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This paper proposes an improved initial alignment method for a strap-down inertial navigation system/global navigation satellite system (SINS/GNSS) integrated navigation system with large misalignment angles. Its methodology is based on the three-dimensional special Euclidean group and extended Kalman filter (SE2(3)/EKF) and aims to overcome the challenges of achieving fast alignment under large misalignment angles using traditional methods. To accurately characterize the state errors of attitude, velocity, and position, these elements are constructed as elements of a Lie group. The nonlinear error on the Lie group can then be well quantified. Additionally, a group vector mixed error model is developed, taking into account the zero bias errors of gyroscopes and accelerometers. Using this new error definition, a GNSS-assisted SINS dynamic initial alignment algorithm is derived, which is based on the invariance of velocity and position measurements. Simulation experiments demonstrate that the alignment method based on SE2(3)/EKF can achieve a higher accuracy in various scenarios with large misalignment angles, while the attitude error can be rapidly reduced to a lower level.

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One of the main methods of the path localization of moving objects is positioning using Global Navigation Satellite Systems (GNSSs) in cooperation with Inertial Navigation Systems (INSs). Its basic task is to provide high availability, in particular in areas with limited access to satellite signals such as forests, tunnels or urban areas. The aim of the article is to carry out the testing and analysis of selected navigation parameters (3D position coordinates (Northing, Easting, and height) and Euler angles (pitch and roll)) of the GNSS/INS system for Unmanned Surface Vehicle (USV) path localization during inland hydrographic surveys. The research used the Ellipse-D GNSS/INS system working in the Real Time Kinematic (RTK) mode in order to determine the position of the "HydroDron" Autonomous Surface Vehicle (ASV). Measurements were conducted on four representative routes with a parallel and spiral arrangement of sounding profiles on Lake Klodno (Poland). Based on the obtained research results, position accuracy measures of the "HydroDron" USV were determined using the Ellipse-D GNSS/INS system. Additionally, it was determined whether USV path localization using a GNSS/INS system working in the RTK mode meets the positioning requirements for inland hydrographic surveys. Research has shown that the Ellipse-D system operating in the RTK mode can be successfully used to position vessels when carrying out inland hydrographic surveys in all International Hydrographic Organization (IHO) Orders (Exclusive, Special, 1a/1b and 2) even when it does not work 100% correctly, e.g., loss of RTK corrections for an extended period of time. In an area with limited coverage of the mobile network operator (30-40% of the time the receiver operated in the differential mode), the positioning accuracy of the "HydroDron" USV using the Ellipse-D GNSS/INS system working in the RTK mode was from 0.877 m to 0.941 m for the R95(2D) measure, depending on the route travelled. Moreover, research has shown that if the Ellipse-D system performed GNSS/INS measurements using the RTK method, the pitch and roll error values amounted to approx. 0.06°, which is almost identical to that recommended by the device manufacturer. However, when working in the differential mode, the pitch and roll error values increased from 0.06° to just over 0.2°.

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A Global Navigation Satellite System (GNSS) is widely used today for both positioning and timing purposes. Many distinct receiver chips are available as Application-Specific Integrated Circuit (ASIC)s off-the-shelf, each tailored to the requirements of various applications. These chips deliver good performance and low energy consumption but offer customers little-to-no transparency about their internal features. This prevents modification, research in GNSS processing chain enhancement (e.g., application of Approximate Computing (AxC) techniques), and design space exploration to find the optimal receiver for a use case. In this paper, we review the GNSS processing chain using SyDR, our open-source GNSS Software-Defined Radio (SDR) designed for algorithm benchmarking, and highlight the limitations of a software-only environment. In return, we propose an evolution to our system, called Hard SyDR to become closer to the hardware layer and access new Key Performance Indicator (KPI)s, such as power/energy consumption and resource utilization. We use High-Level Synthesis (HLS) and the PYNQ platform to ease our development process and provide an overview of their advantages/limitations in our project. Finally, we evaluate the foreseen developments, including how this work can serve as the foundation for an exploration of AxC techniques in future low-power GNSS receivers.

