Due to the inconsistent datum systems between the Global Navigation Satellite System (GNSS) and total station measurement technologies, the processing results of mixed network data combining GNSS baseline data and terrestrial total station observations are inevitably affected by the Deflection of the Vertical (DOV). To reduce the adverse impact of DOV on the accuracy of three-dimensional combined adjustment results, this paper quantitatively evaluates the DOV calculation accuracy of five Earth gravity field models based on the measured DOV data from the GSVS2017 (Geoid Slope Validation Survey) project. Meanwhile, through comprehensive comparative analysis of two existing DOV correction strategies, this paper proposes another method that adopts DOV values calculated by gravity field models as prior constraints to participate in combined adjustment computation. Finally, comparative experiments are designed using measured mixed control network data to verify the effectiveness of different DOV correction strategies in improving the accuracy of combined adjustment results. The main conclusions are drawn as follows: (1) High-degree global Earth gravity field models present high consistency in DOV calculation accuracy, with the Root Mean Square (RMS) better than 2 arcseconds; (2) The weighting method based on Variance Component Estimation (VCE) can effectively improve the internal fitting accuracy of adjustment results; (3) All three DOV correction strategies can enhance the rigor of the adjustment model and optimize the overall adjustment accuracy. Considering both internal and external coincidence accuracy, the scheme that takes DOV components as unknown parameters and incorporates them into the adjustment model achieves the optimal performance.

This paper proposes a bidirectional time-frequency synchronization system based on optically carried satellite navigation signals for point-to-point and point-to-multipoint clock synchronization among distributed coherent receiving nodes on the ground. The system consists of a self-developed modem, an electrical amplifier (EA), a directly modulated laser (DML), an optical fiber, and a photodetector (PD), with transmission between two nodes conducted via a single optical fiber link. By leveraging the spread spectrum gain of satellite navigation signal waveform, the modem transmission power is reduced to as low as -65 dBm. High-precision time-frequency synchronization is achieved by using pseudo-random noise (PRN) code phase to assist carrier phase, enabling the calculation and synchronization of time differences between any two nodes in the distributed coherent reception network. Based on the target time difference estimation, we investigate and compare the closed-loop control performance of PID, second-order phase-locked loop (PLL), and third-order PLL algorithms. Among these, the PID algorithm features independent parameters, directly compensates the phase error with rapid response, and its derivative term mitigates overshoot. Simulation results indicate the PID algorithm exhibits the fastest convergence speed and the smallest oscillation amplitude after stabilization. Consequently, the PID control algorithm combined with a low-pass filter (LPF) algorithm is ultimately adopted, and a digital-to-analog converter (DAC) is used to tune the secondary node's crystal oscillator frequency to achieve point-to-point time-frequency synchronization. Experiments demonstrated that under distributed node clock diversity, the system achieves the best time synchronization stability of 1.89 ps, with frequency stability reaching ≤3.00 × 10-12 at 1 s and ≤3.04 × 10-15 at 103 s. Both theoretical analysis and experimental results validate the correctness and effectiveness of the proposed method.

A software-based path-delay estimation method using single-difference (SD) observations is proposed for enhanced attitude determination in multi-antenna GNSS-over-fiber systems without dedicated delay-monitoring hardware. GNSS signals acquired by multiple remote antennas are transmitted to a central node through a wavelength-division-multiplexed fiber link and measured by an array of GNSS receivers sharing a common local oscillator. This architecture enables phase-coherent measurements of the satellite-common inter-channel path delays. By exploiting their slow temporal variation, the path delays are estimated and smoothed in software, thereby enabling lower-noise SD processing. The method is integrated with an extended long–short ambiguity-resolution algorithm that, from what we believe to be, first obtains a reliable double-difference (DD) initialization and then refines the virtual short-baseline estimate using the filtered path delay and all available SD observations. In the experiment, the ambiguities were successfully resolved over all 1353 valid epochs. Compared with conventional DD processing, the all-antenna SD solution reduced the standard deviations of the East, North, and Up components by 52.73%, 97.34%, and 34.22%, respectively. Using the receiver-reported real-time kinematic (RTK) baselines as the reference, the three-dimensional RMSE decreased from 6.896 to 3.199 mm, corresponding to a reduction of 53.61%. These results demonstrate improvements in both baseline-estimation precision and reference-relative accuracy without dedicated path-delay monitoring hardware.

