Search Results (291)

Reliable ambiguity subset selection is essential for partial ambiguity resolution (PAR) in multi-GNSS and multi-frequency precise point positioning (PPP), as the increasing number of satellite–frequency ambiguities expands the ambiguity search space and reduces ambiguity-fixing reliability in high-dimensional scenarios. To address this issue, this study proposes a multi-factor ranking and screening partial ambiguity resolution (MPAR) algorithm, an entropy-weighted multi-factor ambiguity subset selection algorithm designed for multi-GNSS and multi-frequency undifferenced and uncombined precise point positioning (UDUC PPP). The proposed MPAR algorithm evaluates candidate ambiguities using three quality indicators: signal-to-noise ratio, ambiguity variance, and carrier-phase residual. Min–max normalization is used to eliminate scale differences among the indicators, while entropy-based adaptive weighting is introduced to dynamically determine their relative contributions. Based on the integrated ranking results, ambiguities are divided into easy-to-fix and hard-to-fix subsets, with the hard-to-fix subset further refined through iterative screening before integer fixing. The proposed algorithm was validated using 24 h BDS-3/GPS/Galileo observations collected from 11 globally distributed MGEX stations on day 350 of 2025 under five-, four-, and three-frequency configurations. Its performance was compared with the baseline full ambiguity resolution strategy (FAR), which fixes all candidate ambiguities without subsequent iterative exclusion after an initial fixing failure, as well as elevation-angle-factor-based partial ambiguity resolution (ELE) and variance-factor-based partial ambiguity resolution (VAR). The MPAR algorithm achieved ambiguity-fixing rates of 98.9%, 98.7%, and 99.2% under the three configurations, respectively, exhibiting performance comparable to ELE while outperforming VAR and FAR. Compared with VAR, MPAR increased the average proportions of wide-lane and narrow-lane ambiguity residuals within ±0.1 cycle by 13.6% and 46.4%, respectively. Under the five-frequency configuration, MPAR achieved the best overall performance, with horizontal and vertical convergence times of 9.1 and 8.1 min, respectively. These results demonstrate that the proposed entropy-weighted multi-factor subset selection algorithm improves ambiguity estimation quality and enhances the reliability and convergence performance of high-dimensional multi-GNSS and multi-frequency PPP. Full article

Long and narrow shielded confined spaces, represented by traffic tunnels and underground utility tunnels, constitute critical application scenarios for indoor and underground positioning services. Despite their relatively simple geometric configurations, such environments suffer from severe spatial distortion of geometric dilution of precision (GDOP). Coupled with pervasive low-elevation signal propagation and intensive multipath reflection effects, conventional BeiDou Navigation Satellite System (BDS) positioning services are unable to provide continuous and reliable coverage in these scenarios. To date, existing research on high-precision pseudolite positioning for narrow confined spaces remains largely confined to theoretical analysis and laboratory experimental verification, while systematic studies on application-oriented signal atlas feature network design are significantly insufficient, forming a prominent gap that restricts the practical engineering deployment of relevant technologies. To address the aforementioned technical bottlenecks, this paper proposes a novel BDS pseudolite signal atlas network design method to improve the continuity, stability and comprehensive positioning performance in spatially distorted narrow shielded environments. Field vehicular tests were carried out in actual engineering tunnels and underground utility tunnels to systematically analyze the variation characteristics of raw BDS pseudolite observation data, including pseudorange, carrier phase, carrier-to-noise ratio (C/N₀) and Doppler shift. The test results verified that kinematic Doppler parameters exhibited outstanding stability in complex shielded environments with strong multipath interference. On this basis, a spatial feature model based on kinematic Doppler measurements was constructed, and wavelet denoising technology was adopted to extract effective typical spatial feature parameters. Combined with the deterministic one-to-one mapping relationship between Doppler peak characteristics and spatial positions, a multi-peak kinematic Doppler atlas was established, which eliminates the dependence on pre-deployment data collection, dedicated database construction and offline model training. Furthermore, comprehensively considering multi-dimensional constraints such as spatial environment scale, carrier dynamic characteristics and terminal output rate, the atlas network scheme was optimized to achieve a balanced trade-off among positioning detection accuracy, absolute positioning precision and suppression of the pseudolite near-far effect. Comparative experimental results demonstrate that the proposed BDS pseudolite atlas network effectively resolves the inherent GNSS positioning difficulty in long and narrow shielded spaces. Benefiting from the rational spectral peak configuration strategy, the system can satisfy the continuous and stable positioning requirements of multiple carrier types including motor vehicles and railway locomotives under variable motion speeds and terminal output rates. This study provides a robust and feasible technical solution for high-precision BDS positioning services in long and narrow shielded confined spaces, and holds favorable engineering application prospects for underground navigation scenarios. Full article

