A method for improving the pulse-limited footprint resolution of GNSS-R systems based on bandwidth combination

Abstract

The present application relates to a kind of methods for improving the impulse restriction footprint resolution of GNSS-R system based on bandwidth combination.The global navigation satellite system GNSS signal reflection technology has become an effective means for space-based sea surface wind field inversion, and the wider the signal bandwidth, the higher the impulse restriction footprint resolution.But GNSS-R system all adopts traditional single-band signal method, limited by global navigation satellite system GNSS satellite signal, there is a theoretical upper limit to the signal bandwidth.To solve this problem, the present application proposes a new bandwidth combination method based on combined signal based on autocorrelation signal ambiguity theory.This method processes signals of two or more frequency bands to reduce the width of the main lobe of the autocorrelation function of the GNSS-R system, thereby improving the impulse restriction footprint resolution of the GNSS-R system.Compared with the traditional single-band signal method, the new bandwidth combination method improves the impulse restriction footprint resolution of the GNSS-R system by 1.73 times.

Description

Technical Field

[0001] This invention relates to the field of GNSS-R system remote sensing technology, and in particular to a method for improving the pulse-limited footprint resolution of GNSS-R systems based on bandwidth co-processing. Background Technology

[0002] In recent years, GNSS (Global Navigation Satellite System) signals have been found to be applicable to various environmental remote sensing technologies. For example, Martin-Neira et al., Katzberg et al., and Garrison et al. discovered that the multipath effect of GNSS signals reflected from the sea surface can serve as a new tool for ocean remote sensing. By deploying GNSS reflection signal receivers in Earth orbit to form a GNSS-R (Global Navigation Satellite System Reflectometry) system, a range of remote sensing applications can be carried out using GNSS reflection signals. Among these applications, sea surface wind field inversion has become one of the most popular areas of GNSS-R system remote sensing in recent years.

[0003] Traditional sea surface remote sensing methods employ monostatic radar, which requires specialized transmitters and receivers, as well as large directional antennas to achieve high resolution. In contrast, the GNSS-R system studied in this invention is a bistatic radar system that requires only one receiver, eliminating the need for a transmitter, as the Global Navigation Satellite System (GNSS) satellites provide the transmitted signals. The bistatic structure of the GNSS-R system and the unique characteristics of GNSS signals allow it to obtain ocean surface height characteristics within a mesoscale range without the need for large directional antennas. This characteristic is one of the advantages of the GNSS-R system for sea surface wind field inversion.

[0004] In 1993, Martin-Neira first proposed and described a bistatic GNSS-R system using GPS signals. In 1994, Auber accidentally obtained and reported GPS reflected signals on an airborne platform. These potential remote sensing signals from the ionosphere and sea surface were discovered by Katzberg et al. in 1996. They first theoretically predicted the changes in GPS signals after reflection from the sea surface and land. Subsequently, Garrison et al. demonstrated the feasibility of tracking GNSS reflected signals using a left-hand circularly polarized antenna and a conventional GPS receiver in airborne experiments. In addition, NASA research also proposed using a low-Earth orbit receiving platform to collect GPS signals reflected from the sea surface and conducted multiple airborne flight tests under different sea surface conditions using a delay-mapping receiver. They analyzed the relationship between the reflected signal power curve and sea surface roughness under different time delays, laying the initial theoretical and experimental foundation for inverting sea surface wind speed using GPS reflected signals under airborne conditions. In 1997, Elfouhaily et al., building upon previous research, established a unified directional spectrum for long-wave and short-wave propagation driven by wind, laying the foundation for theoretical model research on sea surface wind field inversion. Zavorotny et al. (2000), through systematic analysis of GPS reflected signal sea wind detection, proposed a mature and now widely used time-delay Doppler two-dimensional power model for GPS reflected signals, namely the ZV model, using bistatic radar equations combined with geometric optics approximation principles, providing a theoretical basis for sea wind detection based on GNSS-R systems. In 2003, Zuffda, using theoretical models and actual airborne data, specifically analyzed the sensitivity of the GPS reflected signal correlation power curve to sea surface wind speed and direction, receiver platform height, satellite elevation angle, and receiver coherence integration time, providing a concrete and clear theoretical basis for better conducting sea surface wind field inversion experiments. NASA, the University of Colorado, the European Space Agency (ESA), and Starlab in Spain have conducted numerous experiments, including those on airborne, spaceborne, and hot air balloon receiving platforms. Wind field information is obtained by matching waveforms from theoretical models with those from actual experiments, and the results are compared and analyzed. In recent years, in addition to waveform matching, methods for wind field inversion under airborne conditions have proposed methods such as Delay-Doppler Maps (DDM) deconvolution and extraction of related geometric parameters. In 2011, Valencia used image processing methods to deconvolve the DDM to obtain scattering coefficients, estimated the mean square slope of the sea surface using these coefficients, and performed wind field inversion based on the relationship between the mean square slope and sea surface wind speed and direction. On the spaceborne side, in 2005, Gleason used measured data to analyze the changes in signal-to-noise ratio and the corresponding altimetry accuracy under different spaceborne platform altitudes and antenna configurations. In 2014, Li et al. used a two-dimensional least squares fitting method and a variable-length iterative method to determine parameters for wind field inversion under spaceborne conditions.In 2015, Clarizia et al. analyzed the mean, variance, leading edge slope, and tail slope of spaceborne DDM and obtained the empirical relationship with wind speed through regression fitting.

[0005] Currently, the feasibility (i.e., sensitivity) of GNSS-R system sea surface wind field inversion technology has been verified; further improving resolution is key to its application. High-resolution GNSS-R system sea surface wind field inversion data can effectively improve the clarity of the retrieved ocean physical models, which is of great significance for refined research on ocean motion. The integrated air-sea navigation and detection team has conducted forward-looking research on the theoretical methods and key technologies for obtaining high-precision, high-resolution ocean gravity fields based on spaceborne GNSS-R system measurement methods, thereby improving the accuracy of underwater gravity matching navigation. Obtaining high-precision, high-resolution sea surface information data based on spaceborne GNSS-R technology is one of the key technologies.