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Carrier phase measurements currently play a crucial role in achieving rapid and highly accurate positioning of global navigation satellite systems (GNSS). Resolving the integer ambiguity correctly is one of the key steps in this process. To address the inefficiency and slow search problem during ambiguity solving, we propose a single-frequency GNSS integer ambiguity solving based on an adaptive genetic particle swarm optimization (AGPSO) algorithm. Initially, we solve for the floating-point solution and its corresponding covariance matrix using the carrier-phase double difference equation. Subsequently, we decorrelate it using the inverse integer Cholesky algorithm. Furthermore, we introduce an improved fitness function to enhance convergence and search performance. Finally, we combine a particle swarm optimization algorithm with adaptive weights to conduct an integer ambiguity search, where each generation selectively undergoes half-random crossover and mutation operations to facilitate escaping local optima. Comparative studies against traditional algorithms and other intelligent algorithms demonstrate that the AGPSO algorithm exhibits faster convergence rates, improved stability in integer ambiguity search results, and in practical experiments the baseline accuracy of the solution is within 0.02 m, which has some application value in the practical situation of short baselines.

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Spoofing interference is one of the most emerging threats to the Global Navigation Satellite System (GNSS); therefore, the research on anti-spoofing technology is of great significance to improving the security of GNSS. For single spoofing source interference, all the spoofing signals are broadcast from the same antenna. When the receiver is in motion, the pseudo-range of spoofing signals changes nonlinearly, while the difference between any two pseudo-ranges changes linearly. Authentic signals do not have this characteristic. On this basis, an anti-spoofing method is proposed by jointly monitoring the linearity of the pseudo-range difference (PRD) sequence and pseudo-range sum (PRS) sequence, which transforms the spoofing detection problem into the sequence linearity detection problem. In this paper, the model of PRD and PRS is derived, the hypothesis based on the linearity of PRD sequence and PRS sequence is given, and the detection performance of the method is evaluated. This method uses the sum of squares of errors (SSE) of linear fitting of the PRD sequence and PRS sequence to construct detection statistics, and has low computational complexity. Simulation results show that this method can effectively detect spoofing interference and distinguish spoofing signals from authentic signals.

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Determining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known fact that the DPLL is stable if the normalized bandwidth, which is the product of the integration time and the noise bandwidth, is much less than one. However, actual limit points are not fixed at exactly one, and they vary with the loop filter order and implementation method. Furthermore, a lower limit on the normalized bandwidth may exist. This paper presents theoretical upper and lower limits for the normalized bandwidth of DPLL in GNSS receivers. The upper limit was obtained by examining the stability of DPLL with a special emphasis on the digital integration methods. The stability was investigated in terms of z-plane root loci with and without the consideration of the computational delay, which is a delay induced by the calculation of the discriminator and the loop filter. The lower limit was analyzed using the DPLL measurement error composed of the thermal noise, oscillator phase noise, and dynamic stress error. By utilizing the carrier-to-noise density ratio threshold which indicates the crossing point between the measurement error and the corresponding threshold, the lower limit of the normalized bandwidth is obtained.

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Ambiguity resolution based on smartphone GNSS measurements can enable various potential applications that currently remain difficult due to ambiguity biases, especially under kinematic conditions. This study proposes an improved ambiguity resolution algorithm, which uses the search-and-shrink procedure coupled with the methods of the multi-epoch double-differenced residual test and the ambiguity majority tests for candidate vectors and ambiguities. By performing a static experiment with Xiaomi Mi 8, the AR efficiency of the proposed method is evaluated. Furthermore, a kinematic test with Google Pixel 5 verifies the effectiveness of the proposed method with improved positioning performance. In conclusion, centimeter-level smartphone positioning accuracy is achieved in both experiments, which is greatly improved compared with the float and traditional AR solutions.