Objective Accurate and stable time synchronization is a fundamental requirement for a wide range of advanced applications, including precision instrumentation, large-scale industrial automation, fault localization in power systems, and intelligent manufacturing. These applications impose stringent requirements on time transfer performance, particularly in terms of low latency, high stability, and robustness against environmental disturbances. Conventional global navigation satellite system (GNSS)-based timing methods benefit from global coverage and mature infrastructure, but their achievable synchronization accuracy is inherently limited by ionospheric delays, satellite clock errors, and multipath effects. In contrast, fiber-based time dissemination provides excellent short-term stability and low phase noise, however, it is still affected by chromatic dispersion, bidirectional link asymmetry, and environmental perturbations such as temperature-induced fiber length fluctuations. To address the limitations of individual timing approaches and to exploit their complementary advantages, this work aims to develop a hybrid time-frequency transfer scheme that integrates the structural robustness of satellite navigation signals with the high stability of optical fiber links. The objective of this paper is to propose, implement, and experimentally demonstrate a microwave-photonics-assisted time synchronization system based on self-generating satellite navigation signal waveforms transmitted over optical fiber, achieving high-precision two-way time and frequency synchronization with excellent engineering feasibility. Methods In the proposed scheme, an FPGA-based signal generation module is designed to generate global positioning system (GPS) L1 and BeiDou B1I baseband signals in real time. Unlike conventional timing methods that rely on externally received satellite signals, the proposed system adopts a self-generating navigation signal architecture. In this architecture, the local reference time is directly embedded into the navigation waveform by precisely aligning the spreading code chip boundaries, using navigation data structure, and using frame timing. This approach ensures that the transmitted signal intrinsically carries accurate timing information, eliminating dependence on external satellite clocks and mitigating associated propagation uncertainties. The generated baseband signals are upconverted to intermediate-frequency and radio-frequency signals, and then electro-optically modulated onto an optical carrier using a microwave photonic link. Then the modulated optical signal is transmitted bidirectionally over a 10 km single-mode fiber, enabling two-way time and frequency transfer. Bidirectional transmission effectively compensates for asymmetry in the optical path and mitigates environmental perturbations such as mechanical stress along the fiber. At the receiving end, an FPGA-based real-time navigation receiver performs signal acquisition, carrier and code tracking, de-spreading, and measurement. Both pseudorange and carrier phase observables are extracted in real time. A hierarchical synchronization strategy is employed: coarse synchronization is established using the recovered transmission and reception timestamps to form a clock offset feedback loop, while fine synchronization is realized using high-resolution pseudorange and carrier phase measurements. The closed-loop interaction between local and remote nodes enables two-way time and frequency synchronization with high precision, effectively suppressing the adverse effects of fiber link asymmetry, chromatic dispersion, and environmental perturbations. Results and Discussions Experimental evaluations were conducted after completing system-level simulations and constructing the test link. Carrier phase measurements were used as the primary observable to assess timing precision and stability. The GPS L1 carrier phase difference results show a standard deviation of 0.00199 cycle, corresponding to a time transfer uncertainty of 1.27 ps at 1575.42 MHz, with a peak-to-peak time synchronization variation below 7.62 ps. For BeiDou signals, the B1I-D1 and B1I-D2 carrier phase difference standard deviations are 0.0016 cycle and 0.0015 cycle, corresponding to time transfer uncertainties of 1.03 ps and 0.96 ps at 1561.098 MHz, respectively. The peak-to-peak synchronization variations are below 6.04 ps and 5.12 ps, respectively. These results indicate that both GPS and BeiDou self-generating navigation signals can provide extremely precise time synchronization when transmitted over a microwave-photonics-assisted optical fiber link. A comparison with representative existing schemes demonstrates that the proposed approach significantly improves time synchronization performance. The optical-carrier navigation waveform scheme outperforms previously reported methods in terms of peak-to-peak timing fluctuations, demonstrating the advantage of embedding time information directly into the transmitted signal while leveraging bidirectional optical fiber transmission. Frequency transfer performance was also evaluated. The system-added frequency instability reaches 3.35 & times;10(-12) s(-1 )and 2.69 & times; 10(-15)/1000 s for GPS L1. For BeiDou B1I-D1, the corresponding values are 3.15 & times;10-12 s-1 and 2.51 & times;10-15/1000 s, while BeiDou B1I-D2 exhibits 2.79 & times;10-(12) s(-1 )and 1.71 & times; 10(-15)/1000 s, respectively, demonstrating excellent long-term frequency stability for all signals. Conclusions The combined time and frequency evaluation shows that the system is capable of maintaining high-precision synchronization over both short-term and long-term intervals, confirming the robustness and reliability of the proposed scheme in practical scenarios. These results demonstrate that the proposed microwave-photonics-assisted hybrid time-frequency transfer scheme based on self-generating satellite navigation signal waveforms over optical fiber achieves high-precision synchronization and strong robustness. By embedding local time information into GPS L1 and BeiDou B1I signals and utilizing bidirectional fiber transmission, the system provides accurate two-way time and frequency transfer with excellent short-and long-term stability, highlighting its engineering feasibility for high-precision time-frequency applications. In the future, this approach can provide a stable time-frequency reference for synchronization between 5G/6G base stations, enhancing network coordination and base station synchronization accuracy. Meanwhile, along high-speed railway lines, it is expected to support distributed base stations and trackside equipment with high-stability time synchronization, thereby improving train positioning accuracy and operational scheduling efficiency.