GNSS array receivers suffer tracking degradation under array nonidealities such as element-position perturbations, channel amplitude/phase errors, and slowly varying manifold mismatch. Conventional blind anti-jamming suppresses interference, but adaptive weight fluctuations can propagate into the correlator domain, increasing cross-branch correlation, causing Early/Late metric imbalance, and reducing Prompt phase consistency. Existing noncoherent combining methods mainly convert multi-branch correlator outputs into scalar energy metrics for code tracking, leaving the carrier loop’s complex Prompt input insufficiently constrained. To address this problem, we propose a blind adaptive joint code–carrier channel-combining method for nonideal arrays. After first-stage anti-jamming, the method estimates an Early/Late correlator-domain covariance matrix and reuses it as a shared statistical constraint. In the code loop, this matrix drives whitened noncoherent energy combining with closed-loop gain normalization to stabilize the DLL discriminator scale. In the carrier loop, it is combined with a Prompt-derived coherent direction to form a covariance-constrained PLL complex input. Simulations under wideband interference, static array errors, and dynamic mismatch show that the proposed J-WNCC reduces both code-phase error and carrier-phase jitter, improving joint tracking robustness in nonideal array environments. Ablation results further reveal a dominant-effect separation: DLL gain normalization mainly calibrates the whitened code-discriminator scale, whereas coherent Prompt combining mainly reconstructs the complex PLL input. Full article

This paper proposes a passive in-orbit calibration method for phased array antennas using GNSS carrier-phase measurements. By performing synchronous observation and exploiting the short-baseline property between the positioning antenna and array elements, the first differencing operation eliminates space propagation errors and clock biases. By further utilizing receiver channel consistency, the second differencing operation cancels out the receiver channel errors, thereby extracting the relative receive-chain phase error of the element under test. Under typical operating conditions, the calibration accuracy can reach an RMS error of approximately $3.02\mathrm{mm}$, corresponding to a phase accuracy of $5.72°$ in the GPS L1 band. This accuracy is close to the $5.625°$ minimum phase step of a 6-bit digital phase shifter, and can be further improved under higher $C/N_0$ and well-controlled residual error conditions. Without requiring a dedicated GNSS band excitation signal, this method avoids co-frequency self-interference with the positioning antenna, which provides an auxiliary approach for in-orbit calibration of phased array receive chains. Full article

In complex urban environments, GNSS satellite signals suffer from severe multipath errors caused by building occlusion and reflection, which significantly degrades the accuracy of precise point positioning (PPP). This paper proposes a deep-learning-based multipath hemispherical grid correction model (DL-MHM) that integrates combined filtering and satellite embedding mechanisms. The model adopts the multi-system interoperable MHM framework to achieve effective multipath error correction. First, pseudorange and carrier phase observation residuals are calculated using the ionosphere-free combination for PPP. Then, a joint median and Kalman filtering scheme is applied to suppress noise in multi-day continuous residual sequences. A transformer-based time-series learning model is constructed, which introduces satellite-specific embedding vectors to characterize the differences between individual satellites and deeply fuse temporal features. This enables the model to adaptively fit the residual variation patterns of different satellites and accurately extract multipath errors. Finally, the multipath components predicted by the deep learning model are incorporated into the multi-system interoperable MHM model to generate the final multipath corrections. Test results show that in heavily obstructed urban scenarios, the root mean square (RMS) values of the east (E), north (N), and up (U) coordinate residuals are improved by 49.27%, 1.80%, and 3.35%, respectively, after DL-MHM correction compared to the uncorrected data. In open-sky environments, the corresponding improvements are 7.70%, 5.48%, and 34.28%. In all experimental scenarios, the proposed method outperforms both the conventional multipath hemispherical map (MHM) model and the convolutional neural network-long short-term memory (CNN-LSTM)-based MHM model in terms of overall multipath correction performance. The experimental results demonstrate that the proposed DL-MHM model can effectively mitigate multipath errors in complex urban scenarios and significantly improve the accuracy of GNSS precise positioning. Full article

