Method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network

Abstract

Method for improving global average altimetry accuracy by weighting based on multi-layer feedforward neural network, including: clarifying the influence of constellation configuration on the altimetry ability of GNSS-R, constructing a weighted prediction model of multi-layer feedforward neural network and verifying it, and finally using this model to predict the altimetry ability of spaceborne GNSS-R. The present invention solves the problem of complex evaluation of the altimetry ability of spaceborne GNSS-R under different simulation conditions, and significantly improves the calculation efficiency of altimetry accuracy.

Description

Technical Field

[0001] The present invention relates to the cross technical fields of satellite altimetry, marine surveying and mapping, etc., in particular to a method for improving the global mean altimetry accuracy by weighting based on a multi-layer feedforward neural network. Background Art

[0002] Altimetry of the sea surface not only plays an important role in the fields of natural environment, ecological economy, etc., but also is one of the most direct means to obtain ocean dynamic environment parameters and ocean gravity field information, and it is of crucial significance for establishing a high-precision global gravity field model in an underwater inertial / gravity integrated navigation system. Currently, the existing conventional sea surface altimetry means mainly include tide gauge altimetry and satellite radar altimetry. However, tide gauge altimetry cannot meet the altimetry accuracy requirements at the global scale, and both of these means have high costs and low spatio-temporal resolutions.

[0003] In recent years, with the gradual improvement of the global GNSS system construction, since the concept of passive reflection and interference system (PARIS) was proposed by Martin-Neira in 1993, using GNSS-R technology for ocean remote sensing and sea surface height measurement has become a new research concept. Currently, the methods for sea surface altimetry using GNSS-R technology mainly include: code-phase altimetry, carrier-phase altimetry, and signal-to-noise ratio altimetry. Currently, experiments are mainly carried out using shore-based and air-based platforms. The code-phase altimetry model is simple and easy to implement, so it is widely applied; carrier-phase altimetry requires signal coherence, but in the case of a large satellite elevation angle, the sea surface reflection signal is usually an incoherent scattering signal; signal-to-noise ratio altimetry uses a common single-antenna signal receiver, has a wide range of applications, effectively reduces the cost, and the inversion accuracy is usually at the decimeter level. In terms of shore-based observations, in 1995, Anderson et al. first proposed the GPS satellite signal interferometry results and compared them with the tide gauge results, and found that the measurement accuracy was about 12 cm; Johan et al. proposed a tide gauge based on GNSS signals, using the carrier-phase method, and the inversion accuracy could reach 4 cm. In terms of air-based observations, Ruffini et al. collected GPS reflection signals under a vortex sea condition with a wind speed of 10 m / s and an effective wave height of 2 m using a low-altitude airborne platform, and performed code-phase tracking processing on the test data. The inversion sea surface height accuracy reached the decimeter level, and the spatial resolution was 20 km; Carreno-Luengo et al. demonstrated through airborne experiments that compared with the GPS C / A code, the GPS P(Y) code sea surface altimetry technology based on semi-codeless technology improved the altimetry accuracy by 1.4 to 2.4 times.

[0004] The current research on sea surface altimetry using GNSS-R constellations mainly focuses on the CYGNSS constellation. The CYGNSS constellation consists of 8 low-Earth orbit satellites with an orbital altitude of 500 km, an orbital inclination of 35°, and an average revisit time predicted to reach 6 hours. It can cover the area between 35° north and south latitudes of the global ocean all-weather and without gaps. In 2019, Li Weiqiang et al. used CYGNSS data to generate reflected waveforms of GPS L1, Galileo E1, and Beidou 3B1 band signals. By applying a delay correction model for sea surface height inversion, the bistatic delay observations were converted into sea surface height measurements and compared with the mean sea surface height model. In 2020, Jake et al. used the DDM data of CYGNSS to perform sea surface height inversion in the waters near Indonesia and proposed the priority design factors for future GNSS-R altimetry missions. Alex et al. carried out tracking and observation processing on the CYGNSS satellite orbits and used improved orbits combined with ionospheric delay models and tropospheric delay models to reduce the sea surface height anomalies relative to the DTU10 mean sea surface. These results all provide effective support for the development of future GNSS-R missions dedicated to ocean altimetry applications.

[0005] Currently, the GNSS-R sea surface altimetry mode based on spaceborne platforms is mainly limited in the following aspects: ① A single satellite cannot achieve uninterrupted detection in a specific range. ② Using multiple satellites to form a constellation can improve the GNSS-R global mean sea surface altimetry accuracy, but there is currently a lack of existing simulation research results and it is impossible to specifically evaluate the sea surface altimetry accuracy in this mode. Considering the above problems, the spaceborne GNSS-R altimetry platform based on satellite constellations can play the following observation advantages: ① Achieve all-day and all-weather uninterrupted continuous detection in a specific area. Compared with a single satellite, using a constellation for cooperation between satellites helps to achieve global or regional observations and data collection, meeting the sea surface altimetry accuracy and spatial resolution of 5-8 cm required for tasks such as underwater navigation. ② Have a large number of signal sources. On-orbit or planned navigation satellites provide rich free and public signals, which is conducive to achieving large-scale high-spatial-resolution, short revisit cycle data collection and surface parameter inversion. ③ The influence of bad weather such as rainfall and fog on L-band signals is small, which is conducive to achieving long-term continuous all-weather observations. ④ Adopt a heterogenous observation mode without a transmitter, so the complexity of the observation device such as volume, cost, and mass is reduced.

[0006] It can be seen that the networking of high-precision GNSS-R altimetry constellations is an inevitable trend for future GNSS-R altimetry. Establishing a global mean sea surface altimetry accuracy prediction model based on a satellite constellation can fill the research gap in this mode and specifically evaluate its sea surface altimetry ability. With the rapid development of machine learning, artificial neural network technology has once again attracted people's attention. This technology has a high non-linear mapping ability. Therefore, combining the global mean sea surface altimetry accuracy prediction model with artificial neural networks will surely improve the accuracy and practicality of the prediction model.

