Multi-frequency Signal Research Articles

Towards Real-Time Integrated Water Vapor Estimates with Triple-Frequency Galileo Observations and CNES Products

Integrated water vapor (IWV) is a crucial parameter for tropospheric sounding and weather prediction applications. IWV is essentially calculated using observations from global navigation satellite systems (GNSS). Presently, the Galileo satellite system is further developed, including more visible satellites that transmit multi-frequency signals. This study aims to evaluate the accuracy of real-time IWV estimated from a triple-frequency Galileo-only precise point positioning (PPP) processing model utilizing E1, E5a, E5b, and E5 observations, which is not addressed by the previous studies. For this purpose, Galileo datasets from 10 global reference stations spanning various 4-week periods in the winter, spring, summer, and fall seasons are acquired. To process the acquired datasets, dual- and triple-frequency ionosphere-free PPP solutions are used, including E1E5a PPP, E1E5aE5b PPP, and E1E5E5b PPP solutions. The publicly available real-time products from the Centre National d’Etudes Spatiales (CNES) are utilized. The real-time IWV values are computed and then validated with the European Centre for Medium-Range Weather Forecasting (ECMWF) reanalysis products (ERA5) counterparts. The findings demonstrate that the root mean square error (RMSE) of the estimated IWV is less than 3.15 kg/m2 with respect to the ECMWF ERA5 counterparts. Furthermore, the E1E5aE5b PPP and E1E5E5b PPP models enhance the IWV’s accuracy by about 11% and 16%, respectively, compared with the E1E5a PPP model.

Multi-frequency weak signal detection based on Liu-like chaotic synchronization system and its hardware circuit implementation

Considering the shortcomings of traditional chaotic systems in weak signal detection methods, such as the high threshold sensitivity requirement and the narrow detection frequency domain. This study proposes a novel three-dimensional chaotic synchronization system, and the dynamical of the system are exhaustively characterized using equilibrium points, phase diagrams, Lyapunov exponential spectra, and bifurcation diagrams. This method involves weak signal detection by means of chaotic synchronization control. Synchronization of a chaotic system using a backstepping synchronization method is used to detect weak signals by analyzing the synchronization error after the introduction of weak signals in a strong noise background. The chaotic system is implemented by hardware circuits, and the simulation of chaotic synchronization control and detection of weak signals from the perspective of circuits is carried out by circuit simulation software. Additionally, the frequency range within which the system is capable of weak signal detection is tested through extensive simulation experiments. Finally, multi-frequency signals detection experiments are performed. The experimental results demonstrate that the system can accurately detect the frequency of weak signals address the limitations of narrow-band detection and multi-frequency signal detection is possible. Meanwhile, the circuit structure proposed in this paper is simple and has some value for engineering applications.

Diffraction efficiency in acousto-optical interaction with short radio pulses

Development of acousto-optic modulators with high diffraction efficiency, which is achieved by using multi-frequency acoustic signals, is of great interest. In this regard, it seems interesting to study the possibility of implementing highly efficient diffraction for wideband signals in the form of radio pulses with short duration. The goal of presented article is to develop a mathematical model based on a quantum description of the interaction between a photon and a phonon, simulate various operating modes of an acousto-optical modulator and compare theoretical results with experimental ones. A comparison between experimental and theoretical results was made, demonstrating the possibility of obtaining high diffraction efficiency (more than 90%) for wideband signals. The proposed method makes it possible to determine the conditions under which maximum diffraction efficiency is observed, and it also seems possible to determine the parameters of the pulse sequence.

Особенности структурного синтеза алгоритмов обработки радиолокационной информации при многочастотном наблюдении

