, and down directions, respectively. With the assistance of inertial sensors, the positioning gap caused by GNSS outages has been compensated. During seven periods of 60 s simulated GNSS data outages, the RMS position errors in the north, east, and down directions were 0.75 m, 0.30 m, and 0.20 m, respectively. [ABSTRACT FROM AUTHOR]

• Measurement noise can be affected by outliers. • A single adaptive or robust filter cannot be applied to all noisy scenes. • The centered error entropy criterion has strong robustness. • Measurement outliers can be detected through Mahalanobis distance. • Robust filters are effective in integrated navigation applications. Due to unpredictable environmental factors, the measurement noise in INS/GNSS integration can be affected by outliers or exhibit statistical uncertainty. A single adaptive or robust filter may not be suitable for all noise scenarios. To address this issue, a new approach called the measurement noise covariance matrix (MNCM) ' R ' modified centered error entropy cubature Kalman filter (RMCEECKF) is proposed in this study. In this method, the MNCM is adjusted based on the innovation sequence, and outliers are detected using the Mahalanobis distance. If outliers are identified, the CEE criterion with strong robustness is applied for the posterior update. Simulation results on INS/GNSS integration demonstrate that the RMCEECKF offers higher estimation accuracy compared to existing methods in scenarios involving outliers, uncertain noise covariance, and outliers under uncertain noise covariance. The inclusion of outlier detection also enhances the computational efficiency of RMCEECKF when compared to the CEECKF. [ABSTRACT FROM AUTHOR]

The proper stochastic model of a global navigation satellite system (GNSS) makes a significant difference on the precise point positioning (PPP)/inertial navigation system (INS) tightly coupled solutions. The empirical Gaussian stochastic model is easily biased by massive gross errors, deteriorating the positioning precisions, especially in the severe GNSS blockage urban environment. In this paper, the distributional characteristics of the gross-error-contaminated observation noise are analyzed by the epoch-differenced (ED) geometry-free (GF) model. The Student's t distribution is used to express the heavy tails of the gross-error-contaminated observation noise. Consequently, a novel sequential Student's t-based robust Kalman filter (SSTRKF) is put forward to adjust the GNSS stochastic model in the urban environment. The proposed method pre-weights all the observations with the a priori residual-derived robust factors. The chi-square test is adopted to distinguish the unreasonable variances. The proposed sequential Student's t-based Kalman filter is conducted for the PPP/INS solutions instead of the standard Kalman filter (KF) when the null hypothesis of the chi-square test is rejected. The results of the road experiments with urban environment simulations reveal that the SSTRKF improves the horizontal and vertical positioning precisions by 57.5% and 62.0% on average compared with the robust Kalman filter (RKF). [ABSTRACT FROM AUTHOR]

The tracking of satellite signals with the passive linearly polarized embedded global navigation satellite system (GNSS) antenna of smartphones in dynamic scenarios is susceptible to the changing multipath and obstructions in urban environments, which lead to a significant decrease in the availability and reliability of GNSS solutions. Accordingly, based on the characteristics of smartphone GNSS and inertial measurement unit (IMU) sensors data in GNSS-degraded environments, we established an IMU-aided uncombined precise point positioning (PPP) mathematical model that is suitable for smartphones. To enhance the reliability of initial alignment in dynamic mode, the step function variances depending on carrier-to-noise density ratio were established with the variances of GNSS measurements, and the inertial navigation system (INS) parameters were initialized while both the velocity of smartphones and the position dilution of precision (PDOP) reached corresponding thresholds. Considering the measurement noise and observations gaps of smartphones, the robust Kalman filter (RKF) with equivalent variance matrix was used for parameter estimation to improve the convergence efficiency of the coupled PPP/INS model. Experimental results indicated that the proposed PPP/INS method can effectively improve the positioning performance of smartphones in GNSS-degraded environments. Compared with the conventional smartphone PPP scheme, the PPP/INS horizontal errors in the eastern and western areas of the long trajectory experiment decreased by 49.37% and 48.29%, respectively. Meanwhile, the trajectory deviation of smartphones can remain stable in the tunnel where GNSS signals are blocked. [ABSTRACT FROM AUTHOR]

The tightly coupled global navigation satellite system (GNSS) precise point positioning (PPP) and inertial navigation system (INS) can provide high-precision position, velocity and attitude information. The coupled system utilizes single receiver, which is particularly suitable for the environment without reference station, such as marine survey. In the former works, the integer ambiguity resolution of PPP/INS in terrestrial environment is researched. However, the GNSS observation is severely affected by the multipath effect in marine environment. In addition, the sideslip caused by wind and sea wave also impact float ambiguity estimation, consequently introducing difficulty for PPP ambiguity fixing. Therefore, the PPP/INS tightly coupled model with fixed ambiguity is proposed for marine survey. The correction model of INS gyroscope bias in closed-loop is deduced in detail. The influence of ship motion noise and multipath in marine environment is reduced by introducing the robust factor to the Kalman filter. The feasibility of the method is verified in a real marine experiment, with a detail evaluation of the data quality and positioning accuracy. The results show that the accuracy of PPP/INS can reach centimeter level after fixing the ambiguity in marine environment. Furthermore, the precise INS-predicted position can significantly shorten the re-fixed time of PPP/INS, which proves the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Inertial navigation is an edge computing-based method for determining the position and orientation of a moving vehicle that operates according to Newton's laws of motion on which all the computations are performed at the edge level without need to other far resources. One of the most crucial struggles in Global Positioning System (GPS) and Inertial Navigation System (INS) fusion algorithms is that the accuracy of the algorithm is reduced during GPS interruptions. In this paper, a low-cost method for GPS/INS fusion and error compensation of the GPS/INS fusion algorithm during GPS interruption is proposed. To further enhance the reliability and performance of the GPS/INS fusion algorithm, a Robust Kalman Filter (RKF) is used to compensate the influence of gross error from INS observations. When GPS data is interrupted, Kalman filter observations will not be updated, and the accuracy of the position will continuously decrease over time. To bridge GPS data interruption, an artificial neural network-based fusion method is proposed to provide missing position information. A well-trained neural network is used to predict and compensate the interrupted position signal error. Finally, to evaluate the effectiveness of the proposed method, an outdoor test using a custom-designed hardware, GPS, and INS sensors is employed. The results indicate that the accuracy of the positioning has improved by 67% in each axis during an interruption. The proposed algorithm can enhance the accuracy of the GPS/INS integrated system in the required navigation performance. [ABSTRACT FROM AUTHOR]

