Method for improving GNSS-R carrier height measurement efficiency based on hierarchical coherence detection

Abstract

The present application relates to the technical field of GNSS-R carrier height measurement, and in particular to a method for improving GNSS-R carrier height measurement efficiency based on hierarchical coherence detection, which introduces a power pre-screening module after the DDM generation process, uses the power waveform characteristics of the central Doppler to preliminarily distinguish the coherence, and only when the pre-screening result shows that there is coherent scattering, the corresponding complex waveform is further extracted and the fine detection based on phase statistics is performed to reduce the invalid complex waveform operation; compared with the prior art, the coherence detection efficiency can be improved without reducing the detection sensitivity.

Description

Technical Field

[0001] This invention relates to the field of GNSS-R carrier height measurement technology, specifically a method for improving the efficiency of GNSS-R carrier height measurement based on hierarchical coherence detection. Background Technology

[0002] Global Navigation Satellite System Reflectometry (GNSS-R) is an emerging passive remote sensing technology. Spaceborne GNSS-R utilizes L-band signals, enabling it to penetrate clouds and rain, achieving all-weather, low-cost global observation. Therefore, it is considered an important means of next-generation Earth observation. Based on different receiver platforms, GNSS-R can be divided into three categories: ground-based, airborne, and spaceborne. Among them, spaceborne GNSS-R has the advantages of short revisit periods and high spatiotemporal resolution, making it a key area of ​​international remote sensing research.

[0003] Sea level height contains information about changes in the Earth's gravitational field. Therefore, by observing the spatiotemporal changes in sea level height, the dynamic processes of the Earth's gravitational field at different scales can be deduced. GNSS-R, as a novel method for sea level altimetry, obtains sea level height by measuring the path changes of satellite signals reflected from the sea surface. This provides observational support for ocean dynamics research, such as global ocean gravity field inversion, sea level change monitoring, and seabed topography exploration. GNSS-R altimetry mainly consists of two observation methods: code phase altimetry and carrier phase altimetry. It is generally believed that the accuracy of GNSS code phase or carrier phase altimetry is approximately 1 / 100 of the chip width or wavelength. Code phase altimetry relies on pseudorange information and has strong anti-interference capabilities, but its accuracy is limited by the chip width, typically only reaching the meter level. In contrast, carrier phase altimetry offers higher measurement accuracy, theoretically achieving centimeter-level or even higher precision. Furthermore, carrier phase altimetry has a higher spatial resolution than code phase altimetry, making it the core development direction for future GNSS-R precision altimetry. However, the stable implementation of carrier phase altimetry fundamentally depends on the coherence of the reflected signal. In real-world observation scenarios, factors such as sea surface disturbances and ocean currents increase the roughness of the reflecting surface, thereby disrupting the coherent structure of the reflected signal. Current GNSS-R satellite receivers (such as CYGNSS, TDS-1, and FY-3E satellites) only generate Delay-Doppler Map (DDM) observations, unable to determine whether the acquired reflection data is coherent, incoherent, or semi-coherent, and lack the ability to identify and label the coherence of complex waveforms in real time. Therefore, coherence detection has become a core prerequisite and key technical issue for improving the accuracy and reliability of GNSS-R carrier phase elevation measurement.

[0004] Existing research has proposed various coherence detection methods. For example, power-based detection methods, including peak amplitude, waveform shape, or power spread, are used to distinguish between coherent and incoherent scattering. However, these power-based coherence detection methods cannot preserve phase information and are not suitable for carrier phase altitude measurement. With the increasing availability of raw intermediate frequency (IF) signals, researchers have begun to explore coherence detection using complex waveforms that contain both amplitude and phase information, such as coherent gain detection, phase statistics detection, and entropy-based detection methods. These complex waveform-based coherence detection methods preserve phase information and can be used for carrier phase altitude measurement. Research by Loria et al. shows that phase statistics-based methods are best suited for determining whether the reflected signal contains sufficient energy for reliable carrier phase estimation. To utilize the higher spatial resolution and phase information of coherent reflections, future receivers will require higher downlink transmission rates for complex waveform data. Studies by Estel et al. have shown that even under the grazing angle geometry most favorable for coherent scattering, and under wind and wave constraints (wind speed below approximately 6 m / s and significant wave height below approximately 1.5 m), only about 33% of trajectories maintain sufficient coherence. Similarly, Roesler et al., based on Spire spaceborne GNSS-R measured data, quantitatively analyzed the coherence of ocean surface reflected signals. Their results indicate that in open sea conditions, only about 1% of reflected signals possess coherent characteristics, meaning a significant proportion of the original observations are incoherent scattering. Therefore, continuous downlink transmission of complex waveform data is infeasible and would be a huge waste of hardware resources. To address this, coherence must be determined in real-time at the spaceborne receiver, and complex waveform data should only be selectively transmitted when coherent scattering is detected, allowing ground processing to fully utilize the observational value of coherent signals.

[0005] Given the need for spaceborne coherent detection, Loria proposed a solution that incorporates a real-time coherent echo detection module into the traditional GNSS-R receiver DDM generation process. By buffering and downloading detected coherent complex waveform samples and auxiliary information, this approach enables subsequent ground processing to obtain higher spatial resolution and more accurate altimetry data with minimal increase in hardware complexity. However, this solution does not consider that the proportion of coherent components in reflected signals is generally low. Directly performing real-time coherence determination based on complex waveforms would result in a large amount of invalid computation and waste of hardware resources. Summary of the Invention

[0006] This invention addresses the problems existing in the prior art by proposing a method for improving GNSS-R carrier height measurement efficiency based on hierarchical coherence detection. This method first performs rapid coherence prediction on the center Doppler power waveform, and then extracts the corresponding complex waveform and performs fine coherence detection only when the power waveform exhibits coherent characteristics. This improves the efficiency of coherence detection without reducing detection sensitivity.