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Interference signals cause position errors and outages to global navigation satellite system (GNSS) receivers. However, to solve these problems, the interference source must be detected, classified, its purpose determined, and localized to eliminate it. Several interference monitoring solutions exist, but these are expensive, resulting in fewer nodes that may miss spatially sparse interference signals. This article introduces a low-cost commercial-off-the-shelf (COTS) GNSS interference monitoring, detection, and classification receiver. It employs machine learning (ML) on tailored signal pre-processing of the raw signal samples and GNSS measurements to facilitate a generalized, high-performance architecture that does not require human-in-the-loop (HIL) calibration. Therefore, the low-cost receivers with high performance can justify significantly more receivers being deployed, resulting in a significantly higher probability of intercept (POI). The architecture of the monitoring system is described in detail in this article, including an analysis of the energy consumption and optimization. Controlled interference scenarios demonstrate detection and classification capabilities exceeding conventional approaches. The ML results show that accurate and reliable detection and classification are possible with COTS hardware.

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This paper evaluates the implementation of a low-complexity adaptive full direct-state Kalman filter (DSKF) for robust tracking of global navigation satellite system (GNSS) signals. The full DSKF includes frequency locked loop (FLL), delay locked loop (DLL), and phase locked loop (PLL) tracking schemes. The DSKF implementation in real-time applications requires a high computational cost. Additionally, the DSKF performance decays in time-varying scenarios where the statistical distribution of the measurements changes due to noise, signal dynamics, multi-path, and non-line-of-sight effects. This study derives the full lookup table (LUT)-DSKF: a simplified full DSKF considering the steady-state convergence of the Kalman gain. Moreover, an extended version of the loop-bandwidth control algorithm (LBCA) is presented to adapt the response time of the full LUT-DSKF. This adaptive tracking technique aims to increase the synchronization robustness in time-varying scenarios. The proposed tracking architecture is implemented in an GNSS hardware receiver with an open software interface. Different configurations of the adaptive full LUT-DSKF are evaluated in simulated scenarios with different dynamics and noise cases for each implementation. The results confirm that the LBCA used in the FLL-assisted-PLL (FAP) is essential to maintain a position, velocity, and time (PVT) fix in high dynamics.

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Global navigation satellite systems (GNSSs) and ultra-wideband (UWB) ranging are two central research topics in the field of positioning and navigation. In this study, a GNSS/UWB fusion method is investigated in GNSS-challenged environments or for the transition between outdoor and indoor environments. UWB augments the GNSS positioning solution in these environments. GNSS stop-and-go measurements were carried out simultaneously to UWB range observations within the network of grid points used for testing. The influence of UWB range measurements on the GNSS solution is examined with three weighted least squares (WLS) approaches. The first WLS variant relies solely on the UWB range measurements. The second approach includes a measurement model that utilizes GNSS only. The third model fuses both approaches into a single multi-sensor model. As part of the raw data evaluation, static GNSS observations processed with precise ephemerides were used to define the ground truth. In order to extract the grid test points from the collected raw data in the measured network, clustering methods were applied. A self-developed clustering approach extending density-based spatial clustering of applications with noise (DBSCAN) was employed for this purpose. The results of the GNSS/UWB fusion approach show an improvement in positioning performance compared to the UWB-only approach, in the range of a few centimeters to the decimeter level when grid points were placed within the area enclosed by the UWB anchor points. However, grid points outside this area indicated a decrease in accuracy in the range of about 90 cm. The precision generally remained within 5 cm for points located within the anchor points.