Accurate attitude measurement is crucial for small platforms such as unmanned aerial vehicles and portable devices. However, traditional high-precision global navigation satellite system (GNSS) heading determination equipment often fails to meet the strict volume and cost constraints due to their long baselines and high costs. To address this issue, this paper proposes a low-cost and compact GNSS heading determination method based on ultra-short baselines. This method relies solely on carrier phase observations and fully utilizes the geometric characteristics of ultra-short baselines. It directly solves the integer cycle ambiguity using the Rounding method. Based on the theory of hypothesis testing, an analytical relationship model between baseline length and observation noise and the fixed success rate of integer cycle ambiguity is quantitatively established. Experiments show that while significantly reducing the size and hardware cost of the equipment, accurate headings can still be calculated, effectively addressing the application limitations of single-antenna heading determination in static/low-speed scenarios. This research provides an engineering-able system solution for cost and volume-sensitive applications.

This deep learning model architecture research proposes a multi-channel Deep Learning-based Automatic Modulation Recognition model (DL-AMR), which integrates Convolutional Neural Networks (CNNs) and Gated Recurrent Units (GRUs) to extract features from both the time and frequency domains. The model leverages the strengths of CNNs for local feature extraction, RNNs for temporal correlation modeling, and Transformer encoders for global context representation. The proposed model, using a unified architecture, outperforms existing State-Of-The-Art (SOTA) methods on the RML2016.10a, RML2016.10b, and HisarMod2019.1 datasets, achieving an average accuracy improvement of up to 0:79% under high Signal-to-Noise Ratio (SNR) conditions. On the RML2018.01a dataset, the model’s average recognition accuracy is only 0:14% lower than that of the best-performing existing model. Experimental results demonstrate that the proposed model exhibits enhanced generalizability compared to other models when faced with complex and dynamic communication environments. In addition, to address the challenge of mixed-signal recognition, this study introduces array antenna beamforming at the receiver side, employing spatial filtering techniques to separate composite signals with identical frequencies but different directions. Experimental results show that the proposed method consistently achieves over 90% recognition accuracy in two distinct communication scenarios. Moreover, when recognizing signals processed by perturbed beamforming algorithms, the proposed model demonstrates superior robustness to signal distortion and loss. Compared to SOTA models, it achieves an average reduction of 34:32% and a maximum reduction of 45:99% in recognition accuracy degradation.