[0007] Different from the existing research results of predecessors, the present invention proposes a global mean sea surface altimetry accuracy index, aiming to construct a reasonable observation constellation configuration and improve the GNSS-R global mean sea surface altimetry accuracy, revealing the influence mechanism of constellation configuration parameters on the global mean sea surface altimetry accuracy; by combining a multi-layer feedforward neural network and an ADAM optimization algorithm, constructing a new type of multi-layer feedforward neural network weighted joint prediction model, and proposing an optimized constellation configuration scheme, so as to meet the altimetry accuracy requirements for underwater navigation. Summary of the Invention

[0008] The object of the present invention is: a method for improving global mean altimetry accuracy based on weighted multi-layer feedforward neural networks. It solves the problem that the altimetry ability of spaceborne GNSS-R based on a satellite constellation cannot be quickly evaluated under different simulation conditions, improves the calculation efficiency of the global mean sea surface altimetry accuracy, and gives the best constellation simulation parameters to meet the altimetry accuracy requirements for underwater navigation.

[0009] The technical solution of the present invention is:

[0010] A method for improving global mean altimetry accuracy based on weighted multi-layer feedforward neural networks, comprising:

[0011] Dividing the earth's sea surface into grids to obtain the average altimetry accuracy σ of each grid grid ;

[0012] According to the average altimetry accuracy σ of each grid grid , obtaining the average value of the average altimetry accuracy σ of all grids grid ;

[0013] According to the average value of the average altimetry accuracy σ of all grids grid ; Determining the spaceborne GNSS-R global mean sea surface altimetry accuracy σ global ;

[0014] Establishing a global mean sea surface altimetry accuracy prediction model;

[0015] Verify the feasibility of the global mean sea surface height measurement accuracy prediction model to obtain a global mean sea surface height measurement accuracy prediction model that meets the verification conditions;

[0016] Use the global mean sea surface height measurement accuracy prediction model that meets the verification conditions to perform simulation calculations under different simulation ranges to obtain multiple global mean sea surface height measurement accuracy prediction results;

[0017] Screen the obtained multiple global mean sea surface height measurement accuracy prediction results, and screen out the prediction results that meet the value range of the sea surface height measurement accuracy for underwater navigation as the screening results;

[0018] The orbital altitude, orbital inclination, number of satellites, and simulation period corresponding to the screening results are used as the constellation design plan. Use the obtained constellation design plan to design and launch the GNSS-R altimetry constellation, and finally obtain the measured value of the global mean sea surface height measurement accuracy.

[0019] Preferably, the method for obtaining the average measurement accuracy σ of each grid is as follows: grid Specifically:

[0020]

[0021] Among them, represents the average value of the mean square error σ of the sea surface height measurements of all single specular reflection points in the grid, and n is the number of single specular reflection points included in each divided grid. ssh

[0022] Preferably,

[0023]

[0024] ′

[0025] Among them, σ ssh is the mean square error of the sea surface height measurement of the single specular reflection point in each grid, P Z (0) and P Z (0) are the amplitude of the average power and the slope of the power waveform at the single specular reflection point in each grid, c is the speed of light in vacuum, SNR is the signal correlation power, N incoh is the number of non-coherent accumulations, and ε ele is the elevation angle of the single specular reflection point.

[0026] Preferably,

[0027] Preferably, the global mean sea surface height measurement accuracy prediction model is specifically:

[0028] ​y = -0.4018×tansig(-0.0463x1 - 1.6060x2 - 1.1038x3 + 1.1773x4 + 2.2772)

[0029] + 0.9281×tansig(1.4336x1 - 0.0311x2 - 1.3815x3 + 1.1050x4 - 1.5181)

[0030] - 0.1666×tansig(-0.5657x1 - 1.0521x2 + 1.4176x3 - 1.3226x4 + 0.7591)

[0031] + 0.8444×tansig(0.8738x1 - 1.8850x2 - 0.3772x3 + 0.8525x4)

[0032] + 0.2531×tansig(-1.5508x1 + 1.0884x2 - 0.1054x3 - 1.2590x4 - 0.7591)

[0033] + 0.4047×tansig(-0.0039x1 - 1.3172x2 - 1.8088x3 - 0.4230x4 - 1.5181)

[0034] + 0.1091×tansig(-1.4974x1 + 0.9534x2 - 0.4286x3 - 1.3605x4 - 2.2772)

[0035] - 0.2366

[0036] where y equals σ global , x1 is the orbital altitude, x2 is the orbital inclination, x3 is the number of satellites, and x4 is the simulation period.

[0037] Preferably, the verification condition is any one of the holistic evaluation index, mean absolute error, mean absolute percentage error, or root mean square error.

[0038] Preferably, the verification condition is a method for verifying the global mean sea surface height measurement prediction model using the holistic evaluation index, specifically:

[0039]

[0040] where is the spaceborne GNSS-R global mean sea surface height measurement σ corresponding to the i-th sample global ; y i (i = 1, 2,..., k) is the true data of the global mean sea surface height measurement corresponding to the i-th sample; k is the number of samples;

[0041] When R 2 is greater than 0.99, a global mean sea surface height measurement accuracy prediction model that meets the verification conditions is obtained.

[0042] Preferably, the orbital altitude, orbital inclination, number of satellites, and simulation period are simulated and calculated at a specific simulation step size under different simulation ranges, so as to obtain multiple global mean sea surface height measurement accuracy prediction results;

[0043] Among them, the simulation range of the orbital altitude is 300 km - 800 km, and the step size is 1 km; the simulation range of the orbital inclination is 70° - 97.5°, and the step size is 0.5°; the simulation range of the number of satellites is 1 - 8, and the step size is 1; the value range of the simulation period is 1 - 3 years, and the step size is 1 year.

[0044] Preferably, the value range requirement for the sea surface height measurement accuracy of underwater navigation is that the value range of the global mean sea surface height measurement accuracy prediction result is 5 - 8 cm.

[0045] The advantages of the present invention compared with the prior art are as follows:

[0046] The present invention uses a multi-layer feedforward neural network combined with the ADAM algorithm to establish a prediction model, quantitatively estimate the altimetry ability of spaceborne GNSS-R, so as to greatly reduce the simulation time in this altimetry mode, and quickly give the specific constellation configuration parameters and simulation period that meet the requirements of underwater navigation altimetry accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the GNSS-R antenna coverage area.

