CN113420424B - Computing method for cross track direction and along track direction spatial resolution of GNSS-R mirror reflection point - Google Patents

Computing method for cross track direction and along track direction spatial resolution of GNSS-R mirror reflection point Download PDF

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CN113420424B
CN113420424B CN202110619742.2A CN202110619742A CN113420424B CN 113420424 B CN113420424 B CN 113420424B CN 202110619742 A CN202110619742 A CN 202110619742A CN 113420424 B CN113420424 B CN 113420424B
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CN113420424A (en
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夏俊明
孙越强
白伟华
杜起飞
王先毅
尹聪
黄飞雄
孟祥广
柳聪亮
胡鹏
刘黎军
蔡跃荣
李伟
曹光伟
吴春俊
刘成
李福�
乔颢
程双双
张璐璐
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National Space Science Center of CAS
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Abstract

The application discloses a method for calculating the space resolution of the cross track direction and the along track direction of a GNSS-R mirror reflection point, which comprises the following steps: calculating an ambiguity function value of a space region around the specular reflection point by taking the time delay and Doppler values at the GNSS-R specular reflection point as reference values; calculating an effective scattering area of the specular reflection point by a threshold method according to the ambiguity function value; the effective scattering area of the specular reflection point is equivalent to an ellipse with the center at the specular reflection point; calculating equations of two tangential lines which are parallel to the motion speed direction of the specular reflection point and tangential to the ellipse; according to the equation of the two tangents, calculating to obtain the cross track spatial resolution at the specular reflection point; the ellipse is equivalent to a parallelogram with equal area, and the bottom side length of the parallelogram is calculated; and calculating the product of the movement speed of the specular reflection point and the incoherent integration time, and calculating the orbital spatial resolution of the GNSS-R specular reflection point according to the size relation between the product and the bottom edge length of the parallelogram.

Description

Computing method for cross track direction and along track direction spatial resolution of GNSS-R mirror reflection point
Technical Field
The application relates to the technical field of GNSS reflected signal remote sensing, in particular to a calculation method of the cross track direction and the along track direction spatial resolution of a GNSS-R mirror reflection point.
Background
Since the 90 s of the 20 th century, the GNSS-R technology (Global Navigation Satellite Systems Reflectometry) has gradually evolved into a new type of remote sensing technology over the earth. The technology can be applied to remote sensing detection in the fields of sea surface wind field, sea surface height, sea surface effective wave height, sea ice coverage, sea ice concentration, soil humidity and the like by simultaneously receiving direct signals and ground reflection signals emitted by GNSS satellites, and has the advantages of rich signal sources, all-day time, all-weather and the like.
The GNSS-R technology belongs to a double-base radar remote sensing mode, and is a space-base GNSS-R double-base radar remote sensing mode composed of a GNSS satellite, a ground surface reflecting surface and a Low Earth Orbit satellite (LEO) receiver, and since the ground surface reflecting surface is usually rough, the GNSS ground reflecting signals received by the LEO satellite are essentially a series of multipath signals after being reflected by a large area of the ground around a specular reflection point. The spatial resolution at the specular reflection point is closely related to a number of factors, such as receiver altitude, speed, incoherent integration time, angle of incidence and azimuth angle of the GNSS satellites. Currently, the calculation of the spatial resolution of the GNSS-R specular reflection point usually equivalent the effective observation area to a square, and the size of the spatial resolution is represented by the square side length. Since the reflected signals received by the GNSS-R satellites may appear in different azimuth directions, the effective observation area of the GNSS-R specular reflection point is actually closer to a parallelogram, and if the current equivalent square GNSS-R spatial resolution calculation method is adopted, the effect of the azimuth angle of the GNSS satellite on the observed spatial resolution of the specular reflection point cannot be accurately reflected.
Disclosure of Invention
The application aims to overcome the defects of the prior art and provides a method for calculating the spatial resolution of the cross track direction and the along track direction of a GNSS-R mirror reflection point.