[0007] This invention achieves its purpose through the following measures: A method for improving the efficiency of GNSS-R carrier height measurement based on hierarchical coherence detection is characterized by introducing a power pre-screening module after the DDM generation process. This module uses the power waveform characteristics of the center Doppler to initially determine coherence. Only when the pre-screening results indicate the presence of coherent scattering is the corresponding complex waveform further extracted and fine detection based on phase statistics performed to reduce invalid complex waveform calculations. Specifically, the method includes the following steps: the coherence pre-detection module comprises steps one to three, and the fine detection module comprises step four. Step 1: Cross-correlate the data and use open-loop tracking to obtain the reflected signal parameters to process the reflected intermediate frequency, as shown in the following formula: (1), in, Indicates the start time of the cross-correlation; This indicates the delay of each waveform; Indicates the coherent integration time; Represented as a locally generated PRN code; Indicates the reflected intermediate frequency signal; Represents the complex waveform of the reflected signal; Step 2: Coherent and incoherent accumulation. The formulas for coherent and incoherent accumulation are as follows: (2), (3), in, This represents the coherent integral complex waveform of the reflected signal. Indicates the number of coherent accumulations. t The start time, Indicates the coherent accumulation time. This is the power waveform after incoherent averaging of the reflected signal. Indicates the number of incoherent accumulations; Step 3: Energy Concentration Cross Point Index (ECI). The formula for calculating the Energy Concentration Cross Point Index is as follows: (7), Where k* represents the index of the position where the curve is closest to the reference line, and ECI represents the energy concentration intersection index, which is used to measure the degree of energy concentration. The closer the ECI value is to 0.5, the more dispersed the reflected energy distribution, indicating that the waveform has weak coherence; the closer the ECI value is to 1, the more concentrated the energy, indicating that the waveform has strong coherence characteristics. Based on the statistical analysis of coherent observation data, the discrimination threshold of ECI is set to 0.8; when the ECI is greater than this threshold, the echo is judged to have coherent characteristics and enters the subsequent coherence processing process. Step 4: Calculate the phase statistics. The complex waveform used is generated by coherently accumulating the received signal from the spaceborne GNSS-R over 50 ms, which preserves the phase continuity characteristics corresponding to coherent reflection while suppressing phase noise. (8), in, express t time The peak value of the coherent integral complex waveform. Indicates taking the complex phase. Indicates phase expansion, Indicates the untangling phase. (9), in, Indicates phase difference, The length CL of the circle is represented by the following formula: (10) For coherent reflection, the reflected signal changes smoothly and continuously over time. Therefore, the temporal change of phase is deterministic, and the phase increments of adjacent epochs have a consistent direction. The vector obtained by mapping this to the unit circle exhibits a concentrated direction. The closer it is to 1, the more inversely, for incoherent scattering, the more random the phase change, and the more uniformly the unit vector distributed on the circumference, with directions canceling each other out. Close to 0.

[0008] This invention uses a combination of a sea surface mean height model and a tidal model as a reference benchmark to evaluate the altimetry accuracy of the carrier phase altimetry method. The sea surface mean height is achieved using the DTU21 mean sea surface model, while the tidal correction term incorporates the TPXO9 global tidal model. The reference sea surface height is expressed as the sum of the mean sea surface height and the tidal term. (11), in, This represents the reference sea level height of the DTU21 model after tidal correction; This represents the average sea level height calculated by the DTU21 model; This represents the tidal correction calculated by the TPXO9 model.

[0009] The carrier phase height measurement formula in this invention is as follows: (12), (13) (14) in, This represents the distance delay difference between the direct and reflected signals calculated by the open-loop tracking model. Indicates the ambiguity of the integer period. Indicates the carrier wavelength. Represents the carrier phase residual. Indicates the bistatic delay of observations. This represents the geometric delay between the direct signal and the reflected signal. Indicates tropospheric delay, Indicates ionospheric delay, This represents the bistatic delay in modeling. Indicates the angle of incidence. This indicates the relative surface height above the reference surface.

[0010] Carrier phase integer ambiguity in this invention It is not an independent estimate for each epoch, but rather an average integer ambiguity calculated over a continuous coherent observation period based on a sea surface reference model.

[0011] This invention selects the Pearson correlation coefficient (PCC), root mean square error (RMSE), and mean absolute error (MAE) to evaluate the overall performance of carrier phase altimetry inversion for sponge height, which are expressed as follows: (15) (16) (17) in, Indicates the total number of observations; and These are measured values ​​and simulated values, respectively. It is the average of the measured values; It is the average of the simulated values.

[0012] This invention addresses the challenges of real-time coherence determination of reflected signals from carrier-phase sea surface altimetry in spaceborne GNSS-R and the low computational efficiency of existing coherence detection methods. It proposes a novel hierarchical coherence detection method to improve coherence detection efficiency while maintaining physical consistency and supporting high-precision carrier-phase altimetry applications. Following the traditional GNSS-R waveform generation process, it proposes a low-computational-cost coherence pre-screening method using the Energy Concentration Intersection Index (ECI) based on power waveform morphology. Furthermore, it utilizes the circular length... Using statistical analysis with reference to length (CL), a stable threshold was determined. Under a fixed error rate of 5%, the ECI thresholds corresponding to multiple CYGNSS ocean tracks were concentrated in the range of 0.81 to 0.85. In addition, based on power prediction, fine coherence detection based on phase statistics was carried out only on echoes that might have coherent scattering, thereby significantly reducing invalid complex waveform calculations. Under the test condition of a maximum number of tracks of 335, compared with the traditional full-volume phase coherence detection method, the total calculation time was reduced from 467.60 s to 431.58 s, and the overall calculation efficiency was improved by about 7.7%. The method was applied to the carrier phase altimetry experiment of actual CYGNSS spaceborne intermediate frequency data, and multiple continuous coherent tracks were successfully identified. The root mean square error of the inverted sea surface height and the reference height was 0.16 to 0.35 m, achieving stable decimeter-level accuracy. The results show that the proposed novel hierarchical coherence detection method can improve processing efficiency while ensuring the reliability of carrier phase altimetry, providing key technical support for future spaceborne GNSS-R precision altimetry and coherent scattering applications. Attached Figure Description

[0013] Figure 1 This is a comparison diagram between the present invention and traditional coherence detection methods, in which... Figure 1 (a) is a flowchart of the present invention and conventional methods; (b) is a schematic diagram of the processing architecture of the conventional method; and (c) is a schematic diagram of the processing architecture of the present invention.