Setting and solving the problem of structural synthesis of the algorithm for detecting and measuring parameters of mobile objects against the background of correlated interference and noise in multi-frequency radar surveillance systems based on multibeam digital antenna arrays are considered. The processing algorithm is synthesized under the assumption of Gaussian observation statistics with separate spatial and temporal characteristics of signals and interference. As part of the study, a phenomenological model of the radar situation was developed, adequate to the formation of observations in multi-frequency space-time signal processing systems against the background of correlated interference and noise. On its basis, a structure of an optimal, in terms of Bayesian quality criteria, algorithm for detecting a multi-part signal at the outputs of multipath digital antenna arrays is obtained. On the basis of the adaptive Bayesian approach, ways of solving the problem of detecting and measuring parameters of mobile objects in conditions of multi-frequency observations with parametric a priori uncertainty about interference characteristics are determined. Recommendations on selection of adaptive algorithms for radar information processing in case of non-stationary observations are given. The results of structural synthesis make it possible to present processing in the form of a multichannel system in space, time and radial speed. Sufficient statistics on the set of radiation frequencies are accumulated. This view opens up a wide range of possibilities for using parallel computing systems. It is shown that the obtained algorithms can serve as the basis for detecting the beginning of maneuvering of an observation object at the stage of primary processing of radar information.

Real-time uncombined PPP using BDS-3 PPP-B2b products with different multi-frequency integrations and refined stochastic model

BDS-3 geostationary orbit (GEO) satellites broadcast PPP-B2b real-time precise products to support real-time precise point positioning (RT-PPP) without dependence on the ground network communication. Since all BDS-3 satellites can provide multi-frequency signals, we investigate the effect of different multi-frequency integrations and the refinement of multi-frequency stochastic model for PPP-B2b RT-PPP. Given that the retrieval of PPP-B2b real-time precise corrections relies on the B1C and B2b frequencies, this study first investigates the kinematic uncombined (UC) RT-PPP performance of the B1C/B2b integration with a comparison to the conventional B1I/B3I integration. The results indicate that the convergence time (with a convergence threshold of 20 cm) of the RT-PPP with the B1C/B2b integration is shortened by 16 %, 15 %, and 12 % over the B1I/B3I integration in the east, north, and up directions, respectively. Further, this study compares the kinematic UC RT-PPP performance of the B1C/B2b dual-frequency integration, B1C/B2b/B3I triple-frequency integration, and B1C/B2b/B3I/B1I/B2a five-frequency integration. Compared with the dual-frequency integration, the positioning performance of the triple-frequency integration is slightly improved. By contrast, the performance improvement of the five-frequency integration is more significant, which can reach 6 %, 32 %, and 9 % for the convergence time, and 11 %, 9 %, and 6 % for the positioning accuracy in three directions, respectively. To further enhance the multi-frequency PPP performance, a refined stochastic model for the BDS-3 five-frequency integrated PPP-B2b RT-PPP is proposed by taking the inconsistency of signal quality among multi-frequency signals into account. After applying the refined stochastic model, the convergence time of the five-frequency kinematic RT-PPP is shortened by 10 %, 14 %, and 9 % to 32, 7, and 19 min in east, north, and up directions, respectively. The positioning accuracy (the root mean square of all the positioning errors excluding the first two hours) of the five-frequency RT-PPP with the refined stochastic model can reach the optimal level, which is 9.9, 6.5, and 14.0 cm in three directions, respectively.

Research on the prediction of breakdown voltage of transformer oil based on multi-frequency ultrasound and GWO-RF algorithm

Transformer oil serves as a critical insulating medium within electrical transformers, with breakdown voltage acting as a crucial indicator to assess both the quality of the oil and its insulation characteristics. In this study, 175 groups of transformer oil samples were selected for experimentation. Breakdown voltage was measured, and signals were subsequently collected following the propagation of multi-frequency ultrasonic signals through the oil samples. The study examines the relationship between the amplitude-frequency response, phase-frequency response of multi-frequency ultrasonic acoustic parameters, and breakdown voltage in transformer oil samples. A prediction model for oil sample breakdown voltage was established using the grey wolf optimization algorithm to optimize the random forest algorithm (GWO-RF), with ultrasonic parameters as inputs and transformer oil breakdown voltage as the output. The original 175 datasets were divided into 140 training sets, 20 validation sets, and 15 test sets. The predictive model achieved an average percentage error of 4.04% and a prediction accuracy of 95.96% on the test set, surpassing the performance of the established random forest algorithm (RF) and the sparrow search algorithm optimized random forest algorithm (SSA-RF) for predicting breakdown voltage.