[0006] Depending on the signal processing method used to acquire the time delay, GNSS-R systems for sea surface wind field inversion are mainly divided into cGNSS-R (conventional GNSS-R) systems and iGNSS-R systems. The cGNSS-R system obtains the time delay by correlating the reflected signal with a locally generated copy of the transmitted signal after Doppler frequency shift compensation for a certain period (usually 1 ms). Currently implemented spaceborne GNSS-R scattering systems all employ cGNSS-R technology, such as UK-DMC (UK Disaster Monitoring Constellation, launched September 27, 2003), TDS-1 (TechDemoSat-1, launched July 8, 2014), 3Cat-2 (launched August 15, 2016), CYGNSS (Cyclone Global Navigation Satellite System, launched December 15, 2016), and BuFeng-1 Constellation (launched June 5, 2019). However, since the aforementioned spaceborne GNSS-R systems all use a single C / A code frequency band with a relatively narrow bandwidth (2.046MHz), this limits their pulse-limited footprint resolution. To overcome this bandwidth limitation, Martin-Neira et al. proposed the iGNSS-R concept and related models. iGNSS-R does not require knowledge of the ranging code structure; it directly correlates the reflected signal with the direct signal to obtain time delay information. Therefore, iGNSS-R technology can extract all spectral components from the GNSS transmitted signal of the Global Navigation Satellite System (GNSS), improving the clarity of the autocorrelation function and thus improving the pulse-limited footprint resolution. However, iGNSS-R sea surface wind field inversion is also directly related to SNR. Since correlating the direct and reflected signals and increasing the signal bandwidth introduce higher thermal noise, a higher-gain direct / reflected signal receiving antenna is needed to improve SNR. Furthermore, iGNSS-R cannot distinguish GNSS satellites based on the code structure; it requires antennas to synthesize multiple variable-pointing beams to simultaneously acquire and track multiple GNSS reflected signals. Therefore, spaceborne iGNSS-R sea surface wind field inversion systems are better suited to using high-gain (directivity coefficient greater than 20 dBi) digital multi-beam phased array antennas. This makes iGNSS-R systems more complex and more expensive than cGNSS-R systems. Furthermore, due to the inherent bandwidth limitations of GNSS signals, even using a single-band iGNSS-R method, the bandwidth is limited to within 25 MHz, corresponding to a pulse-limited footprint resolution of ~5 km. This still falls short of the 1-2 km pulse-limited footprint resolution requirements of future high-resolution sea surface wind field inversion systems.

[0007] With the development of GNSS signals, GNSS systems have introduced new signal modulation methods and wider bandwidth signals to optimize tracking performance. Among them, the Galileo satellite navigation system uses ALT-BOC signal modulation, with the E5 frequency signal as the background, and combines the E5a and E5b signal components at two frequencies into a multi-carrier composite broadband (51.15MHz) signal with upper and lower sideband structures. This signal's bandwidth is at least twice that of previous GNSS signals, providing a new opportunity to improve the pulse-limited footprint resolution of sea surface wind field inversion in spaceborne GNSS-R systems. Furthermore, Galileo's E5a and E5b signals have an open encoding method, allowing GNSS-R systems based on E5a and E5b signals to adopt a cGNSS-R approach, thereby reducing the complexity and cost of the GNSS-R system while maintaining sea surface wind field inversion performance.

[0008] Therefore, there is an urgent need for a method to improve the resolution of pulse-limited footprints, thereby improving the clarity of GNSS-R system remote sensing technology, which is of great significance for the detailed study of physical parameters such as ocean, land surface, and vegetation. Summary of the Invention

[0009] The present invention is proposed to alleviate or solve at least one aspect or point of the above-mentioned problems.

[0010] The present invention provides a method for improving the pulse-limited footprint resolution of a GNSS-R system based on bandwidth co-processing, comprising the following steps:

[0011] By combining satellite signals with essentially the same signal structure in the Global Navigation Satellite System (GNSS), a combined signal is formed. After the combined signal with a wider bandwidth is reflected, it is received by the GNSS-R system. After coherence with the GNSS signal copy data pre-stored in the GNSS-R system, the resulting constrained pulse size is smaller and the resolution is higher than that of a single signal.

[0012] A combined signal is a combination of two or more satellite signals with essentially the same signal structure. These signals can originate from the same system or different systems.

[0013] Preferably, in the Global Navigation Satellite System (GNSS), the center frequencies fc1 and fc2 of satellite signals with essentially the same signal structure are required to be more than half the sum of the bandwidths fs1 and fs2 of the two satellite signals, but not more than the sum of the bandwidths fs1 and fs2 of the two satellite signals.

[0014] Where fc1 and fc2 are the center frequencies of two signals from a Global Navigation Satellite System (GNSS) satellite, and fs1 and fs2 are the bandwidths of two signals from a GNSS satellite.

[0015] Preferably, the signals in the Global Navigation Satellite System (GNSS) with essentially the same signal structure are two signals, E5a and E5b, from the Galileo system's E5 band navigation signal. E5a and E5b have the same bandwidth and are combined into a single wideband signal. E5a and E5b are broadcast at two center frequencies of 1176.45MHz and 1207.14MHz, respectively. Both E5a and E5b consist of two quadrature components. The alternating binary offset carrier (ALT-BOC) technique is used to combine E5a and E5b into a constant envelope signal.

[0016] Preferably, the E5a signal is the lower sideband of ALT-BOC (E5a / b), which can be regarded as a QPSK (10) with data and pilot orthogonality; the E5b signal is the upper sideband of the E5 signal, and its orthogonal components E5bI and E5bQ can both be regarded as BPSK.

[0017] Preferably, the bandwidth of both the E5a and E5b signals is 20.46MHz. Based on the signal frequency, it can be seen that when the two signals are combined into a single E5a / b combined broadband signal, the bandwidth can reach 51.15MHz. Preferably, the only factor limiting the pulse footprint size of the E5a / b combined broadband signal is the square of the autocorrelation function Λ.

[0018] The GNSS-R system signal model used in this invention is based on the Kirchhoff approximation. The Kirchhoff approximation shows that a relatively "smooth" small patch of rough surface sample can be approximated by the tangent plane at any point on the sample. For a certain time t0, the cross-correlation coefficient of the received reflected signal u with respect to different time delay values ​​τ can be expressed as an integral.

[0019]

[0020] Among them, T i Let a(t) represent the integration time, and let τ represent a chip time interval. c The direct signal waveform within, f c Let represent the frequency offset factor, used to compensate for the Doppler frequency offset of the reflected signal. From formula (1), it can be seen that the maximum cross-correlation value between the direct signal waveform a(t) and the reflected signal waveform u(t) occurs at the Doppler frequency offset, which has been completely compensated, and the time series of the two signals are perfectly aligned.

[0021] Establish a coordinate system where the specular reflection point is the origin, the xoy plane is the tangent plane on the Earth's surface passing through the specular reflection point, and the z-axis is the normal direction of the specular reflection point. The GNSS scattered signal from the Global Navigation Satellite System reaching the GNSS-R system receiver can be modeled by integrating over the mean sea surface:

[0022]

[0023] in, This indicates the beam pattern of the GNSS-R system receiving antenna at the scattering point. The gain in direction, a(t) represents the PRN code function, c represents the speed of light, and R T (t) and R R (t) represents the distance from any scattering point within the scintillation region to the transmitter and receiver, respectively, where the coordinates of the scattering point are... in This represents the altitude of the scattering point. Since the scintillation zone is usually small, the sea surface within the scintillation zone can be approximated as a flat plane. Therefore, the Earth's curvature of the sea surface within the scintillation zone can be ignored, and the sea surface within the scintillation zone can be considered as a small patch of sea surface. Where x and y represent the coordinates of the scattering point on the Earth's surface, and z represents the altitude of the scattering point.