While the Cooley-Tukey (CT) algorithm serves as the cornerstone of Fast Fourier Transform (FFT) implementations, existing optimizations primarily target CPU and GPU architectures, leaving significant performance gaps for Neural Processing Units (NPUs). Ascend NPUs excel in AI-centric matrix computations but face challenges in FFT performance due to memory bandwidth constraints and the hierarchy of the Unified Buffer (UB). This paper introduces DRFFT, a high-performance framework tailored for the Ascend architecture, featuring proposed dynamic-radix and double-radix mechanisms. The dynamic-radix algorithm optimizes factor decomposition and auxiliary data generation (PLAN) towards the Cube core size of Ascend NPU, while the double-radix strategy mitigates I/O bottlenecks by hierarchically partitioning computations into GM-radix and UB-radix stages according to the UB size and the memory layout of the sequences. While traditional FFT theory prioritizes minimizing arithmetic operations, our implementation prioritizes architectural alignment with the 16 & times; 16 Cube Units, demonstrating that computational density outweighs operation count in NPUbased environments. Both the granularity (size) and the hierarchical sequence (order) of the decomposed radices in the Cooley-Tukey algorithm are critical constraints when optimizing for the hardware-limited memory and compute primitives of Ascend NPUs to achieve peak performance. By maximizing on-chip UB utilization, this approach restricts Global Memory (GM) interactions to essential frequency minimums, significantly accelerating long-sequence processing. Experimental evaluations demonstrate that DRFFT achieves competitive performance against GPU (up to 1.5 & times; vs. cuFFT) and TPU (up to 3 & times;) libraries under the tested workloads, while validating fundamental acceleration over legacy CPU baselines. Notably, DRFFT achieves about 5 & times; speedup over existing Ascend-based implementations (e.g., MV-2FFT) and maintains high efficiency on the evaluated composite non-power-of-2 sequences with only 11% performance degradation, compared to the 20% similar to 45% typical of other libraries. These results establish DRFFT as an efficient solution for NPU-based scientific computing under the targeted workloads.

One of the key technologies that enables the wideband radio frequency signal sensing in the frequency range is the microwave photonics system, which has low-loss transmission and electromagnetic immunity. The other is compressive sensing, which reduces the sampling rate to the level of the spectrum sparsity and matches the speed of fine digital signal processing (DSP). The photonics-assisted spatial-frequency joint compressive sensing system for sparse multiband radio frequency signals with dual-electrode Mach-Zehnder modulators (DEMZMs) is proposed and verified. First, a multi-antenna array is used for sensing the radio frequency signals in both the frequency and spatial domains. The reference antenna in the array is connected to m random demodulator (RD) channels with m different pseudo-random binary sequence (PRBS), which forms a typical modulated wideband converter (MWC) architecture. Second, the rest of the antenna elements are connected to a single RD channel with the same PRBS, which simplifies the system architecture and reduces hardware complexity. Each RD channel is based on a single DEMZM, which also helps simplify the system. Third, the subsampled digital signals are used to reconstruct the target waveform and extract spatial direction-of-arrival (DOA) information with the simultaneous orthogonal matching pursuit (SOMP) algorithm. The simulation results show that sparse multiband radio frequency signals' waveforms for both communications and radar applications within 5 GHz are successfully reconstructed, from which the frequency information is extracted. The spatial DOA is also extracted within 1∘ with the time delay sensing capability of the proposed architecture. The bit error rate (BER) of reconstructed quaternary phase-shift keying (QPSK) baseband symbols achieved 10-5 under 0 dB signal-to-noise ratio (SNR) with 35 antenna elements.