[0014] Figure 2 This is a schematic diagram of the geometric principle of sea surface altitude inversion in spaceborne GNSS-R.

[0015] Figure 3 This is a schematic diagram illustrating the calculation of the energy concentration intersection index method in this invention, wherein... Figure 3 In the diagram, (a) is the normalized waveform; (b) is the energy concentration intersection index of the normalized waveform.

[0016] Figure 4 This is the result of fine coherence detection based on phase statistics in this invention, wherein Figure 4In the diagram, (a) represents the change in circle length over time; (b) represents the polar coordinate representation of the coherent phase change rate; and (c) represents the polar coordinate representation of the incoherent phase change rate.

[0017] Figure 5 The ECI threshold is determined statistically based on CL coherent reference in this invention, wherein... Figure 5 In the figure, (a) is the ECI distribution based on the CL condition, (b) is the ROC curve, and (c) is the time alignment curve between CL and aggregated ECI.

[0018] Figure 6 This describes the improvement in computation time and efficiency of two coherence detection methods under different trajectory number conditions in the embodiments of the present invention.

[0019] Figure 7 This refers to the location of the mirror point trajectory region in the coherence result of this embodiment of the invention.

[0020] Figure 8 This is a comparison of the carrier phase residual with the normalized value of the reference sea level height in an embodiment of the present invention, wherein... Figure 8 (a) is trajectory 1; (b) is trajectory 2; (c) is trajectory 3; (d) is trajectory 4.

[0021] Figure 9 These are the height measurement inversion results of four coherent trajectories in this embodiment of the invention, wherein... Figure 9 (a) is trajectory 1; (b) is trajectory 2; (c) is trajectory 3; (d) is trajectory 4. Detailed Implementation

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] This invention proposes a novel hierarchical coherence detection method aimed at improving the efficiency of coherence detection for spaceborne GNSS-R reflected signals. Unlike traditional methods, this invention introduces a power pre-screening module after the traditional DDM generation process. This module utilizes the power waveform characteristics of the center Doppler to initially determine coherence. Only when the pre-screening results indicate the potential presence of coherent scattering does the corresponding complex waveform need to be further extracted and fine-tuned based on phase statistics performed. By introducing a computationally low-cost power pre-screening module after DDM generation, this method significantly reduces invalid complex waveform calculations, lowering the real-time processing burden without compromising coherence detection sensitivity. This provides a feasible technical approach for the efficient implementation of precision altimetry and coherent scattering detection in future spaceborne GNSS-R missions.

[0024] Coherence detection is a prerequisite for carrier phase altimetry. However, existing spaceborne GNSS-R receivers generally lack dedicated coherence detection modules, and existing coherence discrimination methods suffer from significant efficiency limitations, failing to meet the requirements of real-time spaceborne processing. Therefore, it is necessary to design a novel hierarchical coherence detection method. This method first utilizes computationally inexpensive observations for rapid prediction, and then performs refined coherence analysis on data exhibiting coherence characteristics, significantly improving overall detection efficiency. This proposed method will provide crucial technical support for the real-time coherent processing and precise altimetry capabilities of future spaceborne GNSS-R receivers.

[0025] The novel hierarchical coherence detection method proposed in this example mainly consists of the following steps: Step 1: Data cross-correlation; Step 2: Coherent and incoherent accumulation; Step 3: Energy Concentration Intersection Index (ECI); Step 4: Calculation of phase statistics. The coherence pre-detection module comprises steps 1, 2, and 3, while the refined detection module is step 4. The specific formulas are as follows: Step 1: Cross-correlate the data and use open-loop tracking to obtain the reflected signal parameters to process the reflected intermediate frequency, as shown in the following formula: (1), Where, represents the start time of the cross-correlation; This indicates the delay of each waveform; Indicates the coherent integration time; Represented as a locally generated PRN code; Indicates the reflected intermediate frequency signal; This represents the complex waveform of the reflected signal.

[0026] Step 2: Coherent and Incoherent Accumulation: In GNSS-R signal processing, to improve the detection capability and signal-to-noise ratio (SNR) of reflected signals, a combination of coherent and incoherent accumulation enhancement strategies is typically employed. The formulas for coherent and incoherent accumulation are as follows: (2), (3), in, This represents the coherent integral complex waveform of the reflected signal. Indicates the number of coherent accumulations. t The start time, Indicates the coherent accumulation time. This is the power waveform after incoherent averaging of the reflected signal. Indicates the number of incoherent accumulations; Step 3: Energy Concentration Intersection Index: This example proposes an energy concentration intersection index for coherent detection of power waveforms. The power waveform used is obtained by coherently accumulating the received signal from the spaceborne GNSS-R for 1 ms, and then performing incoherent accumulation for 1000 ms on this basis. The formula for the energy concentration intersection index is derived as follows.

