Global Positioning System Outages Research Articles

Improving the performance of GPS/INS integration during GPS outage with incremental regularized LSTM learning

Global Positioning System (GPS)/Inertial Navigation System (INS) integration is a widely used technique for navigation and positioning applications. It combines the advantages of GPS and INS to provide accurate and reliable information. However, the GPS/INS integration suffers from performance degradation during a GPS outage, which occurs when natural or artificial factors block the GPS signal. The novelty of this paper is improving GPS/INS integration performance during GPS outages using Incremental Regularized LSTM (IncRLSTM) learning. Incremental learning is a learning paradigm that can be learned from streaming data online and updating the model parameters without forgetting the previous ones. Also, regularization is a technique that prevents overfitting and improves the generalization of the network by adding some constraints or penalties to the model. IncRLSTM learning models the GPS signal as a multi-objective regression and corrects the INS output with the Faded Memory Kalman filter. The results on real-world datasets significantly show the reduction of positioning errors by an average of 72 % during GPS outages and the improvement of the accuracy and robustness of GPS/INS integration by an average of 58 % compared with existing methods. Moreover, IncRLSTM presents, on average, a 10 % improvement compared to the existing methods.

A hybrid optimization method based on extreme learning machine aided factor graph for INS/GPS information fusion during GPS outages

To enhance the navigation capability of the microelectromechanical system (MEMS)-based inertial navigation system (INS)/global positioning system (GPS) integrated system under satellite denied, a hybrid optimization navigation method using minimal learning parameter (MLP) to improve extreme learning machine (ELM) aided adaptive factor graph (AFG) is proposed. The proposed method mainly contains two innovative optimizations: (1) Fully considering the key parameters of each sensor in the INS/GPS integrated navigation system, the factor graph technology is introduced to develop an information fusion model for the system. Based on the maximum correlation entropy criterion and adaptive technology, the existing factor graph method for information fusion is optimized to solve the problem that the abnormal output of each sensor in the INS/GPS integrated system caused by complex environments affects the accuracy of information fusion, thus enhancing the robustness and navigation performance of the INS/GPS integrated system; (2) Moreover, ELM is optimized by MLP to predict the velocity and position observation information of the INS/GPS integrated system and tackle the performance deterioration of the system during GPS outages. The structural parameters of ELM are optimized with the MLP method, aiming to abate the computational burden of the traditional neural network (NN) to avoid “dimension explosion”, as well as enhance the generalization ability and robustness of the network to make it learn from the uncertainty of the system smoothly and quickly. Relevant ground vehicle experiments are designed to evaluate the proposed method. The experimental results demonstrate that the proposed strategy has superior performance and is more feasible for real-time implementation than other comparison approaches.

A switched adaptive strategy for state estimation in MEMS-based inertial navigation systems with application for a flight test

Abstract This paper proposes a switched model to improve the estimation of Euler angles and decrease the inertial navigation system (INS) error, when the centrifugal acceleration occurs. Depending on the situation, one of the subsystems of the proposed switched model is activated for the estimation procedure. During global positioning system (GPS) outages, an extended Kalman filter (EKF) operates in the prediction mode and corrects the INS information, based on the system error model. Compared with previous works, the main advantages of the proposed switched-based adaptive EKF (SAEKF) method are (i) elimination of INS error, during the centrifugal acceleration, and (ii) high accuracy in estimating the attitude and positioning, particularly during GPS outages. To validate the efficiency of the proposed method in various trajectories, an experimental flight test is performed and discussed, involving a microelectromechanical (MEMS)-based INS. The comparative study shows that the proposed method considerably improves the accuracy in various scenarios.

