CN112904325A - Double-star offshore target positioning method based on microwave forwarding - Google Patents
Double-star offshore target positioning method based on microwave forwarding Download PDFInfo
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Abstract
The invention discloses a double-star offshore target positioning method based on microwave forwarding, which comprises the following steps: radiation source microwave signals emitted by the marine radiation source are received by two satellites and forwarded to N ground radar stations; respectively measuring arrival time difference and arrival frequency difference from the marine radiation source to N ground radar stations according to the radiation source microwave signals received by each radar station; establishing a radiation source position information equation set according to the earth spherical model, the arrival time difference and the arrival frequency difference obtained by measurement; analyzing and solving a radiation source position information equation set to obtain radiation source position information; and carrying out positioning fuzzy point elimination processing on the radiation source position information. According to the method, the two satellites are used for receiving the microwave signals from the marine radiation source, the satellites do not process the microwave signals of the radiation source, the microwave signals of the radiation source are directly forwarded to the ground radar station, and the ground radar station carries out parameter measurement on the received signals.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a double-star offshore target positioning method based on microwave forwarding.
Background
The scout positioning can be divided into passive scout positioning and active scout positioning according to whether the scout machine transmits signals. The passive positioning of the signal source has the characteristics of long action distance, high concealment and strong survival capability, and is widely researched at home and abroad.
The multi-station passive positioning mainly obtains the position of a radiation source through positioning parameters, wherein the multi-station passive positioning mainly comprises multi-station time difference positioning, multi-station frequency difference positioning, multi-station direction finding cross positioning, time difference and frequency difference combined positioning and the like. The satellite electronic reconnaissance positioning technology for the marine radiation source has great significance for information countermeasure. The double-satellite time difference and frequency difference positioning method utilizes two satellites to respectively and passively receive signals of a marine radiation source, and then calculates the position of a radiation source target according to the arrival time difference and the frequency difference of the signals. However, since the measured arrival time difference and frequency difference are both nonlinear functions related to the position of the radiation source, it means that solving the position of the radiation source is equivalent to solving a ternary high-order nonlinear equation system, and the conventional method is to solve the position of the radiation source by using a multidimensional search method.
However, the multidimensional search method has a large calculation amount, is easily affected by the initial value of the search to obtain a local optimal solution, and has a large positioning error.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a double-star offshore target positioning method based on microwave forwarding.
One embodiment of the invention provides a double-star offshore target positioning method based on microwave forwarding, which comprises the following steps:
and 5, carrying out positioning fuzzy point elimination processing on the radiation source position information.
In one embodiment of the present invention, the radiation source microwave signal received by each ground radar station in step 1 is represented as:
wherein the content of the first and second substances,
represents a radiation source microwave signal S from a marine radiation source received by an ith satellite retransmission radar station jiDenotes the ith satellite, j denotes the jth radar station,
representing the distance from the marine radiation source to the ith satellite at time t,
representing the distance from the ith satellite to radar station j at time t, and c represents the speed of light.
In one embodiment of the present invention, step 2 comprises:
step 2.1, measuring and obtaining the arrival time difference from the marine radiation source to the N ground radar stations according to the radiation source microwave signals received by the N ground radar stations;
and 2.2, measuring according to the radiation source microwave signals received by the N ground radar stations to obtain the arrival frequency difference from the marine radiation source to the N ground radar stations.
In one embodiment of the invention, step 2.1 comprises:
step 2.1.1, establishing a time difference equation of the radiation source position of each ground radar station according to the position parameters of the two satellites and the position of each ground radar station;
step 2.1.2, carrying out frequency domain correlation processing on the radiation source microwave signals received by each ground radar station to obtain radiation source microwave signals received by a plurality of effective ground radar stations;
and 2.1.3, carrying out weighted average on the radiation source microwave signals received by the plurality of effective ground radar stations according to the time difference equation of the radiation source positions of the ground radar stations to obtain the arrival time difference from the marine radiation source to the N ground radar stations.
In one embodiment of the invention, the equation of the time difference of the source position of each ground radar station in step 2.1.1 is expressed as:
wherein the content of the first and second substances,
representing the time difference between the radiation source microwave signal being forwarded through two satellites to radar station j.