Hybrid vibration isolator based on piezoelectric actuator and metal rubber and its adaptive control method

To achieve vibration isolation across the entire working frequency range, this paper proposes a novel hybrid vibration isolator combining metal rubber and piezoelectric actuators, along with an adaptive active control algorithm. The passive isolation system allows for manual adjustment of stiffness and damping based on the preload, overcoming the issue of fixed stiffness and damping in traditional passive isolation units. For the active isolation system, an improved Filtered-x Normalized Least Mean Squares with adaptive step size active control algorithm is proposed, overcoming the problem of narrow frequency range applicability in traditional active control algorithms. A hybrid model of electromechanical coupling and hysteresis for the piezoelectric actuator is developed for the secondary path in the algorithm. Experimental results confirm that the hybrid isolator possesses vibration isolation capabilities within the 5–500 Hz working frequency range, with vibration suppression at the first and second resonance frequencies improved by 98.9% and 92.2%, respectively, compared to the passive system. Additionally, the hybrid isolator effectively suppresses complex multifrequency signals and demonstrates robustness and adaptability. This research provides advanced technological means to address complex vibration problems, and establishes both theoretical and practical foundations for multi-degree-of-freedom vibration isolation.

High-resolution wide-swath SAR imaging with multifrequency pulse diversity mode in azimuth multichannel system

ABSTRACT High-resolution wide-swath (HRWS) imaging has emerged as a focal point in synthetic aperture radar (SAR) research. However, conventional SAR systems face challenges in achieving both high azimuth resolution and wide swath simultaneously due to the minimum antenna area constraint. In this paper, we propose a HRWS imaging method based on multifrequency pulse diversity (MFPD) and azimuth multichannel (AMC) technique, capable of resolving range and Doppler ambiguities concurrently. In MFPD mode, range ambiguous echoes can be separated by matched filters in the range frequency domain, as multifrequency pulses are transmitted by a single channel in the transmitter. To further enhance the ambiguity resolution ability of the system and address azimuth incoherence, a novel scheme applying the MFPD to AMC system is proposed, categorized into two distinct scenarios. 1) Uniform Sampling: This scenario satisfies the displaced phase centre antenna condition. Under this condition, high range resolution imaging can be achieved through spectrum splicing in range frequency domain, simultaneously resolving Doppler ambiguity. 2) Non-uniform Sampling: In this scenario, the ambiguous echoes are processed by spatial digital beamforming and spectrum splicing in two-dimensional frequency domain. Finally, the HRWS imaging can be obtained by performing the traditional SAR algorithm. Furthermore, the proposed method can synthesize a wideband signal from multifrequency signals, thereby enhancing the feasibility of super-high-resolution imaging. Simulation results demonstrate the effectiveness of the proposed method.

Noise-resistant multi-frequency phase local radionavigation system based radio interference transmitters

Formulation of the problem. The widespread use of electronic warfare has led to significant difficulties in the use of consumer navigation equipment (CNE) of global navigation satellite systems (GNSS). Local radio navigation systems, alternatives to GNSS, are characterized by low accuracy and low noise immunity. At the same time, a spatially distributed system of radio interference transmitters CNE GNSS, using wide-band multi-frequency BPSK signals, can be used to organize a noise-resistant LRNS, in which phase measurements will be used to increase the accuracy of measurements. Purpose. The purpose of this work is to justify the requirements for a local radio navigation system based on spatially distributed radio interference transmitters NAP GNSS, using the noise-resistant method of multi-frequency phase radio navigation. Results. An interference-resistant method of multi-frequency phase radio navigation is presented, and the requirements for a local radio navigation system based on this method are substantiated. For the given typical characteristics of NAP GNSS radio interference transmitters, the value of the frequency detuning of the spectral components of the multi-frequency signal was obtained, at which the best positioning accuracy is achieved. Practical significance. The results obtained can be used to organize a noise-resistant multi-frequency phase local radio navigation system based on NAP GNSS radio interference transmitters.

The damage localization method in the composite panel by multifrequency guided wave signal using parallel network

Fiber-reinforced composite materials find extensive application in the realm of aeronautics; nonetheless, during operational phases, structural integrity may be compromised due to external impacts or extreme environmental conditions. Consequently, the imperative is the necessity of vigilantly monitoring the structural state. The structural health monitoring (SHM) technology based on ultrasonic guided waves can achieve long-distance and wide-ranging damage detection utilizing a minimal number of cost-effective piezoelectric transducers. However, traditional damage identification methods necessitate the analysis of the multi-modal characteristics of guided waves and the deployment of dense sensor arrays. In this paper, we propose a network model that leverages multi-frequency guided-wave signals to achieve spatiotemporal parallelism, incorporating residual blocks and convolutional attention mechanisms (GCRA). This model accurately estimates damage locations with an $R^2$ value of 0.9147. The average error for the six randomly selected damage locations is 0.4275 cm. The results demonstrate that the GCRA facilitates the identification of damaged positions with a high degree of confidence.

