Robust Onboard Orbit Determination Through Error Kalman Filtering

In urban road environments, global navigation satellite system (GNSS) signals may be interrupted due to occlusion by buildings and obstacles, resulting in reduced accuracy and discontinuity of combined GNSS/inertial navigation system (INS) positioning. Improving the accuracy and robustness of combined GNSS/INS positioning systems for land vehicles in the presence of GNSS interruptions is a challenging task. The main objective of this paper is to develop a method for predicting GNSS information during GNSS outages based on a long short-term memory (LSTM) neural network to assist in factor graph-based combined GNSS/INS localization, which can provide a reliable combined localization solution during GNSS signal outages. In an environment with good GNSS signals, a factor graph fusion algorithm is used for data fusion of the combined positioning system, and an LSTM neural network prediction model is trained, and model parameters are determined using the INS velocity, inertial measurement unit (IMU) output, and GNSS position incremental data. In an environment with interrupted GNSS signals, the LSTM model is used to predict the GNSS positional increments and generate the pseudo-GNSS information and the solved results of INS for combined localization. In order to verify the performance and effectiveness of the proposed method, we conducted real-world road test experiments on land vehicles installed with GNSS receivers and inertial sensors. The experimental results show that, compared with the traditional combined GNSS/INS factor graph localization method, the proposed method can provide more accurate and robust localization results even in environments with frequent GNSS signal loss.

Now a days, Unmanned Aerial Vehicles (UAVs) have been exploited in numerous civil and military aspects such as disaster management and border monitoring. Although most of these UAVs are equipped with Global Navigation Satellite System (GNSS) / Inertial Navigation System (INS) reliable integrated system for localization proposes, they are susceptible to lose their GNSS signals under some environmental and artificial challenging circumstances such as, flying in urban areas, jamming, and spoofing. In such complicated scenarios, the navigation solution will degrade rapidly due to the accumulated INS drift errors. Although various aiding sensors such as cameras, and radar are employed to mitigate the INS drift errors, their estimated positioning accuracy is still affected by some factors. This paper presents a nested optimal filter approach (G-H filter, Extended Kalman Filter (EKF)) for UAVs in GNSS denied environment, to enhance the estimated positioning accuracy by integrating the Radar Odometry (RO)/INS/MAG to sustain a reliable navigation solution during GNSS outage. First, the UAV relative velocity is calculated based on image processing approach from the radar range doppler map, then the G-H filter is deployed to improve the accuracy of the vehicle estimated forward velocities based on the vehicle dynamic characteristics to reduce the effect of unrealistic velocity estimate from the radar. These improved velocities are then fused with the Inertial Measurement Unit (IMU), magnetometer, and barometer via EKF to mitigate the positioning RMS errors during the GNSS signals outages. The experimental results demonstrate the proposed system's ability to notably enhance the 3D positioning accuracy during the GNSS signal outage by more than 99% when compared to a stand-alone IMU dead reckoning solution.

With the ever-increasing number of small satellites launched into space, on-board orbit determination is becoming more and more important. Precise satellite positions are needed for constellation maintenance, formation flying, communication optimization, collision avoidance and Earth observation. In addition, accurate time information is required for the functioning of the instruments on board. Low-cost off-the-shelf Global Navigation Satellite System (GNSS) receivers and antennas, adapted to the small size and weight of the satellite, allow precise on-board orbit determination and time synchronization for even the smallest satellites.We analysed more than one year of on-board navigation solutions (NAVSOL) from 8 Astrocast CubeSats, which are equipped with our multi-GNSS single-frequency payload. Based on the residuals from a dynamic orbit fitting, we found that the quality of the NAVSOL from the Astrocast satellites varies strongly both over time and between satellites, with an RMS ranging from a few meters to several tens of meters.In this study, we focus on three main effects that influence the quality of the NAVSOL from the Astrocast satellites: (1) The orbit-fit residuals show a positive radial offset in the range of about 6 m to 15 m, which is caused by ionospheric refraction. Our data show that GNSS signals at negative elevations are very strongly affected by the ionospheric refraction and thus account for the major part of the radial offset. (2) Discrepancies between the NAVSOL positions and velocities, and simulations with a GNSS signal generator show a once-per-revolution periodicity in the out-of-plane component, with amplitudes of 2 m and 5 cm/s in position and velocity, respectively. This effect is probably due to an inappropriate dynamic model used in the real-time navigation algorithm of the GNSS receiver. (3) Depending on the location of the GNSS antenna on board the satellite, the noise level varies by a multiple. This is assumed to be due to the antenna orientations, interference of the GNSS signals with electromagnetic waves coming from the satellite platform, signal attenuation during the transmission from the antenna to the receiver and differences in the soldering or tuning of the individual GNSS antennas.These findings help us refine hardware configurations and firmware settings in preparation for future Astrocast satellites or other nanosatellite missions. By eliminating or minimizing the mentioned effects, we expect to consistently achieve an accuracy on the level of a few meters for the real-time navigation solution of commercial off-the-shelf single-frequency GNSS receivers in space.

