A method for calculating statistical characteristics of target RCS under sea surface multipath effect

Abstract

The application discloses a kind of sea surface multipath effect under target RCS statistical characteristics calculation method, belong to radar application technical field, including the complex RCS data of the target pitch angle direction under given clean background and sea surface specular reflection coefficient data;Under the sea surface multipath effect, the statistical characteristics of target total RCS, namely the fluctuation mean and variance of target total RCS;According to the total RCS function of target with the phase difference of relative direct path as variable, the probability density function of the total RCS of target in the form of numerical function is carried out random test and statistics by Monte Carlo method.The application adopts the above-mentioned sea surface multipath effect under target RCS statistical characteristics calculation method, can quickly calculate the statistical characteristics of target RCS under sea surface multipath effect according to target complex RCS and sea surface specular reflection coefficient, and quickly calculates the total RCS probability density function of target under sea surface multipath effect by Monte Carlo simulation.

Description

Technical Field

[0001] This invention relates to the field of radar application technology, and in particular to a method for calculating the statistical characteristics of target RCS under sea surface multipath effect. Background Technology

[0002] In near-shore environments, radar target detection must consider the multipath effect of the sea surface. The echo generated by radar waves directly illuminating the target and the echo reflected from the sea surface are superimposed at the receiver, causing fluctuations in the target's RCS. The classic model for studying the multipath effect of the sea surface is the "four-path" echo model. For the incident wave, there are two main paths: one is the radar wave directly illuminating the target, and the other is the radar wave illuminating the target after a first reflection from the sea surface. For the scattered wave, there are two main paths: one is the direct return to the radar, and the other is the return to the radar after a first reflection from the sea surface. Combining the two main paths of the incident wave and the two main paths of the scattered wave yields the "four-path" signal model. In fact, in addition to the above four main paths, there are other higher-order reflection paths, but the contribution of higher-order reflection paths to the target echo signal is very small and can be ignored. Based on this, using the monostatic and bistatic equivalence theorem and assuming that the specular reflections from the sea surface are mutually coupled, the model can be further simplified to a "three-path" model. The total RCS of the target under the multipath effect can be calculated based on the RCS of the three paths of the target, the specular reflection coefficient of the sea surface, and the path length of each path.

[0003] However, existing methods cannot further analyze the statistical characteristics of target RCS as a function of distance, especially for sea-skimming vehicles, whose distance relative to radar changes rapidly, causing the RCS to fluctuate continuously. The radar's detection performance against sea-skimming vehicles is closely related to the target's statistical RCS characteristics. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the statistical characteristics of target RCS under the multipath effect of the sea surface. It can quickly calculate the statistical characteristics of target RCS under the multipath effect of the sea surface based on the target's complex RCS and the specular reflection coefficient of the sea surface. The total RCS probability density function of the target under the multipath effect of the sea surface can be quickly calculated through Monte Carlo simulation.

[0005] To achieve the above objectives, this invention provides a method for calculating the statistical characteristics of target RCS under sea surface multipath effects, comprising the following steps:

[0006] S1. Given the complex RCS data of the target pitch angle direction and the specular reflection coefficient data of the sea surface at each ground-scraping angle against a clean background;

[0007] S2. Calculate the mean and variance of the total RCS of the target: The calculation method is to substitute the target complex RCS data and the sea surface specular reflection coefficient into the mean and variance formula to calculate the statistical characteristics of the total RCS of the target under the sea surface multipath effect, which is the mean and variance of the total RCS of the target.

[0008] S3. Based on the target total RCS function with the phase difference of the relatively direct path as the variable, conduct random trials using the Monte Carlo method and statistically calculate the probability density function of the target total RCS in numerical form.