In order to achieve the above objective, the present application provides a method for calculating the spatial resolution of the cross-track direction and the along-track direction of a GNSS-R specular reflection point, the method comprising:
calculating an ambiguity function value of a space region around the specular reflection point by taking the time delay and Doppler values at the GNSS-R specular reflection point as reference values;
calculating an effective scattering area of the specular reflection point by a threshold method according to the ambiguity function value;
the effective scattering area of the specular reflection point is equivalent to an ellipse with the center at the specular reflection point;
calculating equations of two tangential lines which are parallel to the motion speed direction of the specular reflection point and tangential to the ellipse;
according to the equation of the two tangents, calculating to obtain the cross track spatial resolution at the specular reflection point;
the ellipse is equivalent to a parallelogram with equal area, and the bottom side length of the parallelogram is calculated;
and calculating the product of the movement speed of the specular reflection point and the incoherent integration time, and calculating the orbital spatial resolution of the GNSS-R specular reflection point according to the size relation between the product and the bottom edge length of the parallelogram.
As an improvement of the above method, the delay and doppler values at the GNSS-R specular reflection point are used as reference values to calculate the ambiguity function value of the spatial region around the specular reflection point; the method specifically comprises the following steps:
with time delay tau at the point of specular reflection of GNSS-R ref And Doppler value f ref As a reference value, calculating an ambiguity function value WAF of a space region around the GNSS-R specular reflection point as follows:
WAF(τ-τ ref ，f-f ref )＝Λ 2 (τ-τ ref )S 2 (f-f ref )
wherein f represents Doppler frequency of the reflection signal of any reflection point, tau represents propagation delay of the reflection signal of any reflection point, and Λ and S are respectively an autocorrelation function and a Doppler filtering Sinc function of a pseudo-random code adopted by GNSS-R:
wherein T is i For the receiver coherent integration time.
As an improvement of the method, the effective scattering area of the specular reflection point is calculated by a threshold method according to the ambiguity function value; the method specifically comprises the following steps:
taking the largest ambiguity function value WAF from the ambiguity function values WAF max ；
By threshold method, will be greater than WAF max The spatial region of/2 is defined as the effective observation area of the specular reflection point.
As an improvement of the above method, the effective scattering area of the specular reflection point is equivalent to an ellipse centered at the specular reflection point; the method specifically comprises the following steps:
the effective observation area of the GNSS-R specular reflection point is equivalent to an ellipse centered at the GNSS-R specular reflection point, and any point (x, y) of the ellipse satisfies the following formula:
a is an elliptic long half axis and is equal to the maximum value between any two points on the boundary of an effective scattering area; b is the minor axis of the ellipse, which is equal to the minimum value between any two points on the boundary of the effective scattering area, alpha is the included angle between the major axis of the ellipse and the X axis, and theta is the included angle between the connecting line between the point (X, y) and the origin and the X axis.
As a modification of the above method, the equation of two tangents parallel to the direction of the movement speed of the specular reflection point and tangential to the ellipse is calculated; the method specifically comprises the following steps:
velocity of motion V at specular reflection point sp When the direction is not parallel to the Y axis:
two tangent lines y 1 ，y 2 Satisfies the following formula:
wherein the slopes of the two tangents are k, and k is equal to the speed V at the specular reflection point sp Slope of vector, c 1 And c 2 The intercept of the two tangent lines satisfies the following formula:
wherein, the parameter values at two tangent points of the two tangents tangent to the ellipse are respectively theta and theta+pi, and the parameter value theta is:
velocity of motion V at specular reflection point sp The direction is parallel to the Y axis:
two tangent lines x 1 ，x 2 Satisfies the following formula:
c 3 and c 4 The intercept of the two tangent lines satisfies the following formula:
wherein, the parameter values at two tangent points of the two tangents tangent to the ellipse are respectively theta and theta+pi, and the parameter value theta is:
as an improvement of the method, the cross-track spatial resolution at the specular reflection point is calculated according to the equation of the two tangent lines; the method specifically comprises the following steps:
velocity of motion V at specular reflection point sp When the direction is not parallel to the Y axis, the cross track spatial resolution R at the specular reflection point is obtained by two tangent lines cross The method comprises the following steps:
when the mirror surfaceVelocity of motion V at reflection point sp When the direction is parallel to the Y axis, the cross track spatial resolution R at the specular reflection point is obtained by two tangent lines cross The method comprises the following steps:
R cross ＝|c 3 -c 4 |。
as an improvement of the above method, the ellipse is equivalent to a parallelogram with equal area, and the bottom side length of the parallelogram is calculated; the method specifically comprises the following steps:
the ellipse is equivalent to a parallelogram with equal area, the center is coincident with the specular reflection point and the bottom edge is parallel to the speed direction of the specular reflection point, and the bottom edge length L of the parallelogram is as follows:
as an improvement of the method, the product of the movement speed of the specular reflection point and incoherent integration time is calculated, and the orbital spatial resolution of the GNSS-R specular reflection point is calculated according to the size relation between the product and the bottom edge length of the parallelogram; the method specifically comprises the following steps:
according to the movement velocity V of the specular reflection point sp Product V of incoherent integration time T sp T, and the bottom side length L of the parallelogram to obtain the cross track direction and the along track direction spatial resolution R of the GNSS-R specular reflection point parallel The method comprises the following steps:
compared with the prior art, the application has the advantages that:
1. the application equivalent the oval effective scattering area of the GNSS-R mirror reflection point to a parallelogram model with equal area, the center coincident with the mirror reflection point and the bottom parallel to the moving speed direction of the mirror reflection point, and provides a technical scheme for calculating the cross direction and the along-track spatial resolution of the GNSS-R mirror reflection point based on the equivalent parallelogram model;
2. according to the application, the cross track direction and the along track spatial resolution of the GNSS-R mirror reflection point under different threshold conditions can be calculated by modifying the threshold value of the ambiguity function value defined by the effective observation area of the GNSS-R mirror reflection point;
3. the application provides a technical scheme for describing the spatial resolution of the specular reflection point by using the spatial resolution of the two dimensions of the orbital direction and the cross-track direction at the GNSS-R specular reflection point, which is to make the elliptical effective scattering area of the GNSS-R specular reflection point equivalent to a parallelogram model, and can more accurately reflect the influence of the azimuth angle of the GNSS satellite on the spatial resolution at the GNSS-R specular reflection point.
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FIG. 1 is a flow chart of a method for calculating the cross-track and along-track spatial resolutions of GNSS-R specular reflection points according to the present application;
FIG. 2 is a graph of the ambiguity function for a region of space around a GNSS-R specular reflection point;
FIG. 3 is a schematic view of an effective observation area of an elliptical GNSS-R specular reflection spot and its major and minor axes;
FIG. 4 is a schematic illustration of the distance between two tangents and tangents parallel to the direction of the velocity of motion of the specular reflection point in an elliptical effective observation area of the GNSS-R specular reflection point;
FIG. 5 is an equivalent parallelogram and base of an elliptical effective observation area of a GNSS-R specular reflection point;
FIG. 6 is the spatial resolution along the rail and across the rail when the GNSS-R specular reflection spot motion velocity multiplied by the incoherent integration time is less than the parallelogram base length;
FIG. 7 is the along-track and cross-track spatial resolutions when the GNSS-R specular reflection point motion velocity multiplied by the incoherent integration time is greater than the parallelogram base length.
Detailed Description
The application provides a new technology for calculating the space resolution of the cross track direction and the along track direction of GNSS-R by adopting a parallelogram equivalent approximate model. The concrete explanation is as follows:
(1) Using time delay τ at the point of specular reflection of GNSS-R ref And Doppler value J ref Is prepared from ginsengAnd (3) calculating the ambiguity function value WAF of the space region around the GNSS-R specular reflection point by taking the value into account.
The ambiguity function WAF of GNSS-R describes the magnitude of contributions of different reflector elements to the reference point receiver observations within the reflector spatial region. The mathematical expression of the ambiguity function of GNSS-R is:
WAF(τ-τ ref ，f-f ref )＝Λ 2 (τ-τ ref )S 2 (f-f ref ) (1)
where f represents the Doppler frequency of the reflected signal at any reflection point, τ represents the propagation delay of the reflected signal at any reflection point, and Λ and S are the autocorrelation function and the Doppler filtering Sinc function of the pseudo-random code employed by GNSS-R, respectively. The Sinc function of the doppler filter is related to the receiver coherent integration time Ti:
(2) And calculating the effective scattering area of the specular reflection point according to the WAF value by adopting a threshold method. Will contribute more than WAF in all reflective surface elements max The spatial region of/2 is defined as the effective observation region of the GNSS-R specular reflection point, wherein WAF max Is the maximum ambiguity function value.