Enhancing the integration of the GPS/INS during GPS outage using LWT-IncRGRU

A common technique for navigation and positioning applications is the Global Positioning System (GPS)/Inertial Navigation System (INS) integration, which combines the strengths of GPS and INS to offer accurate and reliable information. However, the performance of the GPS/INS integration deteriorates during a GPS outage, which happens when natural or artificial factors block the GPS signal. The novelty of this paper is improving GPS/INS integration performance during GPS outages using Incremental Regularized Gated Recurrent Unit (IncRGRU) learning and Lifting Wavelet Transform (LWT). Incremental learning is a learning paradigm that can update the model parameters online from streaming data without forgetting the previous ones. Moreover, regularization is a technique that improves the network's generalization and avoids overfitting by adding some constraints or penalties to the model. In this way, the GPS signal is modeled by IncRGRU learning, and the Kalman filter corrects the INS output. Furthermore, LWT removes the noise from the sensors' signals. This algorithm has lower complexity and can work in real-time compared to conventional wavelet transforms. The performance of GPS/INS integration during GPS outages and the accuracy and robustness of GPS/INS integration is significantly improved by using LWT-IncRGRU on real-world datasets. The positioning errors are reduced by an average of 76% during GPS outages, and an average of 69% improves the GPS/INS integration compared to existing methods.

Dead Reckoning in Emergency Vehicle Preemption System Using Deep Output Kernel Learning and Extended Kalman Filter

Emergency Vehicle Preemption (EVP) system plays an important role in reducing the response time of emergency vehicles by around 15–50%. Emergency Vehicle location estimation during Global Positioning System (GPS) outages is a challenging task in EVP. To address this issue, a location estimation scheme has been proposed by applying deep output kernel learning and extended Kalman filter using Inertial Measurement Unit (IMU) dead reckoning. The proposed scheme reduces the error in the estimation of velocity, attitude, and position by dynamically adapting the noise parameters of the extended Kalman filter. This system provides navigation solutions for emergency vehicles. Initially, four test routes were selected and the Position, velocity and attitude (pitch and roll angle) were measured and applied to the proposed scheme. Training and testing were conducted for the measured datasets. The performance of the proposed scheme was measured using five statistical methods during training and testing, and a comparison was made with other existing methods. The simulation results show that the proposed scheme performed well, in the four test routes. Finally, two different case studies were conducted using the proposed scheme and the performance was compared with three other methods. According to the results, the proposed scheme showed improvements in detection accuracy compared to the existing methods during GPS outages of 71.94% and 62.83% for Trajectory-1 and Trajectory-2, respectively.

Robust ConvNet-Kalman Filter Integration for Mitigating GPS Jamming and Spoofing Attacks Basing on Inertial Navigation System Data

GPS (Global Positioning System) is the most accurate system for various applications, especially in transportation. However, GPS is critically vulnerable due to its reliance on radio signals, which can be exploited by hackers through intentional attacks like spoofing and jamming, leading to potentially dangerous disruptions for both humans and services. Moreover, GPS systems can also experience accidental disruptions in urban environments, where signals from multiple satellites may be blocked by buildings, severely affecting the receiver's accuracy. This paper presents a robust method designed to mitigate GPS outages caused by both jamming and spoofing by integrating inertial data. The proposed method leverages two key components: convolutional neural networks (ConvNet) and the Kalman filter (KF). A carefully optimized deep layer in the ConvNet is employed to correct errors in the inertial navigation system (INS). The findings indicate a considerable enhancement in accuracy, with the proposed method reducing the RMSE by 77.68% compared to standalone GPS and by 98.34% compared to standalone INS. This significant improvement underscores the proposed approach's performance in maintaining reliable navigation in environments where GPS signals are compromised

Geometric trust-based secure localization technique for resiliency of GPS outage and location error in vehicular cyber-physical systems (VCPS)

Management of vehicle traffic is a challenging task as it is non-deterministic by nature. Vehicular Cyber-Physical Systems (VCPS) is the emerging field of dynamics of vehicle management. Vehicle localization is considered an important task in VCPS. Many researchers proposed methodologies for this based on the Global Positioning System (GPS) which poses few location identification errors. Also, there are more vulnerabilities to the existing vehicular positioning system due to Zig-Zag attacks and bad-mouth attacks. In this work, an error-free and secure environment for communication between dynamically moving vehicle models has been proposed. In our proposed model a localization technique based on mathematical geometry which is capable of GPS outages and encompasses the dynamism of vehicle and on-road trajectory has been developed. The proposed model includes Extended Kalman filter-based routing to predict the neighbouring vehicle position. To avoid vulnerabilities created by the malicious nodes, a trust-based computation is performed by each node on its neighbours perceiving the authenticity of received messages. To validate the methodology, NS2 tool has been used to simulate the VCPS and to test the efficiency with different scenarios such as erroneous location, GPS outage, and malicious attack. The result shows that the proposed approach is more optimal and secure than the existing methodologies.