[0048] Figure 2 It is a structure diagram of a three-layer feedforward neural network.

[0049] Figure 3 It is a flow chart for improving the global mean sea surface height measurement accuracy of GNSS-R satellites based on a new combined multi-layer feedforward neural network weighted joint prediction model.

[0050] Figure 4 It is a curve graph of the single-point measurement accuracy varying with the elevation angle under different GNSS signal sources.

[0051] Figure 5 It is a curve graph of the global mean sea surface height measurement accuracy of a single satellite varying with latitude at different orbital altitudes.

[0052] Figure 6 It is a curve graph of the global mean sea surface height measurement accuracy of a single satellite varying with longitude at different orbital altitudes.

[0053] Figure 7Global average sea surface altimetry accuracy of a single satellite versus latitude at different orbital inclinations.

[0054] Figure 8 Global average sea surface altimetry accuracy of a single satellite versus longitude at different orbital inclinations.

[0055] Figure 9 Comparison chart of predicted values and actual values of the new combined multi-layer feedforward neural network weighted combined prediction model.

[0056] Figure 10 Training times and effect diagram of the neural network dataset.

[0057] Figure 11 Effect diagram of neural network fitting.

[0058] Figure 12 Global average sea surface altimetry accuracy versus orbital altitude under different satellite numbers predicted by the new combined multi-layer feedforward neural network weighted combined prediction model. Detailed implementation

[0059] The present invention relates to a method for improving global average altimetry accuracy based on weighted multi-layer feedforward neural networks. GNSS-R sea surface altimetry based on satellite constellation platforms has become a new research direction and an inevitable trend. Using this technology can meet the altimetry accuracy requirements at the global scale for underwater navigation. Currently, there is still a research gap in global sea surface altimetry in this mode, and its altimetry ability cannot be specifically evaluated. Therefore, it is necessary to construct a satellite constellation for global sea surface altimetry requirements and establish a corresponding altimetry accuracy prediction model, so as to quantitatively estimate the altimetry ability of constellations with different configuration parameters. First, calculate the global average sea surface altimetry accuracy under different constellation configuration parameters (orbital altitude, orbital inclination, and number of satellites) and simulation periods, analyze the influence mechanism of different constellation configuration parameters on accuracy, and establish a new combined multi-layer feedforward neural network weighted combined prediction model; secondly, verify the fitting degree of the prediction model, test the model performance ability, and calculate the R2 value of the model to be 0.9989 and the mean square error to be 0.0007, indicating that the prediction ability of the accuracy prediction model is good; finally, use the new combined multi-layer feedforward neural network weighted combined prediction model for prediction, and comprehensively consider research results and real costs and other factors, it can be concluded that when the constellation is set with an orbital altitude of 500 km, an orbital inclination of 97.5°, and the number of satellites is 6, and the simulation period is one year, the altimetry accuracy can reach 0.0659 m, which can meet the underwater navigation accuracy requirements, thus providing a reference basis for subsequent research on GNSS-R sea surface altimetry using satellite constellations.

[0060] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will further describe in detail the common implementation manners of the present invention with reference to the accompanying drawings, such asFigure 3 As shown below, the specific steps are as follows:

[0061] 1) According to the global average sea surface height measurement accuracy of spaceborne GNSS-R, discuss the influence mechanisms of orbital altitude, orbital inclination, number of satellites, and simulation period on this accuracy;

[0062] The global average sea surface height measurement accuracy σ of the spaceborne GNSS-R global Calculation formula:

[0063]

[0064] Among them, represents the average value of the average measurement accuracies σ of all grids grid of σ, grid σ is the average measurement accuracy of each grid after dividing the Earth's sea surface into 20km×20km grids (this grid division method is an empirical value) grid , specifically:

[0065]

[0066] Among them, represents the average value of the mean square errors σ of the sea surface height measurements at all single specular reflection points in the grid ssh of σ, ssh σ is the mean square error of the sea surface height measurement at each single specular reflection point in each grid, that is, the single-point measurement accuracy:

[0067]

[0068] ′

[0069] Among them, σ ssh is the mean square error of the sea surface height measurement at each single specular reflection point in each grid, P Z (0) and P Z (0) are the amplitude of the average power and the slope of the power waveform at each single specular reflection point in each grid, c is the speed of light in vacuum, is defined as the altimetry sensitivity, SNR is the signal correlation power, N incoh is the number of non-coherent accumulations, ε ele is the elevation angle of the single specular reflection point (affected by orbital altitude and orbital inclination); σ grid is the average measurement accuracy of each grid after dividing the globe into grids, n is the number of single specular reflection points included in each divided grid. The number of n is related to the time length of the simulation period. The longer the simulation period, the larger the number of n. n is affected by the number of satellites. The more satellites, the larger the number of n.

[0070] 2) According to the above influence mechanism, combined with the multi-layer feedforward neural network and the ADAM optimization algorithm, continuously update the weights and thresholds of the neural network to establish a global mean sea surface height measurement accuracy prediction model;

[0071] The expression of the established global mean sea surface height measurement accuracy prediction model is:

[0072] y = -0.4018×tansig(-0.0463x1 - 1.6060x2 - 1.1038x3 + 1.1773x4 + 2.2772)

[0073] + 0.9281×tansig(1.4336x1 - 0.0311x2 - 1.3815x3 + 1.1050x4 - 1.5181)

[0074] - 0.1666×tansig(-0.5657x1 - 1.0521x2 + 1.4176x3 - 1.3226x4 + 0.7591)

[0075] + 0.8444×tansig(0.8738x1 - 1.8850x2 - 0.3772x3 + 0.8525x4)

[0076] + 0.2531×tansig(-1.5508x1 + 1.0884x2 - 0.1054x3 - 1.2590x4 - 0.7591)

[0077] + 0.4047×tansig(-0.0039x1 - 1.3172x2 - 1.8088x3 - 0.4230x4 - 1.5181)

[0078] + 0.1091×tansig(-1.4974x1 + 0.9534x2 - 0.4286x3 - 1.3605x4 - 2.2772)

[0079] - 0.2366

[0080] where y is σ in step 1 global , x1 is the orbital altitude, x2 is the orbital inclination, x3 is the number of satellites, and x4 is the simulation period.