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The paper presents a framework to emulate spacecraft orbits using GNSS hardware in the loop that enables the evaluation of new orbital positioning algorithms. The framework software generates the spacecraft orbit and the GNSS signals, including the most common perturbations. These signals are modulated and transmitted by a software-defined radio and received by a commercial GPS receiver. The system is validated using a test orbit, where the GPS receiver accurately determines the spacecraft positions. Moreover, using raw data provided by the receiver, the spacecraft positions have also been determined by software for a low earth orbit, in which civil GPS receivers do not work.

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Integrity monitoring (IM) is essential if GNSS positioning technologies are to be fully trusted by future intelligent transport systems. A tighter and conservative stochastic model can shrink protection levels in the position domain and therefore enhance the user-level integrity. In this study, the stochastic models for vehicle-based GNSS positioning are refined in three respects: (1) Gaussian bounds of precise orbit and clock error products from the International GNSS Service are used; (2) a variable standard deviation to characterize the residual tropospheric delay after model correction is adopted; and (3) an elevation-dependent model describing the receiver-related errors is adaptively refined using least-squares variance component estimation. The refined stochastic models are used for positioning and IM under the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) framework, which is considered the basis for multi-constellation GNSS navigation to support air navigation in the future. These refinements are assessed via global simulations and real data experiments. Different schemes are designed and tested to evaluate the corresponding enhancements on ARAIM availability for both aviation and ground vehicle-based positioning applications.

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To date, no universal modelling technique is available to mitigate the effect of site-specific multipaths in high-precision global navigation satellite system (GNSS) data processing. Multipaths affect both carrier-phase and code/pseudorange measurements, and the errors can propagate and cause position biases. This paper presents the use of an Eccosorb AN-W-79 microwave-absorbing material mounted around a GNSS antenna that reflects less than -17 dB of normal incident energy above a frequency of 600 MHz. To verify the feasibility and effectiveness of the Eccosorb, we installed two close stations by continuously operating multi-GNSS (BeiDou, GLONASS, Galileo and GPS) in a challenging location. One station is equipped with the Eccosorb AN-W-79, covering a square area of 3.35 m2 around the antenna, and the second station operates without it. The standard deviation reductions from single point positioning estimates are significant for all the individual GNSS solutions for the station equipped with microwave-absorbing material. The reductions are as follows: for GPS, between 15% and 23%; for Galileo, between 22% and 45%; for GLONASS, 22%; and for BeiDou, 4%. Furthermore, we assess the influence of multipaths by analysing the linear combinations of code and carrier phase measurements for various GNSS frequencies. The Galileo code multipath shows a reduction of more than 60% for the station with microwave-absorbing material. For GLONASS, particularly for the GLOM3X and GLOM1P code multipath combinations, the reduction reaches 50%, depending on the observation code types. For BeiDou, the reduction is more than 30%, and for GPS, it reaches between 20% and 40%. The Eccosorb AN-W-79 microwave-absorbing material shows convincing results in reducing the code multipath noise level. Again, using microwave-absorbing material leads to an improvement between 15% and 60% in carrier phase cycle slips. The carrier-phase multipath contents on the post-fit residuals from the processed GNSS solutions show a relative RMS reduction of 13% for Galileo and 9% for GLONASS and GPS when using the microwave-absorbing material. This study also presents power spectral contents from residual signal-to-noise ratio time series using Morlet wavelet transformation. The power spectra from the antenna with the Eccosorb AN-W-79 have the smallest magnitude, demonstrating the capacity of microwave-absorbing materials to lessen the multipath influence while not eliminating it.

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Increasing the number of satellites in a global navigation satellite system (GNSS) improves the positioning accuracy and increases availability. However, it reduces the positioning accuracy improvement rate and increases the calculation loads, which can cause battery usage problems in mobile devices using a GNSS. An appropriate satellite selection method is required. One current method entails the use of ideal satellite placement with respect to the minimum geometric dilution of precision (GDOP). In this study, the described ideal satellite placement with the minimum GDOP were divided in terms of the horizontal dilution of precision (HDOP) and vertical dilution of precision (VDOP). HDOP and VDOP were mathematically derived and analyzed. The derived formula was verified using simulations. The analysis was performed with actual dual GNSS satellite data. The satellites adjacent to the ideal placement were selected and the DOP was calculated. Simply selecting satellites closest to the ideal placement afforded large values for HDOP and VDOP. This issue was addressed using a satellite changing algorithm considering the dual GNSS, resulting in reduced values of the HDOP and VDOP.