Passive IR-UWB Localization System for UAV-Based Electric Facility Inspection During GPS Outage

A practical localization system is proposed for a substation inspection unmanned aerial vehicle (UAV) performing its mission under global positioning system (GPS) signal blockage. The sensor hardware consists of a single transmitter and a cruciform receiver array, which produces the range difference (RD) information used for UAV positioning. The use of impulse-radio ultra wide-band (IR-UWB) devices secures the robustness against RF interference often caused by an exogenous electromagnetic field. With this hardware configuration, the UAV localization can be formulated as the state estimation problem for an uncertain linear state space model and be solved by using the computationally efficient robust weighted least squares (RWLS) estimator. Since the standard RWLS estimator could be sensitive to the imperfectness of prior knowledge on the noise statistic, a geometric constraint expressed in terms of a UAV position is exploited to secure the reliable localization performance in practice. Through experimental results, it is verified that the proposed solution provides reliable UAV positioning performance despite using the imperfect measurement noise statistics for the localization system.

A Novel ML-Aided Methodology for SINS/GPS Integrated Navigation Systems during GPS Outages

To improve the navigation accuracy for land vehicles during global positioning system (GPS) outages, a machine learning (ML) aided methodology to integrate a strap-down inertial navigation system (SINS) and GPS system is proposed, as follows. When a GPS signal is available, an online sequential extreme learning machine with a dynamic forgetting factor (DOS-ELM) algorithm is used to train the mapping model between the SINS’ acceleration, specific force, speed/position increments outputs, and the GPS’ speed/position increments. When a GPS signal is unavailable, GPS speed/velocity measurements are replaced with prediction output of the well-trained DOS-ELM module’s prediction output, and information fusion with the SINS reduces the degree of system error divergence. A land vehicle field experiment’s actual sensor data were collected online, and the DOS-ELM-aided methodology for the SINS/GPS integrated navigation systems was applied. The simulation results indicate that the proposed methodology can reduce the degree of system error divergence and then obtain accurate and reliable navigation information during GPS outages.

Virtual global positioning system construction approach for unmanned surface vessel based on Dempster–Shafer theory and broad learning framework

AbstractIntegrated navigation systems made up of a strap-down inertial navigation system (SINS) and global positioning system (GPS) are increasingly being used to improve the position, speed, and attitude information of unmanned surface vessels (USV). However, a GPS outage could occur due to the dependence of GPS performance on the external environment and the number of available satellites. This study uses an innovative combination of Dempster–Shafer (DS) theory and broad learning (BL) method to design a SINS/GPS integrated navigation system. First, the velocity and position information derived from the SINS and their corresponding GPS were fused using DS fusion rules, while the SINS error was modelled using the BL method. A ‘virtual’ GPS was then designed using the proposed DS–BL approach to provide the speed and position information when the GPS signal was interrupted, thereby ensuring the continuous navigation of the USV. The results of both simulation and sea trial demonstrate that the proposed virtual GPS estimation approach is effective, and the navigational accuracy of the proposed method is superior to other methods.

Deep Learning-Enabled Fusion to Bridge GPS Outages for INS/GPS Integrated Navigation

The low cost inertial navigation system (INS) suffers from bias and measurement noise, which would result in poor navigation accuracy during global positioning system (GPS) outages. Aiming to bridge GPS outages duration and enhance the navigation performance, a deep learning network architecture named GPS/INS neural network (GI-NN) is proposed in this paper to assist the INS. The GI-NN combines a convolutional neural network and a gated recurrent unit neural network to extract spatial features from inertial measurement unit (IMU) signals and track their temporal characteristics. The relationship among the attitude, specific force, angular rate and the GPS position increment is modelled, while the current and previous IMU data are used to estimate the dynamics of the vehicle by GI-NN. Numerical simulations, real field tests and public data tests are performed to evaluate the effectiveness of the proposed algorithm. Compared with the traditional machine learning algorithms, the results illustrate that the proposed method can provide more accurate and reliable navigation solutions in GPS denied environments.