[0009] Preferably, in S1, acquiring the complex RCS data in the target pitch direction includes the following steps:

[0010] S11. Simplify the "four-path" signal model into a "three-path" signal model;

[0011] S12. Calculate the path length of each path in the "three-path" signal model;

[0012] The radar, the sea surface reflection point, and the target are located at the three vertices of a triangle, and the distance between the radar and the sea surface reflection point is... The distance between the sea surface reflection point and the target is The distance between the radar and the target is The elevation angles of both the radar and the target observed at the sea surface reflection point are... The elevation angle of the radar at the target location and the depression angle of the sea surface reflection point are both... The target is at an altitude of 100 meters above sea level. ;

[0013] Path 1 Distance ;

[0014] Path 2 Distance ;

[0015] Path 3 Distance ;

[0016] S13. The scattering field of each path is represented by the target body scattering field as follows:

[0017] ;

[0018] ;

[0019] ;

[0020] in, The specular reflection coefficient of the sea surface. Given the radar wavenumber, the total scattered field is:

[0021] ;

[0022] S14. Obtain complex RCS data in the target pitch direction;

[0023] Normalizing the relative incident wave energy, the total complex RCS of the target is obtained as follows:

[0024] ;

[0025] in, For radar wave number, For the target total RCS under multipath effects, , , The corresponding target pitch angles are respectively The directional complex RCS, the horizontal complex RCS, and the target elevation angle are... Directional complex RCS.

[0026] Preferably, in S11, the "four-path" signal model is as follows: Path 1 is the direct echo path, where the radar emits electromagnetic waves that directly illuminate the target, generating scattered waves that return directly to the radar. The scattered field generated by Path 1 is denoted as... Paths 2 and 3 are single-reflection echoes. Path 2 involves the radar transmitting electromagnetic waves that directly strike the target, generating scattered waves that reflect once off the sea surface before returning to the radar. Path 3 involves the radar transmitting electromagnetic waves that reflect once off the sea surface before striking the target, generating scattered waves that return directly to the radar. The scattered fields generated by paths 2 and 3 are denoted as follows: and Path 4 is a secondary reflection echo. The electromagnetic waves emitted by the radar are reflected once by the sea surface before striking the target, generating scattered waves that are reflected once more back to the radar. The scattered field generated by path 4 is denoted as... The scattered field at the radar receiving antenna is the superposition of four-path scattered fields, i.e. .

[0027] Preferably, in S11, the "three-path" signal model specifically refers to the following: In the "four-path" signal model, paths 2 and 3 scatter the target bistatically, and the bistatic angles are the same. According to the monostatic-bistatic equivalence theorem, when the bistatic angle is small, the bistatic scattering is approximately equivalent to monostatic scattering along the angle bisector of the bistatic angle. That is, the target scattering of paths 2 and 3 is set as target scattering along the horizontal direction. At the same time, the specular reflection coefficient of the rough sea surface is set to be mutually coupled, that is, the specular reflection coefficient of the sea surface in paths 2 and 3 is the same. Therefore, it is considered that the scattered fields of paths 2 and 3 are the same. The total scattered field is simplified to ;

[0028] Redefining path 1 as a direct path, its scattering field is: Path 2 is a primary reflection path, and its scattered field is... Path 3 is a secondary reflection path, and its scattered field is... The total scattered field is .

[0029] Preferably, in S2, the calculation process of the mean and variance of the target total RCS includes the following steps:

[0030] S21. The phase of the scattered field under each path changes with the distance R, and the total RCS of the target fluctuates continuously with the distance R. The phase factor of the total complex RCS is extracted as follows:

[0031] ;

[0032] S22. Using the direct path phase as a reference, express other phases as phase differences relative to the direct path:

[0033] ;

[0034] S23. Simplify the phase difference in S22, let:

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] in, ， This represents the phase difference between the primary and secondary reflection paths relative to the direct path, caused by path difference. ， This represents the phase difference between the primary and secondary reflection paths relative to the direct path, caused by scattering from the target body in different directions. Based on the path relationship, we have... The simplified phase difference result is:

[0040] ;

[0041] S24. Under the multipath effect, the total RCS of the target can be considered as the vector sum of the RCS of each path. According to geometric relationships, the total RCS function of the target, with the phase difference relative to the direct path as the variable, is:

[0042]

[0043] ;

[0044] S25. For a given target, during a single radar detection cycle, assuming the sea surface is stationary and the radar illumination angle remains constant, the target's total RCS is considered to be the phase difference caused by the path difference. A function of the independent variable, As a random variable, the mean and variance of the target total RCS are calculated as follows:

[0045] ;

[0046] .

[0047] Preferably, in S3, the random variable is adjusted according to the target total RCS expression. Perform Monte Carlo simulation.