[0024] In addition, g in formula (2) represents the propagation and scattering process.

[0025]

[0026] Where V represents the Fresnel reflection coefficient; Let q represent the scattering vector, where k = 2π / λ represents the radiation wavenumber, and q represents the scattering vector. z Represents the scattering vector The magnitude of the sea level normal component at the point of reflection of the mirror. The unit vector representing the incident wave. The unit vector representing the scattered wave, where i represents the imaginary unit, has a value equal to... Substituting equation (3) into equation (2), and then into equation (1), the instantaneous signal can be expressed as equation (4):

[0027]

[0028] The function Λ represents the autocorrelation function of the PRN code of a GNSS satellite:

[0029]

[0030] The Doppler spread function S(Δf) can be approximated as a sinc function:

[0031]

[0032] The greatest correlation between the received reflected signal and the signal replica in the GNSS-R system occurs when the signal after Doppler frequency shift compensation is aligned with the receiver replica a. If the received signal comes from sea surface reflection, the reflected signal u can be represented as the sum of multiple paths, which contain different time delays and different Doppler frequency shifts. According to formulas (5) and (6), the maximum value of the cross-correlation function between the direct signal and the reflected signal can only be obtained when the time delay and Doppler of the direct signal and the reflected signal are corrected. The same delay corresponds to the concentric rings in the sea surface scintillation zone, and this area can be directly reached by the GNSS signal link of the Global Navigation Satellite System (GNSS). After obtaining the navigation and positioning signal of the GNSS-R system, it is calculated that the average power of the delayed signal can be obtained by integrating its inner product over time T. i The inner average is obtained

[0033]

[0034] Substituting equation (4) into equation (7), we can obtain the average power expression for the time delay τ and frequency offset Δf, assuming the cumulative time T. i Within the scintillation zone, the elevation of all scattering points is consistent:

[0035]

[0036] This equation is called the bistatic radar equation, and the parameters... Represents the scattering point The normalized biradial scattering cross section at sea level, where Represents the scattering point The scattering vector at that location, and also in formula (8)

[0037]

[0038] Indicates pulse-limited footprints,

[0039] Using a low-gain antenna, the antenna gain is assumed to be within the scintillation region. constant Therefore, the integral factor representing the antenna gain in formula (8) It can be removed. Within the scintillation region, the frequency difference Δf between the Doppler frequency offset and the compensation frequency remains 0. Then, according to formula (6), the variable S is close to 1, indicating complete Doppler frequency offset compensation. Under typical conditions of altitude, speed, and number of accumulations for a GNSS receiver in a global navigation satellite system, the accumulation time T i ~1ms, therefore, we can further assume S=1. After reasonable simplification, the only factor determining the pulse-limited footprint size is Λ. 2 ,

[0040] Preferably, the E5a / b combined broadband signal has increased signal bandwidth, reducing the main lobe width of the PRN autocorrelation function. The autocorrelation function of the PRN signal is the Fourier transform of its power spectral density (PSD), i.e.

[0041] Λ PRN (τ)=F{P PRN (f)} (10)

[0042] Where represents the autocorrelation function of the PRN signal, represents the Fourier transform operator, and represents the power spectral density of the PRN signal. The PRN signal can be considered as a BPSK or QPSK signal, and its power spectral density is considered to be a sinc squared function, i.e.

[0043]

[0044] Where represents the signal bandwidth, represents the center frequency of the carrier, and the Fourier transform of the squared sinc function is known to be a triangular wave function, i.e.

[0045]

[0046] Where represents the triangular wavefunction model with a base length of (i.e., to ), therefore its main lobe width is .

[0047] Substituting equations (12) and (11) into equation (10), we obtain the autocorrelation function expression for the PRN signal.

[0048]

[0049] As shown in formula (13), the main lobe width of the PRN signal autocorrelation function is inversely proportional to the signal bandwidth. By increasing the signal bandwidth, the main lobe width of the PRN signal autocorrelation function can be reduced.

[0050] Preferably, the main lobe width of the combined E5a / b wideband signal autocorrelation function is 1 / 3 of the main lobe width of the E5a signal autocorrelation function.

[0051] Since E5a and E5b signals have the same bandwidth, and the PSDs of BPSK and QPSK signals both follow the sinc function rule, the PSD of the joint E5a / b signal can be defined as follows:

[0052]

[0053] in, and These represent the signal bandwidths of E5a and E5b, respectively, and their values ​​are... and These represent the carrier center frequencies of E5a and E5b, respectively. Since E5a and E5b have the same signal bandwidth...

[0054]

[0055] Substituting formula (15) into formula (14), we get

[0056]

[0057] The autocorrelation function of the joint E5a and E5b signal is the Fourier transform of its PSD, i.e.

[0058]

[0059] Based on the operational characteristics of the Fourier transform, and (where Δf) c =30.69MHz), then we can obtain

[0060]

[0061] According to formula (12), the Fourier transform of the sinc square function is a function with a base length of... height f s The triangular function, since the PSD of the E5a signal is a sinc square function, the region within this triangle represents the main lobe of the autocorrelation function of the E5a signal, and its main lobe width is...

[0062]

[0063] Substitute formula (12) into formula (18), and then adjust the complex terms in the formula. Take the real part

[0064]

[0065] For the E5 signal's two subbands, E5a and E5b, both have a signal bandwidth of f. s =20.46MHz, and the center frequency interval between the two sub-bands E5a and E5b is Δf. c =30.69MHz, the region between the first pair of minimum values ​​of the autocorrelation function is the main lobe of the E5a / b joint signal autocorrelation function, and its main lobe width is

[0066]

[0067] f s and Δf cSubstituting the specific values, we obtain that the main lobe width of the autocorrelation function of the E5a signal is 97.8 ns, the main lobe width of the autocorrelation function of the E5a / b joint signal is 32.6 ns, and the main lobe width of the autocorrelation function of the E5a and E5b joint signal is 1 / 3 of the main lobe width of the autocorrelation function of the E5a signal.

[0068] Preferably, in the GNSS-R system, the size of the pulse-limited footprint is proportional to the square root of the main lobe width of the signal's autocorrelation function, and the size of the pulse-limited footprint can be calculated by the following formula.

[0069]

[0070] Where a and b represent the major and minor semi-axis of the pulse-limited footprint ellipse, respectively, and θ R BW represents the elevation angle of the satellite in the GNSS-R system; BW represents the main lobe width of the signal's autocorrelation function.