(3) And the effective scattering area at the specular reflection point is equivalent to an ellipse with the center at the specular reflection point, the major axis of the ellipse is equal to the maximum value between any two points on the boundary of the effective scattering area, and the minor axis of the ellipse is equal to the minimum value between any two points on the boundary of the effective scattering area.
The parametric equation for an ellipse is that,
wherein X and Y are coordinates of an X axis and a Y axis corresponding to any point of the ellipse, a is the size of a major axis of the ellipse, b is the size of a minor axis of the ellipse, alpha is the included angle between the major axis of the ellipse and the X axis, and theta is the included angle between the connecting line between any point of the ellipse and the origin and the X axis.
(4) And calculating tangential equations of two tangential lines which are parallel to the motion speed direction of the specular reflection point and tangential to the ellipse.
Let the slope of the tangent be k, which is equal to the velocity V at the point of specular reflection sp The slope of the vector. Let the parameter values at the tangent points of the tangent line and the ellipse be respectively theta and theta+pi, and the calculation formula of the parameter value theta be
a. Velocity of motion V at specular reflection point sp When the direction is not parallel to the Y axis
Substituting θ and θ+pi into the parameter equation to obtain two tangent equations
c 1 And c 2 The two kinds of the materials are respectively that,
b. velocity V at specular reflection point sp In a direction parallel to the Y-axis
After substituting θ and θ+pi into the parameter equation, two tangent equations can be obtained
c 3 And c 4 The two kinds of the materials are respectively that,
(5) Calculating the distance between two tangent equations, wherein the distance is the cross track spatial resolution at the GNSS-R specular reflection point;
(6) The ellipse is equivalent to a parallelogram with equal area, the center is coincident with the specular reflection point, and the bottom edge is parallel to the speed direction of the specular reflection point, and the bottom edge length L of the parallelogram is calculated;
(7) According to the movement velocity V of the specular reflection point sp Product V of incoherent integration time T sp T, calculating the orbital spatial resolution R of the GNSS-R specular reflection point according to the size relation between the T and the parallelogram bottom edge length L patallel ，
The technical scheme of the application is described in detail below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1, embodiment 1 of the present application proposes a method for calculating the spatial resolution of the cross-track direction and the along-track direction of the GNSS-R specular reflection point. The method comprises the following specific steps:
(1) Calculating the specular reflection point time delay tau by using the formulas (1) and (2) ref And Doppler value f ref As a reference value, an ambiguity function value WAF of a spatial region around the GNSS-R specular reflection point is calculated, as shown in fig. 2.
(2) Calculating the effective scattering area of the specular reflection point according to the WAF value by using a threshold method, wherein the contribution of the effective scattering area in all the reflection surface elements is larger than WAF max The space area of/2 is the effective observation area corresponding to the GNSS-R product, wherein WAF max For maximum ambiguity function values, the effective observation area of the GNSS-R specular reflection point ellipse is as the area within the thickened ellipse in FIG. 3As shown.
(3) And the effective scattering area at the specular reflection point is equivalent to an ellipse with the center at the specular reflection point, the major axis of the ellipse is equal to the maximum value between any two points on the boundary of the effective scattering area, and the minor axis of the ellipse is equal to the minimum value between any two points on the boundary of the effective scattering area. The long and short axes of the GNSS-R specular reflection spot ellipses are shown as bold line segments in FIG. 3.
(4) And (3) to (8) calculating two tangent equations parallel to the motion speed direction of the specular reflection point and tangential to the ellipse. Two tangents parallel to the direction of the motion speed of the specular reflection point of the effective observation area of the oval shape of the GNSS-R specular reflection point are shown as two parallel dashed lines in fig. 4.
(5) Calculating the distance between two tangent equations by using a formula (9), wherein the distance is the cross track spatial resolution at the GNSS-R specular reflection point; the distance between two tangents parallel to the direction of the speed of movement of the specular reflection point of the effective observation area of the GNSS-R specular reflection point ellipse is shown by the double arrow between the two parallel dashed lines in fig. 4.