[0081] 3) Verify the accuracy prediction model determined in step 2 to determine the feasibility of the model;

[0082] The feasibility verification index is any one of the overall evaluation index (R 2 ), mean absolute error (MAE), mean absolute percentage error (MAPE), or root mean square error (RMSE), where:

[0083]

[0084] Among them, is the predicted data of the i-th global mean sea surface height measurement accuracy; y i (i = 1, 2, …, k) is the true data of the i-th global mean sea surface height measurement accuracy; k is the number of y in step 2.

[0085] When R 2 = 1, the predicted value is equal to the true value; when R 2 is infinitely close to 1 (generally greater than 0.99), it indicates that the performance of the multi-layer feedforward network prediction model is better.

[0086] 4) After determining the feasibility, use the model that meets the feasibility to calculate the y value at different simulation ranges with a specific simulation step size for the orbital altitude (simulation range 300 km - 800 km, step size 1 km), orbital inclination (simulation range 70° - 97.5°, step size 0.5°), number of satellites (simulation range 1 - 8 satellites, step size 1 satellite), and simulation period (1 - 3 years, step size 1 year), and obtain multiple global mean sea surface height measurement accuracy prediction results;

[0087] 5) Screen the multiple global mean sea surface height measurement accuracy prediction results obtained in step 4), and screen out the prediction results that meet the value range of the sea surface height measurement accuracy for underwater navigation as the screening results;

[0088] 6) Obtain the orbital altitude, orbital inclination, number of satellites, and simulation period corresponding to the screening results as the constellation design plan, and use the obtained constellation design plan to design and launch the GNSS-R altimetry constellation, and finally obtain the measured value of the global mean sea surface height measurement accuracy.

[0089] Embodiment

[0090] 1. Data

[0091] (1) GNSS satellite precise ephemeris

[0092] Based on the precise ephemeris provided by the International GNSS Service (IGS), the three-dimensional coordinates of GPS, GLONASS, GALILEO, and BDS satellites in the geocentric coordinate system are obtained respectively. The IGS precise ephemeris adopts the SP3 format, and the content includes satellite positions, satellite clock records, satellite running speeds, etc. Since the SP3 precise ephemeris provides satellite positions every 15 minutes, in order to unify with the set -R satellite sampling time, it is necessary to obtain the three-dimensional coordinates of the GNSS satellite orbit sampling points through the Legendre polynomial interpolation method to obtain the high-precision positioning of GNSS satellites.

[0093] (2) Satellite simulation conditions

[0094] This invention draws on the TechDemoSat-1 satellite successfully launched into orbit on July 8, 2014 by Surrey Satellite Technology Limited (SSTL) in the UK for providing on-orbit technology verification services. This satellite is in a sun-synchronous orbit with an altitude of 635 km, and is mainly equipped with a new generation of on-board GNSS remote sensing instrument receiver (SGR-ReSI), which can track, record and process the surface reflection signals of 4 GPS L1, L2C and other navigation satellites. All the data of this satellite are recorded on the MERRByS website (www.merrbys.co.uk). Simulation analysis is carried out based on the satellite orbit parameters and antenna observation mode. Using the control variable method, when analyzing the influence of a certain constellation configuration parameter on the height measurement accuracy, other configuration parameters are kept unchanged.

[0095] 2. Construction of a new combined multi-layer feedforward neural network weighted combined prediction model

[0096] The rapid undulating changes on the ocean surface have a certain impact on the sea surface height measurement accuracy, and its uncertainty is mainly reflected in the uncertainty of the waveform. In the process of retrieving sea surface height information using sea surface reflection signals, the broadening and deformation of the scattered signal power waveform generated by the rough sea surface are the main factors affecting the height measurement accuracy. Secondly, when GNSS signal scattering occurs on the rough sea surface, the receiver will receive reflection signals from multiple different directions, and the reflection area here is the specular area. The specular area near the specular reflection point has multiplicative noise called speckle noise, which is also a key factor affecting the height measurement accuracy. Therefore, by improving the signal-to-noise ratio (SNR) of a single specular reflection point, the global sea surface height measurement accuracy can be improved.

[0097] In addition, as an on-board platform for GNSS-R signal receivers, it is difficult for a single satellite to achieve uninterrupted detection in a specific range. Its coverage area always changes with the flight time, and this change is strictly affected by orbit parameters such as orbit altitude and orbit inclination. Therefore, it is usually difficult to achieve global or regional observation and data collection with just one satellite. The satellites in a constellation are all deployed in space and form a relatively stable spatial configuration, and there is also a relatively stable spatio-temporal relationship between satellites. Through the mutual cooperation between constellations, the satellite constellation can greatly improve the ground coverage range and the efficiency of ground observation such as communication and navigation on the basis of a single satellite. Therefore, by revealing the influence mechanism of constellation configuration parameters such as orbit inclination, orbit altitude, and the number of satellites and the simulation period on the global average sea surface height measurement accuracy, a satellite constellation configuration scheme that meets the height measurement requirements can be constructed based on a typical Walker constellation, so as to estimate the different height measurement accuracies that can be obtained under different conditions.

[0098] (1) Geometric Model for Sea Surface Altimetry

[0099] For orbital parameters, due to the characteristics of low-earth orbit satellites such as low antenna transmission power, high resolution, small delay, and short revisit period, and the uniform ground resolution of satellites in near-circular orbits, the satellite constellations for earth observation usually consist of multiple near-circular LEO satellites. Here, referring to the TDS-1 mission, the main orbital parameters of the GNSS-R constellation are set the same as it.

[0100] For the antenna observation mode, the spaceborne GNSS-R payload generally includes: one or two left-hand circular polarization antennas (LHCP), one right-hand circular polarization antenna (RHCP), and a dedicated GNSS-R receiver. Among them, the LHCP antenna is used to receive GNSS signals reflected from the earth's surface. The size and position of the reflected ground coverage are closely related to the beam width and surface direction of each LHCP antenna. The antenna beam width of the TDS-1 mission is 34°×35° at the GPS L1 frequency. In this invention, the same antenna observation mode as the TDS-1 satellite is also adopted.