[0071] As can be seen from formula (22), the size of the pulse-limited footprint is proportional to the square root of the main lobe width of the autocorrelation function of the signal.

[0072] Preferably, the size of the pulse-limited footprint of the E5a / b combined broadband signal is 0.58 times the size of the pulse-limited footprint of the E5a signal.

[0073] Pulse-constrained footprint resolution refers to the size of the smallest distinguishable unit during remote sensing, determined by the pulse-constrained footprint size. Pulse-constrained footprint resolution is expressed by the following formula:

[0074]

[0075] Where ε a ε b Let a and b represent the pulse-limited footprint resolution along the long and short sides of the pulse-limited footprint ellipse, respectively. In formula (23), the smaller the size of the major semi-axis a and minor semi-axis b of the pulse-limited footprint ellipse, the smaller the size of the smallest unit that can be distinguished in the remote sensing process, and the more refined the remote sensing information that can be obtained, thus improving the pulse-limited footprint resolution. The improvement factor of the pulse-limited footprint resolution can be expressed by formula (24).

[0076]

[0077] Where dε a ,dε b These represent the factors that improve the resolution of pulse-limited footprints along the long and short sides of the pulse-limited footprint ellipse, respectively. The pulse-limited footprint resolution of the combined E5a and E5b signals is 1.73 times higher than that of the E5a signal alone.

[0078] This invention combines two or more satellite signals, which have equivalent bandwidth. The combined signal increases the signal bandwidth, leading to a reduction in the main lobe width of the signal autocorrelation function and a larger pulse-limited footprint size, thereby improving pulse-limited footprint resolution and enhancing the performance of GNSS-R system remote sensing technology. Attached Figure Description

[0079] Figure 1 GNSS-R system principle.

[0080] Figure 2 Geometric relationships of the GNSS-R system.

[0081] Figure 3 Galileo E5 signal power spectral density.

[0082] Figure 4 Schematic diagram of the antenna structure of the E5a / b combined signal GNSS-R system.

[0083] Figure 5 Simulation curves of antenna voltage standing wave ratio for E5a / b joint bandwidth GNSS-R system.

[0084] Figure 6 Simulated radiation pattern of antenna for E5a / b joint bandwidth GNSS-R system.

[0085] Figure 7 Joint Signal GNSS-R System Antenna Verification Prototype.

[0086] Figure 8 Autocorrelation function curves of the E5a / b combined signal and the E5a signal alone.

[0087] Figure 9 Comparison of footprints limited by combined signal and individual E5a signal pulses. Detailed Implementation

[0088] The following description of embodiments of the present invention with reference to the accompanying drawings is intended to explain the overall inventive concept of the invention and should not be construed as a limitation thereof. In this invention, the same reference numerals denote the same or similar parts.

[0089] The features described herein may be implemented in various forms and should not be construed as limited to the examples described herein. Rather, the examples described herein are provided only to illustrate some of the many feasible ways in which the methods, apparatuses, and / or systems described herein will become clear upon understanding the disclosure of the invention.

[0090] Although terms such as “first,” “second,” and “third” may be used herein to describe various components, assemblies, regions, layers, or parts, these components, assemblies, regions, layers, or parts should not be limited by these terms. Rather, these terms are used only to distinguish one component, assembly, region, layer, or part from another.

[0091] In the specification, when an element (such as a layer, region, or substrate) is described as being "on" another element, "connected to," or "bonded to" another element, the element may be directly "on" another element, directly "connected to," or "bonded to" the other element, or one or more other elements may be present in between. Conversely, when an element is described as being "directly on" another element, "directly connected to," or "directly bonded to" another element, no other elements may be present in between.

[0092] The terminology used herein is for the purpose of describing various examples only and is not intended to limit disclosure. Unless the context clearly indicates otherwise, the singular form is intended to include the plural form as well. The terms “comprising,” “including,” and “having” indicate the presence of the described features, quantities, operations, components, elements, and / or combinations thereof, but do not preclude the presence or addition of one or more other features, quantities, operations, components, elements, and / or combinations thereof.

[0093] To enable those skilled in the art to utilize the content of this invention, the following exemplary embodiments may be provided in conjunction with specific application scenarios, specific systems, device and component parameters, and specific connection methods. However, these embodiments are merely examples for those skilled in the art, and the general principles defined herein can be applied to other embodiments and application scenarios without departing from the spirit and scope of this invention.

[0094] According to an exemplary embodiment of the present invention: Figure 1-9As shown, the Galileo system navigation E5 band signal is a satellite signal with a basically the same signal structure as other GNSS (Global Navigation Satellite System) signals. It consists of two signals, E5a and E5b, broadcast at two center frequencies of 1176.45MHz and 1207.14MHz, respectively. Both E5a and E5b are composed of two quadrature components. The two signals are combined into a constant envelope signal using the alternating binary offset carrier (ALT-BOC) technique. The E5a signal is the lower sideband of the ALT-BOC (E5a / b) and can be regarded as a QPSK (10) with data and pilot orthogonality. The E5b signal is the upper sideband of the E5 signal, and its quadrature components E5bI and E5bQ can be regarded as BPSK. The bandwidth of both E5a and E5b signals is 20.46MHz. According to the signal frequency, the bandwidth can reach 51.15MHz when the two signals are combined into a wideband signal (E5a / b combined signal). After reflection, the combined signal is received by the GNSS-R system. After coherence with the GNSS signal copy data of the Global Navigation Satellite System within the GNSS-R system, a larger confined pulse size and higher resolution are obtained compared to the single signal, which improves the sea surface wind field inversion performance of the GNSS-R system.

[0095] According to an exemplary embodiment of the present invention:

[0096] The pulse-limited footprint size of the combined broadband signal of the two signals E5a and E5b in the Galileo system navigation E5 band is limited only by the square of the autocorrelation function.

[0097] This invention employs the theoretical model proposed by Zavorotny et al. to predict the structure of the reflected signal received by the GNSS-R system receiver after the GNSS signal is reflected from the sea surface. The principle of the GNSS-R system is as follows: Figure 1 As shown. In Figure 1 In the GNSS-R system scenario shown, the strongest scattered signal originates only from a finite region around a nominal sea-level specular reflection point (i.e., the "scintillation zone"). The scattered signal outside the scintillation zone is very weak Bragg scattering, therefore this invention does not consider this type of scattering. This physical background leads this invention to use the Kirchhoff approximation of the geometrical optics limit for theoretical modeling of GNSS scattered signals in a global navigation satellite system.