(6) The ellipse is equivalent to a parallelogram with equal area, coincident center and specular reflection point and bottom parallel to the speed direction of the specular reflection point, and the bottom side length of the parallelogram is calculated according to formula (10). The equivalent parallelogram and base length of the effective observation area of the GNSS-R specular reflection spot ellipse are shown in FIG. 5.
(7) According to the movement velocity V of the specular reflection point sp Product V of incoherent integration time T sp And (3) calculating the orbital spatial resolution of the GNSS-R specular reflection point according to a formula (11) according to the size relation between T and the parallelogram bottom side length L.
The spatial resolution along the orbit and along the cross orbit when the velocity of the movement of the GNSS-R specular reflection point multiplied by the incoherent integration time is smaller than the length of the bottom side of the parallelogram is shown by the double arrow line segment in FIG. 6.
The spatial resolution along the orbit and cross-orbit when the velocity of the GNSS-R specular reflection point motion multiplied by the incoherent integration time is greater than the length of the base of the parallelogram, as indicated by the double-arrow line segment in fig. 7.
The scheme comprises the following technical characteristics:
an effective observation area of a GNSS-R specular reflection point is defined as an area with a ambiguity function value greater than 1/2 of a maximum ambiguity function value in a scattering area taking the specular reflection point as a reference point;
2, approximating the boundary of an effective observation area of the GNSS-R specular reflection point to an ellipse with the center coincident with the specular reflection point, wherein the major axis of the ellipse is equal to the maximum value between any two points on the boundary of the effective scattering area, and the minor axis of the ellipse is equal to the minimum value between any two points on the boundary of the effective scattering area;
the effective observation area of the GNSS-R specular reflection point is equivalent to a parallelogram with equal area, the center coinciding with the specular reflection point and the bottom side parallel to the motion speed direction of the specular reflection point;
4, calculating a formula of the cross track spatial resolution of the GNSS-R specular reflection point is a formula (9);
and 5, calculating a formula of the spatial resolution of the GNSS-R specular reflection point along the track direction is formula (11).
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present application and are not limiting. Although the present application has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present application, which is intended to be covered by the appended claims.

Claims (6)

1. A method for calculating the orbital and along-the-track spatial resolution of a GNSS-R specular reflection point, the method comprising:
calculating an ambiguity function value of a space region around the specular reflection point by taking the time delay and Doppler values at the GNSS-R specular reflection point as reference values;
calculating an effective scattering area of the specular reflection point by a threshold method according to the ambiguity function value;
the effective scattering area of the specular reflection point is equivalent to an ellipse with the center at the specular reflection point;
calculating equations of two tangential lines which are parallel to the motion speed direction of the specular reflection point and tangential to the ellipse;
according to the equation of the two tangents, calculating to obtain the cross track spatial resolution at the specular reflection point;
the ellipse is equivalent to a parallelogram with equal area, and the bottom side length of the parallelogram is calculated;
calculating the product of the motion speed of the specular reflection point and incoherent integration time, and calculating to obtain the orbital spatial resolution of the GNSS-R specular reflection point according to the size relation between the product and the bottom edge length of the parallelogram;
the equation of two tangent lines which are parallel to the motion speed direction of the specular reflection point and tangential to the ellipse is calculated; the method specifically comprises the following steps:
velocity of motion V at specular reflection point sp When the direction is not parallel to the Y axis:
two tangent lines y 1 ，y 2 Satisfies the following formula:
wherein the slopes of the two tangential lines are k, and k is equal to the motion speed V at the specular reflection point sp Slope of vector, c 1 And c 2 The intercept of the two tangent lines satisfies the following formula:
a is an elliptic long half axis and is equal to the maximum value between any two points on the boundary of an effective scattering area; b is an ellipse minor axis and is equal to the minimum value of the distance between any two points on the boundary of the effective scattering area, alpha is the included angle between the major axis of the ellipse and the X axis, and theta is the included angle between the connecting line between any point (X, y) of the ellipse and the origin and the X axis;
