Carrier phase method for estimating lake ice thickness of satellite-borne GNSS-R original intermediate frequency signal

Abstract

The invention discloses a carrier phase method for satellite-borne GNSS-R original intermediate frequency signal lake ice thickness estimation, and the method comprises the following steps: S1, receiving a GPS reflection signal from the surface of an ice layer, and obtaining original sampling data through a Raw IF mode; s2, removing a ranging code and navigation data in the signal to obtain a carrier signal; s3, calculating the propagation path length of the signal in the ice layer, wherein the effective wavelength of the signal in the ice layer is determined by the dielectric constant of ice; s4, constructing a local reference signal, and obtaining an ice layer phase through complex correlation calculation; s5, unpacking the phase to obtain a continuous phase; s6, calculating the ice layer path length and the ice layer thickness according to the continuous phase; and S7, correcting ionosphere, troposphere and orbit errors. Through carrier phase measurement and error correction technologies, the ice layer thickness measurement method which is efficient, low in cost and high in precision can be provided, the ice layer thickness measurement method is suitable for lake surface ice layer monitoring, and important data support can be provided for climate change research and ice layer simulation.

Description

Technical Field

[0001] The present invention relates to the technical fields of GNSS remote sensing and lake cryosphere remote sensing, and particularly to a method for measuring the thickness of the ice layer on the lake surface by using the CYGNSS (Cyclone Global Navigation Satellite System) satellite system through the carrier phase altimeter technology. Background Art

[0002] Existing methods for measuring the thickness of the ice layer on the lake surface include technologies such as using radar altimeters, laser altimeters, and gravity measurements. However, these methods have problems such as high cost, limited measurement coverage, or inability to directly measure the draft of the ice layer. The CYGNSS satellite system can achieve high-precision measurement of the lake ice layer thickness at low cost by receiving GPS reflected signals, and has better time and space coverage capabilities. Related research work has been carried out on spaceborne GNSS-R raw intermediate frequency signals in aspects such as ice sheet altimetry, sea surface altimetry, lake water level estimation, lake ice surface altimetry, and inland water body detection. However, there is less research on using spaceborne GNSS-R raw intermediate frequency signals to measure the thickness of the ice layer on the lake surface, and there has even been no widely applicable specific measurement method.

[0003] In view of this, the present invention provides a carrier phase method for estimating the thickness of lake ice using spaceborne GNSS-R raw intermediate frequency signals. Summary of the Invention

[0004] The object of the present invention is to provide a method for measuring the ice layer thickness by using the CYGNSS carrier phase altimeter technology. By extracting the carrier phase information of the GPS signal reflected at the ice / water interface, the draft of the ice layer is calculated, and then the ice layer thickness is deduced. This method can achieve high-precision measurement in a short time and effectively correct ionospheric, tropospheric, and orbital errors.

[0005] Compared with the prior art, the beneficial effects of the present invention include:

[0006] Low cost: Using the existing GPS signals without the need to additionally transmit radar or laser signals.

[0007] High precision: High-precision measurement of the thickness of the ice layer on the lake surface can be achieved through carrier phase measurement and phase unwrapping technology.

[0008] Wide coverage: The CYGNSS satellite constellation design can provide high-frequency measurement coverage.

[0009] Direct measurement: It can directly measure the draft of the ice layer without indirectly calculating through other parameters.

[0010] A carrier phase method for estimating lake ice thickness from on - board GNSS - R raw intermediate frequency signals. The technical solution includes the following steps:

[0011] Step S1: Receive GPS reflected signals from the ice layer surface and obtain raw sampling data through the Raw IF mode;

[0012] Step S2: Remove the ranging code and navigation data in the signal to obtain the carrier signal;

[0013] Step S3: Calculate the propagation path length of the signal in the ice layer, where the effective wavelength of the signal in the ice layer is determined by the dielectric constant of the ice;

[0014] Step S4: Construct a local reference signal and obtain the ice layer phase through complex correlation calculation;

[0015] Step S5: Unwrap the phase to obtain the continuous phase;

[0016] Step S6: Calculate the ice layer path length and ice layer thickness based on the continuous phase;

[0017] Step S7: Correct the ionospheric, tropospheric and orbit errors.

[0018] Preferably, the formula for the effective wavelength of the signal in the ice layer is:

[0019]

[0020] In the formula, λ is the GPS L1 wavelength, and ε i ' ce is the real part of the dielectric constant of the ice.