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High-precision position estimations of agricultural mobile robots (AMRs) are crucial for implementing control instructions. Although the global navigation satellite system (GNSS) and real-time kinematic GNSS (RTK-GNSS) provide high-precision positioning, the AMR accuracy decreases when the signals interfere with buildings or trees. An improved position estimation algorithm based on multisensor fusion and autoencoder neural network is proposed. The multisensor, RTK-GNSS, inertial-measurement-unit, and dual-rotary-encoder data are fused with Extended Kalman filter (EKF). To optimize the EKF noise matrix, the autoencoder and radial basis function (ARBF) neural network was used for modeling the state equation noise and EKF measurement equation. A multisensor AMR test platform was constructed for static experiments to estimate the circular error probability and twice-the-distance root-mean-squared criteria. Dynamic experiments were conducted on road, grass, and field environments. To validate the robustness of the proposed algorithm, abnormal working conditions of the sensors were tested on the road. The results showed that the positioning estimation accuracy was improved compared to the RTK-GNSS in all three environments. When the RTK-GNSS signal experienced interference or rotary encoders failed, the system could still improve the position estimation accuracy. The proposed system and optimization algorithm are thus significant for improving AMR position prediction performance.

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This paper evaluates the performance of robust adaptive tracking techniques with the direct-state Kalman filter (DSKF) used in modern digital global navigation satellite system (GNSS) receivers. Under the assumption of a well-known Gaussian distributed model of the states and the measurements, the DSKF adapts its coefficients optimally to achieve the minimum mean square error (MMSE). In time-varying scenarios, the measurements' distribution changes over time due to noise, signal dynamics, multipath, and non-line-of-sight effects. These kinds of scenarios make difficult the search for a suitable measurement and process noise model, leading to a sub-optimal solution of the DSKF. The loop-bandwidth control algorithm (LBCA) can adapt the DSKF according to the time-varying scenario and improve its performance significantly. This study introduces two methods to adapt the DSKF using the LBCA: The LBCA-based DSKF and the LBCA-based lookup table (LUT)-DSKF. The former method adapts the steady-state process noise variance based on the LBCA's loop bandwidth update. In contrast, the latter directly relates the loop bandwidth with the steady-state Kalman gains. The presented techniques are compared with the well-known state-of-the-art carrier-to-noise density ratio (C/N0)-based DSKF. These adaptive tracking techniques are implemented in an open software interface GNSS hardware receiver. For each implementation, the receiver's tracking performance and the system performance are evaluated in simulated scenarios with different dynamics and noise cases. Results confirm that the LBCA can be successfully applied to adapt the DSKF. The LBCA-based LUT-DSKF exhibits superior static and dynamic system performance compared to other adaptive tracking techniques using the DSKF while achieving the lowest complexity.

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The performance of global navigation satellite system (GNSS) receivers is significantly affected by interference signals. For this reason, several research groups have proposed methods to mitigate the effect of different kinds of jammers. One effective method for wide-band interference mitigation (IM) is the high-rate DFT-based data manipulator (HDDM) pulse blanker (PB). It provides good performance to pulsed and frequency sparse interference. However, it and many other methods have poor performance against wide-band noise signals, which are not frequency-sparse. This article proposes to include automatic gain control (AGC) in the HDDM structure to attenuate the signal instead of removing it: the HDDM-AGC. It overcomes the wide-band noise limitation for IM at the cost of limiting mitigation capability to other signals. Previous studies with this approach were limited to only measuring the carrier-to-noise density ratio (C/N0) performance of tracking, but this article extends the analysis to include the impact of the HDDM-AGC algorithm on the position, velocity, and time (PVT) solution. It allows an end-to-end evaluation and impact assessment of mitigation to a GNSS receiver. This study compares two commercial receivers: one high-end and one low-cost, with and without HDDM IM against laboratory-generated interference signals. The results show that the HDDM-AGC provides a PVT availability and precision comparable to high-end commercial receivers with integrated mitigation for most interference types. For pulse interferences, its performance is superior. Further, it is shown that degradation is minimized against wide-band noise interferences. Regarding low-cost receivers, the PVT availability can be increased up to 40% by applying an external HDDM-AGC.