[0027] (1) Calculate the energy distribution: given Normalized delay power distribution: Normalized to probability: (4), in, Indicates the first Normalized power of each delay unit, Indicates the total number of delay units. Indicates the first Energy percentage of each delay unit; (2) Sort by energy percentage from smallest to largest: (5), in, express The result after sorting by value from smallest to largest is the [number]. One element; (3) Calculate the cumulative sum of energy percentages: (6), in, Indicates the order before The percentage of cumulative energy per delay unit.

[0028] (4) The energy concentration intersection index is defined as the x-coordinate of the point that makes the curve closest to the reference line, and the calculation formula is as follows: (7), Where k* represents the index of the position where the curve is closest to the reference line, and ECI represents the energy concentration intersection index, used to measure the degree of energy concentration. The closer the ECI value is to 0.5, the more dispersed the reflected energy distribution, indicating weaker waveform coherence; the closer the ECI value is to 1, the more concentrated the energy, indicating that the waveform has strong coherence characteristics. Based on the statistical analysis of coherent observation data, this invention sets the discrimination threshold of ECI to 0.8; the relevant demonstration will be given later. When the ECI is greater than this threshold, the echo is determined to have coherent characteristics and enters the subsequent coherent processing flow.

[0029] (4) Calculate phase statistics: After determining that the reflected power waveform has coherent characteristics based on the energy concentration intersection index, step (4) further introduces the phase statistics method to perform refined detection of the degree of coherence. This step is based on the peak phase of the complex waveform and its statistical characteristics to perform higher resolution coherence identification of the reflected signal. The complex waveform used in this invention is generated by coherently accumulating the satellite-borne GNSS-R received signal for 50 ms. While suppressing phase noise, it retains the phase continuity characteristics corresponding to coherent reflection, providing a reliable basis for subsequent phase statistical analysis.

[0030] (8), in, express t time The peak value of the coherent integral complex waveform. Indicates taking the complex phase. Indicates phase expansion, This indicates the untangling phase.

[0031] (9), in, This indicates the phase difference.

[0032] The formula for representing the circular length (CL) is as follows: (10) For coherent reflection, the reflected signal changes smoothly and continuously over time; therefore, the temporal variation of the phase is deterministic, and the phase increments of adjacent epochs have a consistent direction. The vector obtained by mapping this to the unit circle exhibits a clear concentration of directions. The closer it is to 1. Conversely, for incoherent scattering, the phase change is approximately random, its unit vector is uniformly distributed on the circumference, and their directions cancel each other out, therefore... The closer it is to 0.

[0033] Figure 1This paper compares the traditional full-quantity coherence detection method with the novel hierarchical coherence detection method proposed in this invention, highlighting the differences in processing flow and receiver architecture. Traditional methods directly perform fine coherence detection based on phase statistics on all observation samples after generating complex waveforms, failing to distinguish the differences in coherence at the reflection echo level, which easily leads to a large amount of invalid computation in spaceborne observations. The proposed method introduces a power domain pre-detection module after the DDM generation process, using the characteristics of the incoherent accumulated power waveform to quickly make an initial judgment on coherence, and only further extracting complex waveforms and performing fine detection on echoes that may exhibit coherent scattering. This hierarchical strategy effectively reduces the number of complex waveform coherence detection triggers without changing the physical criteria for coherence. Compared with the traditional full-quantity detection architecture based on complex waveforms, the novel hierarchical processing architecture significantly reduces the real-time processing burden and downlink requirements for invalid data on spaceborne systems. This method provides an efficient implementation path for spaceborne GNSS-R carrier phase altimetry and coherent scattering detection.

[0034] This example uses a Complex Waveform (cWF) intermediate frequency (IF) data product processed and released by the Institute of Space Sciences (ICE-CSIC / IEEC) in Catalonia. This data product is generated from raw GNSS-R IF data processed by a ground-based software receiver, preserving key information such as the amplitude and carrier phase of the reflected signal, and features a high time sampling rate. The dataset consists of cWF data files and their corresponding metadata files. The cWF files contain complex waveform sequences of the direct and reflected signals, while the metadata files provide observation geometry, transmitter and receiver orbit parameters, and mirror point position information, providing a crucial data foundation for subsequent research on the coherence characteristics of the reflected signal and carrier phase altimetry methods.

[0035] To evaluate the accuracy of sea level retrieval using carrier phase altimetry, it is typically necessary to compare and verify the retrieval results with independent measured sea level data. However, due to the scarcity of measured sea level data, this invention uses a combination of a sea level mean height model and a tidal model as a reference benchmark to evaluate the altimetry accuracy of the carrier phase altimetry method. Specifically, the sea level mean height is based on the DTU21 sea level mean model published by the Technical University of Denmark (DTU), while the tidal correction term incorporates the TPXO9 global tidal model. Based on this, the reference sea level height can be expressed as the sum of the sea level mean height and the tidal term.

[0036] (11), in, This represents the reference sea level height of the DTU21 model after tidal correction; This represents the average sea level height calculated by the DTU21 model; This represents the tidal correction calculated by the TPXO9 model.

[0037] This example demonstrates sea surface altimetry analysis based on the bistatic observation geometry of a spaceborne GNSS-R system. The observation geometric relationships are as follows: Figure 2 As shown. In this bistatic system, signals from GNSS satellites are reflected after incident on the sea surface and received by the CYGNSS onboard receiver. To characterize the signal propagation process, this example uses the WGS-84 reference ellipsoid as the ideal reflecting surface and constructs a virtual reflection path model for the GNSS signal. The corresponding virtual path is illustrated in the diagram below. Figure 2 As shown. Given that the actual signal propagation path is affected by atmospheric effects such as ionospheric and tropospheric delays, corresponding atmospheric corrections are introduced in the modeling process to reduce their impact on the accuracy of sea surface height inversion. Specifically, the ionospheric delay is corrected using the Global Ionospheric Map (GIM), and the tropospheric delay is corrected using the UNB3M model. Based on this, this example references the carrier phase GNSS-R altimeter model proposed by Li et al., and, combined with the phase observation definition and symbol conventions used in this example, adjusts the carrier phase altimeter formula accordingly. Its mathematical expression is shown below: (12), (13) (14) in, This represents the distance delay difference between the direct and reflected signals calculated by the open-loop tracking model. Indicates the ambiguity of the integer period. Indicates the carrier wavelength. Represents the carrier phase residual. Indicates the bistatic delay of observations. This represents the geometric delay between the direct signal and the reflected signal. Indicates tropospheric delay, Indicates ionospheric delay, This represents the bistatic delay in modeling. Indicates the angle of incidence. This represents the relative surface height above the reference surface. It should be noted that the carrier phase integer ambiguity in this invention... It is not an independent estimate for each epoch, but rather an average integer ambiguity calculated over a continuous coherent observation period based on a sea surface reference model.