With advancements in reusable liquid rocket engine technology to meet the diverse demands of space missions, engine systems have become increasingly complex. In most cases, these engines rely on stable open-loop control and closed-loop regulation systems. However, due to the high degree of coupling and nonlinear dynamics within the system, most transient adjustments still depend on open-loop control. Open-loop control often fails to provide the optimal control strategy when encountering external disturbances. To address this issue, we introduce the intrinsically motivated twin delayed deep deterministic (TD3) algorithm, specifically designed for the startup process of LOX/Kerosene high-pressure staged combustion engine. This approach leverages intrinsic motivation to enable the algorithm to adapt to the abrupt parameter changes during the start-up process. A series of comprehensive experiments were conducted to verify the effectiveness of our method. The experimental results demonstrate that our method outperforms both the PID method and previous researchers' reinforcement learning methods based on the TD3 algorithm and DDPG, achieving a faster and more stable start-up process and significantly enhancing engine performance.

Inspired by the unconstrained PPE (UPPE) formulation [Liu, Liu, Pego 2007 Comm. Pure Appl. Math., 60 pp. 1443], we previously proposed the GePUP formulation [Zhang 2016 J. Sci. Comput., 67 pp. 1134] for numerically solving incompressible Navier-Stokes equations (INSE) on no-slip domains. In this paper, we propose GePUP-E and GePUP-ES, variants of GePUP that feature (a) electric boundary conditions with no explicit enforcement of the no-penetration condition, (b) equivalence to the no-slip INSE, (c) exponential decay of the divergence of an initially non-solenoidal velocity, and (d) monotonic decrease of the kinetic energy. Different from UPPE, the GePUP-E and GePUP-ES formulations are of strong forms and are designed for finite volume/difference methods under the framework of method of lines. Furthermore, we develop semi-discrete algorithms that preserve (c) and (d) and fully discrete algorithms that are fourth-order accurate for velocity both in time and in space. These algorithms employ algebraically stable time integrators in a black-box manner and only consist of solving a sequence of linear equations in each time step. Results of numerical tests confirm our analysis.

Buck-boost output, low leakage current, and electrolytic capacitor-less are three important requirements for single-phase nonisolated ac-dc converters. Existing topologies can only meet some of these requirements and involve a large number of components. Through topology derivation, this article proposes a single-phase common-ground ac-dc converter that meets all three requirements simultaneously, with three switches, two diodes, two inductors, and two film capacitors. The proposed topology features a common-ground structure, short-circuiting the parasitic capacitance between the grid and the load, thereby suppressing the leakage current. To mitigate the impact of pulsating power on grid current and output voltage, a harmonic suppression algorithm (HSA) is introduced, controlling harmonics in the dq frame at N times the fundamental frequency. Finally, a 500-W experimental prototype was built, with an output capacitance of 20 mu F, an rms leakage current of only 2.15 mA, and an efficiency of 96.54%. With the HSA, the total harmonic distortion of the grid current was reduced from 33.6% to 3.1%, and the output voltage ripple was reduced from 30 to 3.6 V.

Transparent objects play a vital role in modern industries and find widespread applications across various engineering scenarios. However, capturing accurate depth maps of transparent objects remains challenging due to their reflective and refractive properties, which pose difficulties for most commercial-grade optical sensors. In this paper, we propose a novel depth estimation method called DFNet-Trans, designed to estimate depth from a noisy RGB-D image input. Initially, a multiscale feature fusion module (FFM) is incorporated into the existing depth estimation network to generate the initial depth map. Subsequently, we enhance the network by adding a confidence branch and a mask branch on the same encoder, enabling improved distortion correction and real scene restoration in the depth estimation. Based on the framework representation, missing depth can be completed. Comprehensive experiments demonstrate that the proposed approach significantly outperforms the current state-of-the-art methods on the recently popular large-scale real dataset TransCG. the proposed approach achieves a remarkable 27.7% reduction in RMSE and a notable 34.6% reduction in REL. The generalization experiment shows that the proposed approach outperforms existing methods when generalized to an unknown real dataset.