[0021] Preferably, the formula for the ice layer thickness is:

[0022]

[0023] In the formula, R ice (t) is the path length of the signal in the ice layer.

[0024] Furthermore, the path length R ice (t) of the signal in the ice layer can be obtained through carrier phase measurement:

[0025]

[0026] Preferably, the error correction includes:

[0027] a. Correct the ionospheric delay;

[0028] b. Correct the tropospheric delay;

[0029] c. Correct the satellite orbit error.

[0030] The corrected carrier phase φ ice,corrected can be expressed as:

[0031] φ ice,corrected (t) = φ measured (t) - φ iono (t) - φ tropo (t) - φ orbit (t) (4)

[0032] In the formula, φ measured (t) is the measured original carrier phase, φ iono (t) is the phase error caused by ionospheric delay, φ tropo (t) is the phase error caused by tropospheric delay, φ orbit (t) is the phase error caused by orbit error.

[0033] The ionospheric delay is corrected using the Global Ionosphere Map (GIM) of the International GNSS Service. The corrected phase error is:

[0034]

[0035] Among them,

[0036]

[0037] In the formula, f is the GPS L1 frequency (1575.42 MHz), TEC is the Total Electron Content, obtained through GIM, that is, calculated by the following formula:

[0038] TEC = sTEC1 + sTEC2 - sTEC D (7)

[0039] In the formula, sTEC D represents the slant Total Electron Content (sTEC) along the direct signal path, and sTEC1 and sTEC2 represent the sTEC along the incident path and the reflected path respectively. sTEC is calculated by GIM and calculated by the following formula:

[0040]

[0041] In the formula, α is the proportionality factor of the ionospheric density above the CYGNSS (or TDS - 1) orbit, γ is the elevation angle of the incident ray at the Ionospheric Piercing Point (IPP), vTEC is the vertical TEC at the IPP obtained from GIM, and the subscripts 1, 2, and D represent the incident path, the reflected path, and the direct path respectively. The values of α1, α2, and α are determined based on the International Reference Ionosphere (IRI) 2020 model. D value.

[0042] The tropospheric delay of the reflected signal is modeled by the following equation using VMF3 and its corresponding tropospheric delay product on a 1°×1° grid:

[0043] ΔT tropo =2·[ZHD×m dry (θ(t))+ZWD×m wet (θ(t))] (9)

[0044] where ZHD and ZWD are the dry and wet tropospheric delays respectively, m dry and m wet are the mapping functions of the dry and wet tropospheric delays respectively, and θ(t) is the satellite elevation angle at time t.

[0045] The phase error after tropospheric delay correction is then:

[0046]

[0047] Satellite orbit error correction includes GNSS satellite orbit error and GNSS-R satellite orbit error. For GNSS satellite orbit error correction, the precise GNSS satellite orbit deviation is obtained from the final orbit of the Center for Orbit Determination in Europe (CODE). For GNSS-R satellite orbit error, due to the lack of precise orbit information of CYGNSS, the orbit error is approximated by a linear trend, i.e., the GNSS-R satellite orbit error is parameterized as a linear function of time:

[0048]

[0049] where a0 and a1 are estimated by least squares fitting, i.e.,

[0050]

[0051] where, is the residual phase distance measurement value of the open-loop tracking output, t k is the timestamp, and M is the number of GNSS reflected signal carrier phase samples.

[0052] The phase error after orbit error correction is then:

[0053]

[0054] Finally, the calculation formula for the ice thickness is further corrected to:

[0055] BRIEF DESCRIPTION OF THE DRAWINGS

[0056] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly introduced below.

[0057] Figure 1 This is the flowchart of the carrier phase method for estimating lake ice thickness from the raw intermediate frequency signal of spaceborne GNSS-R provided in the embodiments of the present invention.

[0058] Figure 2 This is the geometric model of the propagation path of the reflected signal at the ice / water interface provided in the embodiments of the present invention.

[0059] Figure 3 This is the ice thickness measurement result for simulating 4 different true ice thicknesses (0.5 m, 1 m, 2 m, 3 m) under the first error scenario (TEC = 10, tropospheric delay = 0.0023, orbit error = 0.1) in the embodiments of the present invention.