[0048] Therefore, this invention employs the aforementioned method for calculating the statistical characteristics of target RCS under sea surface multipath effects. Based on the classical sea surface multipath model, it further derives a formula for calculating the statistical characteristics of target RCS, enabling rapid calculation of the target RCS statistical characteristics under sea surface multipath effects based on the target's complex RCS and the sea surface specular reflection coefficient. The total RCS function derived in this invention, using relative phase difference as the independent variable, can be rapidly calculated using Monte Carlo simulation to determine the total RCS probability density function of the target under sea surface multipath effects.

[0049] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0050] Figure 1 This is a flowchart of an embodiment of the method for calculating the statistical characteristics of target RCS under the multipath effect of the sea surface according to the present invention;

[0051] Figure 2 This is a diagram of a "four-path" signal model from an embodiment of the method for calculating the statistical characteristics of target RCS under the multipath effect of the sea surface according to the present invention.

[0052] Figure 3 This is a schematic diagram of the path length and target scattering in the "three-path" model of an embodiment of the method for calculating the statistical characteristics of target RCS under the multipath effect of the sea surface according to the present invention;

[0053] Figure 4 This is a schematic diagram of the RCS vectors of each path in an embodiment of the method for calculating the statistical characteristics of target RCS under the multipath effect of the sea surface according to the present invention;

[0054] Figure 5 This is an embodiment of the method for calculating the statistical characteristics of target RCS under the multipath effect of the sea surface according to the present invention. It is the probability density function of the total RCS of the target under the multipath effect of the sea surface. Detailed Implementation

[0055] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0057] Example 1

[0058] This invention provides a method for calculating the statistical characteristics of target RCS under sea surface multipath effects. The overall process is as follows: Figure 1 As shown, it includes the following steps:

[0059] S1. Given the complex RCS data of the target in the pitch direction against a clean background and the specular reflection coefficient data of the sea surface at various ground-brushing angles. Obtaining the complex RCS data of the target in the pitch direction includes the following steps:

[0060] S11. Simplify the "four-path" signal model into a "three-path" signal model. The "four-path" signal model is as follows: Figure 2 As shown. Path 1 is the direct echo path, where the radar emits electromagnetic waves that directly illuminate the target, generating scattered waves that return directly to the radar. Paths 2 and 3 are single-reflection echoes. Path 2 involves the radar emitting electromagnetic waves that directly illuminate the target, generating scattered waves that reflect once off the sea surface before returning to the radar; Path 3 involves the radar emitting electromagnetic waves that reflect once off the sea surface before illuminating the target, generating scattered waves that return directly to the radar. Path 4 is the double-reflection echo, where the radar emitting electromagnetic waves reflects once off the sea surface before illuminating the target, generating scattered waves that reflect once off the sea surface before returning to the radar. The scattered fields generated by paths 1-4 are denoted as follows: , , , The scattered field at the radar receiving antenna is the superposition of four-path scattered fields, that is... .

[0061] Of the four paths, paths 1 and 4 involve monostatic scattering of the target, while paths 2 and 3 involve bistatic scattering with the same bistatic angle. According to the monostatic-bistatic equivalence theorem, when the bistatic angle is small, bistatic scattering is approximately equivalent to monostatic scattering along the angle bisector of the bistatic angle. Therefore, the target scattering along paths 2 and 3 is assumed to be horizontal. Simultaneously, the specular reflection coefficients of the rough sea surface are assumed to be mutually coupled, meaning the specular reflection coefficients of the sea surface are the same in paths 2 and 3. Therefore, the scattered fields of paths 2 and 3 can be considered identical. The total scattered field is .

[0062] The "four-path" signal model is simplified to a "three-path" signal model. Path 1 is redefined as a direct path, and its scattered field is: Path 2 is a primary reflection path, and its scattered field is... Path 3 is a secondary reflection path, and its scattered field is... The total scattered field is .

[0063] S12. Calculate the path length of each path in the "three-path" signal model. A schematic diagram of the path length and target scattering in the "three-path" signal model is shown below. Figure 3 As shown. The distances for each path are:

[0064] ;

[0065] ;

[0066] .

[0067] S13. The scattering field of each path is represented by the target body scattering field as follows:

[0068] ;

[0069] ;

[0070] ;

[0071] in, The specular reflection coefficient of the sea surface. Given the radar wavenumber, the total scattered field is:

[0072] .