[0098] The GNSS-R system signal model based on the Kirchhoff approximation used in this invention has been adopted by Beckham et al., Rytov et al., Clifford et al., Bass et al., Voronovich et al., and is applicable to short-wavelength, bistatic, rough surface scattering problems. The Kirchhoff approximation shows that a relatively "smooth" small patch of rough surface can be approximated as a tangent plane at any point on that sample. For a given time t0, the cross-correlation coefficient of the received reflected signal u with respect to different time delay values ​​τ can be expressed as an integral.

[0099]

[0100] Among them, T i Let a(t) represent the integration time, and let τ represent a chip time interval. c The waveform of the direct signal within. c denoted as frequency offset factor, used to compensate for the Doppler frequency offset of the reflected signal. As can be seen from formula (1), the maximum cross-correlation value between the direct signal waveform a(t) and the reflected signal waveform u(t) occurs at the Doppler frequency offset, which has been fully compensated, and the time series of the two signals are perfectly aligned.

[0101] Establish as Figure 2 The coordinate system shown is defined by the specular reflection point as its origin, the xoy plane as the tangent plane on the Earth's surface passing through the specular reflection point, and the z-axis as the normal direction to the specular reflection point. The GNSS scattered signal from the Global Navigation Satellite System reaching the GNSS-R system receiver can be modeled using an integral taken over the mean sea surface:

[0102]

[0103] in, This indicates the beam pattern of the GNSS-R system receiving antenna at the scattering point. The gain in direction, a(t) represents the PRN code function, and c represents the speed of light. R T (t) and R R (t) represents the distance from any scattering point within the scintillation region to the transmitter and receiver, respectively, where the coordinates of the scattering point are... in This indicates the altitude of the scattering point. Since the scintillation zone is typically small, the sea surface within it can be approximated as a flat plane, thus ignoring the Earth's curvature and treating it as a small patch of sea surface. Therefore, it can be considered... Where x and y represent the coordinates of the scattering point on the Earth's surface, and z represents the altitude of the scattering point.

[0104] In addition, g in formula (2) represents the propagation and scattering process.

[0105]

[0106] Where V represents the Fresnel reflection coefficient; q represents the scattering vector, where k = 2π / λ represents the radiation wavenumber; z Represents the scattering vector The magnitude of the sea level normal component at the point of reflection of the mirror; The unit vector representing the incident wave. The unit vector representing the scattered wave; i represents the imaginary unit, whose value is equal to... Substituting equation (3) into equation (2), and then into equation (1), the instantaneous signal can be expressed as equation (4):

[0107]

[0108] The function Λ represents the autocorrelation function of the PRN code of a GNSS satellite:

[0109]

[0110] The Doppler spread function S(Δf) can be approximated as a sinc function:

[0111]

[0112] The greatest correlation between the received reflected signal and the signal replica within the GNSS-R system occurs when the signal, after Doppler shift compensation, is aligned with the receiver replica a. If the received signal originates from sea surface reflection, the reflected signal u can be represented as the sum of multiple paths containing different time delays and different Doppler shifts. According to formulas (5) and (6), the maximum value of the cross-correlation function between the direct and reflected signals can only be obtained when the time delays and Doppler shifts of the direct and reflected signals are corrected. The same delay corresponds to concentric rings within the sea surface scintillation zone, which can be obtained through the GNSS direct signal link of the Global Navigation Satellite System (GNSS) and then calculated. Finally, the average power of the delayed signal can be obtained by integrating its inner product over time T. i The inner average is obtained

[0113]

[0114] Substituting equation (4) into equation (7), we obtain the average power expression for the time delay τ and frequency offset Δf. Assume the cumulative time T... i Within the scintillation zone, the elevation of all scattering points is consistent:

[0115]

[0116] This equation is called the bistatic radar equation. Parameters Represents the scattering point The normalized biradial scattering cross section at sea level, where Represents the scattering point The scattering vector at that location. Additionally, in formula (8)...

[0117]

[0118] This indicates that the pulse limits the footprint.

[0119] Since a low-gain antenna is used, the antenna gain in the scintillation region can be approximated. constant Therefore, the integral factor representing the antenna gain in formula (8) It can be removed. If the frequency difference Δf between the Doppler frequency offset and the compensation frequency remains 0 within the scintillation region, then according to formula (6), the variable S is close to 1, indicating complete Doppler frequency offset compensation. Under typical conditions of altitude, speed, and number of accumulations for a GNSS receiver in a global navigation satellite system, the accumulation time T i ~1ms. Therefore, we can further assume S=1. After reasonable simplification, the only factor determining the pulse-limited footprint size in this invention is Λ. 2 .

[0120] According to an exemplary embodiment of the present invention:

[0121] The main lobe width of the autocorrelation function of the two signals E5a and E5b in the Galileo system navigation E5 band is 1 / 3 of the main lobe width of the autocorrelation function of the E5a signal.

[0122] This invention considers the width of the autocorrelation function of the PRN signal. In general, the main power of the autocorrelation function Λ is concentrated within its main lobe; therefore, when analyzing the size of the pulse-limited footprint, the main lobe width of Λ is primarily considered. According to the Wiener-Khinchin theorem, the autocorrelation function of the PRN signal is the Fourier transform of its power spectral density (PSD), i.e.

[0123] Λ PRN (τ)=F{P PRN (f)} (10)

[0124] Among them, Λ PRN (τ) denotes the autocorrelation function of the PRN signal; F{·} denotes the Fourier transform operator; P PRN(f) represents the power spectral density of the PRN signal. The PRN signal can be considered as a BPSK or QPSK signal, and its power spectral density can be considered as a sinc squared function, i.e.

[0125]

[0126] Among them, f s f represents the signal bandwidth. c This represents the center frequency of the carrier wave. It is known that the Fourier transform of the square sinc function is a trigonometric wave function, i.e.

[0127]

[0128] Where, tri(τf s ) indicates that the length of the base is (Right now arrive The trigonometric wave function model is given, therefore its main lobe width is...

[0129] Substituting equations (12) and (11) into equation (10), we obtain the autocorrelation function expression for the PRN signal.

[0130]

[0131] As can be seen from formula (13), the main lobe width of the PRN signal autocorrelation function is related to the signal bandwidth f. s Inversely proportional. Increasing the signal bandwidth can reduce the main lobe width of the PRN signal's autocorrelation function. However, in the GNSS-R system, the PRN signal originates from GNSS satellites, and its bandwidth is affected by the bandwidth of the GNSS satellite signals. Using a single signal has a theoretical upper limit on the main lobe width of the autocorrelation function. However, GNSS satellites contain signals with essentially the same signal structure. Combining multiple of these signals can form a composite signal, which possesses equivalent bandwidth functionality.