Estimator-Based GPS Attitude and Angular Velocity Determination

In this paper, the estimator-based Global Positioning System (GPS) attitude and angular velocity determination is presented. Outputs of the attitude estimator include the attitude angles and attitude rates or body angular velocities, depending on the design of estimator. Traditionally as a position, velocity and time sensor, the GPS also offers a free attitude-determination interferometer. GPS research and applications to the field of attitude determination using carrier phase or Doppler measurement has been extensively conducted. The raw attitude solution using the interferometry technique based on the least-squares approach is inherently noisy. The estimator such as the Kalman filter (KF) or extended Kalman filter (EKF) can be incorporated into the GPS interferometer, potentially providing several advantages, such as accuracy improvement, reliability enhancement, and real-time characteristics. Three estimator-based approaches are investigated for performance comparison, including (1) KF with measurement involving attitude angles only; (2) EKF with measurements based on attitude angles only; (3) EKF with measurements involving both attitude angles and body angular rates. The assistance from body mounted gyroscopes, if available, can be utilized as the measurements for further performance improvement, especially useful for the case of signal-challenged environment, such as the GPS outages. Modeling of the dynamic process involving the body angular rates and derivation of the related algorithm will be presented. Simulation results for various estimator-based approaches are conducted; performance comparison is presented for the case of GPS outages.

GPS/INS Integration During GPS Outages Using Machine Learning Augmented with Kalman Filter

Nowadays a tremendous progress has been witnessed in Global Positioning System (GPS) and Inertial Navigation System (INS). The Global Positioning System provides information as long as there is an unobstructed line of sight and it suffers from multipath effect. To enhance the performance of an integrated Global Positioning System and Inertial Navigation System (GPS/INS) during GPS outages, a novel hybrid fusion algorithm is proposed to provide a pseudo position information to assist the integrated navigation system. A new model that directly relates the velocity, angular rate and specific force of INS to the increments of the GPS position is established. Combined with a Kalman filter the hybrid system is able to predict and estimate a pseud GPS position when GPS signal is unavailable. Field test data are collected to experimentally evaluate the proposed model. In this paper, the obtained GPS/INS datasets are pre-processed and semi-supervised machine learning technique has been used. These datasets are then passed into Kalman filtering for the estimation/prediction of GPS positions which were lost due to GPS outages. Hence, to bridge out the gaps of GPS outages Kalman Filter plays a major role in prediction. The comparative results of Kaman filter and extended Kalman filter are computed. The simulation results show that the GPS positions have been predicted taking into account some factors/measurements of a vehicle, the trajectory of the vehicle, the entire simulation was done using Anaconda (Jupyter Notebook).

A Vehicle-Model-Aided Navigation Reconstruction Method for a Multicopter during a GPS Outage

The integrated navigation of inertial navigation systems (INS) and the Global Positioning System (GPS) is essential for small unmanned aerial vehicles (UAVs) such as multicopters, providing steady and accurate position, velocity, and attitude information. Nevertheless, decreasing navigation accuracy is a serious threat to flight safety due to the long-term drift error of INS in the absence of GPS measurements. To bridge the GPS outage for multicopters, this paper proposes a novel navigation reconstruction method for small multicopters, which combines the vehicle dynamic model and micro-electro-mechanical system (MEMS) sensors. Firstly, an induced drag model is introduced into the dynamic model of the vehicle, and an efficient online parameter identification method is designed to estimate the model parameters quickly. Secondly, the body velocity can be calculated from the vehicle model and accelerometer measurement. In addition, the nongravitational acceleration estimated from body velocity and radar height are utilized to yield a more accurate attitude estimate. Fusing the information of the attitude, body velocity, magnetic heading, and radar height, a navigation system based on an error-state Kalman filter is reconstructed. Then, an adaptive measurement covariance algorithm based on a fuzzy logic system is designed to reduce the weight due to the disturbed acceleration. Finally, the hardware-in-loop experiment is carried out to demonstrate the effectiveness of the proposed method. Simulation results show that the proposed navigation reconstruction algorithm aided by the vehicle model can significantly improve navigation accuracy during a GPS outage.