In one embodiment of the invention, step 2.2 comprises:
2.2.1, establishing a frequency difference equation of the radiation source position of each ground radar station according to the speed parameters of the two satellites and the position of each ground radar station;
step 2.2.2, carrying out frequency domain correlation processing on the radiation source microwave signals received by each ground radar station to obtain radiation source microwave signals received by a plurality of effective ground radar stations;
and 2.2.3, carrying out weighted average on the radiation source microwave signals received by the plurality of effective ground radar stations according to a frequency difference equation of the radiation source positions of the ground radar stations to obtain the arrival frequency difference from the marine radiation source to the N ground radar stations.
In one embodiment of the invention, the frequency difference equation for the position of the radiation source for each ground radar station in step 2.2.1 is expressed as:
wherein the content of the first and second substances,
representing the frequency difference of the radiation source microwave signal forwarded via two satellites to radar station j,
representing the radial velocity from the marine source to the ith satellite at time t,
representing the radial velocity from the ith satellite to radar station j at time t.
In one embodiment of the present invention, the set of radiation source position information equations established in step 3 is expressed as:
wherein (x, y, z) represents the position coordinates of the marine radiation source, (x)i,yi,zi) Representing the positions of two satellites, (v)xi,vyi,vzi) Representing the velocity, R, of two satelliteseRepresenting earth radius and H elevation observations.
In one embodiment of the present invention, step 4 comprises:
step 4.1, constructing a marine radiation source to satellite S according to the radiation source position information equation set1A univariate sextant equation of distance;
step 4.2, constructing a radiation source position information estimation equation according to the radiation source position information equation set and the one-element six-order equation;
and 4.3, solving the radiation source position information estimation equation to estimate the radiation source position information.
In one embodiment of the invention, the radiation source position information estimation equation constructed in step 4.2 is expressed as:
wherein the content of the first and second substances,
representing the position coordinates of the source of the radiation at sea,
a matrix representing the position and velocity of the satellite,
representing the altitude matrix of the satellite, H representing the altitude observation, HiIndicating the altitude, R, of the ith satelliteeRepresenting the radius of the earth, Fi＝vxixi+vyiyi+vziziIn order for the intermediate variable to be known,
a time difference matrix is represented which is,
representing a time difference-frequency difference matrix, mT＝[vx1,vy1,vz1]A-1M-[a1,0,0]A matrix of intermediate coefficients is represented which,
representing a first intermediate coefficient, a2＝-[vx1,vy1,vz1]A-1n represents a second intermediate coefficient which is,
represents a distance matrix, r1Representing the distance S of the marine radiation source to the satellite1。
Compared with the prior art, the invention has the beneficial effects that:
according to the double-satellite offshore target positioning method based on microwave forwarding, the microwave signals from the offshore radiation sources are received through the two satellites, the satellites do not process the microwave signals of the radiation sources, the microwave signals of the radiation sources are directly forwarded to the ground radar station, the ground radar station conducts parameter measurement on the received signals, and the method effectively reduces the calculation amount of satellite processing data.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic flowchart of a method for positioning a double-star offshore target based on microwave forwarding according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a satellite positioning model provided by an embodiment of the invention;
FIG. 3 is a schematic diagram of a simulation scenario provided by an embodiment of the invention;
fig. 4 is a schematic diagram of a solution result of a radiation source position information equation set provided by the embodiment of the present invention;
fig. 5 is a schematic view of analysis of positioning errors of different time difference errors and frequency difference errors in the method for positioning a double-star offshore target based on microwave forwarding according to the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Example one
Referring to fig. 1, fig. 1 is a schematic flowchart of a method for positioning a double-star offshore target based on microwave forwarding according to an embodiment of the present invention. The embodiment provides a double-star offshore target positioning method based on microwave forwarding, which comprises the following steps:
and step 1, N ground radar stations receive radiation source microwave signals, wherein the radiation source microwave signals sent by the marine radiation source are received by two satellites and are forwarded to the N ground radar stations, and N is an integer larger than 0.