Controllable multi-soliton spectral tunneling by airy pulses in photonic crystal fiber

A straightforward method to induce tunable multi-soliton spectral tunneling (SST) using a finite energy Airy pulse in a photonic crystal fiber (PCF) featuring three zero-dispersion wavelengths is proposed numerically in the paper. The study reveals that the distinctive multi-envelope structure of the Airy pulse enables the control of tunneling distances, properties, and soliton numbers through modulation of its attenuation factor and peak intensity. Notably, the SST process involving the Airy pulse generates multiple blue-shifted and red-shifted dispersion waves, along with associated trapping waves, contributing to the formation of an ultra-flat and ultra-wide supercontinuum. Furthermore, the velocity and efficiency of multi-SST can be manipulated to enhance the overall tunability of the phenomenon. The findings underscore the potential application of Airy pulse-driven SST in secure multi-frequency signal transmission and controlled supercontinuum generation, with the tunability of these processes being governed by the specific attenuation factor and peak power settings of the input Airy pulse. This work advances the understanding of multi-SST dynamics in PCFs and provides a theoretical framework for exploiting these dynamics in practical information security and optical spectrum management contexts.

Topological rainbow trapping of shear horizontal waves in a phononic crystal plate with tapered surface

Topological interface states have localized field enhancement characteristics. Integrating them with the concept of rainbow trapping undoubtedly be a more effective method for elastic energy localization and collection. In this paper, the tunable interface state of shear horizontal (SH) waves is realized in a one-dimensional (1D) phononic crystal (PC) plate by modifying the structural parameters of unit cells with tapered surfaces, where the interface state emerges in the overlapping band gaps of two types of unit cells with different Zak phases. Furthermore, we assembled seven types of unit cells with gradient variations, achieving topological rainbow trapping. Meanwhile, the robustness of the rainbow state has been demonstrated, and more separated frequencies are obtained by changing the order of these unit cells. The results of the study demonstrate that the highly localized, compact, and broadband tunable topological rainbow system we designed holds promise for applications in areas such as elastic energy harvesting, filtering, and multi-frequency signal processing.

GNSS Reflectometry-Based Ocean Altimetry: State of the Art and Future Trends

For the past 20 years, Global Navigation Satellite System reflectometry (GNSS-R) technology has successfully shown its potential for remote sensing of the Earth’s surface, including ocean and land surfaces. It is a multistatic radar that uses the GNSS signals reflected from the Earth’s surface to extract land and ocean characteristics. Because of its numerous advantages such as low cost, multiple signal sources, and all-day/weather and high-spatiotemporal-resolution observations, this new technology has attracted the attention of many researchers. One of its most promising applications is GNSS-R ocean altimetry, which can complement existing techniques such as tide gauging and radar satellite altimetry. Since this technology for ocean altimetry was first proposed in 1993, increasing progress has been made including diverse methods for processing reflected signals (such as GNSS interferometric reflectometry, conventional GNSS-R, and interferometric GNSS-R), different instruments (such as an RHCP antenna with one geodetic receiver, a linearly polarized antenna, and a system of simultaneously used RHCP and LHCP antennas with a dedicated receiver), and different platform applications (such as ground-based, air-borne, or space-borne). The development of multi-mode and multi-frequency GNSS, especially for constructing the Chinese BeiDou Global Navigation Satellite System (BDS-3), has enabled more free signals to be used to further promote GNSS-R applications. The GNSS has evolved from its initial use of GPS L1 and L2 signals to include other GNSS bands and multi-GNSS signals. Using more advanced, multi-frequency, and multi-mode signals will bring new opportunities to develop GNSS-R technology. In this paper, studies of GNSS-R altimetry are reviewed from four perspectives: (1) classifications according to different data processing methods, (2) different platforms, (3) development of different receivers, and (4) our work. We overview the current status of GNSS-R altimetry and describe its fundamental principles, experiments, recent applications to ocean altimetry, and future directions.