The demand for reliable Positioning, Navigation, and Timing (PNT) solutions is rapidly increasing due to the growing need for precision, efficiency, and safety in unmanned systems. As operations become more autonomous, the reliance on accurate and continuous PNT data becomes critical for maintaining system integrity. The Global Navigation Satellite System (GNSS), while serving as the primary global PNT service, is vulnerable to interference, jamming, and spoofing attacks. This raises serious concerns, particularly for safety-critical applications, and urgently requires resilient Alternative PNT (A-PNT) solutions. An existing worldwide infrastructure, the Distance Measuring Equipment (DME) system, is considered one of the most promising candidates for A-PNT to address GNSS vulnerabilities. Utilising the carrier phase of the DME signal enables distance measurements with centimetre-level accuracy. However, due to the pulse system nature of DME transmissions and the sparsity of phase observations, conventional carrier tracking loops such as PLLs and FLLs struggle to maintain a reliable phase lock. To address these challenges, this work proposes a zero-crossing-integrated Kalman filter-based approach to track the DME carrier signal at an irregular rate. The performance of the proposed algorithm is validated through a series of drone tests at Cranfield University, UK. The validation results demonstrate that the proposed enhanced carrier tracking approach consistently delivers stable and accurate performance. Full article

In this contribution, we introduce the concept of Fourier ambiguity resolution. We show how it is rooted in the principle of integer equivariant (IE) estimation and in its periodic representation. As a result, we present a general Fourier representation of IE-estimators. As the IE-class is the largest class of estimators used in GNSS ambiguity resolution, the periodic representation opens up a broad spectrum of new applications, both in the field of parameter estimation and in that of statistical testing. The representation also applies to the integer class, with its popular estimators of integer-rounding, integer-bootstrapping, and integer least-squares, as well as to their integer-aperture variants. In this contribution, we consider the periodic representation of the best integer equivariant (BIE) estimator. It is shown how this minimum mean squared error IE-estimator can be represented in both the spatial and frequency domains and how preference for one of the two representations should be based on the GNSS carrier-phase ambiguity precision. We also present a hybrid form of the BIE-estimator and show how the spatial and frequency representations can be mixed so as to do justice to the practical situation when carrier-phase ambiguity vectors consist of ambiguities having a wide range of varying precision. Full article

Low earth orbit (LEO)-enhanced global navigation satellite systems (GNSSs) (LeGNSSs) have emerged as a promising paradigm for next-generation precise point positioning (PPP). However, the highly dynamic nature of LEO satellites results in significant ionospheric variations with more frequent cycle slips. Thus, identifying fractional cycle slips and evaluating false alarms present significant challenges. In this paper, we propose an ionospheric preprocessing generalized combination (IPGC) method to improve the reliability of cycle slip detection. The ionospheric delay in the carrier phase is mitigated using the NeQuick model. Additionally, a set of specifically designed coefficients is used to combine LEO and GNSS observations, which increases the sensitivity of cycle slip detection. The simulation results indicate that the proposed method can effectively eliminate ionospheric interference of up to 4 cycles in LEO satellite cycle slip detection and can accurately detect all combinations of cycle slips with a maximum deviation of $0.14$ cycles. Compared with solutions without cycle slip repair, this method accelerates the positioning convergence time by $0.96/0.89/1.2$ min on the north/east/up (NEU) components, and the reconvergence efficiency is increased by factors of 10, $5.5$, and 2, respectively. Even with an elevated cutoff angle of ${40}^{\circ }$, the system achieves centimeter-level positioning accuracy ($0.38/1.08/1.86$ cm). These results confirm the effectiveness of the proposed method in LEO satellite cycle slip detection, providing key algorithmic guidance for the practical implementation of PPP in hybrid constellation systems. Full article