Specifically, assuming that a marine radiation source P emits a signal m (t), two satellites receive radiation source microwave signals and only take charge of forwarding without processing, and forward the received radiation source microwave signals to N radar stations located on the ground, where N is an integer greater than 0, and the radiation source microwave signals received by the N radar stations are represented as:
wherein the content of the first and second substances,
represents a radiation source microwave signal received by a marine radiation source signal to a radar station j through an ith satellite, i represents the ith satellite, j represents the jth radar station,
representing the distance from the marine radiation source to the ith satellite at time t,
representing the distance from the ith satellite to radar station j at time t, and c represents the speed of light.
Referring to fig. 2, fig. 2 is a schematic diagram of a satellite positioning model according to an embodiment of the present invention, taking N-3 radar stations as an example, two satellites in fig. 2 are respectively a 1 st satellite S1 and a 2 nd satellite S2, and radiation source microwave signals received by 3 radar stations a, B, and C are respectively represented as follows:
wherein the content of the first and second substances,
representing the distance from the ith satellite to radar station a at time t,
representing the distance from the ith satellite to radar station B at time t,
representing the distance from the ith satellite to radar station C at time t,
representing the received signal of the radiation source P signal to the radar station a via the ith satellite,
representing the received signal of the radiation source P signal to the radar station B via the ith satellite,
representing the received signal of the radiation source P signal to the radar station C via the i-th satellite.
And 2, respectively measuring and obtaining the arrival time difference and the arrival frequency difference from the marine radiation source to the N ground radar stations according to the radiation source microwave signals received by the N ground radar stations.
Specifically, step 2 of this embodiment includes step 2.1 and step 2.2:
and 2.1, measuring and obtaining the arrival time difference from the marine radiation source to the N ground radar stations according to the radiation source microwave signals received by the N ground radar stations.
Specifically, step 2.1 of this embodiment includes step 2.1.1, step 2.1.2, and step 2.1.3:
and 2.1.1, establishing a time difference equation of the radiation source position of each ground radar station according to the position parameters of the two satellites and the position of each ground radar station.
Specifically, the equation of the time difference of the radiation source position of each ground radar station, which is established according to the position parameters of two satellites and the position of each ground radar station, is expressed as:
wherein the content of the first and second substances,
representing the time difference between the radiation source microwave signal being forwarded through two satellites to radar station j.
Referring to fig. 2 again, the equation of the time difference of the radiation source positions of the 3 radar stations a, B, and C in fig. 2 is respectively expressed as:
wherein the content of the first and second substances,
representing the time difference between the marine radiation source signal and the radar station a forwarded via two satellites,
representing the time difference between the marine radiation source signal and the radar station B forwarded via two satellites,
representing the time difference between the marine radiation source signal and the radar station C, as forwarded through two satellites.
And 2.1.2, carrying out frequency domain correlation processing on the radiation source microwave signals received by each ground radar station to obtain a plurality of radiation source microwave signals received by effective ground radar stations.
Specifically, since the positions of the satellites and the positions of the ground radar stations are known quantities, the first half of the equation of time difference of equation (3) is known, and the equation containing the unknown quantities is expressed as:
according to a formula (1), each ground radar station receives a radiation source microwave signal, frequency domain correlation processing is carried out on the radiation source microwave signals, whether the jth ground radar station receives the radiation source microwave signals forwarded by the satellite is judged, if the correlation peak detection is larger than or equal to a preset threshold value, the preset threshold value is set according to actual conditions, the jth ground radar station is considered to receive the radiation source microwave signals forwarded by the satellite, the radiation source microwave signals forwarded by the satellite received by the jth ground radar station are effective signals, if the correlation peak detection is smaller than the preset threshold value, the radiation source microwave signals forwarded by the satellite received by the jth ground radar station are abandoned, and the N ground radar stations respectively carry out frequency domain correlation processing to obtain the radiation source microwave signals received by a plurality of effective ground radar stations.
And 2.1.3, carrying out weighted average on the radiation source microwave signals received by the effective ground radar stations according to the time difference equation of the radiation source positions of the ground radar stations to obtain the arrival time difference from the marine radiation source to the N ground radar stations.
Specifically, in step 2.1.2 of this embodiment, radiation source microwave signals received by a plurality of effective ground radar stations are obtained, the effective number of this embodiment is recorded as M, and specifically, weighted averaging is performed on the radiation source microwave signals received by the plurality of effective ground radar stations according to a time difference equation of the radiation source position of the ground radar station, so that the arrival time difference from the marine radiation source to the N ground radar stations is expressed as:
and 2.2, measuring according to the radiation source microwave signals received by the N ground radar stations to obtain the arrival frequency difference from the marine radiation source to the N ground radar stations.