An improved wide-lane ambiguity resolution method for kinematic smartphone positioning

Abstract The release of GNSS raw data on Android smartphones provides the potential for high-precision smartphone positioning using multi-constellation and multi-frequency signals. However, severe multipath and low observation quality in kinematic environments make double-differenced uncombined ambiguities difficult to resolve reliably. To address this, the paper proposes an improved wide-lane (WL) integer ambiguity resolution (IAR) method that combines integer rounding and the Least-Square AMBiguity Decorrelation Adjustment (LAMBDA) methods. The proposed method achieved fix rates of 57% to 70% in challenging environments, with an average improvement of 7 · 7% in horizontal positioning accuracy compared to the float solution. The traditional partial integer rounding method only improved accuracy by 1 · 1%.

Multi-frequency signal acquisition and phase measurement in space gravitational wave detection.

To enhance the accuracy of phase measurement and to prevent tracking errors, it is crucial to effectively read the multi-frequency signal in space gravitational wave detection. In this paper, a novel signal acquisition method called the multi-frequency acquisition algorithm is proposed and implemented. Different from the traditional single-frequency acquisition, the signal characteristics of amplitude and frequency are both considered to better distinguish different frequency components. A phasemeter integrated with the acquisition method and narrow-bandwidth digital phase-locked loop is constructed for the method test and verification. The results show that the multi-frequency acquisition unit can capture all the frequencies of an input signal in several milliseconds. The precision is better than ±200Hz under a low SNR (signal-to-noise ratio) of 0 dB. The phase noise can reach 2 µrad/Hz1/2 in the frequency range of 0.1-1Hz and satisfy the requirement of the space gravitational wave detection in all frequency ranges.

Binary multi-frequency signal for accurate and rapid electrochemical impedance spectroscopy acquisition in lithium-ion batteries

Electrochemical Impedance Spectroscopy (EIS) plays a crucial role in characterizing the internal electrochemical states of lithium-ion batteries and proves to be effective for estimating battery states. Traditional EIS measurement, however, requires expensive electrochemical workstations with time-consuming signal injection, especially in low-frequency regions, thus limiting its practical applications. Here we show that applying our proposed pulse-like Binary Multi-Frequency Signals (BMFS) as the excitation signal in the EIS measurement, which simultaneously possesses numerous frequency components and maintains high energy at each frequency component, will significantly improve test speed while retaining accuracy. The applicability of the BMFS under various cathode material types, including nickel cobalt manganese (NCM), lithium cobalt oxide (LCO), and lithium iron phosphate (LFP) is demonstrated. The robustness of the signal is experimentally verified through varying C-rates and measurement window lengths. The BMFS, requiring only 30 s per test, can achieve test results with an amplitude error of 1% and a phase error of 1° as compared with those obtained from traditional EIS tests. Moreover, BMFS can also be applied in online EIS measurement scenarios, favorable for real-world applications. This work enables accurate and rapid acquisition of EIS results, which is currently expensive and time-consuming to obtain, ensuring a faster and more nuanced characterization of the internal states of many battery systems in an affordable and accessible manner, especially in data-driven and machine-learning approaches.

Effects of Equatorial Plasma Bubbles on Multi-GNSS Signals: A Case Study over South China

Equatorial plasma bubbles (EPBs) occur frequently in low-latitude areas and have a non-negligible impact on navigation satellite signals. To systematically analyze the effects of a single EPB event on multi-frequency signals of GPS, Galileo, GLONASS, and BDS, all-sky airglow images over South China are jointly used to visually determine the EPB structure and depletion degree. The results reveal that scintillations, or GNSS signal fluctuations, are directly linked to EPBs and that the intensity of scintillation is positively correlated with the airglow depletion intensity. The center of the airglow depletion often corresponds to stronger GNSS scintillation, while the edge of the bubble, which is considered to have the largest density gradient, corresponds to relatively smaller scintillation instead. This work also systematically analyzes the responses of multi-constellation and multi-frequency signals to EPBs. The results show that the L2 and L5 frequencies are more susceptible than the L1 frequency is. For different constellations, Galileo’s signal has the best tracking stability during an EPB event compared with GPS, GLONASS, and BDS. The results provide a reference for dual-frequency signal selection in precise positioning or TEC calculation, that is, L1C and L2L for GPS, L1C and L5Q for Galileo, L1P and L2C for GLONASS, and L1P and L5P for BDS. Notably, BDS-2 is significantly weaker than BDS-3. And inclined geosynchronous orbit (IGSO) satellites have abnormal data error rates, which should be related to the special signal path trajectory of the IGSO satellite.