[0101] This invention needs to define an antenna coverage range and select appropriate GNSS signals for each LEO satellite. Figure 1 It is a schematic diagram of the GNSS-R antenna coverage. Among them, point P and point P' are both specular reflection points, point O is the center of the earth; β is the elevation beam width of the antenna, Φ is the geocentric angle between the GNSS-R LEO satellite and the specular reflection point, θ is the geocentric angle between the GNSS-R LEO satellite and the GNSS satellite, and α min is the minimum coverage elevation angle of the antenna; h is the orbital height of the GNSS-R LEO satellite, H is the orbital height of the GNSS satellite, and R is the average radius of the earth. The area between P and P' is the antenna-reflected ground coverage area.

[0102] From the geometric model combined with trigonometric function relationships, it can be obtained that:

[0103]

[0104] It can be seen that the size of the angle θ between the GNSS satellite and the LEO satellite mainly depends on H and α, that is, θ changes with the height of different GNSS satellites, where the range of H is 19100 - 35900 km.

[0105] (2) Calculation of Specular Reflection Point

[0106] Currently, the mirror reflection point algorithms mainly include the S.C. Wu algorithm, the Gleason algorithm, the line segment bisection method, etc. In this invention, the bisection method is selected to calculate the mirror reflection point. Through the bisection algorithm, the angles between the receiver and the mirror reflection point and between the GNSS satellite and the mirror reflection point that satisfy the Fresnel condition are iteratively solved, and then the results obtained by iteration are substituted into the GNSS-R geometric relationship to solve the specific coordinates of the mirror reflection point.

[0107] (3) Calculation of the correlation power of the reflected signal

[0108] Due to the existence of noise, the scattered signal correlation power model usually refers to the first-order statistical average, that is, the correlation power after non-coherent accumulation, which is a function of two variables, the time delay τ and the Doppler f. c Here, we choose the Z-V model to simulate the correlation power waveform of the reflected signal at the receiver end, and the theoretical expression of the scattered signal power at any time can be obtained:

[0109]

[0110] Among them, P T represents the power of the GNSS transmitter, λ represents the electromagnetic wavelength of the GNSS signal, T i represents the coherent integration time, ρ represents the position information of the mirror reflection point, G T (ρ) and G R (ρ) represent the antenna power gain of the GNSS transmitter and the antenna power gain of the spaceborne receiver respectively, R TP and R PR represent the geometric distances from the navigation satellite and the LEO satellite to the mirror reflection point respectively, Δτ(ρ) represents the time delay difference between the local replica signal and the incoming wave signal, Δf(ρ) represents the Doppler frequency difference between the local replica signal and the incoming wave signal, and σ0(ρ) is the normalized bistatic scattering coefficient, and Λ represents the Woodward ambiguity function (WAF). σ0(ρ) can be expressed as:

[0111]

[0112] In the formula, P PDF (·) is the probability density function of the sea surface slope. From equations (3.2) and (3.3), it can be seen that the contribution of the scattered signal mainly comes from the intersection area of four spatial regions: the antenna coverage area determined by G T (ρ) and G R (ρ), the equal-delay area determined by the characteristics of the Λ 2 function, the equal-Doppler area determined by |S| 2 , and the illumination area related to the sea surface roughness determined by P PDF .

[0113] (4) Calculation of the altimetry accuracy of the global mean sea surface

[0114] The mean square error σ of the sea surface height measurement at the single mirror reflection point ssh The calculation formula is as follows:

[0115]

[0116] In the formula, P Z (0) and P Z (0)' are the amplitude of the average power and the slope of the power waveform at the mirror reflection point, c is the speed of light in vacuum, is defined as the altimetry sensitivity, indicating the change of the altimetry result with the ratio of the magnitude of the correlation power of the reflected signal and its change rate. It can be seen from the altimetry mean square error model that the altimetry mean square error is related to the signal correlation power SNR, the non-coherent accumulation times N incoh , the height angle ε of the mirror reflection point ele , the maximum slope P of the leading edge of the delay waveform Z (0)' and the corresponding average power P at the mirror reflection point Z (0). When only thermal noise is considered, SNR can be expressed as:

[0117]

[0118] Among them, k is the Boltzmann constant K = 1.3806505×10 -23 J / K; T is the equivalent temperature of the receiver, and B is the signal bandwidth of the receiver.

[0119] After the altimetry accuracy calculation of the single mirror reflection point is completed, the earth is divided into 0.2°×0.2° (20km×20km) grids. All the calculated mirror reflection points are projected into the divided grids according to their longitude and latitude coordinates. After the division is completed, the number of points and the single-point accuracy in each grid are counted, and the average altimetry accuracy of each grid can be obtained:

[0120]

[0121] In the formula, n is the number of mirror reflection points in the grid. The finally calculated altimetry accuracy of the global mean sea surface is:

[0122]

[0123] (5) Prediction model of the altimetry accuracy of the global mean sea surface

[0124] Currently, the feasibility of GNSS-R global sea surface altimetry based on the constellation platform has been verified, but there is a lack of specific evaluation of its altimetry ability. Moreover, due to the large amount of simulation work, if large-scale and small-step simulations are carried out over a long simulation period, the time consumed will be measured in years. Therefore, the present invention selects to establish a global mean sea surface altimetry accuracy prediction model using a multi-layer feedforward neural network, so as to facilitate subsequent accurate and efficient quantitative evaluation of the altimetry ability of the satellite constellation, and thus select the best constellation configuration and simulation time that can meet the current altimetry accuracy requirements.

[0125] The multi-layer feedforward neural network includes an input layer, a hidden layer and an output layer, and it obtains the expected output result by adjusting the weight thresholds between the neural network nodes. The specific neural network structure diagram is as Figure 2 shown. The learning method of the multi-layer feedforward neural network includes: transmitting information layer by layer in a forward manner, and backpropagating the error between the output result and the expected result layer by layer in a reverse manner, and then adjusting the connection weights between the neuron nodes. Through such repeated cyclic processing, the multi-layer feedforward neural network is trained, and finally the optimal multi-layer feedforward neural network model can be obtained.