Specifically, step 2.2 includes step 2.2.1, step 2.2.2, step 2.2.3:
and 2.2.1, establishing a frequency difference equation of the radiation source position of each ground radar station according to the speed parameters of the two satellites and the position of each ground radar station.
Specifically, the frequency difference equation of the radiation source position of each ground radar station, which is established according to the velocity parameters of two satellites and the position of each ground radar station in the embodiment, is expressed as:
wherein the content of the first and second substances,
representing the frequency difference of the radiation source microwave signal forwarded via two satellites to radar station j,
representing the radial velocity from the marine source to the ith satellite at time t,
representing the radial velocity from the ith satellite to radar station j at time t.
Referring to fig. 2 again, the frequency difference equations of the radiation source positions of the 3 radar stations a, B, and C in fig. 2 are respectively expressed as:
where, lambda denotes the wavelength of the signal,
representing the frequency difference of the radiation source microwave signal emitted by the marine radiation source and forwarded to the radar station A through two satellites,
representing the frequency difference of the radiation source microwave signal emitted by the marine radiation source and forwarded to the radar station B through two satellites,
representing radiation source microwaves emitted by a marine radiation sourceThe signal is forwarded via two satellites to a frequency difference up to radar station C,
indicating the satellite S at time t1Up to the radial velocity of the radar station a,
indicating the satellite S at time t2Up to the radial velocity of the radar station a,
indicating the satellite S at time t1Up to the radial velocity of the radar station B,
indicating the satellite S at time t2Up to the radial velocity of the radar station B,
indicating the satellite S at time t1Up to the radial velocity of the radar station C,
indicating the satellite S at time t2Up to the radial velocity of the radar station C,
indicating that the marine radiation source arrives at the satellite S at time t1The radial velocity of the magnetic field generating device,
indicating that the marine radiation source arrives at the satellite S at time t2The radial velocity of (a).
And 2.2.2, carrying out frequency domain correlation processing on the radiation source microwave signals received by each ground radar station to obtain a plurality of radiation source microwave signals received by the effective ground radar stations.
Specifically, since the velocity of the satellite and the position of the ground radar station are known quantities, the first half of the frequency difference equation of equation (7) is known, and the equation containing the unknown quantities is expressed as:
according to a formula (1), each ground radar station receives a radiation source microwave signal, frequency domain correlation processing is carried out on the radiation source microwave signals, whether the jth ground radar station receives the radiation source microwave signals forwarded by the satellite is judged, if the correlation peak detection is larger than or equal to a preset threshold value, the preset threshold value is set according to actual conditions, the jth ground radar station is considered to receive the radiation source microwave signals forwarded by the satellite, the radiation source microwave signals forwarded by the satellite received by the jth ground radar station are effective signals, if the correlation peak detection is smaller than the preset threshold value, the radiation source microwave signals forwarded by the satellite received by the jth ground radar station are abandoned, and the N ground radar stations respectively carry out frequency domain correlation processing to obtain the radiation source microwave signals received by a plurality of effective ground radar stations.
And 2.2.3, carrying out weighted average on the radiation source microwave signals received by the effective ground radar stations according to a frequency difference equation of the radiation source positions of the ground radar stations to obtain the arrival frequency difference from the marine radiation source to the N ground radar stations.
Specifically, in step 2.2.2 of this embodiment, radiation source microwave signals received by a plurality of effective ground radar stations are obtained, the effective number of this embodiment is denoted as M, and specifically, the radiation source microwave signals received by the plurality of effective ground radar stations are weighted and averaged according to a frequency difference equation of a radiation source position of the ground radar station, so that an arrival frequency difference from the marine radiation source to the N ground radar stations is expressed as:
and 3, establishing a radiation source position information equation set according to the earth spherical model, the measured arrival time difference and the measured arrival frequency difference.
