CN108491613B - Signal reflection field calculation method for sea surface low-angle target radar - Google Patents
Signal reflection field calculation method for sea surface low-angle target radar Download PDFInfo
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Abstract
A signal reflection field calculation method for sea surface low-angle target radar adopts an iteration mode, sets a target function as the logarithm of the ratio of an incident angle to a reflection angle, further gradually iterates the initial value of the set distance between the radar and a reflection point, and changes the distance between the radar and the reflection point which is closest to an actual value, thereby realizing the accurate calculation of the position of the specified reflection point when only the height of a radar antenna, the height of a target and the distance between the radar and the target are specified. In addition, the reflection coefficient is set as the product of the ground reflection coefficient, the diffusion factor and the specular scattering factor, so that the reflection coefficient of the signal reflection field is further effectively determined, and the purpose of accurately calculating the signal reflection field is achieved.
Description
Technical Field
The invention relates to a signal reflection field calculation method, in particular to a signal reflection field calculation method for a sea surface low-angle target radar.
Background
In free space, only one ray, namely a straight ray, is used for the radar wave to reach a target; but at sea level, there are also sea surface reflection lines between the radar and the target, in addition to the direct lines, as shown in fig. 1. In low-angle glancing projection, the directivities of the antenna in the direction of a straight ray and the direction of a reflected ray are almost the same, and the reflection RCS of a target is also almost unchanged, so that the field intensity of the reflected ray and the field intensity of the straight ray are comparable, and under the strong interference of the two rays, the receiving field presents strong fluctuation along with the change of distance.
Under the condition that the height of the radar antenna and the height of the target are determined, if the distance between the radar and the reflection point and the distance between the target and the reflection point are specified, the parameters of the straight rays and the reflection lines can be obtained by utilizing the existing formula. However, if only the height of the radar antenna, the height of the target, and the distance between the radar and the target are specified, the position of the reflection point cannot be analytically specified, that is, the distance between the radar and the reflection point and the distance between the target and the reflection point are analytically determined, and the parameters of the direct ray and the reflection line are difficult to calculate.
Therefore, it is necessary to research a signal reflection field calculation method for a sea surface low-angle target radar, which can accurately calculate the position of a specified reflection point and determine the reflection coefficient of a signal reflection field when only the height of a radar antenna, the height of a target and the distance between the radar and the target are specified.
Disclosure of Invention
The object of the present invention is to overcome the above-mentioned shortcomings of the prior art and to provide a method for calculating a signal reflection field of a low-angle target radar on the sea surface, which can accurately calculate the position of a specified reflection point and can determine the reflection coefficient of the signal reflection field when only the height of the radar antenna, the height of the target and the distance between the radar and the target are specified.
The technical scheme of the invention is as follows:
a signal reflection field calculation method for a sea surface low-angle target radar comprises the following steps:
firstly, selecting an initial value of the distance between the radar and a reflection point, and determining the initial value by using the line-of-sight distance of the radar and the line-of-sight distance of a target, wherein the initial value of the distance between the radar and the reflection point is as follows: dividing the line-of-sight distance of the radar by the sum of the line-of-sight distance of the radar and the line-of-sight distance of the target, and multiplying the sum by the distance between the radar and the target;
secondly, selecting a target function, and calculating the distance between the radar and a reflection point by adopting an iteration mode;
thirdly, substituting the distance between the radar and the target and the distance between the radar and the reflection point into a formula to calculate the distance between the target and the reflection point;
fourthly, substituting the distance between the radar and the reflection point, the distance between the target and the reflection point and the distance between the radar and the target into a formula to calculate parameters of a straight ray and a reflection ray;
and fifthly, substituting the distance between the radar and the reflection point, the distance between the target and the reflection point and the distance between the radar and the target into a reflection coefficient calculation formula to calculate the reflection coefficient.
Further, the target function is the logarithm of the ratio of the incident angle to the reflection angle, and the ratio function of the incident angle to the reflection angle is calculated by substituting the initial value of the distance from the radar to the reflection point into a formula; and defining a certain error value, iterating the objective function towards zero step by step, and when the absolute value of the objective function is smaller than the error value, considering the distance between the radar and the reflection point as a real distance.