[0126] The number of neurons in the input layer of the multi-layer feedforward neural network is determined by the number of input data variables. In the present invention, the configuration parameters of the satellite constellation (orbital altitude, orbital inclination and number of satellites) and the simulation period are used as input nodes, that is, the number of nodes in the input layer is 4; the finally calculated global mean sea surface altimetry accuracy is used as the output node, that is, the number of nodes in the output layer is 1.

[0127] For the selection of the training function, considering the disadvantages of slow convergence speed and easy to fall into local minima of the neural network, the present invention selects the LM (Levenberg Marquardt) algorithm. The LM algorithm is a combination of the gradient descent method and the Gauss-Newton method. It has both the local convergence of the Gauss-Newton method and the global characteristics of the gradient method, and has the advantages of fast convergence speed and high stability when the number of network parameters is relatively small, so that the number of network iterations can be reduced

[49] ; for the selection of the transfer function, the present invention uses the non-linear transfer function tansig for the input layer and the hidden layer of the network, and the linear function purelin for the output layer to keep the range of the output.

[0128] Aiming at the disadvantages of the gradient descent method, the present invention introduces the ADAM optimization algorithm. This algorithm combines the advantages of the GDM and RMSprop optimizers, and can dynamically adjust the adaptive learning rates of different parameters to update the weights and thresholds of the multi-layer feedforward neural network. The Adam optimization algorithm calculates the first moment estimate m of the gradient g t and the second moment estimate v t, thus correcting the first - order moment estimation bias and the second - order moment estimation bias, and finally correcting the weight threshold of the network. Among them, m t and v t are calculated as follows:

[0129] m t =β1·m t-1 +(1 - β1)·dk (3.8)

[0130] v t =β2·v t-1 +(1 - β2)·dk 2 (3.9)

[0131] Among them, m t and v t represent the first - order and second - order moment estimations after iteration respectively; β1 and β2 represent the exponential weighted average parameters; dk and dk 2 represent the gradient value and the square of the gradient value of the neural network weight or threshold respectively. The finally updated weights and thresholds can be expressed as:

[0132]

[0133]

[0134] Among them, w t and b t are the updated neural network weights and thresholds, α is the learning rate, and δ is the smoothing term.

[0135] To evaluate the performance of the finally established multi - layer feed - forward neural network prediction model, an overall evaluation index R 2 , that is, the coefficient of determination, is introduced to evaluate the generalization ability of the network model. Its definition formula is as follows:

[0136]

[0137] In the formula: is the predicted data of the i - th sample; y i (i = 1, 2, …, n) is the true data of the i - th sample; n is the number of samples. When the value of R 2 is closer to 1, it indicates that the performance of the multi - layer feed - forward network prediction model is better.

[0138] 3. Results and Discussion

[0139] For a satellite constellation, when discussing time scales greater than one orbital repeat period, the right ascension of the ascending node, the argument of perigee, and the true anomaly have little impact on the final results. Therefore, the present invention selects the satellite orbital altitude, orbital inclination, and the number of satellites as constellation configuration parameters respectively, and considering the simulation period, discusses the impact on the global mean sea surface height measurement accuracy. After clarifying the influence mechanism of each parameter, a global mean sea surface height measurement accuracy prediction model based on the satellite constellation is established using a multi-layer feedforward neural network.

[0140] The present invention conducts analysis and discussion based on the TDS-1 satellite orbit and antenna parameters. The satellite sampling time is 1 s, and a one-month simulation analysis and calculation are carried out using GPS L1 C / A, GLONASS L1OC, GALILEO E1A, and BDS-3B1 I signals. According to the single-point height measurement accuracy calculation formula (3.4), the analysis of different GNSS satellite signals yields the results as Figure 3 shown, that is, the height measurement accuracies of different GNSS satellite signals are different, and the single-point height measurement accuracy increases with the increase of the elevation angle of the specular reflection point.

[0141] (1) Results of height measurement accuracy at different orbital altitudes

[0142] When setting the discussion range of the orbital altitude, the application purpose of the satellite, the impact of the space debris environment, and the impact of link loss are mainly considered. When the satellite constellation is deployed at 800 km, 1100 km, and 1400 km, the space debris generated by their mutual collisions will stay in the space debris environment for a long time and cause a relatively serious impact on the environment, while when the satellite orbital altitude is 500 km, the impact on the space debris environment is the smallest; at the same time, the ultra-long distance between satellites or between the satellite and the ground leads to a large delay in information transmission, and the link loss also increases; in addition, when the satellite orbital altitude is lower, affected by the atmospheric density and resistance, its lifespan will be shortened. Therefore, when setting the constellation orbital altitude, many factors such as the height measurement accuracy requirement, signal transmission loss, and satellite lifespan should be comprehensively considered. The present invention sets the discussion range of the orbital altitude as 400 - 800 km, with a step size of 50 km, and discusses the influence mechanism of the orbital altitude on the global mean sea surface height measurement accuracy under the condition of only a single satellite when the orbital inclination is 97.5°. The variations of the global mean sea surface height measurement accuracy of a single satellite in the latitude direction and longitude direction at different orbital altitudes are respectively as Figure 5 and 6 shown.

[0143] From Figure 5 and Figure 6The results show that in terms of latitude distribution, the global average sea surface measurement accuracy is relatively high in the mid - low latitude regions and relatively low in the high - latitude regions. The latitude distribution range is related to the inclination angle of LEO satellites. The peak part of the latitude distribution represents a sharp increase in the number of specular reflection points in this area, but all are at low elevation angles. In terms of longitude distribution, the global average sea surface measurement accuracy changes little with longitude and is relatively evenly distributed within the longitude range. However, there is a slight decrease in accuracy around 100°E longitude. The reason for this phenomenon is the existence of GEO and IGSO satellites in the Beidou - 3 satellite navigation system. The longitude of the sub - satellite point trajectory intersection of the three IGSO satellites is 118°E, and the phase difference between the three satellites is 120°; the fixed positions of the three GEO satellites are 80°E, 110.5°E, and 140°E respectively. The existence of GEO and IGSO satellites enhances the coverage of the Beidou navigation system in the East Asian region, so the distribution of specular reflection points in this area is also relatively dense.