Specifically, in this embodiment, a radiation source position information equation set is established according to a spherical earth model, a measured arrival time difference and an arrival frequency difference, and the established radiation source position information equation set is expressed as:
wherein (x, y, z) represents the position coordinates of the marine radiation source, (x)i,yi,zi) Representing the positions of two satellites, (v)xi,vyi,vzi) Representing the velocity, R, of two satelliteseThe radius of the earth, H is an elevation observation value, and H can make a reasonable assumption on the height of the target according to experience or auxiliary information.
And 4, resolving the radiation source position information equation set to obtain radiation source position information.
Specifically, the step 4 of solving the radiation source position information equation set includes step 4.1 and step 4.2:
step 4.1, constructing a marine radiation source to satellite S according to the radiation source position information equation set1A one-dimensional six-degree equation of distance.
Specifically, the present embodiment uses the spherical earth model x in formula (11)2+y2+z2＝(Re+H)2The ternary high-order nonlinear equation is simplified to r1The first order six equation of (a) is expressed as:
λ6r1 6+λ5r1 5+λ4r1 4+λ3r1 3+λ2r1 2+λ6r1 6+λ1r1+r0＝0 (12)
wherein r is1Representing a source of radiation at sea to a satellite S1A distance of (a) < lambda >i(i is 1,2 … 6) is a coefficient of each order.
The present embodiment sets a distance r1Initial value and a precision e, continuously iterated by using Newton's iterative algorithmUntil the approximate accuracy e is met, the distance r is obtained1. Except that the distance r is obtained by using a classical Newton iterative algorithm1Besides, the unary sextuple equation can be solved through the constructed numerical solution, so that
Is a distance matrix obtained by solving a six-degree equation of a unitary1And then a distance matrix r is obtained.
And 4.2, constructing a radiation source position information estimation equation according to the radiation source position information equation set and the unary sextuple equation.
Specifically, according to equation (11), a position velocity matrix a is constructed by the position information and the velocity information of two satellites, and the position velocity matrix a is expressed as:
wherein (x)i,yi,zi) (v) position of two satellitesxi,vyi,vzi) The velocity of two satellites.
Meanwhile, a height matrix h of the satellite is constructed, and the height matrix h is expressed as:
wherein H represents an elevation observation value, HiHeight of the ith satellite, ReIs the radius of the earth, Fi＝vxixi+vyiyi+vziziFor known intermediate variables, τ is the arrival time difference obtained by equation (6), and f is the arrival frequency difference obtained by equation (10).
And using the arrival time difference and the arrival frequency difference from the marine radiation source to the N ground radar stations obtained by the forwarding measurement of the two satellites to construct a time difference matrix N, wherein the time difference matrix N is expressed as:
meanwhile, a time difference frequency difference matrix M is constructed, and is expressed as:
and (3) according to the formula (13), the formula (14), the formula (15), the formula (16) and the formula (12), the formula (11) is reduced again, and finally, a radiation source position information estimation equation is obtained, wherein the radiation source position information estimation equation is expressed as:
wherein the content of the first and second substances,
representing the position coordinate of the source of the radiation at sea, mT＝[vx1,vy1,vz1]A-1M-[a1,0,0]Representing a matrix of intermediate coefficients, a1The first intermediate coefficient is represented by a first number,
a2represents a second intermediate coefficient, a2＝-[vx1,vy1,vz1]A-1n，
Represents a distance matrix, r1Representing a source of radiation at sea to a satellite S1The distance of (c).
And 4.3, solving a radiation source position information estimation equation to estimate the radiation source position information.
Specifically, the radiation source position information estimation equation obtained by simplifying the formula (17) is solved, so that the radiation source position information is estimated
And 5, carrying out positioning fuzzy point elimination processing on the radiation source position information.
Specifically, the present embodiment generates a fuzzy solution when solving the estimation of the radiation source position information, and there are two main reasons for generating the fuzzy solution: firstly, because the added root is introduced in the process of solving the radiation source position information estimation equation, the fuzzy solution can be removed by a method of examining the root of the equation set; and another is that because the positioning curved surfaces of two satellites have a plurality of intersection points, the ambiguity solution must introduce other information to distinguish, such as adding direction-finding information or using the observation results of a plurality of orbital planes to resolve ambiguity.
In order to verify the effectiveness of the microwave-forwarding-based two-star offshore target positioning method provided in this embodiment, the following simulation experiments are used to further prove the effectiveness.