Carrier-phase ambiguity validation is essential to ensure the reliability of integer ambiguity resolution in high-precision GNSS positioning. Although integer equivariant (IE) estimators provide optimal integer candidates within their class, noise and model limitations may lead to incorrect fixing. Validation procedures are therefore crucial for safeguarding the transition from float to fixed solutions, particularly in high-precision and safety-critical applications. In this contribution we introduce the concept of Fourier ambiguity validation and show how it is rooted in the principles of integer aperture (IA) estimation and its periodic representation. Unlike classical integer estimators that always return an integer solution, IA estimators introduce adjustable acceptance regions in the float ambiguity domain and fix ambiguities only when sufficient statistical evidence is present. As a result we present a general Fourier representation of IA estimators and provide an analytical description of the probabilistic properties of integer-aperture bootstrapping. We also present a hybrid description and show how the spatial and frequency representations can be mixed so as to do justice to the practical situation when carrier-phase ambiguities have a wide range of varying precision. Full article

In Global Navigation Satellite Systems (GNSS), high-precision position coordinates are typically determined by establishing a double-difference carrier phase observation model and resolving the integer ambiguities within it. Therefore, the ability to fix integer ambiguities rapidly and accurately is a critical challenge in carrier phase measurements. To address the problem of double-difference integer ambiguity, this paper proposes a Hybrid Adaptive Differential Evolution Grey Wolf Optimizer (HADE-GWO) algorithm. Comparative experiments focusing on computation speed and stability were conducted against the GWO, LAMBDA, and M-LAMBDA algorithms. The results show that while achieving the same fixing success rate as the LAMBDA and M-LAMBDA algorithms, the HADE-GWO algorithm finds the optimal ambiguity solution in less time. To validate the high-dimensional ambiguity resolution capability of the HADE-GWO algorithm, 6-dimensional and 12-dimensional integer ambiguity resolution tests were performed. The outcomes indicate that the HADE-GWO algorithm possesses excellent high-dimensional resolution capabilities. Finally, an application experiment was conducted using single-frequency data from GPS and BeiDou (BDS) systems. The results demonstrate that the algorithm can achieve centimeter-level positioning accuracy in a combined single-frequency GPS+BDS solution. Full article

Arctic-specific limitations, including a limited number of visible satellites with unfavorable distribution, and the fact that during Arctic navigation, Global Navigation Satellite System (GNSS) signals suffer from significant multipath interference caused by sea ice, icebergs, ship superstructures, and low-elevation satellite signals reflected off the sea surface, have rendered conventional positioning solutions inadequate for maritime navigation safety requirements. To address these challenges, this paper implements a vector tracking loop (VTL) architecture incorporating forward–backward Kalman filtering to improve the estimation accuracy of carrier and code phase errors while proposing a scalar sequential integrity monitoring algorithm that enables identification and exclusion of faulty satellite signals to further enhance position estimation accuracy. The faulty satellite signals refer to satellite signals containing significant deviations that cannot be corrected by conventional models. The experiment uses a navigation scheme with commercial receivers as a reference. To verify the effectiveness of the proposed method at different latitudes, it was tested with real-world data from the Arctic; two sets of tests were conducted at latitudes between 70 and 80° and above 80°. The results show that the optimized navigation method improved positioning accuracy by 65.9% and 56.8% compared with existing methods in the two test groups, respectively, effectively enhancing positioning accuracy in the Arctic environment. Full article

This paper examines precise timestamping of LoRaWAN messages (particularly beacons) to enable wide-area synchronization for end devices without GNSS. The need for accuracy demands hardware-level timestamping architectures, possibly using time-domain cross-correlation (matched filtering) against internally generated chirp references. Focusing on Time-of-Arrival (TOA) estimation from raw IQ samples, the authors analyze effects of non-idealities—additive white Gaussian noise (AWGN), Carrier Frequency Offset (CFO), Sampling Phase and Frequency Offset (SPO and SFO, respectively), and radio parameters such as spreading factor (SF) and sampling rate of the baseband signals. A MATLAB (R2020) simulation mimics preamble detection and Start-of-Frame Delimiter (SFD) timestamping while sweeping SF (7, 9, 12), sampling rates (0.25–10 MSa/s), SNR (−20 to +20 dB), and CFO/SFO offsets (−10–10 ppm frequency deviation). Errors are evaluated in terms of mean and dispersion, the latter represented by the P95–P5 range metric. Results show that oversampling not only improves temporal resolution, but sub-microsecond error dispersion can be achieved with high sampling rates in favorable SNR and SF cases. Indeed, SPO and SNR greatly contribute to error dispersion. On the other hand, higher SF values increase correlation robustness at the cost of longer chirps, making SFO a dominant error source; ±10 ppm SFO can induce roughly ±3 μs SFD bias for SF12. CFO largely cancels after up-/down-chirp averaging. As a concluding remark, matched-filter hardware timestamping can ensure sub-μs errors thanks to oversampling but requires SFO compensation for accurate real-world synchronization in practice. Full article