[0060] Figure 4 This is the ice thickness measurement result for simulating 4 different true ice thicknesses (0.5 m, 1 m, 2 m, 3 m) under the second error scenario (TEC = 20, tropospheric delay = 0.0046, orbit error = 0.2) in the embodiments of the present invention.

[0061] Figure 5 This is the ice thickness measurement result for simulating 4 different true ice thicknesses (0.5 m, 1 m, 2 m, 3 m) under the third error scenario (TEC = 30, tropospheric delay = 0.0023, orbit error = 0.1) in the embodiments of the present invention.

[0062] Figure 6 This is the ice thickness measurement result for simulating 4 different true ice thicknesses (0.5 m, 1 m, 2 m, 3 m) under the fourth error scenario (TEC = 10, tropospheric delay = 0.0046, orbit error = 0.2) in the embodiments of the present invention.

[0063] Figure 7 This is the ice thickness measurement result for simulating 4 different true ice thicknesses (0.5 m, 1 m, 2 m, 3 m) under the fifth error scenario (TEC = 20, tropospheric delay = 0.0023, orbit error = 0.2) in the embodiments of the present invention.

[0064] Figure 8 This is the ice thickness measurement result for simulating 4 different true ice thicknesses (0.5 m, 1 m, 2 m, 3 m) under the sixth error scenario (TEC = 30, tropospheric delay = 0.0046, orbit error = 0.2) in the embodiments of the present invention. Detailed implementation manners

[0065] The present invention will be described in detail below with reference to the accompanying drawings and by way of examples. Each example is provided by way of explanation of the present invention rather than a limitation thereof. In fact, those skilled in the art will appreciate that modifications and variations can be made to the present invention without departing from the scope or spirit thereof. For example, features described as part of one embodiment can be used in another embodiment to yield yet another embodiment. Accordingly, it is intended that the present invention cover such modifications and variations that fall within the scope of the appended claims and their equivalents.

[0066] The present invention provides a method for constructing a spaceborne GNSS-R wave period estimation model, which will be described in detail below with reference to the accompanying drawings:

[0067] Example 1

[0068] To verify the feasibility of the method provided by the present invention, simulation data is used to simulate the process of the CYGNSS carrier phase altimeter measuring the thickness of lake ice, and corrections for ionospheric, tropospheric, and orbital errors are considered. Finally, a measurement result graph of the ice thickness is plotted, and the measurement results under 6 different error scenarios for different true ice thicknesses (0.5 m, 1 m, 2 m, 3 m) are analyzed and summarized to evaluate the feasibility of the algorithm provided by the present invention.

[0069] The specific implementation manner of the present invention includes the following specific steps.

[0070] 1. Signal reception and preprocessing

[0071] The CYGNSS satellite receives the GPS reflected signal from the ice surface and obtains the original sampling data in the Raw IF mode. After removing the ranging code and navigation data from the signal, the carrier signal is obtained:

[0072] s(t) = C n cos(2πf IF t - φ(t)) (1)

[0073] In the formula, C n is the signal amplitude, f IF is the intermediate frequency, and φ(t) is the carrier phase.

[0074] φ(t) is related to the propagation path length R(t) of the signal, and the expression is as follows:

[0075]

[0076] In the formula, λ is the wavelength of the GPS L1 signal.

[0077] Considering the signal path of the ice layer, the total path length can be expressed as:

[0078] R(t) = R0(t) + Rice (t) (3)

[0079] Wherein, R0(t) is the path length of the signal in free space, and R ice (t) is the path length of the signal in the ice layer, which is related to the ice layer thickness.

[0080] Therefore, the total phase of the signal can be expressed as:

[0081]

[0082] 2. Calculation of the path length of the lake ice layer

[0083] The formula for calculating the effective wavelength of the signal in the ice layer is:

[0084]

[0085] Wherein, λ is the GPS L1 wavelength, and ε i ' ce is the real part of the dielectric constant of ice.

[0086] The formula for calculating the ice layer thickness is:

[0087]

[0088] Then the path length of the signal in the ice layer is:

[0089]

[0090] 3. Carrier phase extraction

[0091] In order to extract the ice layer thickness, it is necessary to separate R from the measured phase ice (t), then a local reference signal can be constructed:

[0092] s'(t) = C n cos(2πf IF t - φ'(t)) (8)

[0093] Wherein, φ'(t) is the estimated free space phase.