Detection and repair of BDS six-frequency cycle slips based on recursive filtering and integer constraint method

The multi-frequency signals of the Beidou system are very helpful for positioning, but in data processing, the detection and repair of multi-frequency cycle slips also face certain challenges. A recursive filtering and integer constraint cycle slip detection and repair method for the Beidou six-frequency is proposed in this paper. This method utilises five sets of combination coefficients of six-frequency and three sets of dual-frequency combinations, and detects and repairs cycle slips through integer constraints of cycle slip estimation. The proposed method has been validated by data with a sampling rate of 1 Hz, and can detect the position and size of cycle slips at various frequencies, whether it is random cycle slips or small cycle slips of equal size less than 2 cycles, with a detection success rate of 100%.

Multi-Frequency GPR Data Fusion through a Joint Sliding Window and Wavelet Transform-Weighting Method for Top-Coal Structure Detection

Top-coal structure detection is an important basis for realizing effective mining in fully mechanized cave faces. However, the top-coal structure is very complex and often contains multi-layer gangues, which seriously influence the level of effective mining. For these reasons, this paper proposes a novel multi-frequency ground-penetrating radar (GPR) data-fusing method through a joint sliding window and wavelet transform weighting method to accurately detect the top-coal structure. It possesses the advantages of both high resolution and great detection depth, and it can also integrate multi-frequency GPR data into one composite profile to interpret the internal structure information of top coal in detail. The detection procedure is implemented following several steps: First of all, the multi-frequency GPR data are preprocessed and aligned through a band-pass filter and a zero offset elimination method to establish their spatial correspondences. Secondly, the proposed method is used to determine the time-varying weight values of each frequency GPR signal according to the wavelet energy proportion within the sliding window; also, the edge detection algorithm is introduced to improve the fusion efficiency of the wavelet transform so as to realize the effective fusion of the multi-frequency GPR data. Thirdly, a reflection intensity model of multi-frequency GPR signals traveling in the top-coal is established by using the stratified identification method, and then, the detailed top-coal structure can be inversely interpreted. Finally, the quantitative evaluation criteria, information entropy (IE), space–frequency (SF) and Laplacian gradient (LG), are used to evaluate the multi-frequency GPR data fusion’s effectiveness in laboratory and field environments. The experimental results show that, compared with the genetic, time-varying and wavelet transform fusion method, the fusion performance of the presented method possesses higher values in the IE, SF and LG evaluation criteria, and it also has both the merits of high resolution and great detection depth.

Multi-frequency probabilistic imaging fusion for impact localization on aircraft composite structures

Since the internal barely visible damage of aircraft composite structures caused by the impact is a critical problem, impact monitoring is essential for the integrity and reliability of aircraft composite structures. This paper presents a multi-frequency probabilistic imaging fusion method for localizing impacts on aircraft composite structures. To capture the impact signals, a network of distributed sensors is mounted on the structure. The impact signals are then processed using the continuous wavelet transform (CWT) to extract the multi-frequency narrowband Lamb wave signals. The time difference of arrival (TDOA), a key feature of the impact source, is measured using averaging techniques employed in the normalized variance sequence. Subsequently, a probabilistic imaging function is established, and the TDOA of narrowband Lamb wave signals at each frequency is used as the feature input to generate the multi-frequency probabilistic imaging results. To determine the performance of the imaging results at each frequency, an efficiency index is introduced, allowing for the retention or abandonment of the imaging results. By utilizing the retained multi-frequency probabilistic imaging results, the proposed method achieves impact localization through imaging fusion. Experimental verification is conducted on a stiffened aircraft composite panel, and a comparison is made with two existing methods: the hyperbolic locus imaging method and the virtual time reversal imaging method. The results show that the proposed method can significantly improve localization accuracy compared to the existing methods, and is effective even in the presence of measurement noise.