A Mixed Optimization Method Based on Adaptive Kalman Filter and Wavelet Neural Network for INS/GPS During GPS Outages

To improve the navigation performance of the navigation system combining inertial navigation system (INS) and global positioning system (GPS) under complicated environments, especially GPS outages, a navigation method - wavelet neural network based on random forest regression (RFR-WNN) to assist adaptive Kalman filter (AKF) - is proposed. AKF is employed to correct INS errors, the Kalman filter is improved by introducing adaptive factor, to suppress the influence of the complex environment and random errors on the filtering accuracy; RFR-WNN is used to construct a high-precision prediction model when GPS works well, and to provide the required observations for AKF update when GPS outages. To solve the problem that the single neural network structure is easy to cause the overfitting, unstable and low prediction accuracy due to the lack of comprehensive training samples, RFR is introduced to optimize the single WNN, which can improve the generalization ability and prediction accuracy. In order to verify the effectiveness and advancement of the proposed method, vehicle navigation experiments were carried out, the results indicate that the proposed method has better navigation accuracy and performance than compared methods during GPS outages, and this advantage is more obvious in the case that fewer samples are collected.

Vehicle Localization During GPS Outages With Extended Kalman Filter and Deep Learning

Integration of microelectromechanical system-based inertial navigation system (MEMS-INS) and global positioning system (GPS) is a promising approach to vehicle localization. However, such a scheme may have poor performance during GPS outages and is less robust to measurement noises in changeable urban environments. In this article, we give an improved extended Kalman filter (IEKF) using an adaptation mechanism to eliminate the influence of noises in MEMS-INS and mitigate dependence on the process model. Especially, to guarantee accurate position estimation of the INS, a deep learning framework with multiple long short-term memory (multi-LSTM) modules is proposed to predict the increment of the vehicle position based on Gaussian mixture model (GMM) and Kullback-Leibler (KL) distance. The IEKF and the multi-LSTM are then combined together to optimize vehicle positioning accuracy during GPS outages in changeable urban environments. Numerical simulations and real-world experiments have demonstrated the effectiveness of the combined IEKF and multi-LSTM method, with the root-mean-square error (RMSE) of predicted position reduced by up to 93.9%. Or specifically, the RMSEs during GPS outages with durations 30, 60, and 120 s are 2.34, 2.69, and 3.08 m, respectively, which obviously outperform the existing method.

Assisting UAV Localization Via Deep Contextual Image Matching

In this article, we aim to explore the potential of using onboard cameras and pre-stored geo-referenced imagery for Unmanned Aerial Vehicle (UAV) localization. Such a vision-based localization enhancing system is of vital importance, particularly in situations where the integrity of the global positioning system (GPS) is in question (i.e., in the occurrence of GPS outages, jamming, etc.). To this end, we propose a complete trainable pipeline to localize an aerial image in a pre-stored orthomosaic map in the context of UAV localization. The proposed deep architecture extracts the features from the aerial imagery and localizes it in a pre-ordained, larger, and geotagged image. The idea is to train a deep learning model to find neighborhood consensus patterns that encapsulate the local patterns in the neighborhood of the established dense feature correspondences by introducing semi-local constraints. We qualitatively and quantitatively evaluate the performance of our approach on real UAV imagery. The training and testing data is acquired via multiple flights over different regions. The source code along with the entire dataset, including the annotations of the collected images has been made public. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> https://github.com/m-hamza-mughal/Aerial-Template-Matching. Up-to our knowledge, such a dataset is novel and first of its kind which consists of 2052 high-resolution aerial images acquired at different times over three different areas in Pakistan spanning a total area of around 2 km <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