[0144] It can be seen from Figures 4 - 6 the results that the orbital altitude has an impact on the global average sea surface measurement accuracy, but the impact is relatively small. According to the GNSS - R spatial geometric relationship, within the current orbital altitude range, the higher the satellite orbital altitude, the more specular reflection points with high elevation angles can be generated, and the corresponding global average sea surface measurement accuracy is higher. However, since the GNSS - R signal travels a relatively long distance from the transmitter to the receiver, the effects of the ionosphere, troposphere, etc. need to be considered in the propagation path. Therefore, based on the calculation results, considering the signal transmission path loss, space debris environment, and the impact of the atmosphere on satellite life, etc., the designed constellation orbital altitude is finally selected as 500 km.

[0145] (2) Measurement accuracy results under different orbital inclinations

[0146] When setting the discussion range of the orbital altitude, the latitude coverage range of the detection target is mainly considered. Finally, the discussion range of the orbital inclination of the present invention is set to 70° - 95°, and the step size is set to 5°; according to the above - mentioned discussion results of the orbital altitude, when the orbital altitude is 500 km, the influence mechanism of the orbital inclination on the global average sea surface measurement accuracy under the condition of a single satellite is discussed. The changes in the global average sea surface measurement accuracy of a single satellite in the latitude and longitude directions under different orbital inclinations are respectively as Figure 6 and Figure 7 shown. Combining Figure 7 and Figure 8 the results, it can be seen that:

[0147] At different orbital inclinations, the distribution characteristics of the global average sea surface height measurement accuracy of a single satellite in the latitude and longitude directions are the same as those described above. Moreover, the larger the orbital inclination of the LEO satellite, the wider the latitude range of the distribution of its specular reflection points. The orbital inclination has a great influence on the sea surface height measurement accuracy. When the orbital inclination is 70°-90°, as the satellite orbital inclination increases, the global average sea surface height measurement accuracy decreases, but the sea surface height measurement range is wider; when the orbital inclination is 90°-95°, as the satellite orbital inclination increases, the global average sea surface height measurement accuracy increases, but the sea surface height measurement range shrinks. This result is mainly because as the satellite orbital inclination continuously increases, the coverage range of the global specular reflection points increases, resulting in a decrease in the global average measurement accuracy.

[0148] When the satellite is at the sun-synchronous orbit inclination, the satellite can operate under the same illumination conditions every day. While having a stable power supply, the fixed illumination can also bring a stable temperature environment to the satellite, reducing the design cost of the satellite in dealing with temperature environment changes. Considering the above factors, the designed constellation orbital inclination is finally selected as 97.5°.

[0149] (3) Sea surface height measurement accuracy results under different numbers of satellites

[0150] The discussion range of the number of satellites in the constellation is set to 2, 4, 6, and 8. Combining the above discussion content, the satellite orbital height is set to 500 km, and the orbital inclination is set to 97.5°. The global average sea surface height measurement accuracies of three Walker constellation configurations (δ constellation, rose constellation, and star constellation) are calculated under different numbers of satellites. It can be seen that different Walker constellation configurations have little influence on the global average sea surface height measurement accuracy, and the more satellites there are, the higher the global average sea surface height measurement accuracy.

[0151] (4) Sea surface height measurement accuracy results under different simulation periods

[0152] When the simulation period is one month, the sea surface height measurement accuracy only reaches the decimeter level, still unable to meet the sea surface height measurement accuracy requirements for underwater navigation. Therefore, in the present invention, the simulation period is extended to 1 year and 3 years respectively. Considering that the Walker constellation configuration has little influence on the accuracy, only the global average sea surface height measurement accuracy of the δ constellation configuration under different simulation periods is calculated. It can be seen that the longer the simulation period, the higher the corresponding global average sea surface height measurement accuracy. (5) Verification and application of the new combined multi-layer feedforward neural network weighted combined prediction model

[0153] When the number of constellation satellites is 8 and the simulation period is 1 year, the required accuracy of 5 - 8 cm for underwater navigation has been met. Therefore, it is speculated that when the number of constellation satellites is between 4 and 8, the required accuracy can also be achieved. However, due to the lack of simulation data, the altimetry ability of the constellation cannot be quantitatively estimated. Therefore, the present invention can train and discuss the four factors affecting altimetry accuracy discussed above by using a new combined multi-layer feedforward neural network weighted combined prediction model, so as to obtain the optimal constellation design scheme that meets the altimetry requirements. Here, the selected orbital height is 400 - 800 km, and the discussion step size is 50 km; the orbital inclination is 70 - 97.5°, and the discussion step size is 5°; the number of satellites is 1, 2, 4, 8; the simulation periods are 1 year and 3 years. 90% of the data is randomly selected as the training sample.

[0154] Figure 9 It is a comparison chart of the global mean sea surface altimetry accuracy output by the new combined multi-layer feedforward neural network weighted combined prediction model and the actual simulation accuracy results. It can be seen that in the test set samples, the model prediction value and the actual simulation value are relatively close, and the determination coefficient R 2 is 0.9989, indicating that the new combined multi-layer feedforward neural network weighted combined prediction model is relatively accurate in predicting the global mean sea surface altimetry accuracy. At the same time, the results of the mean absolute error (MAE), mean absolute percentage error (MAPE), mean square error (MSE), and root mean square error (RMSE) are all small, which also indicates that the multi-layer feedforward neural network prediction model performs well.