[0094] The ice layer phase is obtained through complex correlation calculation:

[0095]

[0096] Wherein, I and Q are obtained by calculating the complex correlation (I and Q components) of the real signal and the reference signal, and the expressions are:

[0097]

[0098] 4. Phase unwrapping and ice layer thickness calculation

[0099] For the phase φ ice,wrapped (t), perform the unwrap process to obtain the continuous phase φ ice,unwrapped (t). Finally, the path length R

[0100] of the signal in the ice layer ice (t) can be obtained through carrier phase measurement:

[0101]

[0102] 5. Error correction

[0103] Error correction includes: correcting ionospheric delay, correcting tropospheric delay, and correcting satellite orbit error. Therefore, the corrected

[0104] carrier phase φ ice,corrected (t) can be expressed as:

[0105] φ ice,corrected (t) = φ measured (t) - φ iono (t) - φ tropo (t) - φ orbit (t) (12)

[0106] In the formula, φ measured (t) is the measured original carrier phase, φ iono (t) is the phase error caused by ionospheric delay, φ tropo (t) is the phase error caused by tropospheric delay, φ orbit (t) is the phase error caused by orbit error.

[0107] (1) Correcting ionospheric delay

[0108] The ionospheric delay is corrected using the International GNSS Service Global Ionospheric Map (GIM). The corrected phase error is:

[0109]

[0110] Among them,

[0111]

[0112] In the formula, f is the GPS L1 frequency (1575.42 MHz), TEC is the total electron content, obtained through GIM, that is, calculated by the following formula:

[0113] TEC = sTEC1 + sTEC2 - sTEC D (15)

[0114] In the formula, sTECD Indicates the total slant electron content (sTEC) along the direct signal path. sTEC1 and sTEC2 represent the sTEC along the incident path and the reflected path respectively. sTEC is calculated by GIM. The geometric model of the propagation path of the reflected signal at the ice / water interface is as shown in the appendix Figure 2 and is calculated by the following formula

[0115]

[0116] where α is the proportionality factor of the ionospheric density above the CYGNSS (or TDS-1) orbit, γ is the elevation angle of the incident ray at the ionospheric pierce point (IPP), vTEC is the vertical TEC at the IPP obtained from GIM, and the subscripts 1, 2, and D represent the incident path, the reflected path, and the direct path respectively. The values of α1, α2, and α are determined based on the International Reference Ionosphere (IRI) 2020 model D values

[0117] (2) Tropospheric delay correction

[0118] The tropospheric delay of the reflected signal is modeled by VMF3 and its corresponding tropospheric delay product of 1°×1° grid by the following formula

[0119] ΔT tropo = 2[ZHD×m dry (θ(t)) + ZWD×m wet (θ(t))] (17)

[0120] where ZHD and ZWD are the dry and wet tropospheric delays respectively, m dry and m wet are the mapping functions of the dry and wet tropospheric delays respectively, and θ(t) is the satellite elevation angle at time t

[0121] Then the phase error after tropospheric delay correction is

[0122]

[0123] (3) Satellite orbit error correction

[0124] Satellite orbit error correction includes GNSS satellite orbit error and GNSS-R satellite orbit error. For GNSS satellite orbit error correction, accurate GNSS satellite orbit deviations are obtained from the final orbits of the Center for Orbit Determination in Europe (CODE). For GNSS-R satellite orbit error, due to the lack of accurate CYGNSS orbit information, the orbit error is approximated by a linear trend, that is, the GNSS-R satellite orbit error is parameterized as a linear function of time

[0125]

[0126] Wherein, a0 and a1 are estimated by least squares fitting, that is

[0127]

[0128] Wherein, is the residual phase distance measurement value of the open-loop tracking output, t k is the timestamp, and M is the number of GNSS reflected signal carrier phase samplings.