[0038] To quantitatively evaluate the overall performance of carrier phase altimetry inversion for sea surface height retrieval, this example selects multiple statistical evaluation indicators for comprehensive analysis of the inversion results. The Pearson Correlation Coefficient (PCC) is used to characterize the correlation between the retrieved sea surface height sequence and the reference height sequence, reflecting their consistency in trend. The Root Mean Square Error (RMSE) measures the overall deviation of the inversion results from the reference value, exhibiting higher sensitivity to larger errors. The Mean Absolute Error (MAE) characterizes the average magnitude of error in a single observation. (15) (16) (17) in, Indicates the total number of observations; and These are measured values ​​and simulated values, respectively. It is the average of the measured values; It is the average of the simulated values.

[0039] Figure 3 This demonstrates the ability of the energy concentration intersection index method to distinguish between coherent and incoherent reflection waveforms. (By...) Figure 3 (a) It can be seen that the normalized power of the coherent waveform is highly concentrated near the main peak in the delay dimension, with a narrow main lobe and rapid energy decay, reflecting the energy concentration characteristics under the dominance of specular reflection; in contrast, the incoherent waveform exhibits obvious delay extension, with power distributed in multiple delay units, reflecting the multipath superposition effect caused by scattering from the rough sea surface. Figure 3 (b) The results of the energy concentration intersection index calculation for the corresponding waveforms are presented. The cumulative energy curve of the coherent waveform can achieve a high energy ratio within a small number of delay units, and its intersection with the reference line is close to 1, corresponding to a large ECI value (0.932). In contrast, the energy accumulation process of the incoherent waveform is relatively smooth, the intersection point is significantly shifted to the left, and the ECI value is significantly reduced (0.648). These results indicate that ECI can effectively characterize the overall energy concentration of the power waveform in the delay dimension, thus enabling a clear distinction between coherent and incoherent scattering in the power domain.

[0040] Figure 4 The results of fine coherence detection based on phase statistics and their physical meaning are presented. Figure 4(a) presents the sequential characteristics of the circular length (CL) over time. The circular length is used to quantify the directional consistency of the phase increment on a unit circle, and its value ranges from 0 to 1. When the reflected signal remains stably coherent, the phase changes of adjacent epochs exhibit strong directional consistency, and the corresponding CL value remains close to 1 over a relatively long period. Roesler et al., based on statistical analysis of spaceborne GNSS-R phases, pointed out that when the circular length is greater than 0.9, the phase increment exhibits significant directional concentration in polar coordinate space, and this state can be determined as a completely coherent reflection. In the section where coherence is weakened or lost, the CL value decreases significantly, reflecting that the phase increment direction gradually diverges and the phase consistency is disrupted. Figure 4 (b) and Figure 4 (c) The polar coordinate distribution characteristics of the phase difference between adjacent epochs on the unit circle are presented under coherent and incoherent states, respectively. In the coherent case, the phase increment exhibits a significant directional clustering on the circumference, and its vector synthesis result has a large magnitude, thus corresponding to a higher circle length. In the incoherent case, the phase increment is approximately randomly distributed across the entire circumference, with the directional components canceling each other out, resulting in a significant reduction in the synthesized vector and a corresponding decrease in the circle length. This result indicates that the circle length can effectively characterize the directional consistency of the phase sequence and its time-varying characteristics, and can serve as an important statistical measure to distinguish between coherent and incoherent reflections, providing a reliable and physically meaningful criterion for refined phase decision-making in the hierarchical coherence detection framework.

[0041] In this example, based on CYG05_PRN25 trajectory data, the circle length is used as a reference index for phase consistency to define the "coherent / incoherent" time window: when CL > 0.9, it is determined to be a coherent window; otherwise (CL ≤ 0.9), it is determined to be an incoherent window. Since the calculation of CL is based on the phase increment after 50 ms coherent integration and is statistically analyzed within a sliding window, its time support length is not consistent with ECI (calculated from the waveform morphology of incoherent integration). To achieve comparability, the study first statistically aggregates ECI within each CL time window (taking the median of ECI within that window as the representative value), thereby mapping ECI onto the time axis of CL. Figure 5 (c)).

[0042] Figure 5(a) shows the ECI conditional distribution under the aforementioned CL reference label conditions: the blue histogram represents the distribution of "ECI aggregate values ​​appearing in the incoherent window (CL≤0.9)," and the orange histogram represents the distribution of "ECI aggregate values ​​appearing in the coherent window (CL>0.9)." It can be observed that the ECI distribution within the coherent window shifts significantly to the right and becomes more concentrated, indicating that in the region with strong phase consistency, the waveform power morphology exhibits stronger energy concentration and stability characteristics. Meanwhile, the ECI distribution in the incoherent window is more dispersed and extends to a lower value range, reflecting stronger randomness in the waveform morphology under phase instability conditions. It is noteworthy that the two types of distributions still overlap to some extent in the high ECI region, indicating that the single-window power morphology (ECI) alone is not completely equivalent to the phase consistency index (CL): even within a window with CL≤0.9, a high ECI may occur due to energy focusing and other reasons. Therefore, this example adopts a threshold determination strategy constrained by the false alarm rate, rather than subjectively selecting a threshold.