This paper proposes a cooperative localization method based on time-division processing of interferometric measurements, in which the receiver updates the signals from multiple UAVs in separate time slots, thereby reducing spectrum usage and baseband hardware overhead. A Kalman-enhanced tracking loop is designed to achieve high-precision carrier-phase and Doppler estimation under low-SNR conditions. For angle estimation, a time-division update strategy is employed such that the receiver performs full carrier tracking for only one UAV in each time slot, while the carrier phases of the remaining UAVs are extrapolated from the Doppler states estimated in the previous epoch. This avoids the hardware complexity associated with maintaining multiple parallel tracking loops. By fusing the estimated azimuth, elevation, and pseudorange measurements with the master UAV’s high-precision GNSS observations, a factor-graph-based sliding-window cooperative localization algorithm is constructed. Simulation results show that the proposed method improves the RMSE of carrier-phase and Doppler estimation by nearly an order of magnitude compared with the traditional FLL-assisted PLL. The system maintains angle estimation accuracy better than 0.01° within a four-node configuration and achieves centimeter-level ranging accuracy when SNR ≥ 0 dB. In a cooperative flight scenario with one master and three follower UAVs, the method consistently delivers sub-decimeter 3D localization accuracy. Full article

Accurate and robust positioning is a critical enabler for Unmanned Aerial Vehicle (UAV) applications, ranging from mapping and inspection to emerging Urban Air Mobility (UAM). While Global Navigation Satellite Systems (GNSS) remain the backbone of absolute positioning, their performance is severely constrained by UAV platform characteristics and complex low-altitude environments. This paper presents a system-level review of GNSS-based UAV positioning. Instead of treating GNSS in isolation, we first link mission requirements and platform constraints, such as aggressive dynamics and Size, Weight, and Power (SWaP) limitations, to specific positioning challenges. We then critically evaluate the spectrum of GNSS techniques, from standalone and Satellite-Based Augmentation System (SBAS) modes to high-precision carrier-phase methods including Real-Time Kinematic (RTK), Post-Processed Kinematic (PPK), Precise Point Positioning (PPP), and PPP-RTK. Furthermore, we discuss multi-sensor fusion with inertial, visual, and Light Detection and Ranging (LiDAR) sensors to mitigate vulnerabilities in urban canyons and GNSS-denied conditions. Finally, we outline key challenges and future directions, highlighting integrity-aware architectures, Artificial Intelligence (AI)-enhanced signal processing, and multi-layer Positioning, Navigation, and Timing (PNT) concepts. The review provides a structured framework and system-level insights to guide resilient navigation for UAV operations in low-altitude airspace. Full article

Global Navigation Satellite System (GNSS) signal acquisition in high-dynamic environments faces significant challenges due to large Doppler frequency offsets and stringent computational constraints. This paper proposes a frequency-domain compressed acquisition algorithm that reformulates the conventional two-dimensional code-phase/Doppler search as a set of independent one-dimensional sparse recovery problems. Doppler uncertainty is modeled as sparsity in a discretized frequency dictionary, and a low-coherence measurement matrix is designed offline via projected gradient descent with a two-stage annealing strategy. The resulting matrix significantly reduces maximum coherence and supports reliable sparse recovery from a small number of compressed measurements. During online operation, the receiver forms compressed observations for all code phases through efficient matrix operations and recovers sparse Doppler spectra using lightweight orthogonal matching pursuit. Simulation results show that the proposed method achieves a several-fold reduction in computational cost compared with classical parallel code-phase search while maintaining high detection probability at low carrier-to-noise density ratios and under large Doppler offsets, providing an effective solution for resource-constrained GNSS receivers in high-dynamic scenarios. Full article