Time series data widely exist in public services, industrial environments, and military applications. Traditionally, the transmission of a huge volume of data for analytic tasks poses challenges, particularly in mobile environments with limited computing and communication resources. Semantic communication emerges as a solution for intelligently extracting various features from source data and efficiently transmitting task-related information to receivers, thereby reducing bandwidth consumption significantly. In this paper, we introduce a novel federated semantic communication system tailored for forecasting-oriented time series transmission tasks. The correlation of source data collected from terminal devices is mined and the corresponding semantic information is transmitted to an edge server for collaborative inference. To optimize the semantic analysis process, we devise a deep decomposition block at the transmitter side, decomposing time series into trend and multiple period components. This reduces noise interference from wireless channels, enhancing the overall transmission quality. For effective training and collaborative inference, we propose a Federated Mixture of period Routers (FedMoR) architecture. Within each channel encoder, period routers are divided into private and public ones. Private routers extract specialized features from individually collected data, mitigating accuracy degradation. Public routers share knowledge across all transmitters, enhancing temporal analysis robustness. Simulation results demonstrate that the proposed system outperforms two traditional technique-based and two semantic communication-based baselines under three common channels. The system achieves low mean square errors on five widely-used real-world time series forecasting datasets, particularly in the low signal-to-noise ratio regime.

In the context of promoting intelligence and informatization, multimodal perception surveillance systems have become a promising solution for comprehensive environmental monitoring across different dimensions. However, these systems face key challenges in processing and transmitting heterogeneous data from various perceptrons, which requires effective resource allocation strategies. This paper addresses this challenge by integrating non-orthogonal multiple access (NOMA) into the communication framework of multimodal perception surveillance systems to improve the efficiency of multimodal data transmission. Specifically, this paper proposes a new search algorithm that combines binary space compression with cross entropy (CE) algorithm to optimize the efficient allocation of limited spectrum resources and the successive interference cancellation (SIC) ordering of the perceptrons. The proposed ordering compression-based CE (OCCE) algorithm treats the binary encoding of SIC ordering as a stochastic learning process, which significantly reduces computational complexity while ensuring the accuracy of the optimal solution. Meanwhile, we also obtained an iterative analytical formula for the optimal transmit-powers of the perceptrons through mathematical analysis. The numerical results verify the effectiveness of the proposed algorithm in optimizing the resource allocation of the multimodal perception surveillance system, as well as its superior performance in terms of accuracy and computational efficiency.

A photonics-assisted compressive sensing (CS) array system based on uniform linear array (ULA) for wideband sparse radio frequency (RF) signals acquisition and direction of arrival (DOA) estimation is proposed. Each branch of the system consists of two cascaded Mach-Zehnder modulators (MZMs), an integrator, and a low-rate analog-to-digital converter (ADC). The modulated pseudo-random binary sequence (PRBS) is the same across each coherent branch, so that the simultaneous orthogonal matching pursuit (SOMP) algorithm and the orthogonal matching pursuit (OMP) algorithms are sued to estimate the frequency and DOA. The introduction of multiple coherent branches not only enable the estimation of DOA but also improve the accuracy of the frequency recovery. The frequency estimation accuracy of multi-tone signals reaches 0.01 GHz, and the angle estimation accuracy reaches 1° at the signal noise ratio (SNR) of 10 dB in the simulations and experiments, which demonstrate the feasibility of the proposed method in joint frequency and DOA estimation.