[0043] To quantitatively determine the discrimination threshold of ECI, this example uses CL>0.9 as the reference truth value label, and constructs a Receiver Operating Characteristic Curve (ROC) using the aggregated ECI as the discrimination score. Figure 5 (b)). At each candidate threshold T, if If the result is positive, it is considered relevant; otherwise, it is considered inrelevant, and the True Positive Rate (TPR) is calculated accordingly. With the False Positive Rate (FPR) In this example, FPR=5% is chosen as the operating point to control false alarms; that is, the threshold is defined as the 95th quantile of the distribution of incoherent samples. Figure 5 (a) and Figure 5 (b) The corresponding threshold for this dataset is approximately (As shown by the dashed line) This means that the time window will only be considered coherent when the ECI reaches a high level, thus ensuring that the false alarm rate under incoherent conditions is limited to approximately 5%. Meanwhile, the ROC curve still shows a high TPR at this operating point. Figure 5 (b) indicates that, under strict control of false alarms, ECI can still identify most of the coherent windows defined by CL, demonstrating ECI's effective sensitivity to coherent events and strong distinguishing ability.

[0044] Finally, from the perspective of time series ( Figure 5(c) This provides a more intuitive understanding of the relationship between the two types of indicators and the necessity of the time alignment strategy. The blue line in the figure represents CL (left axis), and the red line represents the aggregated ECI (right axis), with reference lines for CL=0.9 and the ECI threshold respectively. It can be seen that when CL is significantly higher than 0.9 and remains stable, ECI synchronously exhibits a high value and remains relatively stable; when CL decreases and enters an incoherent state, ECI also decreases overall. It is important to emphasize that the change in ECI may exhibit a slight time lag or smoothing effect relative to CL. This is due to the time support introduced by ECI aggregation (taking statistics within the CL window), rather than an algorithmic error. This result indicates that, within the framework of using CL as a phase consistency reference, waveform-based ECI can determine a stable threshold through a controlled false alarm rate (FPR=5%), achieving effective detection of coherent intervals; simultaneously, the time support difference should be explicitly handled through methods such as window aggregation to enable consistent and interpretable comparisons between the two types of indicators.

[0045] This example presents the ECI threshold determined based on three independent CYGNSS ocean observation datasets under a fixed false positive rate (FPR=5%), where CL>0.9 is used as the reference standard for phase consistency to define the coherent time window. Although there are significant differences in satellite number, observation time, and the number of coherent time windows among the different datasets, the obtained ECI thresholds are all concentrated in a narrow range of 0.81 to 0.85, indicating that under the controlled false positive rate constraint, the ECI threshold is insensitive to specific orbits and observation conditions, exhibiting good stability and consistency. At this threshold level, the TPR performance of different datasets varies. For the CYG05_PRN25 and CYG04_PRN25 datasets, the TPR is close to or reaches 1, indicating that most of the coherent time windows defined by CL>0.9 simultaneously exhibit highly concentrated waveform power morphology; while in the CYG01_PRN15 dataset, although the number of coherent time windows is larger, its TPR is significantly lower, indicating that phase consistency does not necessarily correspond to strong morphological coherence. This result demonstrates that ECI is a more conservative coherence criterion than CL, primarily used to identify "strongly coherent" reflection events that simultaneously possess phase stability and high power concentration. Based on the statistical results from the aforementioned multi-dataset datasets, this invention selects ECI≈0.8 as a unified coherence discrimination threshold. This threshold can control the misclassification rate of incoherent time windows to within approximately 5% under different orbital and observational conditions, while maintaining a high recognition capability for strongly coherent events. Therefore, it can serve as a reasonable basis for ECI coherence discrimination in this invention.

[0046] Depend on Figure 6It can be seen that, under the condition of a maximum number of intermediate frequency trajectories of 335, the total computation time of the traditional full-quantity coherence detection method is 467.60 s, while the computation time of the novel hierarchical coherence detection method proposed in this invention is 431.58 s, achieving an overall computational efficiency improvement of 7.7%. Figure 6 The computation time trends for different numbers of trajectories show that the computation time for both methods increases approximately linearly with the increase in the number of mid-frequency trajectories, indicating that the computational complexity of both algorithms is mainly constrained by the linearity of the trajectory size. However, throughout the entire test range, the computation time of the novel hierarchical coherence detection method is consistently lower than that of the traditional full-data coherence detection method, and the difference between the two remains relatively stable with the increase in the number of trajectories, reflecting that the hierarchical detection strategy has a stable efficiency advantage under different data scales. Meanwhile, Figure 6 The efficiency improvement rate given on the right axis indicates that the new method has a high relative improvement when the number of trajectories is small, then gradually stabilizes as the number of trajectories increases, and finally converges at around 7.7%. This hierarchical coherence detection method effectively reduces redundant complex waveform coherence calculations through power domain pre-screening, significantly reducing the overall computational overhead while ensuring the physical consistency of detection, demonstrating good scalability and potential for spaceborne real-time processing applications.

[0047] according to Figure 7 It can be seen that the coherent trajectory recognition effect of the new hierarchical coherence detection method under actual spaceborne observation conditions can be analyzed. Figure 7 Using Sentinel-2 optical remote sensing imagery as a background, this paper presents the spatial distribution of coherent reflection trajectories identified within the study area. The study area is located in the Bahamas and adjacent seas, where the sea surface is relatively open and relatively flat, providing favorable conditions for stable specular reflection and coherent scattering. It can be seen that four continuous coherent trajectories were identified based on the hierarchical coherence detection method. Each trajectory exhibits good spatial continuity and a consistent direction, without significant spatial dispersion or random jumps. This invention provides basic information about the corresponding trajectories, showing a coherence duration of approximately 5–15 s and reflecting surfaces all being ocean, satisfying the basic physical conditions for continuous carrier phase tracking. These results demonstrate that the novel hierarchical coherence detection method can effectively extract coherent trajectories with clear physical meaning from real spaceborne GNSS-R data, providing a reliable data foundation for subsequent carrier phase continuity maintenance and high-precision sea surface altimetry inversion.