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To obtain single-receiver Global Navigation Satellite System (GNSS) parameter solutions, the PPP-RTK user-filter combines measurements with time-correlated corrections that are separately computed by the filter of an external provider. The consequence of exercising such double-filtering is that the Kalman filter's standard assumption of having uncorrelated measurements in time becomes violated. This leads the user-filter to lose its 'minimum variance' property, thereby delivering imprecise parameter solutions. The solutions' precision-loss becomes more pronounced when one experiences an increase in the correction latency, i.e., the delay in time after the corrections are estimated and the time they are applied to the user measurements. In this contribution, we propose a new multi-epoch formulation for the PPP-RTK user-filter upon which both the uncertainty and the temporal correlation of the corrections are incorporated. By a proper augmentation of the user-filter state-vector, the corrections are jointly measurement-updated with the user parameter solutions. Supported by numerical results, the proposed formulation is shown to outperform its commonly used counterpart in the minimum-variance sense.

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The integration of geospatial data in hydrography, performed using different measurement systems, involves combining several study results to provide a comprehensive analysis. Each of the hydroacoustic and optoelectronic systems is characterised by a different spatial reference system and the method for technical implementation of the measurement. Therefore, the integration of hydrographic data requires that problems in selected fields of electronics, geodesy and physics (acoustics and optics) be solved. The aim of this review is to present selected fusion methods applying the data derived from Global Navigation Satellite System (GNSS), Real Time Kinematic (RTK) measurements, hydrographic surveys, a photogrammetric pass using unmanned vehicles and Terrestrial Laser Scanning (TLS) and compare their accuracy. An additional goal is the evalution of data integration methods according to the International Hydrographic Organization (IHO) S-44 standard. The publication is supplemented by implementation examples of the integration of geospatial data in the Geographic Information System (GIS). The methods described indicate the lack of a uniform methodology for data fusion due to differences in both the spatial reference systems and the techniques used. However, the integration of hydroacoustic and optoelectronic data allows for high accuracy geospatial data to be obtained. This is confirmed by the methods cited, in which the accuracy of integrated geospatial data was in the order of several centimetres.

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Since radio frequency interference (RFI) seriously degrades the performance of a global navigation satellite system (GNSS) receiver, interference detection becomes very important for GNSS receivers. In this paper, a novel rearranged wavelet-Hough transform (RWHT) method is proposed in GNSS interference detection, which is obtained by the combination of rearranged wavelet transform and Hough transform (HT). The proposed RWHT method is tested for detecting sweep interference and continuous wave (CW) interference, the major types of GNSS interfering signals generated by a GNSS jammer in a controlled test bench experiment. The performance of the proposed RWHT method is compared with the conventional techniques such as Wigner-Ville distribution (WVD) and Wigner-Hough transform (WHT). The analysis results show that the proposed RWHT method reduces the influence of cross-item problem and improves the energy aggregation property in GNSS interference detection. When compared with the WHT approach, this proposed RWHT method presents about 90.3% and 30.8% performance improvement in the initial frequency and chirp rate estimation of the GNSS sweep interfering signal, respectively. These results can be further considered to be the proof of the validity and effectiveness of the developed GNSS interference detection method using RWHT.