the parameter values at two tangent points of the two tangents tangent to the ellipse are respectively theta and theta+pi, and the parameter value theta is:
velocity of motion V at specular reflection point sp The direction is parallel to the Y axis:
two tangent lines x 1 ，x 2 Satisfies the following formula:
c 3 and c 4 The intercept of the two tangent lines satisfies the following formula:
wherein, the parameter values at two tangent points of the two tangents tangent to the ellipse are respectively theta and theta+pi, and the parameter value theta is:
calculating to obtain the cross track spatial resolution at the specular reflection point according to the equation of the two tangents; the method specifically comprises the following steps:
velocity of motion V at specular reflection point sp When the direction is not parallel to the Y axis, the cross track spatial resolution R at the specular reflection point is obtained by two tangent lines cross The method comprises the following steps:
velocity of motion V at specular reflection point sp When the direction is parallel to the Y axis, the cross track spatial resolution R at the specular reflection point is obtained by two tangent lines cross The method comprises the following steps:
R cross ＝|c 3 -c 4 |。
2. the method for calculating the spatial resolution of the cross-track direction and the along-track direction of the GNSS-R specular reflection point according to claim 1, wherein the ambiguity function value of the spatial region around the specular reflection point is calculated by taking the time delay and the Doppler value at the GNSS-R specular reflection point as reference values; the method specifically comprises the following steps:
with time delay tau at the point of specular reflection of GNSS-R ref And Doppler value f ref As a reference value, calculating an ambiguity function value WAF of a space region around the GNSS-R specular reflection point as follows:
WAF(τ-τ ref ,f-f ref )＝Λ 2 (τ-τ ref )S 2 (f-f ref )
wherein f represents Doppler frequency of the reflection signal of any reflection point, tau represents propagation delay of the reflection signal of any reflection point, and Λ and S are respectively an autocorrelation function and a Doppler filtering Sinc function of a pseudo-random code adopted by GNSS-R:
wherein T is i For the receiver coherent integration time.
3. The method for calculating the cross-track and along-track spatial resolutions of GNSS-R specular reflection points according to claim 2, wherein the effective scattering area of the specular reflection points is calculated by a thresholding method according to a ambiguity function value; the method specifically comprises the following steps:
taking the largest ambiguity function value WAF from the ambiguity function values WAF max ；
By threshold method, will be greater than WAF max The spatial region of/2 is defined as the effective observation area of the specular reflection point.
4. A method for calculating the cross-track and along-track spatial resolutions of GNSS-R specular reflection points according to claim 3, wherein the effective scattering area of the specular reflection points is equivalent to an ellipse centered at the specular reflection point; the method specifically comprises the following steps:
the effective observation area of the GNSS-R specular reflection point is equivalent to an ellipse centered at the GNSS-R specular reflection point, and any point (x, y) of the ellipse satisfies the following formula:
a is an elliptic long half axis and is equal to the maximum value between any two points on the boundary of an effective scattering area; b is the minor axis of the ellipse, which is equal to the minimum value between any two points on the boundary of the effective scattering area, alpha is the included angle between the major axis of the ellipse and the X axis, and theta is the included angle between the connecting line between the point (X, y) and the origin and the X axis.
5. The method for calculating the spatial resolutions of the cross-track direction and the along-track direction of the GNSS-R specular reflection points according to claim 1, wherein the ellipse is equivalent to a parallelogram with equal area, and the bottom side length of the parallelogram is calculated; the method specifically comprises the following steps:
the ellipse is equivalent to a parallelogram with equal area, the center is coincident with the specular reflection point and the bottom edge is parallel to the speed direction of the specular reflection point, and the bottom edge length L of the parallelogram is as follows:
6. the method for calculating the spatial resolution of the GNSS-R specular reflection point along the track according to claim 5, wherein the calculating the product of the motion speed of the specular reflection point and the incoherent integration time calculates the spatial resolution of the GNSS-R specular reflection point along the track according to the magnitude relation between the product and the bottom edge length of the parallelogram; the method specifically comprises the following steps:
based on specular reflection pointsVelocity of motion V sp Product V of incoherent integration time T sp T, and the bottom side length L of the parallelogram to obtain the orbital spatial resolution R of the GNSS-R specular reflection point parallel The method comprises the following steps:
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