[0132] The Galileo system navigation E5 band signal is a set of signals with the above characteristics. It consists of two signals, E5a and E5b, broadcast at two center frequencies of 1176.45MHz and 1207.14MHz, respectively. Both E5a and E5b are composed of two quadrature components. The two alternating binary offset carrier (ALT-BOC) technology is used to combine E5a and E5b into a constant envelope signal. The E5a signal is the lower sideband of the ALT-BOC (E5a / b) and can be regarded as a QPSK (10) with data and pilot orthogonality. The E5b signal is the upper sideband of the E5 signal, and its quadrature components E5bI and E5bQ can be regarded as BPSK. Both E5a and E5b signals have a bandwidth of 20.46MHz. According to the signal frequency, when the two signals are combined into a broadband signal (E5a / b combined signal), the bandwidth can reach 51.15MHz. This is the maximum bandwidth that GNSS signals of the current global navigation satellite system can achieve, which is beneficial to improving the sea surface wind field inversion performance of the GNSS-R system.

[0133] Since E5a and E5b signals have the same bandwidth, and the PSDs of BPSK and QPSK signals both follow the sinc function rule, the PSD of the joint E5a / b signal can be defined as follows:

[0134]

[0135] in, and These represent the signal bandwidths of E5a and E5b, respectively, and their values ​​are... and These represent the carrier center frequencies of E5a and E5b, respectively.

[0136] Since E5a and E5b have the same signal bandwidth...

[0137]

[0138] Substituting formula (15) into formula (14), we get

[0139]

[0140] According to the Wiener-Khinchin theorem, the autocorrelation function of the joint E5a and E5b signal is the Fourier transform of its PSD, i.e.

[0141]

[0142] Based on the operational characteristics of the Fourier transform, and (where Δf) c=30.69MHz), then we can obtain

[0143]

[0144] According to formula (12), the Fourier transform of the sinc square function is a function with a base length of... height f s The triangular function. Since the PSD of the E5a signal is a sinc square function, the region within this triangle represents the main lobe of the autocorrelation function of the E5a signal, and its main lobe width is...

[0145]

[0146] Substitute formula (12) into formula (18), and then adjust the complex terms in the formula. Take the real part

[0147]

[0148] For the E5 signal's two subbands, E5a and E5b, both have a signal bandwidth of f. s =20.46MHz. Furthermore, the center frequency interval between the two sub-bands, E5a and E5b, is Δf. c =30.69MHz. The region between the first pair of minimum values ​​of the autocorrelation function is the main lobe of the E5a / b joint signal autocorrelation function, and its main lobe width is...

[0149]

[0150] f s and Δf c Substituting the specific values, we obtain that the main lobe width of the autocorrelation function of the E5a signal is 97.8 ns, and the main lobe width of the autocorrelation function of the E5a / b joint signal is 32.6 ns. The main lobe width of the autocorrelation function of the E5a and E5b joint signal is 1 / 3 of the main lobe width of the autocorrelation function of the E5a signal.

[0151] According to an exemplary embodiment of the present invention:

[0152] The pulse-limited footprint resolution of the combined E5a and E5b signals of the Galileo system navigation E5 band is 1.73 times higher than that of the pulse-limited footprint resolution of the E5a signal alone.

[0153] After completing the main lobe width analysis of the autocorrelation function of the Galileo / GNSS-R system joint signal, the pulse-delimited footprint size analysis of this joint signal can be carried out. For the GNSS-R system, the size of its pulse-delimited footprint can be calculated by the following formula.

[0154]

[0155] Where a and b represent the major and minor semi-axis of the pulse-limited footprint ellipse, respectively; θ R BW represents the elevation angle of the satellite in the GNSS-R system; BW represents the main lobe width of the autocorrelation function of the signal.

[0156] From formula (22), it can be seen that the size of the pulse-limited footprint is proportional to the square root of the main lobe width of the autocorrelation function of the signal. As discussed earlier, the main lobe width of the autocorrelation function of the combined Galileo E5a and E5b signal is 1 / 3 of the main lobe width of the autocorrelation function of the individual E5a signal. Therefore, the size of the pulse-limited footprint of the combined E5a and E5b signal is [a fraction of the pulse-limited footprint size of the E5a signal]. times.

[0157] Pulse-constrained footprint resolution refers to the size of the smallest distinguishable unit during remote sensing, determined by the size of the pulse-constrained footprint. The pulse-constrained footprint resolution is expressed by the following formula:

[0158]

[0159] Where ε a ε b Let a and b represent the pulse-limited footprint resolution along the long and short sides of the pulse-limited footprint ellipse, respectively. In formula (23), the smaller the dimensions of the major semi-axis a and minor semi-axis b of the pulse-limited footprint ellipse, the smaller the size of the smallest distinguishable unit in the remote sensing process, and the more refined the remote sensing information obtained, thus improving the pulse-limited footprint resolution. The improvement factor of the pulse-limited footprint resolution can be expressed by formula (24).

[0160]

[0161] Where dε a ,dε b These represent the factors that improve the resolution of pulse-limited footprints along the long and short sides of the pulse-limited footprint ellipse, respectively. The pulse-limited footprint resolution of the combined E5a and E5b signals is improved compared to the pulse-limited footprint resolution of the E5a signal alone. times.

[0162] According to formula (22), the main factor for improving the pulse-limited footprint resolution is the bandwidth of the E5a / b combined signal. The bandwidth of the E5a / b combined signal is 52MHz, which is twice the bandwidth of the E5a signal alone. However, the bandwidth of traditional single-band GNSS-R system antennas generally does not exceed 25MHz, which cannot meet the bandwidth requirements of the combined signal. Therefore, research on combined bandwidth GNSS-R system antennas is needed.

[0163] To verify the design correctness of the E5a / b combined signal bandwidth antenna, this invention designed and fabricated an E5a / b combined signal bandwidth antenna verification prototype, and tested its voltage standing wave ratio (VSWR) and radiation pattern performance. To ensure the accuracy of the antenna verification prototype's test results, the VSWR and radiation pattern tests were conducted in an anechoic chamber to shield the antenna performance from the influence of the external environment. Subsequently, the simulation results and test results of the E5a / b combined bandwidth antenna verification prototype were compared.

[0164] Furthermore, to verify the effect of the E5a / b combined signal on the pulse-limited footprint resolution of the GNSS-R system, this invention inputs the measured signal bandwidth values ​​of the combined bandwidth antenna verification prototype under the conditions of receiving the E5a / b combined signal and the E5a signal alone into the simulation environment, calculates the pulse-limited footprint resolution of the two bandwidths in the environment, and compares them.

[0165] Validation data for the method of this invention:

[0166] 1. Antenna verification prototype design

[0167] To verify the method of this invention, a combined signal GNSS-R system antenna was designed, with the structure as follows: Figure 4 As shown, the antenna consists of a radiating element, a feed network, a support structure, and an RF cable.