[0073] S14. Obtain complex RCS data in the target pitch direction;

[0074] Normalizing the relative incident wave energy, the total complex RCS of the target is obtained as follows:

[0075] ;

[0076] in, For radar wave number, For the target total RCS under multipath effects, , ， The corresponding target pitch angles are respectively The directional complex RCS, the horizontal complex RCS, and the target elevation angle are... Directional complex RCS.

[0077] S2. Calculate the mean and variance of the total RCS of the target: The calculation method is to substitute the target complex RCS data and the sea surface specular reflection coefficient into the mean and variance formula to calculate the statistical characteristics of the total RCS of the target under the sea surface multipath effect, which are the mean and variance of the total RCS of the target.

[0078] The calculation process for the mean and variance of the target total RCS includes the following steps:

[0079] S21. The phase of the scattered field under each path changes with the distance R, and the total RCS of the target fluctuates continuously with the distance R. The phase factor of the total complex RCS is extracted as follows:

[0080] .

[0081] S22. Using the direct path phase as a reference, express other phases as phase differences relative to the direct path:

[0082] .

[0083] S23. Simplify the phase difference in S22, let:

[0084] ;

[0085] ;

[0086] ;

[0087] ;

[0088] in, , This represents the phase difference between the primary and secondary reflection paths relative to the direct path, caused by path difference. , This represents the phase difference between the primary and secondary reflection paths relative to the direct path, caused by scattering from the target body in different directions. Based on the path relationship, we have... The simplified phase difference result is:

[0089] .

[0090] S24. Under the multipath effect, the total RCS of the target is considered as the vector sum of the RCS of each path, such as... Figure 4 As shown, based on geometric relationships, the target total RCS function, with the phase difference relative to the direct path as the variable, is:

[0091]

[0092] .

[0093] S25. For a given target, during a single radar detection cycle, assuming the sea surface is stationary and the radar illumination angle remains constant, the target's total RCS is considered to be the phase difference caused by the path difference. A function of the independent variable, As a random variable, the mean and variance of the target total RCS are calculated as follows:

[0094] ;

[0095] .

[0096] S3. Based on the objective total RCS function, for random variables By performing Monte Carlo simulations and statistically analyzing the results, the numerical function form of the target RCS probability density function can be obtained. For example, when , , When this is achieved, the total RCS probability density function of the target can be obtained as follows: Figure 5 As shown.

[0097] Therefore, this invention employs the aforementioned method for calculating the statistical characteristics of target RCS under sea surface multipath effects. Based on the classical sea surface multipath model, it further derives a formula for calculating the statistical characteristics of target RCS, enabling rapid calculation of the target RCS statistical characteristics under sea surface multipath effects based on the target's complex RCS and the sea surface specular reflection coefficient. The total RCS function derived in this invention, using relative phase difference as the independent variable, can be rapidly calculated using Monte Carlo simulation to determine the total RCS probability density function of the target under sea surface multipath effects.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for calculating the statistical characteristics of target RCS under sea surface multipath effects, characterized in that: Includes the following steps: S1. Given the complex RCS data of the target pitch angle direction and the specular reflection coefficient data of the sea surface at each ground-scraping angle against a clean background; S2. Calculate the mean and variance of the total RCS of the target: The calculation method is to substitute the target complex RCS data and the sea surface specular reflection coefficient into the mean and variance formula to calculate the statistical characteristics of the total RCS of the target under the sea surface multipath effect, which is the mean and variance of the total RCS of the target. The calculation process includes the following steps: S21. The phase of the scattered field under each path changes with the distance R between the radar and the target. The total RCS of the target fluctuates continuously with the distance R. The phase factor of the total complex RCS is extracted as follows: ； in, The specular reflection coefficient of the sea surface. Radar wave number; For the target total RCS under multipath effects, , , The corresponding target pitch angles are respectively The directional complex RCS, the horizontal complex RCS, and the target elevation angle are... Directional RCS; , , The distances for the three paths are respectively; S22. Using the direct path phase as a reference, express other phases as phase differences relative to the direct path: ； S23. Simplify the phase difference in S22, let: ； ； ； ； in, ， This represents the phase difference between the primary and secondary reflection paths relative to the direct path, caused by path difference. ， This represents the phase difference between the primary and secondary reflection paths relative to the direct path, caused by scattering from the target body in different directions. Based on the path relationship, we have... The simplified phase difference result is: ； S24. Under the multipath effect, the total RCS of the target can be considered as the vector sum of the RCS of each path. According to geometric relationships, the total RCS function of the target, with the phase difference relative to the direct path as the variable, is: ； S25. For a given target, during a single radar detection cycle, assuming the sea surface is stationary and the radar illumination angle remains constant, the target's total RCS is considered to be the phase difference caused by the path difference. A function of the independent variable, As a random variable, the mean and variance of the target total RCS are calculated as follows: ； ； S3. Based on the target total RCS function with the phase difference of the relatively direct path as the variable, conduct random trials using the Monte Carlo method and statistically calculate the probability density function of the target total RCS in numerical form.