People have to move between indoor and outdoor frequently in city scenarios. The global navigation satellite system signal cannot provide reliable indoor positioning services. To solve the problem, this article proposes a seamless positioning system based on an inverse global navigation satellite system signal, which can extend the global navigation satellite system service into the indoor scenario. In this method, a signal source is arranged at a key position in the room, and the inverse global navigation satellite system signal is transmitted to the global navigation satellite system receiver to obtain a preset positioning result. The indoor positioning service is continued with the inertial navigation system after leaving the key position. The inverse global navigation satellite system seamless positioning system proposed in this article can unify indoor and outdoor positioning using the same receiver. The receiver does not need to re-receive navigation information when the scene changes, which avoids the switching process. Through the design of signal layer coverage, the receiver is in a warm start state, and the users can quickly fix the position when the scenario changes, realizing quick access in a true sense. This enables the ordinary commercial global navigation satellite system receiver to obtain indoor positioning capability without modification, and the algorithm can perform accurate positioning indoors and outdoors without switching.

Due to the low signal power, the Global Navigation Satellite System (GNSS) signal is vulnerable to interference and even cannot be captured or tracked in harsh environments. As an alternative, the Low Earth Orbit (LEO) satellite has been widely used in the navigation field due to the advantages of low cost and strong signals. It is becoming a significant component of the new combined navigation system with GNSS. The combination of an LEO Doppler signal and GNSS observables can improve the positioning accuracy and high-precision positioning convergence time of the GNSS receiver. However, the GNSS signal receiving capability cannot be improved from this data fusion level. We propose a novel assisted structure where GNSS signal acquisition and Doppler tracking are assisted by LEO Doppler positioning. The receiver uses the LEO signal to achieve Doppler positioning firstly. Then, the coarse position with the GNSS navigation messages received from LEO, as well as the estimated clock information, is used to assist in the acquisition and tracking of GNSS. In this way, the GNSS receiver’s sensitivity can get the benefit from this integrated system. The paper presents the structure of the assisted receiver and analyzes the assisted GNSS signal acquisition and carrier tracking performance in detail. Simulation experiments of this assisted structure are carried out to verify its superiority of acquisition and tracking sensitivity in comparison with standalone GNSS receivers. Theoretical analysis and experimental results show that the proposed acquisition method can achieve 90% detection probability at a carrier-to-noise ratio (C/N0) of 15 dB-Hz, which is about 8 dB higher than the conventional acquisition method without assistance; the proposed tracking method can track weak signals of 5 dB-Hz, which is about 4 dB higher than the conventional method. Therefore, this novel LEO-assisted receiver has significantly improved weak signal acquisition and tracking sensitivity.

Abstract. Typically, in situations where Global Navigation Satellite System (GNSS) signals are unavailable, navigation systems rely on integrating GNSS and inertial navigation system (INS) data. While such integration can provide accurate positioning during short GNSS signal outages, it cannot sustain prolonged GNSS outages. The reason for this is that the system's performance depends solely on the INS and can result in significant errors over time. To address this issue, additional onboard sensors are necessary. This study proposes a navigation system that integrates INS and LiDAR simultaneous localization and mapping (SLAM) using an extended Kalman filter (EKF). The system was tested using the raw KITTI dataset in various outdoor driving scenarios without GNSS signals. It is shown that the proposed system significantly outperformed the INS-only system, with an average RMSE improvement of around 93% and 58% in the horizontal and the up directions, respectively.

Under the high dynamic conditions, Global Navigation Satellite System (GNSS) signals produce great Doppler frequency shifts, which hinders the fast acquisition of signals. Inertial Navigation System (INS)-aided acquisition can improve the acquisition performance, whereas the accuracy of Doppler shift and code phase estimation are mainly determined by the INS precision. The relation between the INS accuracy and Doppler shift estimation error has been derived, while the relation between the INS accuracy and code phase estimation error has not been deduced. In this paper, in order to theoretically analyze the effects of INS errors on the performance of Doppler shift and code phase estimations, the connections between them are re-deduced. Moreover, the curves of the corresponding relations are given for the first time. Then, in order to have a better verification of the INS-aided acquisition, a high dynamic scenario is designed. Furthermore, by using the deduced mathematical relation, the effects of different grade INS on the GNSS (including Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS)) signal acquisition are analyzed. Experimental results demonstrate that the INS-aided acquisition can reduce the search range of local frequency and code phase, and achieve fast acquisition. According to the experimental results, a suitable INS can be chosen for the deeply coupled integration.

Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) are the most commonly used navigation systems. They both have unique advantages and disadvantages. GNSS is capable of generating precise navigation solutions while enough satellites are in view. However, the GNSS signals are sensitive to the environment. While the signals is attenuated, the GNSS receiver will fail to provide reliable navigation solutions. INS is an advanced navigation system built based on Newton's law. Due to the random noises contained in the Inertial Measurement Unit (IMU), the INS navigation solutions errors diverge over time. Therefore, effective integration of the two common systems can obtain better navigation results than any individual system. In this paper, for enhancing the GNSS/INS tightly integration system with low cost, multiple receivers were employed in the tight integration. Pseudo-range and Pseudo-range rates from the multiple receivers were employed to compose the measurement vector of the integration filter. In order to reduce the computation load, a measurement difference method was proposed. The state vector dimension could be reduced with the measurement difference scheme. Both simulation and field test were carried out for evaluating the performance of the proposed method. Since it was hard to obtain GNSS raw measurements from commercial receivers, self-developed DSP+FPGA (Digital Signal Processor, DSP; Field Programmable Gate Array, FPGA) based GNSS receivers were employed in the field test. The statistical analysis of the results showed that the positioning errors decreased with the receiver's amount increasing. In addition, a measurement difference method was proposed to reduce the state vector dimension for saving the computation load with the identical navigation solutions accuracy.

Drones are becoming increasingly significant for vast applications, such as firefighting, and rescue. While flying in challenging environments, reliable Global Navigation Satellite System (GNSS) measurements cannot be guaranteed all the time, and the Inertial Navigation System (INS) navigation solution will deteriorate dramatically. Although different aiding sensors, such as cameras, are proposed to reduce the effect of these drift errors, the positioning accuracy by using these techniques is still affected by some challenges, such as the lack of the observed features, inconsistent matches, illumination, and environmental conditions. This paper presents an integrated navigation system for Unmanned Aerial Vehicles (UAVs) in GNSS denied environments based on a Radar Odometry (RO) and an enhanced Visual Odometry (VO) to handle such challenges since the radar is immune against these issues. The estimated forward velocities of a vehicle from both the RO and the enhanced VO are fused with the Inertial Measurement Unit (IMU), barometer, and magnetometer measurements via an Extended Kalman Filter (EKF) to enhance the navigation accuracy during GNSS signal outages. The RO and VO are integrated into one integrated system to help overcome their limitations, since the RO measurements are affected while flying over non-flat terrain. Therefore, the integration of the VO is important in such scenarios. The experimental results demonstrate the proposed system’s ability to significantly enhance the 3D positioning accuracy during the GNSS signal outage.

A sparse global navigation satellite system (GLONASS) signal acquisition method based on compressive sensing and multiple measurement vectors is proposed. The nonsparse GLONASS signal can be represented sparsely on our proposed dictionary which is designed based on the signal feature. Then, the GLONASS signal is sensed by a normalized orthogonal random matrix and acquired by the improved multiple measurement vectors acquisition algorithm. There are 10 cycles of pseudorandom codes in a navigation message, and these 10 pseudorandom codes have the same row sparse structure. So, the acquisition probability can be raised by row sparse features theoretically. A large number of simulated GLONASS signal experiments show that the acquisition probability increases with the increase in the measurement vector column dimension. Finally, the practical availability of the new method is verified by acquisition experiments with the real record GLONASS signal. The new method can reduce the storage space and energy loss of data transmission. We hope that the new method can be applied to field receivers that need to record and transmit navigation data for a long time.