[0168] The antenna works as follows: the horizontal and vertical signal components of the GNSS reflected signal received by the radiating element are transmitted to the feed network via two radio frequency cables. The feed network then combines the horizontal and vertical signals into a single left-hand circularly polarized signal. This combined signal is then transmitted via the feed port to the radio frequency channel within the GNSS-R system's satellite compartment.

[0169] Figure 5 The figure shows the simulated voltage standing wave ratio (VSWR) curve of the antenna in the combined signal GNSS-R system. As can be seen from the figure, the VSWR of the antenna for both E5a and E5b band signals is better than 1.29. At this point, the energy loss of the antenna for the radio frequency signal is less than 2%, which meets the requirement of simultaneously transmitting E5a and E5b signals.

[0170] Figure 6The figure shows the simulated radiation pattern of the antenna for the joint signal GNSS-R system. As can be seen from the figure, the antenna's 3dB beamwidth is ±45°, which is much larger than the pulse-limiting beamwidth of the GNSS x'c reflected signal. Therefore, the antenna can receive multiple GNSS reflected signals from multiple GNSS systems over a sufficiently large range. By cohering with the GNSS signal replicas within the GNSS-R system, the desired GNSS reflected signals and their time delay information can be obtained, thereby enabling the GNSS-R system's sea surface wind field inversion function.

[0171] 2. Antenna verification prototype testing

[0172] Figure 7 This paper presents a prototype antenna for a joint signal GNSS-R system manufactured according to the design results of this invention. The voltage standing wave ratio (VSWR) and radiation pattern of this prototype were tested in an anechoic chamber. The purpose of testing the VSWR was to verify the antenna's ability to receive GNSS reflected signals within the E5a / b joint bandwidth. The purpose of testing the radiation pattern was to verify the antenna's 3dB beam footprint width, which is significantly larger than the pulse-limited footprint size. Therefore, the antenna can receive multiple GNSS reflected signals over a sufficiently large range. After coherent processing with pre-stored GNSS signal copies within the GNSS-R system, the corresponding GNSS reflected signal information can be extracted, thereby realizing the GNSS-R system's sea surface wind field inversion function. Since the PRN codes of different GNSS satellites are different, reflected signals from different GNSS satellites can be distinguished by correlating with different PRN code copies within the GNSS-R system.

[0173] The Joint Signals GNSS-R system antenna verification prototype was measured in an anechoic chamber using an Agilent E8361A vector network analyzer. The test consisted of two steps: First, the vector network analyzer was directly connected to the feed port of the Joint Signals GNSS-R system antenna verification prototype to obtain the antenna's voltage standing wave ratio (VSWR) test results; then, the Joint Signals GNSS-R system antenna verification prototype was connected to the radiation performance testing system in the anechoic chamber to conduct antenna radiation performance tests, obtaining the test results for the Joint Signals GNSS-R system antenna verification prototype.

[0174] Test results of the joint signal GNSS-R system antenna verification prototype show that its performance meets the requirements for use in the Galileo E5a and E5b frequency bands, and it can be used as a receiving antenna for the Galileo E5a and E5b joint signal GNSS-R system.

[0175] 3. Combined signal pulse limits footprint resolution

[0176] In the verification of pulse-limited footprint size using the joint signal GNSS-R system antenna verification prototype, the main factor is bandwidth. Substituting the test results of the operating frequency (i.e., bandwidth) of the joint signal GNSS-R system antenna verification prototype into the actual environmental parameters yields the resolution of the pulse-limited footprint when using the joint signal GNSS-R system antenna verification prototype. According to formulas (13) and (20), the corresponding autocorrelation function can be obtained by performing an inverse Fourier transform on the power spectral density of the Galileo E5a single-band signal and the Galileo E5a / b joint signal, respectively. To compare and analyze the influence of the E5a / b joint signal on the sea surface wind field inversion of the GNSS-R system, this invention selects the E5a signal as a reference and... Figure 8 The autocorrelation functions for these two signals are given. As can be seen from the figure, due to the fact that cos(2πΔf) in formula (20) c The periodicity of the τ term exhibits a multi-peaked distribution in the autocorrelation function of the E5a / b joint signal, with the main peak being significantly narrower than that of the E5a signal alone. This is beneficial for generating high-precision code tracking and better resolution, making it possible to obtain more accurate pulse-constrained footprint resolution when inverting sea surface wind fields in the GNSS-R system.

[0177] Figure 9 This section compares the pulse-limited footprint size obtained by substituting the parameters of the individual E5a signal and the combined E5a / b signal into the simulation environment. Figure 9 It can be seen that, compared to the E5a signal alone, the nadir pulse-limited footprint size of the E5a / b combined signal is reduced from 3.8km to 2.2km, which is 0.58 times smaller. With the reduction in pulse-limited footprint size, the minimum recognizable pixel size of the GNSS-R system becomes more refined, thereby effectively improving the pulse-limited resolution performance of the GNSS-R system.

[0178] Compared to the E5a signal alone, the pulse-determined footprint size of the GNSS-R system using the combined E5a / b signal decreased from 3.8 km to 2.2 km, a reduction of 0.58 times. The pulse-determined footprint resolution using the combined E5a / b signal, following a reciprocal relationship, increased to 1.72 times that of the E5a signal alone.

[0179] Using combined E5a / b signals is an effective method to improve the pulse-limited footprint resolution of GNSS-R systems. By employing combined E5a / b signals for remote sensing, more refined remote sensing information can be obtained than with E5a signals alone. This technology can support 2km resolution-level GNSS-R system sea surface wind field inversion remote sensing, thereby supporting ongoing global sea surface wind field observations with high pulse-limited footprint resolution based on spaceborne GNSS-R system measurement methods.