[0155] The training process of the multi-layer feedforward neural network is as Figure 10 and Figure 11 shown. Figure 10 It is the training times and effect diagram of the neural network dataset. Figure 10 The circle in it is the best verification position. Figure 11 It is the fitting effect diagram of the neural network. The fitting value is regressed to the true value. The higher the goodness of fit, the better the fitting effect. It can be seen that as the number of iterations increases, the MSE gradually decreases and approaches the minimum value. When the algebra is 20 times, the lowest mean square error appears in the validation set, that is, the model effect is the best at this time. Combining the above-discussed evaluation indicators, the new combined multi-layer feedforward neural network weighted combined prediction model can better evaluate the altimetry ability of the constellation under a given orbital height, orbital inclination, and number of satellites, so as to quantitatively analyze the global mean sea surface altimetry accuracy. At this time, the model expression is:

[0156]

[0157]

[0158] Using this model, the present invention can quantitatively analyze the performance of satellite constellations for sea surface measurement under unknown simulation parameters. The present invention analyzes that when the number of satellites is between 4 and 8 and the simulation period is one year, the underwater navigation accuracy requirements can be met. Therefore, here the present invention uses this model to predict the measurement accuracy at different orbital altitudes and different numbers of satellites. The results are as Figure 12 shown. It can be seen that when the number of satellites is 6 and 7, the measurement accuracy at any orbital altitude can meet the requirements. However, when the number of orbits is 7, the accuracy only increases by about 0.004 cm, and the increase amplitude is small. Therefore, considering the actual cost, the present invention believes that when the orbital altitude is 500 km, the orbital inclination is 97.5°, the number of satellites is 6, and the simulation period is 1 year, this satellite constellation can meet the centimeter-level accuracy required for underwater navigation.

[0159] Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention. Without conflict, the embodiments of the present application and the technical features in the embodiments can be combined with each other.

[0160] The content not detailedly described in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims

1. Method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network, characterized in that, Including: Divide the Earth's sea surface into grids and obtain the average altimetry accuracy σ of each grid grid ; According to the average measurement accuracy σ of each grid grid , the average measurement accuracy σ of all grids is obtained grid and the average value According to the average measurement accuracy σ of all grids grid the average value of determine the global average sea surface measurement accuracy σ of spaceborne GNSS-R global ; Establish a high-precision prediction model for global mean sea surface height measurement; Conduct a feasibility verification on the high-precision prediction model for global mean sea surface height measurement to obtain a high-precision prediction model for global mean sea surface height measurement that meets the verification conditions; Use the high-precision prediction model for global mean sea surface height measurement that meets the verification conditions to perform simulation calculations under different simulation ranges to obtain multiple high-precision prediction results for global mean sea surface height measurement; Screen the obtained multiple high-precision prediction results for global mean sea surface height measurement, and screen out the prediction results that meet the value range of sea surface height measurement for underwater navigation as the screening results; The orbital altitude, orbital inclination, number of satellites, and simulation period corresponding to the screening results are used as the constellation design scheme, and the obtained constellation design scheme is used for the design and launch of the GNSS-R altimetry constellation, and finally the measured value of the global mean sea surface height measurement accuracy is obtained.

2. The method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network according to claim 1, characterized in that, Method for obtaining the average measurement accuracy σ of each grid, specifically: grid ​ Among them, represents the mean square error σ of the sea surface height measurement of all single specular reflection points in the grid ssh , and n is the number of single specular reflection points included in each divided grid.

3. The method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network according to claim 2, characterized in that, Among them, σ ssh is the mean square error of sea surface height measurement at the single mirror reflection point, P Z (0) and P Z (0)' are the amplitude of the average power and the slope of the power waveform at the single mirror reflection point in each grid, c is the speed of light in vacuum, SNR is the signal correlation power, N incoh is the number of non-coherent accumulations, ε ele is the elevation angle of the single mirror reflection point.

4. The method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network according to claim 1, characterized in that, 5. The method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network according to claim 1, characterized in that, The high-precision prediction model for global mean sea surface height measurement is specifically: y = -0.4018×tansig(-0.0463x1 - 1.6060x2 - 1.1038x3 + 1.1773x4 + 2.2772) + 0.9281×tansig(1.4336x1 - 0.0311x2 - 1.3815x3 + 1.1050x4 - 1.5181) - 0.1666×tansig(-0.5657x1 - 1.0521x2 + 1.4176x3 - 1.3226x4 + 0.7591) + 0.8444×tansig(0.8738x1 - 1.8850x2 - 0.3772x3 + 0.8525x4) + 0.2531×tansig(-1.5508x1 + 1.0884x2 - 0.1054x3 - 1.2590x4 - 0.7591) + 0.4047×tansig(-0.0039x1 - 1.3172x2 - 1.8088x3 - 0.4230x4 - 1.5181) + 0.1091×tansig(-1.4974x1 + 0.9534x2 - 0.4286x3 - 1.3605x4 - 2.2772) -0.2366 where y equals σ global , x1 is the orbital altitude, x2 is the orbital inclination, x3 is the number of satellites, and x4 is the simulation period.

6. The method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network according to any one of claims 1 to 5, characterized in that, The verification condition is any one of the overall evaluation index, mean absolute error, mean absolute percentage error, or root mean square error.

7. The method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network according to claim 6, characterized in that, The verification condition is a method for verifying the high-precision prediction model for global mean sea surface height measurement using the overall evaluation index, specifically: Among them, is the spaceborne GNSS-R global mean sea surface measurement accuracy σ corresponding to the i-th sample global ; y i (i = 1, 2, …, k) is the true data of the global mean sea surface measurement accuracy corresponding to the i-th sample; k is the number of samples; When R 2 is greater than 0.99, a global mean sea level measurement accuracy prediction model that meets the verification conditions is obtained.

8. The method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network according to claim 6, characterized in that, Perform simulation calculations on the orbital altitude, orbital inclination, number of satellites, and simulation period at a specific simulation step under different simulation ranges to obtain multiple high-precision prediction results for global mean sea surface height measurement; Among them, the simulation range of the orbital altitude is 300 km - 800 km, and the step size is 1 km; the simulation range of the orbital inclination is 70° - 97.5°, and the step size is 0.5°; the simulation range of the number of satellites is 1 - 8, and the step size is 1; the value range of the simulation period is 1 - 3 years, and the step size is 1 year.

9. The method for improving the global average measurement accuracy by weighting based on a multi-layer feedforward neural network according to claim 6, characterized in that, The value range requirement for the sea surface height measurement accuracy for underwater navigation is that the value range of the high-precision prediction results for global mean sea surface height measurement is 5 - 8 cm.

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