[0129] Then the phase error after orbit error correction is:

[0130]

[0131] Finally, substituting the above formula (11) into formula (6), the lake ice thickness after error correction can be obtained:

[0132]

[0133] Appendix Figures 3 - 8 The measurement results of different true ice thicknesses (0.5 m, 1 m, 2 m, 3 m) simulated by using the technical solution of the present invention are given under 6 different error scenarios. The 6 error scenarios are set as follows:

[0134] Scenario 1: Ice thickness measurement result (TEC = 10, tropospheric delay = 0.0023, orbit error = 0.1)

[0135] Scenario 2: Ice thickness measurement result (TEC = 20, tropospheric delay = 0.0046, orbit error = 0.2)

[0136] Scenario 3: Ice thickness measurement result (TEC = 30, tropospheric delay = 0.0023, orbit error = 0.1)

[0137] Scenario 4: Ice thickness measurement result (TEC = 10, tropospheric delay = 0.0046, orbit error = 0.2)

[0138] Scenario 5: Ice thickness measurement result (TEC = 20, tropospheric delay = 0.0023, orbit error = 0.2)

[0139] Scenario 6: Ice thickness measurement result (TEC = 30, tropospheric delay = 0.0046, orbit error = 0.2)

[0140] From Appendix Figures 3 - 8 The following conclusions can be drawn:

[0141] 1. Effectiveness of error correction

[0142] (1) Ionospheric error correction:

[0143] Ionospheric errors have a significant impact on the measurement results, especially in scenarios with high TEC values (such as 30 TECU). After correcting the ionospheric delay through GIM, the accuracy of the measurement results is significantly improved. In scenarios with low TEC values (such as 10 TECU), the impact of ionospheric errors is smaller, and the corrected results are closer to the true values.

[0144] (2) Tropospheric error correction:

[0145] Tropospheric delays (such as 2.3 milliseconds and 4.6 milliseconds) have a certain impact on the measurement results, especially in scenarios with large tropospheric delays. After correcting the tropospheric delay through the model, the deviation of the measurement results is significantly reduced.

[0146] (3) Orbit error correction: Orbit errors (such as 0.1 meters and 0.2 meters) have a small but significant impact on the measurement results. After correcting the orbit errors with high-precision orbit data, the accuracy of the measurement results is further improved.

[0147] 2. Measurement accuracy under different ice layer thicknesses

[0148] (1) Thin ice layers (0.5 meters and 1 meter): The measurement results of thin ice layers are more affected by errors, especially in scenarios with high TEC values and large tropospheric delays. The deviation between the corrected ice layer thickness and the true value is still large, but error correction significantly improves the measurement accuracy.

[0149] (2) Thick ice layers (2 meters and 3 meters): The measurement results of thick ice layers are relatively more stable, and the deviation from the true value is smaller after error correction. In the case of thick ice layers, the effect of error correction is more significant, and the true ice layer thickness can be better restored.

[0150] 3. Impact of error scenarios on measurement results

[0151] (1) Scenario 1 (small errors): TEC = 10, tropospheric delay = 2.3 milliseconds, orbit error = 0.1 meter.

[0152] The measurement results are very close to the true values, and it is almost impossible to distinguish between the true value and the corrected value after error correction.

[0153] (2) Scenario 2 (medium errors):

[0154] TEC = 20, tropospheric delay = 4.6 milliseconds, orbit error = 0.2 meter. The measurement results are greatly affected by errors, but the deviation from the true value is significantly reduced after correction.

[0155] (3) Scenario 3 (large TEC errors):

[0156] TEC = 30, tropospheric delay = 2.3 milliseconds, orbit error = 0.1 meter. The ionospheric error has a significant impact on the measurement results, and the deviation between the corrected result and the true value is still large.

[0157] (4) Scenario 4 (large tropospheric and orbit errors):

[0158] TEC = 10, tropospheric delay = 4.6 milliseconds, orbit error = 0.2 meter. The tropospheric and orbit errors have a significant impact on the measurement results, and the deviation between the corrected result and the true value decreases.

[0159] (5) Scenario 5 (medium TEC and large orbit error):

[0160] TEC = 20, tropospheric delay = 2.3 milliseconds, orbit error = 0.2 meter. After error correction, the deviation between the measurement result and the true value decreases significantly, but there is still a certain error.

[0161] (6) Scenario 6 (maximum error):

[0162] TEC = 30, tropospheric delay = 4.6 milliseconds, orbit error = 0.2 meter. The measurement result is most affected by the error, and the deviation between the corrected result and the true value is still large, but the error correction significantly improves the measurement accuracy.

[0163] In summary, error correction is crucial for improving the measurement accuracy of ice thickness, especially in scenarios with high TEC values and large tropospheric delays. The simulation data shows that the method provided by the present invention has the potential to significantly improve the accuracy of the measurement results by comprehensively correcting ionospheric, tropospheric, and orbit errors. The present invention provides important theoretical support and practical guidance for measuring the ice thickness of lakes using the CYGNSS carrier phase altimeter.