[0180] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that variations and combinations of elements may be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for improving the pulse-limited footprint resolution of a GNSS-R system based on bandwidth co-processing, characterized in that: By combining satellite signals with essentially the same signal structure from a Global Navigation Satellite System (GNSS), a combined signal is formed. This combined signal, with its increased bandwidth, is reflected and received by the GNSS-R system. After coherence with pre-stored GNSS signal replicas within the GNSS-R system, the resulting constrained pulse size is smaller and has higher resolution compared to individual signals. A combined signal is a combination of two or more satellite signals with essentially the same signal structure. The signals with essentially the same signal structure can come from the same system or different systems. In the Global Navigation Satellite System (GNSS), the center frequencies fc1 and fc2 of satellite signals with essentially the same signal structure must be spaced greater than half the sum of the bandwidths fs1 and fs2 of the two satellite signals, but not exceeding the sum of the bandwidths fs1 and fs2 of the two satellite signals. Where fc1 and fc2 are the center frequencies of two signals of the Global Navigation Satellite System (GNSS) satellite, and fs1 and fs2 are the bandwidths of two signals of the Global Navigation Satellite System (GNSS) satellite. Using a GNSS-R system signal model based on the Kirchhoff approximation, for a certain moment... Regarding the received reflected signal For different delay values The cross-correlation coefficient is expressed as an integral. （1） in, Indicates the integration time. Represents a time period of code chips The direct signal waveform inside, The frequency offset factor is used to compensate for the Doppler frequency offset of the reflected signal. From formula (1), it can be seen that the waveform of the direct signal is... With the reflected signal waveform The maximum cross-correlation value occurs at the Doppler frequency offset, which has been fully compensated for, and the time series of the two signals are perfectly aligned. Establish a coordinate system, where the specular reflection point is the origin, the xoy plane is the tangent plane on the Earth's surface passing through the specular reflection point, and the z-axis is the normal direction of the specular reflection point. The GNSS scattered signal from the Global Navigation Satellite System reaching the GNSS-R system receiver is modeled by integrating over the mean sea surface: （2） in, This indicates the beam pattern of the GNSS-R system receiving antenna at the scattering point. Directional gain, Represents the PRN code function. Represents the speed of light. and Let represent the distances from any scattering point within the scintillation region to the transmitter and receiver, respectively, where the coordinates of the scattering point are . ,in This indicates the altitude of the scattering point. ,in and These represent the coordinates of the scattering point on the Earth's surface. Indicates the altitude of the scattering point. In addition, in formula (2) Representing the propagation and scattering process （3） in, Represents the Fresnel reflection coefficient; Denotes the scattering vector, where Indicates the radiation wavenumber. Represents the scattering vector The magnitude of the sea level normal component at the point of reflection of the mirror. The unit vector representing the incident wave. The unit vector representing the scattered wave. Represents the imaginary unit, whose value is equal to Substituting formula (3) into formula (2), and then into formula (1), the instantaneous signal is expressed as formula (4): （4） function The autocorrelation function of GNSS satellite PRN codes: （5） Doppler spread function Approximately expressed as the sinc function: （6） According to formulas (5) and (6), the maximum value of the cross-correlation function of the direct and reflected signals can be obtained only when the time delay and Doppler of the direct and reflected signals are corrected. The same delay corresponds to the concentric rings in the sea surface scintillation zone. This area can be directly reached via the GNSS signal link of the Global Navigation Satellite System (GNSS). After obtaining the navigation and positioning signal of the GNSS-R system, it is calculated that the average power of the delayed signal is obtained by integrating its inner product over time. The inner average is obtained （7） Substituting equation (4) into equation (7), we obtain the time delay. and frequency offset The average power expression, assuming cumulative time Within the scintillation zone, the elevation of all scattering points is consistent: （8） This equation is called the bistatic radar equation, and the parameters... Represents the scattering point The normalized biradial scattering cross section at sea level, where Represents the scattering point The scattering vector at that location, and in addition, the scattering vector in formula (8) （9） Indicates pulse-limited footprints. A low-gain antenna is used; the antenna gain in the scintillation region is... It is a constant. =1, therefore, the integral factor representing the antenna gain in formula (8) is 1. The frequency difference between the Doppler frequency offset and the compensation frequency within the scintillation region can be removed. If the value remains 0, then according to formula (6), the variable... A value close to 1 indicates complete Doppler frequency offset compensation, with a typical accumulation time under the conditions of altitude, speed, and accumulation count for a GNSS receiver in a Global Navigation Satellite System. ~1 ms, assuming =1, and after reasonable simplification, the only factor determining the pulse-limited footprint size is . .

2. The method according to claim 1, characterized in that: The main lobe width of the combined E5a / b wideband signal autocorrelation function is 1 / 3 of the main lobe width of the E5a signal autocorrelation function. Since E5a and E5b signals have the same bandwidth, and the PSDs of BPSK and QPSK signals both follow the sinc function rule, the PSD of the joint E5a / b signal is defined as follows: （14） in, and These represent the signal bandwidths of E5a and E5b, respectively, and their values ​​are... = =20.46MHz, and These represent the carrier center frequencies of E5a and E5b, respectively. =1175.45MHz, = +30.69MHz = 1207.14MHz Since E5a and E5b have the same signal bandwidth... = = （15） Substituting formula (15) into formula (14), we get... （16） The autocorrelation function of the joint E5a and E5b signal is the Fourier transform of its PSD, i.e. （17） Based on the operational characteristics of the Fourier transform, and = + ,in =30.69MHz, then we can get （18） According to formula (12), the Fourier transform of the sinc square function is a function with a base length of... ,high The triangular function, since the PSD of the E5a signal is a sinc square function, the region within this triangle represents the main lobe of the autocorrelation function of the E5a signal, and its main lobe width is... （19） Substitute formula (12) into formula (18), and then adjust the complex terms in the formula. Take the real part （20） For the E5 signal's two subbands, E5a and E5b, their signal bandwidths are both... =20.46MHz, and the center frequency interval between the two sub-bands E5a and E5b is... =30.69MHz, the region between the first pair of minimum values ​​of the autocorrelation function is the main lobe of the E5a / b joint signal autocorrelation function, and its main lobe width is （21） Will and Substituting the specific values, we can obtain that the main lobe width of the autocorrelation function of the E5a signal is 97.8 ns, the main lobe width of the autocorrelation function of the E5a / b joint signal is 32.6 ns, and the main lobe width of the autocorrelation function of the E5a and E5b joint signal is 1 / 3 of the main lobe width of the autocorrelation function of the E5a signal.

3. The method according to claim 2, characterized in that: In the aforementioned GNSS-R system, the size of the pulse-limited footprint is proportional to the square root of the main lobe width of the signal's autocorrelation function. The size of the pulse-limited footprint is calculated by the following formula. （22） in, , These represent the major and minor semi-axis of the pulse-limited footprint ellipse, respectively. Indicates the elevation angle of satellites in the GNSS-R system; The main lobe width represents the autocorrelation function of the signal. As can be seen from formula (22), the size of the pulse-limited footprint is proportional to the square root of the width of the main lobe of the autocorrelation function of the signal.

4. The method according to claim 3, characterized in that: The size of the pulse-limited footprint of the E5a / b combined broadband signal is 0.58 times the size of the pulse-limited footprint of the E5a signal. Pulse-constrained footprint resolution refers to the size of the smallest distinguishable unit during remote sensing, determined by the pulse-constrained footprint size. Pulse-constrained footprint resolution is expressed by the following formula: （23） in , Let represent the pulse-limited footprint resolution along the long and short sides of the pulse-limited footprint ellipse, respectively. The improvement factor of the pulse-limited footprint resolution is expressed by formula (24). （24） in , These represent the factors that improve the resolution of pulse-limited footprints along the long and short sides of the pulse-limited footprint ellipse, respectively. The pulse-limited footprint resolution of the combined E5a and E5b signals is 1.73 times higher than that of the E5a signal alone.

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