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been very intensively developed and widely applied in multiple areas. To further enhance the reliability and availability of GPS/INS integrated navigation in GPS challenging environment, range observation through ultra-wideband (UWB) is introduced in GPS/INS tightly coupled navigation. An improved robust Kalman filter is proposed and used to resist the influence of gross error from UWB observation in GPS/UWB/IMU tightly coupled navigation. The variance of the squared Mahalanobis distance in moving window is calculated, which brings as new judgement factor for gross errors in order to decrease the rate of false outlier identification. A simulation analysis shows that the improved robust Kalman filter is able to correctly identify gross errors and the rate of false judgment as zero. In order to validate the new robust filter, a real experiment is conducted. The results indicate that the improved robust Kalman filter used in GPS/UWB/INS tightly coupled navigation is able to remove the harmful effect of gross error in UWB observation. It clearly illustrates that the improved robust Kalman filter is very effective, and all the simulated small and large gross errors added to UWB distance observation are successfully identified. [ABSTRACT FROM AUTHOR]

This paper investigates a tightly-coupled Global Position System (GPS)/Ultra-Wideband (UWB)/Inertial Navigation System (INS) cooperative positioning scheme using a Robust Kalman Filter (RKF) supported by V2I communication. The scheme proposes a method that uses range measurements of UWB units transmitted among the terminals as augmentation inputs of the observations. The UWB range inputs are used to reform the GPS observation equations that consist of pseudo-range and Doppler measurements and the updated observation equation is processed in a tightly-coupled GPS/UWB/INS integrated positioning equation using an adaptive Robust Kalman Filter. The result of the trial conducted on the roof of the Nottingham Geospatial Institute (NGI) at the University of Nottingham shows that the integrated solution provides better accuracy and improves the availability of the system in GPS denied environments. RKF can eliminate the effects of gross errors. Additionally, the internal and external reliabilities of the system are enhanced when the UWB observables received from the moving terminals are involved in the positioning algorithm. [ABSTRACT FROM AUTHOR]

Abstract: The necessity recurrently comes up to align a strapdown inertial navigation system (SINS) in a moving vehicle to avoid a long run-up of the inertial system before a start or launch command is issued. This in-motion alignment is therefore achieved by integrating SINS data with some external aiding source such as the Global Positioning System (GPS) by using some form of measurement matching method. Consequently, this paper illustrates a reliable in-motion alignment scheme for a low-cost strapdown inertial measurement unit (SIMU) using a consistent and robust Kalman filter (RKF) structure. An error model of the SINS is derived and the state vector comprises attitude, velocity, position and sensor errors. Velocity information from the GPS with maneuvering is employed as a measurement to the filter. Experimentation results show that the proposed filter is less sensitive to impulsive noise and gives better estimates of the navigation parameters. [Copyright &y& Elsevier]

Accurate localization is a need of rising importance in modern times, often obtained by Global Navigation Satellite Systems (GNSS) receivers. Such receivers, which are usually based on a Kalman filter or an extended Kalman filter (EKF), might suffer greatly from outlier measurements, caused by multipath and/or non-line-of-sight (NLOS) receptions of the original GNSS signals. In order to mitigate these outlier measurements, outlier rejection techniques must be used. In this paper we present a simple yet efficient outlier rejection technique for Kalman filters, which we term Kalman Filter for Outlier Rejection (KFOR). The proposed KFOR was compared against common outlier rejection techniques, and outperformed them in all various scenarios. Some more advantages of the KFOR are further discussed. [ABSTRACT FROM AUTHOR]

The emergence of dual frequency global navigation satellite system (GNSS) chip actively promotes the progress of precise point positioning (PPP) technology in Android smartphones. However, some characteristics of GNSS signals on current smartphones still adversely affect the positioning accuracy of multi-GNSS PPP. In order to reduce the adverse effects on positioning, this paper takes Huawei Mate30 as the experimental object and presents the analysis of multi-GNSS observations from the aspects of carrier-to-noise ratio, cycle slip, gradual accumulation of phase error, and pseudorange residual. Accordingly, we establish a multi-GNSS PPP mathematical model that is more suitable for GNSS observations from a smartphone. The stochastic model is composed of GNSS step function variances depending on carrier-to-noise ratio, and the robust Kalman filter is applied to parameter estimation. The multi-GNSS experimental results show that the proposed PPP method can significantly reduce the effect of poor satellite signal quality on positioning accuracy. Compared with the conventional PPP model, the root mean square (RMS) of GPS/BeiDou (BDS)/GLONASS static PPP horizontal and vertical errors in the initial 10 min decreased by 23.71% and 62.06%, respectively, and the horizontal positioning accuracy reached 10 cm within 100 min. Meanwhile, the kinematic PPP maximum three-dimensional positioning error of GPS/BDS/GLONASS decreased from 16.543 to 10.317 m. [ABSTRACT FROM AUTHOR]