1. Simulation data parameters
Referring to fig. 2 again, and referring to fig. 3, fig. 3 is a schematic diagram of a simulation scenario provided in an embodiment of the present invention, where specific parameters include:
satellite position:
satellite S1East longitude 101.85 degree north latitude 26.07 degree height 600km
Satellite S2East longitude 102.73 degree north latitude 26.25 degree height 600km
Satellite velocity:
satellite S1 [-6636.852,-2107.567,1442.781]m/s
Satellite S2 [-6619.444,-2194.200,1392.497]m/s
Position of the marine emission source target P: east longitude 92 degree north latitude 15 degree
2. Simulation data processing content and result
Referring to fig. 4, fig. 4 is a schematic diagram of a solution result of a radiation source position information equation set according to an embodiment of the present invention, it can be known from fig. 4 that the radiation source position information equation set has two real roots, and it is necessary to determine according to other information to remove one virtual root, that is, to perform positioning ambiguity elimination on the radiation source position information. Finally, please seeFig. 5 and 5 are schematic diagrams illustrating analysis of positioning errors of different time difference errors and frequency difference errors in the microwave-forwarding-based double-satellite offshore target positioning method provided by the embodiment of the present invention, and it can be known from fig. 5 that the distance r is 1ns in time difference error and 1Hz in frequency difference error1The calculated value of (A) is 1763.61826km, the error is-580 m, the calculated position of the target is (-215290.19m, 6156885.91m, 1651338.79m), the error is 644.91m, and through analysis of positioning errors of different time difference errors and frequency difference errors in the graph 5, the influence of the time difference errors on the positioning errors is small, and after the frequency difference errors are larger than 3Hz, the positioning errors are increased rapidly.
To sum up, in the method for positioning a double-star offshore target based on microwave forwarding provided by this embodiment, two satellites are used to receive microwave signals from an offshore radiation source, the satellites do not process the microwave signals of the radiation source, the radiation source microwave signals are directly forwarded to a ground radar station, the ground radar station performs parameter measurement on the received signals, such as time difference, frequency difference and the like, the method provided by this embodiment effectively reduces the calculated amount of satellite processing data, performs time difference and frequency difference parameter estimation on the signals received by each ground radar station, effectively improves the estimation errors of the time difference and the frequency difference by means of weighted averaging, and provides a method for simplifying the nonlinear equation set into a solution of a unary sextuple equation for solving the solution of a ternary high-order nonlinear equation set after obtaining the time difference and frequency difference parameters, thereby solving the problems of large calculated amount, unary sextuple equation caused by multi-dimensional search, The problem of local optimal solution is easily caused, the analytic solution of the radiation source position is obtained by solving a unary sextuple equation, the estimation value of the radiation source target is obtained by root checking and fuzzy judgment, and the accuracy of target positioning is improved.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (10)
1. A double-star offshore target positioning method based on microwave forwarding is characterized by comprising the following steps:
step 1, N ground radar stations receive radiation source microwave signals, wherein the radiation source microwave signals sent by an offshore radiation source are received by two satellites and are forwarded to the N ground radar stations, and N is an integer greater than 0;
step 2, respectively measuring and obtaining arrival time difference and arrival frequency difference from the marine radiation source to the N ground radar stations according to the radiation source microwave signals received by the N ground radar stations;
step 3, establishing a radiation source position information equation set according to the earth spherical model, the measured arrival time difference and the measured arrival frequency difference;
step 4, resolving the radiation source position information equation set to obtain radiation source position information;
and 5, carrying out positioning fuzzy point elimination processing on the radiation source position information.
2. The microwave-retransmission-based double-star offshore target positioning method according to claim 1, wherein the radiation source microwave signal received by each ground radar station in step 1 is represented as:
wherein the content of the first and second substances,
represents a radiation source microwave signal S from a marine radiation source received by an ith satellite retransmission radar station jiDenotes the ith satellite, j denotes the jth radar station,
representing the distance from the marine radiation source to the ith satellite at time t,
representing the distance from the ith satellite to radar station j at time t, and c represents the speed of light.