[0048] Figure 8The variation characteristics of carrier phase residuals and normalized reference sea level height sequences on four typical coherent trajectories are compared and presented. It can be seen that under different trajectory geometric conditions and observation periods, the two types of sequences exhibit high consistency in overall evolution trend, relative fluctuation pattern, and extreme value location. This indicates that in the coherent trajectories screened using the hierarchical coherence detection method, the main variation information contained in the carrier phase residuals has a clear physical correspondence with the actual sea level height changes. From the quantitative correlation index, the correlation coefficients for the four trajectories reach 0.99, 0.99, 0.93, and 0.97 respectively, which are generally at a high level, reflecting a significant positive correlation between the carrier phase residuals and the reference sea level height. Among them, the correlation coefficients of trajectory 1 (Figure (a)) and trajectory 2 (Figure (b)) are close to 1, indicating that under conditions of high coherence quality and relatively stable observation geometry, the carrier phase residuals can almost synchronously characterize the relative change process of sea level height, verifying the high sensitivity of carrier phase observations to sea level height changes. In contrast, trajectories 3 (Figure (c)) and 4 (Figure (d)) have relatively low correlation coefficients, but still exhibit a strong correlation. Overall, Figure 8 The high consistency and high correlation results shown statistically verify the effectiveness of the hierarchical coherence detection method in coherent trajectory screening, and also physically demonstrate that carrier phase residuals can serve as an effective observation reflecting changes in sea surface height.

[0049] according to Figure 9 It can be seen that a more rigorous quantitative and qualitative analysis can be conducted on the performance of coherent trajectories obtained by the novel hierarchical coherence detection method in carrier phase height measurement inversion. Figure 9Comparison results of sea surface height sequences obtained from GNSS-R carrier phase inversion on four typical coherent trajectories with reference sea surface heights are presented. It can be seen that, under the four different trajectory geometry and observation conditions, the inverted sea surface heights generally follow the fluctuation characteristics of the reference sea surface height well in terms of overall variation trend, accurately depicting the continuous variation process of sea surface height. This indicates that the coherent trajectory selection results have high reliability in terms of physical consistency and phase stability. From the quantitative error statistics, the RMSEs for the four trajectories are 0.21 m, 0.21 m, 0.16 m, and 0.35 m, respectively, and the MAEs are 0.25 m, 0.27 m, 0.13 m, and 0.29 m, respectively, with the overall error level consistently within the decimeter range. The above results are in good agreement with the findings of Estel et al.'s study on sea surface altimetry using spaceborne GNSS-R carrier phase under grazing angle geometry. This study indicated that when the scattering process remains coherent, GNSS-R carrier phase altimetry can achieve a combined accuracy of approximately 16 / 20 cm (median / mean) on a 50 ms integration scale. This invention, using the same 50 ms integration time scale, obtained coherent trajectories screened through a graded coherence detection method, also exhibits a carrier phase altimetry inversion error that remains consistently on the decimeter level, verifying the consistency between the two studies in terms of physical mechanisms and measurement performance. Overall, Figure 9 The high sequence consistency shown indicates that GNSS-R carrier phase altimetry inversion can stably achieve decimeter-level accuracy on coherent trajectories selected by the novel hierarchical coherence detection method, and exhibits good robustness under different trajectory conditions. This not only verifies the effectiveness of the hierarchical coherence detection method in coherent trajectory identification, but also demonstrates that it can provide a reliable data foundation for subsequent high-precision carrier phase altimetry inversion, further reflecting the feasibility and application value of this method in practical spaceborne GNSS-R sea surface altimetry applications.

[0050] Along-orbit spatial resolution is a key indicator for evaluating the sea surface altimetry observation capability of GNSS-R. Its magnitude is primarily determined by the projection velocity of the specular reflection point on the Earth's surface and the signal accumulation time. According to the calculation method for along-orbit spatial resolution, it can be approximately expressed as the product of the projection velocity of the specular reflection point on the ground and the accumulation time. For CYGNSS satellites, the average movement speed of the specular reflection point on the Earth's surface is approximately 6 km / s. Therefore, under otherwise identical conditions, a longer accumulation time results in a larger along-orbit spatial sampling interval, leading to a decrease in spatial resolution. Taking CYG05_PRN25 data as an example, this paper compares and analyzes the spatial resolution and altimetry accuracy of carrier phase altimetry and code phase altimetry under different accumulation time conditions. Carrier phase altimetry employs a short-time coherent accumulation of 50 ms, resulting in a spatial resolution of approximately 0.3 km along the track and an RMSE of 0.35 m. In contrast, code phase altimetry typically requires a longer period of incoherent accumulation to suppress noise; under a 1000 ms accumulation condition, its spatial resolution along the track decreases to approximately 6 km, and its RMSE is approximately 8.9 m. These results demonstrate that carrier phase altimetry has significant advantages in both spatial resolution and altimetry accuracy.