Further, the reflection coefficient is a product of a ground reflection coefficient, a diffusion factor and a specular scattering factor, and the diffusion factor is a spherical diffusion factor; they can be calculated from the distance from the radar to the reflection point, the distance from the target to the reflection point and the distance between the radar and the target.
Further, the iteration mode is one of a gradient descent method, a newton method and quasi-newton method, a conjugate gradient method, a heuristic optimization method and a lagrange multiplier method.
Further, the initial value of the distance from the selected radar to the reflection point is:
further, the objective function is: ln (theta)1/θ2)。
Further, the reflection coefficient formula is:
the invention has the beneficial effects that: the invention adopts an iteration mode, sets the target function as the logarithm of the ratio of the incident angle to the reflection angle, further iterates the initial value of the set distance between the radar and the reflection point step by step to become the distance between the radar and the reflection point which is closest to the actual value, thereby realizing the accurate calculation of the position of the specified reflection point when only the height of the radar antenna, the height of the target and the distance between the radar and the target are specified. In addition, the reflection coefficient is set as the product of the ground reflection coefficient, the diffusion factor and the specular scattering factor, so that the reflection coefficient of the signal reflection field is further effectively determined, and the purpose of accurately calculating the signal reflection field is achieved.
Drawings
FIG. 1 is a schematic diagram of sea level reflection lines;
FIG. 2 is a schematic diagram of sea level reflection field calculation;
fig. 3 is a schematic diagram of an iterative approach.
In fig. 1, PQP represents a straight line, PCQP, PQCP represents a primary reflection line, and PCQCP represents a secondary reflection line.
Detailed Description
The invention will be described in further detail below with reference to the drawings and specific examples.
Examples
First, the basic principle of sea surface radar wave rays:
in free space, only one ray, namely a straight ray, is used for a radar wave to reach a target, and the power of a radar receiving signal is as follows:
wherein: pt-transmission power (w)
Gt(θ)，Gr(theta) — transmit and receive antenna gain, theta being the target pointing angle of arrival
Lambda-wavelength (m) of the transmitted signal
σtTarget RCS (m)2)
d-target distance (m)
L (d) -atmospheric attenuation in relation to distance and in relation to elevation angle of target
However, at sea level, there are also sea surface reflection lines between the radar and the target, in addition to the direct lines, as shown in fig. 1.
In low-angle glancing projection, the directivities of the antenna in the direction of a straight ray and the direction of a reflection line are almost the same, and the reflection RCS of a target is also almost unchanged, so that the field intensity of a primary reflection line and a secondary reflection line can be compared with that of the straight ray, and under the strong interference of the two rays, the receiving field shows strong fluctuation along with the change of distance.
Second, a calculation formula of the reflection field:
the distance between the radar and the target is more than tens of kilometers, and although the included angle of the distance to the center of the earth is less than 1 degree, the influence of the curvature of the earth is remarkable. The notion of line-of-sight distance, and the notion of antenna and target height above the horizon, are introduced at this time. Due to the non-uniform refractive index of the atmosphere, there is a refractive index gradient dN/dh and the radiation is slightly curved. To simplify the calculation, the equivalent radius of the earth is defined, and the rays are still calculated as straight lines.