A buck-boost common ground bridgeless power factor correction rectifier (PFC) which can achieve the function of power decoupling has been proposed. The topology realizes the common ground connection between the power grid and the load, so the common-mode current can be completely eliminated. As well as, the converter also has the function of boosting and reducing voltage, which can achieve a wide output voltage range. It is worth mentioning that this converter can achieve the power decoupling function without any electrolytic capacitor or active pulsating-power-buffering. Then, detailed analysis was conducted on the operation mode of the PFC. Finally, the feasibility of this topology was demonstrated through steady-state and dynamic simulation results.

In existing 6D pose estimation methods, there is often a high requirement for the precision of 3D models or UV textures of objects. To address these issues, a new 6D pose estimation algorithm is proposed based on improvements made to the latest object detection algorithm, Yolov7. By extending the prediction networks and modifying the loss function, as well as performing keypoint interpolation, the new 6D pose estimation algorithm is designed. Experimental results demonstrate that the proposed method achieves an ADD (Average Distance of Differences) score of 87.5% on the Linemod dataset, showing a 25% improvement compared to the keypoint-based BB8 method in terms of the ADD score. Specifically, when estimating the pose of transparent objects, the proposed method outperforms the PVNet method by approximately 10%. These results validate the excellent detection performance of the proposed method.

This paper proposes and experimentally validates a large-scale multi-antenna and one-receiver global navigation satellite system (GNSS)-over-fiber differential positioning system using silicon on-chip optical routing. The radio-over-fiber (RoF) distributed antenna architecture is utilized to facilitate remote multipoint GNSS signal acquisition, and RoF transmission links featuring low loss, large bandwidth, and immunity to electromagnetic interference are reaped to achieve the centralized reception of remotely collected GNSS signals at the local end. At this end, a complementary metal-oxide-semiconductor (CMOS)-process-compatible high-speed silicon optical switch chip is fabricated for the periodic switching and differential calculation of GNSS signals over fiber obtained at different monitoring points. Then, a time-division multiplexing-based multi-antenna and one-receiver GNSS positioning system using on-chip optical routing is built. In the experiments, a self-developed 1 X 8 thermo-optic silicon optical switch chip based on a Mach-Zehnder interferometer is employed to build an experimental multi-antenna GNSS positioning system with five remote monitoring points. The RoF transmission distance of the GNSS signals is 10 km. According to the experimental results, the real-time response time of the optical switch chip module is less than 200 mu s. Stable and high-accuracy positioning at five remote monitoring points (10 km away) is achieved without the aid of additional optical amplification. The obtained positioning accuracy in the east (E), north (N), and up (U) directions is all at the millimeter level.

The publisher's note contains a correction to [Opt. Express 29 32333 (2021)10.1364/OE.438439]. The article was corrected on 17 June 2022.

Ambiguity resolution (AR) is a fundamental problem for carrier phase based signal processing tasks to leverage the superhigh precision of wavelength-level range and velocity measurements. With the elaborately designed waveform and coordinated running of the space-based satellite system, the antenna-array observations of global navigation satellite system (GNSS) signals feature a phase measurement model. In this article, the AR of baseline estimation with GNSS carrier phase measurements only in the AR step is examined from an array signal processing perspective. The array-geometry-aided ambiguity resolution approach, coined as AGAR, is proposed for growing the baseline estimation provided by a search-free algorithm to the accuracy of the aperture level in an effective way. First, the single-epoch and search-free $2q$-order AR method is further investigated in size and statistical independence. Second, the conventional phase beampattern is defined to characterize the similarity of carrier phase measurement vector of signals from different directions. Third, a simple and effective ambiguity-lookup-table approach after the conventional phase beampattern is proposed which fulfills the goal of baseline growing to the array aperture level. Fourth, the identifiability, success rate, Cramér–Rao bound (CRB), and computation complexity are analyzed. As a result, the phase-based and complex-based processings are distinguished, resulting in an alternative analytical prediction of outlier probability that well approximates AR’s success rate. The relationship between the success rate of AR and CRB is also clarified. Numerical simulations are carried out to verify the proposed analytical prediction and AR approach. The AR success rate increased from 10% to 93% at a relatively large measurement error of 0.05 cycle.