[0051] The coherence of GNSS-R reflected signals is not a single attribute, but rather manifested simultaneously in the multidimensional characteristics of power pattern, phase stability, and their evolution over time. Power domain indices (such as the energy concentration intersection index) primarily characterize the degree of energy concentration of the reflected echo in the delay dimension, and their physical basis stems from the high concentration of reflected energy near the main peak under specular reflection dominance. Phase domain indices (such as circle length) statistically analyze the consistency of phase increments between adjacent epochs in the time dimension, reflecting the continuous evolution characteristics of the carrier phase during coherent scattering. Experimental results show that within the coherence time window defined by CL>0.9, the distribution of ECI generally exhibits a significant rightward shift, indicating that enhanced phase consistency is usually accompanied by an increase in waveform morphological energy concentration. However, the two types of indices may still show inconsistencies within local time windows, reflecting that morphological coherence and phase coherence are not strictly equivalent at the physical level. Based on the above understanding, this invention adopts a hierarchical criterion that combines the power domain and the phase domain, uses low-dimensional, low-computational-cost morphological features for coherence prediction, and then completes fine discrimination through phase statistics, thus realizing the collaborative characterization and hierarchical discrimination of multidimensional coherence features from a physical perspective.

Claims

1. A method for improving the efficiency of GNSS-R carrier height measurement based on hierarchical coherence detection, characterized in that, Following the DDM generation process, a power pre-screening module is introduced. This module uses the power waveform characteristics of the central Doppler to initially determine coherence. Only when the pre-screening results indicate the presence of coherent scattering is the corresponding complex waveform extracted and fine detection based on phase statistics performed to reduce invalid complex waveform calculations. Specifically, this includes the following steps: the coherence pre-detection module comprises steps one through three, and the fine detection module comprises step four. Step 1: Cross-correlate the data and use open-loop tracking to obtain the reflected signal parameters to process the reflected intermediate frequency, as shown in the following formula: （1）， in, Indicates the start time of the cross-correlation; This indicates the delay of each waveform; Indicates the coherent integration time; Represented as a locally generated PRN code; Indicates the reflected intermediate frequency signal; Represents the complex waveform of the reflected signal; Step 2: Coherent and incoherent accumulation. The formulas for coherent and incoherent accumulation are as follows: （2）， （3）， in, This represents the coherent integral complex waveform of the reflected signal. Indicates the number of coherent accumulations. t The start time, Indicates the coherent accumulation time. This is the power waveform after incoherent averaging of the reflected signal. Indicates the number of incoherent accumulations; Step 3: Energy Concentration Cross Point Index (ECI). The formula for calculating the Energy Concentration Cross Point Index is as follows: （7）， Where k* represents the index of the position where the curve is closest to the reference line, and ECI represents the energy concentration intersection index, which is used to measure the degree of energy concentration. The closer the ECI value is to 0.5, the more dispersed the reflected energy distribution, indicating that the waveform has weak coherence; the closer the ECI value is to 1, the more concentrated the energy, indicating that the waveform has strong coherence characteristics. Based on the statistical analysis of coherent observation data, the discrimination threshold of ECI is set to 0.8; when the ECI is greater than this threshold, the echo is judged to have coherent characteristics and enters the subsequent coherence processing process. Step 4: Calculate the phase statistics. The complex waveform used is generated by coherently accumulating the received signal from the spaceborne GNSS-R over 50 ms, which preserves the phase continuity characteristics corresponding to coherent reflection while suppressing phase noise. （8）， in, express t time The peak value of the coherent integral complex waveform. Indicates taking the complex phase. Indicates phase expansion, Indicates the untangling phase. （9）， in, Indicates phase difference, The length CL of the circle is represented by the following formula: （10）， For coherent reflection, the reflected signal changes smoothly and continuously over time. Therefore, the temporal change of phase is deterministic, and the phase increments of adjacent epochs have a consistent direction. The vector obtained by mapping this to the unit circle exhibits a concentrated direction. The closer it is to 1, the more inversely, for incoherent scattering, the more random the phase change, and the more uniformly the unit vector distributed on the circumference, with directions canceling each other out. Close to 0.

2. The method for improving the efficiency of GNSS-R carrier height measurement based on hierarchical coherence detection according to claim 1, characterized in that, The accuracy of the carrier phase altimetry method is evaluated using a combination of the sea surface mean height model and the tidal model as a reference. The sea surface mean height is calculated using the DTU21 mean sea surface model, while the tidal correction term incorporates the TPXO9 global tidal model. The reference sea surface height is expressed as the sum of the mean sea surface height and the tidal term. （11）， in, This represents the reference sea level height of the DTU21 model after tidal correction; This represents the average sea level height calculated by the DTU21 model; This represents the tidal correction calculated by the TPXO9 model.

3. The method for improving the efficiency of GNSS-R carrier height measurement based on hierarchical coherence detection according to claim 2, characterized in that, The formula for carrier phase height measurement is as follows: （12）， （13）， （14）， in, This represents the distance delay difference between the direct and reflected signals calculated by the open-loop tracking model. Indicates the ambiguity of the integer period. Indicates the carrier wavelength. Represents the carrier phase residual. Indicates the bistatic delay of observations. This represents the geometric delay between the direct signal and the reflected signal. Indicates tropospheric delay, Indicates ionospheric delay, This represents the bistatic delay in modeling. Indicates the angle of incidence. This indicates the relative surface height above the reference surface.

4. The method for improving the efficiency of GNSS-R carrier height measurement based on hierarchical coherence detection according to claim 3, characterized in that, Carrier phase integer ambiguity It is not an independent estimate for each epoch, but rather an average integer ambiguity calculated over a continuous coherent observation period based on a sea surface reference model.

5. The method for improving the efficiency of GNSS-R carrier height measurement based on hierarchical coherence detection according to claim 4, characterized in that, The Pearson correlation coefficient (PCC), root mean square error (RMSE), and mean absolute error (MAE) were selected to evaluate the overall performance of carrier phase altimetry for inverting sponge height, and are respectively expressed as follows: （15）， （16）， （17）， in, Indicates the total number of observations; and These are measured values ​​and simulated values, respectively. It is the average of the measured values; It is the average of the simulated values.

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