The equivalent radius of the earth is:
Re＝kR (2)
r is the true radius of the earth,
R＝6371km (3)
dN/dh is negative, in the standard case: dN/dh ═ 39(N units/km). At this time k＝4/3，Re＝8490km。
As shown in fig. 2, the radar antenna has a height h1Target height of h2Spherical reflection point is C, radar distance from reflection point is d1Distance d between target and reflection point2Distance d between radar and target1+d2The radar height above the tangent plane can be calculated as:
the target height above the tangent plane is:
straight ray PQ length of
The length of the reflection line PCQ is
Angle of depression for straight rays (set h)1>h2) Is composed of
θd＝arctan[(ah1-ah2)/d] (9)
The angle of depression of the reflected ray is
θd＝arctan[(ah1+ah2)/d] (10)
In fig. 2 there are: theta1＝θ2＝θr。
At h1、h2In the case of certainty, if d is specified1、d2Provided that d is equal to d1+d2Less than the line-of-sight distance
Then the parameters of the straight rays and the reflected rays can be obtained by the above formulas. But if only h is specified1、h2D, the position of the reflection point cannot be analytically specified, i.e. d is analytically specified1、d2The parameters of the straight and reflected rays are not easy to calculate. Therefore, in the case of d, the position of the reflection point is numerically determined. There may be a variety of approaches or fits. Here, d is determined by several iterations using a gradient method1、d2。
Thirdly, the method comprises the following specific steps:
first, selecting initial value d of radar distance from reflection point1By line-of-sight distance of radar
Line-of-sight distance to target
Determining an initial value, i.e. an initial value d of the radar distance from the reflection point1Comprises the following steps: line-of-sight distance of radar
Divided by the line-of-sight distance of the radar
Line-of-sight distance to target
Multiplying the sum by the distance d between the radar and the target;
is expressed by the formula:
secondly, selecting a target function, and calculating the distance d between the radar and a reflection point by adopting an iterative mode1(ii) a As shown in FIG. 3, the horizontal axis represents the distance from the radar position, the distance from the radar to the target is d, and the vertical axis representsThe axis being an objective function selected as θ1And theta2Logarithmic ratio of (a), i.e. ln (theta)1/θ2). When the point C moves on the sphere, the tangent line at the point C in fig. 2 is also inclined. When the point C is close to the radar end theta1＞θ2，ln(θ1/θ2) > 0, whereas ln (theta)1/θ2) Is greater than 0. Therefore, when the point C moves, that is, when x has a different value in fig. 3, rt (x) is different, and the point at which rt (x) is 0 is the reflection point. An error value eps may be specified, and when | rt (x) | < eps, the value of x at this time is considered to be the reflection point. At an initial value d1The dots calculate rt (d) using equations (4), (5), (8) and (9)1) Then let d11＝d1+ d, calculating rt (d)11) From this, the gradient value 1/C-rt (d) can be calculated1) As shown in fig. 3, the position where rt is 0 is then calculated from this gradient:
d12＝d1+rt(d1)C
then rt (d) is obtained by calculation using the formulas (3) - (9)12). If rt (d)12) If the value is not met, then the value is determined from rt (d)11)、rt(d12) The iteration continues until a deterministic value is obtained.
Thirdly, the distance d between the radar and the target and the distance d between the radar and the reflection point are compared1Substituting into formula to calculate the distance d between the target and the reflection point2；d＝d1+d2。
Fourthly, the radar is separated from the reflection point by a distance d1Distance d of target from reflection point2And the distance d between the radar and the target, substituting the distance d into a formula to calculate the parameter h of the direct ray and the reflected ray1、h2、θ1、θ2，θ1＝θ2＝θ。
Fifthly, the distance d between the radar and the reflection point1Distance d of target from reflection point2And the distance d between the radar and the target is substituted into a reflection coefficient calculation formula to calculate the reflection coefficient.