3. The microwave-retransmission-based two-star offshore target positioning method according to claim 2, wherein step 2 comprises:
step 2.1, measuring and obtaining the arrival time difference from the marine radiation source to the N ground radar stations according to the radiation source microwave signals received by the N ground radar stations;
and 2.2, measuring according to the radiation source microwave signals received by the N ground radar stations to obtain the arrival frequency difference from the marine radiation source to the N ground radar stations.
4. The microwave-retransmission-based two-star offshore target positioning method according to claim 3, wherein step 2.1 comprises:
step 2.1.1, establishing a time difference equation of the radiation source position of each ground radar station according to the position parameters of the two satellites and the position of each ground radar station;
step 2.1.2, carrying out frequency domain correlation processing on the radiation source microwave signals received by each ground radar station to obtain radiation source microwave signals received by a plurality of effective ground radar stations;
and 2.1.3, carrying out weighted average on the radiation source microwave signals received by the plurality of effective ground radar stations according to the time difference equation of the radiation source positions of the ground radar stations to obtain the arrival time difference from the marine radiation source to the N ground radar stations.
5. The microwave-retransmission-based two-satellite offshore target positioning method according to claim 4, wherein the equation of the time difference of the radiation source position of each ground radar station in step 2.1.1 is expressed as:
wherein the content of the first and second substances,
representing the time difference between the radiation source microwave signal being forwarded through two satellites to radar station j.
6. The microwave-retransmission-based two-star offshore target positioning method according to claim 5, wherein step 2.2 comprises:
2.2.1, establishing a frequency difference equation of the radiation source position of each ground radar station according to the speed parameters of the two satellites and the position of each ground radar station;
step 2.2.2, carrying out frequency domain correlation processing on the radiation source microwave signals received by each ground radar station to obtain radiation source microwave signals received by a plurality of effective ground radar stations;
and 2.2.3, carrying out weighted average on the radiation source microwave signals received by the plurality of effective ground radar stations according to a frequency difference equation of the radiation source positions of the ground radar stations to obtain the arrival frequency difference from the marine radiation source to the N ground radar stations.
7. The method for positioning double-star offshore target based on microwave forward of claim 6, wherein the frequency difference equation of the radiation source position of each ground radar station in step 2.2.1 is expressed as:
wherein the content of the first and second substances,
representing the frequency difference of the radiation source microwave signal forwarded via two satellites to radar station j,
representing the radial velocity from the marine source to the ith satellite at time t,
representing the radial velocity from the ith satellite to radar station j at time t.
8. The microwave-retransmission-based two-star offshore target positioning method according to claim 6, wherein the radiation source position information equation set up in step 3 is expressed as:
wherein (x, y, z) represents the position coordinates of the marine radiation source, (x)i,yi,zi) Representing the positions of two satellites, (v)xi,vyi,vzi) Representing the velocity, R, of two satelliteseRepresenting earth radius and H elevation observations.
9. The microwave-retransmission-based two-star offshore target positioning method according to claim 8, wherein step 4 comprises:
step 4.1, constructing a marine radiation source to satellite S according to the radiation source position information equation set1A univariate sextant equation of distance;
step 4.2, constructing a radiation source position information estimation equation according to the radiation source position information equation set and the one-element six-order equation;
and 4.3, solving the radiation source position information estimation equation to estimate the radiation source position information.
10. The microwave-retransmission-based two-star offshore target positioning method according to claim 9, wherein the radiation source position information estimation equation constructed in step 4.2 is expressed as:
wherein the content of the first and second substances,
representing the position coordinates of the source of the radiation at sea,
a matrix representing the position and velocity of the satellite,
representing the altitude matrix of the satellite, H representing the altitude observation, HiIndicating the altitude, R, of the ith satelliteeRepresenting the radius of the earth, Fi＝vxixi+vyiyi+vziziIn order for the intermediate variable to be known,
a time difference matrix is represented which is,
representing a time difference-frequency difference matrix, mT＝[vx1,vy1,vz1]A-1M-[a1,0,0]A matrix of intermediate coefficients is represented which,
representing a first intermediate coefficient, a2＝-[vx1,vy1,vz1]A-1n represents a second intermediate coefficient which is,
represents a distance matrix, r1Representing a source of radiation at sea to a satellite S1The distance of (c).
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