Support Vector Machine Assisted GPS Navigation in Limited Satellite Visibility

This paper investigates performance improvement via the incorporation of the support vector machine (SVM) into the vector tracking loop (VTL) for the Global Positioning System (GPS) in limited satellite visibility. Unlike the traditional scalar tracking loop (STL), the tracking and navigation modules in the VTL are not independent anymore since the user’s position can be determined by using the information from other satellites and can be predicted on the basis of the states of the user. The method proposed in this paper makes use of the SVM to bridge the GPS signal and prevent the error growth due to signal outage. Similar to the neural network, the SVM is motivated by its ability to approximate an unknown nonlinear input-output mapping through supervised training. The SVM is employed for predicting adequate numerical control oscillator (NCO) inputs, i.e., providing better prediction of residuals for the Doppler frequency and code phase in order to maintain regular operation of the navigation system. When the navigation processing is in good condition, the SVM is at the training stage, and the output information from the discriminator and navigation filter is adopted as the inputs. Other machine learning (ML) algorithms such as the radial basis function neural network (RBFNN) and the Adaptive Network-Based Fuzzy Inference System (ANFIS) are employed for comparison. Performance evaluation for the SVM assisted architecture as compared to the RBFNN- and ANFIS-assisted methods and the un-assisted VTL will be carried out and the performance evaluation during GPS signal outage will be presented. The proposed design is very useful for navigation during the environment of limited satellite visibility to effectively overcome the problem in the environment of GPS outage.

Seamless GPS/Inertial Navigation System Based on Self-Learning Square-Root Cubature Kalman Filter

To improve the seamless navigation ability of an integrated Global Positioning System (GPS)/inertial navigation system in GPS-denied environments, a hybrid navigation strategy called the self-learning square-root- cubature Kalman filter (SL-SRCKF) is proposed in this article. The SL-SRCKF process contains two innovative steps: 1) it provides the traditional SRCKF with a self-learning ability, which means that navigation system observations can be provided continuously, even during long-term GPS outages; and 2) the relationship between the current Kalman filter gains and the optimal estimation error is established, which means that the optimal estimation accuracy can be improved by error compensation. The superiority of the proposed SL-SRCKF strategy is verified via experimental results and prominent advantages of this approach include: 1) the SL-SRCKF comprises two cycle filtering systems that work in a tightly coupled mode, and this allows more accurate error correction results to be obtained during GPS outages; 2) the system's error prediction ability is effectively improved by introducing a long short-term memory, which provides much better performance than other neural networks, such as random forest regression or the recursive neural network; and 3) under different (30, 60, and 100 s) GPS outage conditions, the long-term stability of SL-SRCKF is much better than that of other error correction approaches.

A Novel Hybrid Fusion Algorithm for Low-Cost GPS/INS Integrated Navigation System During GPS Outages

It is the main challenge for Global Positioning System (GPS)/Inertial Navigation System (INS) to achieve reliable and low-cost positioning solutions during GPS outages. A new GPS/INS hybrid method is proposed to bridge GPS outages. Firstly, a data pre-processing algorithm based on empirical mode decomposition (EMD) for wavelet de-noising is developed to reduce the uncertain noise of IMU raw measurements and provide accurate information for subsequent GPS/INS data fusion and training samples. Then, the interactive multi-model extended Kalman filter(IMM-EKF) algorithm is proposed to improve the robustness of Kalman filter output and the accuracy of model training target output. Finally, a new intelligent structure of GPS/INS based on Extreme Learning Machine (ELM) is proposed. When the GPS is available, the IMM-EKF is used to fuse the GPS and de-noised INS data, and the de-noised INS data and the outputs of IMM-EKF are used to train the ELM. During GPS outages, the ELM is used to predict and correct the INS position error. In order to evaluate the effectiveness of the proposed method, 3 tests were performed in the actual field test. The comparison results show that the proposed fusion method can significantly improve the accuracy and reliability of positioning during GPS outages.