Usually, the ground reflection is calculated according to the flat ground, namely the Fresnel reflection coefficient, but at the distance of more than dozens of kilometers, the ground reflection is processed according to the spherical surface, a beam of rays is projected onto the spherical surface, the reflection rays are diffused and have diffusion factors, meanwhile, the ground is rough, only one part of the ground is in mirror scattering, namely the mirror scattering factors, and the rest part of the ground is in diffuse scattering, so that ground clutter is formed. The reflection coefficient is thus the product of three factors:
where gamma is the Fresnel reflection coefficient
In which theta is the grazing angle epsiloneIs the relative complex dielectric constant:
εe＝εr+jεi (14)
for seawater (3.6% salt content), εs(static permittivity), τ (relaxation time), σiThe values of (conductivity) with temperature are given in the following table:
| temperature of | εs | τ | σi |
| 0 | 75.08 | 16.93×10-12 | 2.70×1010 |
| 10 | 72.08 | 12.10×10-12 | 3.74×1010 |
| 20 | 69.08 | 9.15×10-12 | 4.70×1010 |
| 30 | 66.08 | 7.18×10-12 | 5.56×1010 |
| 40 | 63.32 | 5.68×10-12 | 6.58×1010 |
Spherical diffusion factor:
specular scattering factor:
S＝e-μ (18)
σHthe root mean square value of the sea wave height is determined by the sea wind speed. According to statistics, the wind speed at sea is 10-20 (miles per hour) for more than 50%, the sea condition is 3-level sea condition, and the wave height root mean square value is 0.6-1.2 m.
According to the steps (10) to (20), the reflection coefficient of any place can be calculated, and the reflection field strength of the position can be determined.
Therefore, the invention can only stipulate the height h of the radar antenna1Target height h2And the distance d between the radar and the target, the position of the specified reflection point is accurately calculated, and the reflection coefficient of the signal reflection field can be determined.
Claims (7)
1. A signal reflection field calculation method for a sea surface low-angle target radar is characterized by comprising the following steps: the signal reflection field calculation method for the sea surface low-angle target radar comprises the following steps:
firstly, selecting an initial value of the distance between the radar and a reflection point, and determining the initial value by using the line-of-sight distance of the radar and the line-of-sight distance of a target, wherein the initial value of the distance between the radar and the reflection point is as follows: dividing the line-of-sight distance of the radar by the sum of the line-of-sight distance of the radar and the line-of-sight distance of the target, and multiplying the sum by the distance between the radar and the target;
secondly, selecting a target function, and calculating the distance between the radar and a reflection point by adopting an iteration mode;
thirdly, substituting the distance between the radar and the target and the distance between the radar and the reflection point into a formula to calculate the distance between the target and the reflection point;
fourthly, substituting the distance between the radar and the reflection point, the distance between the target and the reflection point and the distance between the radar and the target into a formula to calculate parameters of a straight ray and a reflection ray;
and fifthly, substituting the distance between the radar and the reflection point, the distance between the target and the reflection point and the distance between the radar and the target into a reflection coefficient calculation formula to calculate the reflection coefficient.
2. The method of claim 1, wherein the method comprises the steps of: the target function is the logarithm of the ratio of the incident angle to the reflection angle, and the ratio function of the incident angle to the reflection angle is calculated by substituting the initial value of the distance from the radar to the reflection point into a formula; and defining a certain error value, iterating the objective function towards zero step by step, and when the absolute value of the objective function is smaller than the error value, considering the distance between the radar and the reflection point as a real distance.
3. The signal reflection field calculation method for a sea surface low angle target radar according to claim 1 or 2, characterized in that: the reflection coefficient is the product of a ground reflection coefficient, a diffusion factor and a specular scattering factor, and the diffusion factor is a spherical diffusion factor; they can be calculated from the distance from the radar to the reflection point, the distance from the target to the reflection point and the distance between the radar and the target.
4. The signal reflection field calculation method for a sea surface low angle target radar according to claim 1 or 2, characterized in that: the iteration mode is one of a gradient descent method, a Newton method, a quasi-Newton method, a conjugate gradient method, a heuristic optimization method and a Lagrange multiplier method.
5. The method of claim 1, wherein the method comprises the steps of: the initial value of the distance from the selected radar to the reflection point is as follows:
in the formula, PC1And d represents the distance between the radar and the target.
6. The method of claim 1, wherein the method comprises the steps of: the objective function is: ln (theta 1/theta 2), where theta 1 represents the incident angle and theta 2 represents the reflection angle.
7. The method of claim 1, wherein the method comprises the steps of: the formula of the reflection coefficient is as follows:
wherein
The total reflection coefficient is represented as a whole, Γ is the Fresnel reflection coefficient, D is the spherical diffusion factor, and S is the specular scattering factor.
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