2. The method for calculating the statistical characteristics of target RCS under sea surface multipath effect according to claim 1, characterized in that: In S1, obtaining the complex RCS data in the target pitch direction includes the following steps: S11. Simplify the "four-path" signal model into a "three-path" signal model; S12. Calculate the path length of each path in the "three-path" signal model; The radar, the sea surface reflection point, and the target are located at the three vertices of a triangle, and the distance between the radar and the sea surface reflection point is... The distance between the sea surface reflection point and the target is The distance between the radar and the target is The elevation angles of both the radar and the target observed at the sea surface reflection point are... The elevation angle of the radar at the target location and the depression angle of the sea surface reflection point are both... The target is at an altitude of 100 meters above sea level. ; Path 1 Distance ; Path 2 Distance ; Path 3 Distance ; S13. The scattering field of each path is represented by the target body scattering field as follows: ； ； ； in, The specular reflection coefficient of the sea surface. Given the radar wavenumber, the total scattered field is: ； S14. Obtain complex RCS data in the target pitch direction; Normalizing the relative incident wave energy, the total complex RCS of the target is obtained as follows: ； in, For radar wave number, For the target total RCS under multipath effects, , , The corresponding target pitch angles are respectively The directional complex RCS, the horizontal complex RCS, and the target elevation angle are... Directional RCS.

3. The method for calculating the statistical characteristics of target RCS under sea surface multipath effect according to claim 2, characterized in that: In S11, the "four-path" signal model is as follows: Path 1 is the direct echo path, where the radar emits electromagnetic waves that directly illuminate the target, generating scattered waves that return directly to the radar. The scattered field generated by Path 1 is denoted as... Paths 2 and 3 are single-reflection echoes. Path 2 involves the radar transmitting electromagnetic waves that directly strike the target, generating scattered waves that reflect once off the sea surface before returning to the radar. Path 3 involves the radar transmitting electromagnetic waves that reflect once off the sea surface before striking the target, generating scattered waves that return directly to the radar. The scattered fields generated by paths 2 and 3 are denoted as follows: and Path 4 is a secondary reflection echo. The electromagnetic waves emitted by the radar are reflected once by the sea surface before striking the target, generating scattered waves that are reflected once more back to the radar. The scattered field generated by path 4 is denoted as... ; The scattered field at the radar receiving antenna is the superposition of four-path scattered fields, i.e. .

4. The method for calculating the statistical characteristics of target RCS under sea surface multipath effect according to claim 3, characterized in that: In S11, the "three-path" signal model is specifically as follows: In the "four-path" signal model, paths 2 and 3 scatter the target bistatically, and the bistatic angles are the same. According to the monostatic-bistatic equivalence theorem, when the bistatic angle is small, bistatic scattering is approximately equivalent to monostatic scattering along the angle bisector of the bistatic angle. That is, the target scattering of paths 2 and 3 is set as target scattering along the horizontal direction. At the same time, the specular reflection coefficient of the rough sea surface is set as mutually coupled, that is, the specular reflection coefficient of the sea surface in paths 2 and 3 is the same. Therefore, the scattered fields of paths 2 and 3 are considered to be the same. The total scattered field is simplified to ; Redefining path 1 as a direct path, its scattering field is: Path 2 is a primary reflection path, and its scattered field is... Path 3 is a secondary reflection path, and its scattered field is... The total scattered field is .

5. The method for calculating the statistical characteristics of target RCS under sea surface multipath effect according to claim 4, characterized in that: In S3, the random variable is adjusted according to the target total RCS expression. Perform Monte Carlo simulation.

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