In this paper, we develop a novel method to detect Global Navigation Satellite Systems (GNSS) spoofing for an Automatic Dependent Surveillance-Broadcast (ADS-B) equipped aircraft. The Federal Aviation Administration (FAA) has mandated [18] all civil aircraft to be ADS-B Out equipped by January 1, 2020. The ADS-B Out broadcast sent to Air Traffic Control (ATC) consists of the aircraft's position, velocity, and other aircraft-specific information, all of which being unencrypted, poses a serious integrity threat. With readily available ADS-B trackers [19], [20], a spoofer can accurately track an aircraft to generate a spoofed trajectory that can go undetected [11]. We propose a novel method to modulate the ADS-B Out position broadcast such that a spoofed trajectory generated using the modulated ADS-B will be detectable by comparing Inertial Navigation System (INS) positions against those obtained using the spoofed GNSS signal. The amplitude of ADS-B modulation is selected to exceed the nominal INS error covariance so that spoofing is observable. In this work, we analytically quantify the magnitude of ADS-B modulation that will be sufficient for spoofing detection. During scenarios of GNSS signal jamming and spoofing, reauthentication of a reacquired GNSS signal is necessary to maintain integrity. During a GNSS outage, given enough time, the INS solution drift will grow large enough such that the spoofed GNSS solution might be within the INS error covariance envelope and go undetected. For GNSS outage scenarios we propose continuous modulation of ADS-B position and analytically quantify the magnitude such that spoofing of the GNSS signal is detectable after signal is re-acquired.

A signal of opportunity (SOP)-aided inertial navigation system (INS) framework is presented and studied. The following problem is studied. A mobile receiver with access to global navigation satellite system (GNSS) signals is aiding its onboard INS with GNSS pseudoranges. While navigating, the receiver draws pseudorange observations on ambient unknown terrestrial SOPs and estimates the SOPs' states. GNSS signals become unavailable, at which point the receiver uses the SOPs to aid its INS. It is demonstrated that fusing SOP pseudoranges in a tightly-coupled GNSS-SOP-INS framework produces a superior navigation solution to a traditional tightly-coupled GNSS-INS framework. Moreover, in the absence of GNSS signals, it is demonstrated that aiding the INS via SOPs produces bounded estimation errors. The SOP-aided INS's performance sensitivity is studied over varying quantity and quality of exploited SOPs. Experimental results are presented demonstrating a ground vehicle navigating exclusively with inertial measurement unit (IMU) data and pseudoranges from an unknown terrestrial SOP emanating from a cellular tower.

The Global Navigation Satellite System (GNSS) signals are often blocked or interfered in complex geographical or electromagnetic environments, which may make GNSS receivers unable to provide satisfying navigation and positioning services. There have been many ground-based or space-based GNSS augmentation systems to improve the resilience of GNSS positioning, of which most of them rely on additional infrastructures. In this study, a smartphone-based tightly-coupled positioning method was developed using the images from a build-in monocular camera and GNSS signals. In this method, the feature points with the known coordinates are regarded as 'visual pseudolite' and the distance between the camera and the feature points was calculated according to the photogrammetry approaches and used to estimate the user positioning with GNSS signals. The experimental results showed the feasibility of the tightly-coupled positioning algorithm and reached the positioning accuracy of ±5.56 m (1?), which is significantly higher than that of GNSS-only and vision-only positioning solutions.

The traditional measurement of signal bandwidth using single-carrier frequency sweeping is not suitable for global navigation satellite system (GNSS) signal. A new analysis technique of signal bandwidth with digital signal processing technique has been developed. After the GNSS signal is highly sampled, the spectrum of the actual GNSS signal and the ideal signal generated locally are evaluated in digital domain. The bandwidth of GNSS signal can be calculated. Simulation has been done for the proposed measurement technique using spectrum evaluation algorithm of the Periodogram and the Welch respectively. The simulation results shows that the GNSS signal bandwidth can be accurately estimated after the ideal and actual signal spectrum are evaluated and calculated using the Welch. The simulation results show that The estimating accurate of signal bandwidth can be higher than 99.9% in the case of the proper parameters have been set for Welch.

Measurements of carrier frequency phase differences of global navigation satellite system signals between multiple antennas are used in many coordinate and navigation applications. Global navigation satellite systems signal simulators are used for controlling global navigation satellite systems receiver’s instrumental errors. Therefore, it is necessary to determine the systematic error of the carrier frequency phase of generated signals for signal simulators. For this purpose a new calibration method of global navigation satellite systems simulators was developed. Method is based on refined errors model of generated phase differences of two radio frequency channels of the simulator. The proposed method was implemented using a wideband oscilloscope as an analog-to-digital converter. Approbation of the calibration method was carried out by comparison with the measurement results obtained using the State secondary standard of units of complex transmission coefficients in the range of 0...–60 dB and complex reflection coefficients in the range of 0.002–1 in the frequency range of 0.05–65 GHz (registration No. 2.1.ZZT.0210.2015). The calibration method allows one to determine carrier frequencies phase offsets of navigation signals for global navigation satellite systems simulators with expanded uncertainty (with a coverage factor of 3) of 1°. The proposed method provides the required accuracy of generating phase differences of the carrier frequencies of global navigation satellite systems signals is ensured for modern types of global navigation satellite systems simulators.