[0164] Finally, it should also be noted that the term "comprising", "including" or any other variation is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not explicitly listed, or elements inherent to such process, method, article or device. Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications once they know the basic creative concept. Therefore, the appended claims are intended to be construed as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0165] The above-described embodiments merely represent specific implementation manners of the present application. The description thereof is relatively specific and detailed, but it should not be construed as a limitation to the protection scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the technical solution of the present application, several modifications and improvements can still be made, and these all fall within the protection scope of the present application.

Claims

1. A carrier phase method for estimating the thickness of ice from the original intermediate frequency signal of a satellite-borne GNSS-R, characterized in that: The following steps are involved: Step S1, receiving the GPS reflection signal from the ice surface and obtaining the raw sampling data through the Raw IF mode; Step S2, removing the ranging code and navigation data from the signal to obtain a carrier signal; Step S3, calculating the propagation path length of the signal in the ice layer, wherein the effective wavelength of the signal in the ice layer is determined by the real part of the dielectric constant of the ice, and the calculation formula of the effective wavelength is: Where λ is the GPS L1 wavelength, ε' ice is the real part of the dielectric constant of ice; Step S4, constructing a local reference signal and obtaining the ice layer phase through complex correlation calculation; Step S5, unpacking the phase to obtain a continuous phase; Step S6, calculating the ice layer path length and ice layer thickness according to the continuous phase, the ice layer thickness calculation formula is: in, Among them, φ ice,corrected is the corrected carrier phase; Step S7, correcting the ionosphere, troposphere and orbit errors, the corrected carrier phase: f ice,corrected (t)=φ measured (t)-φ iono (t)-φ tropo (t)-φ orbit (t) (4) Among them, φ measured (t) is the original carrier phase, φ iono (t),φ tropo (t),φ orbit (t) are the phase errors caused by ionosphere, troposphere and orbit errors respectively.

2. The method according to claim 1, characterized in that The ionospheric delay correction adopts the international GNSS service global ionospheric delay map (GIM), and the corrected phase error is: in, Where f is the GPS L1 frequency (1575.42MHz) and TEC is the total electron content, obtained through GIM, which is calculated as follows: TEC=sTEC1+sTEC2-sTEC D (7) Among them, sTEC D represents the tilted total electron content (sTEC) along the direct signal path, sTEC1 and sTEC2 represent the sTEC along the incident path and the reflected path, respectively. sTEC is calculated by GIM and is calculated by the following formula: Where α is the scaling factor of the ionospheric density above the CYGNSS (or TDS-1) orbit, γ is the elevation angle of the incident ray at the ionospheric penetration point (IPP), vTEC is the vertical TEC at the IPP obtained from GIM, and the subscripts 1, 2, and D represent the incident path, reflected path, and direct path, respectively. α1, α2, and α are determined based on the International Reference Ionosphere (IRI) 2020 model. D The value of .

3. The method according to claim 1, characterized in that The tropospheric delay correction is modeled using the VMF3 model and its 1°×1° grid tropospheric delay product by the following formula: Where ZHD and ZWD are the tropospheric dry delay and wet delay, respectively. dry and m wet are the mapping functions of the tropospheric dry delay and wet delay respectively, and θ(t) is the satellite altitude angle at time t. Then the phase error after tropospheric delay correction is:

4. The method according to claim 1, characterized in that: The orbit error correction comprises the following sub-steps: Satellite orbit error correction includes, GNSS satellite orbit error and GNSS-R satellite orbit error, where the GNSS satellite orbit error correction obtains the precise GNSS satellite orbit bias from the final orbit of the European Orbit Determination Center (CODE). For the GNSS-R satellite orbit error, due to the lack of CYGNSS precise orbit information, the orbit error is approximated by a linear trend, that is, the GNSS-R satellite orbit error is parameterized as a linear function of time: In the formula, a0 and a1 are estimated by least squares fitting, that is, In the formula, is the residual phase distance measurement output by the open-loop tracking, t k is the timestamp, and M is the number of carrier phase samples of the GNSS reflection signal. Then the phase error after orbit error correction is:

5. The method according to claim 1, characterized in that The final calculation formula for the ice thickness is:

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