A Spaceborne Radar Radiation Source Localization Method Considering Ionospheric Correction

Abstract

The present invention discloses a method for positioning a spaceborne radar radiation source considering ionospheric correction. An observation equation of a reference station considering only the ionospheric influence is established. The double-difference equation is obtained by pairwise subtraction of the reference station observation equations, thereby eliminating the receiver clock error of the reference station and the receiver clock error of the navigation spaceborne transceiver, and obtaining the double-difference ionospheric delay corresponding to the corresponding sub-reference station. The double-difference ionospheric delays of each sub-reference station are combined with the approximate coordinates of the virtual observation station to obtain the double-difference ionospheric delays of each sub-navigation spaceborne transceiver corresponding to the virtual observation station. Then, short baseline solution is carried out in combination with the coordinates of the radiation source target without ionospheric correction to complete differential positioning and obtain the coordinates of the radiation source target after eliminating the ionospheric delay. The present invention uses the VRS method model to eliminate the influence of the ionosphere, and the positioning result has higher accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of satellite radio navigation, and particularly relates to a method for positioning a spaceborne radar radiation source considering ionospheric correction. Background Art

[0002] The method for positioning a spaceborne radar radiation source, also known as the passive positioning method for a spaceborne radar, does not emit electromagnetic signals by itself. Generally, it uses the electromagnetic signals that already exist in space, and only intercepts and receives the radiation source signals through one or more observation stations (monitoring spaceborne receivers) and measures their signal parameters to determine the position of the radiation source. Monitoring the positioning of a spaceborne radar radiation source has the advantages of strong survivability, good concealment, anti-stealth, strong radiation ability, low cost, etc., can make up for the deficiencies of active detection, and compared with the limitations of ground-based and airborne radars such as small monitoring range and large influence by terrain, the positioning of a spaceborne radar radiation source has the advantages of global coverage ability, small influence by the environment, all-day and all-weather, etc.

[0003] The ionosphere is a region located about 60 to 2000 kilometers above the Earth's surface, mainly a plasma layer composed of a large number of electrons. This layer is strongly affected by solar radiation (especially ultraviolet and X-rays) and cosmic rays, resulting in the ionization of air molecules and atoms to form charged particles. These particles have effects such as delay, dispersion, absorption, and Faraday rotation on the signals passing through the ionosphere, significantly affecting the accuracy of satellite navigation and positioning.

[0004] Virtual Reference Station (VRS) is an advanced network real-time kinematic positioning technology that connects multiple reference stations (i.e., actual satellite observation stations) through a network to provide high-precision and real-time position data services. The virtual reference station VRS can effectively compensate for the positioning deviation caused by factors such as atmospheric delay and satellite orbit error by analyzing the data of multiple actual satellite observation stations in real time, greatly improving the accuracy and reliability of positioning.

[0005] In the field of positioning a spaceborne radar radiation source, few people have studied the error brought by the ionospheric delay to the propagation process of the satellite radiation source positioning ground target. With the gradual increase in the requirement for positioning accuracy, there is an urgent need for high-precision positioning of a spaceborne radar radiation source. Summary of the Invention

[0006] In order to make up for the lack of research on the ionosphere in the propagation process of positioning a spaceborne radar radiation source, the present invention provides a method for positioning a spaceborne radar radiation source considering ionospheric correction, and weakens the ionospheric delay in the signal propagation path based on the method model of VRS.

[0007] The above object of the present invention is achieved by the following solutions:

[0008] A spaceborne radar radiation source positioning method considering ionospheric correction, comprising the following steps:

[0009] Step 1: The radiation source signals simultaneously emitted by the radiation source target reach each monitoring spaceborne receiver; among them, 1 monitoring spaceborne receiver serves as the main monitoring spaceborne receiver, and the remaining monitoring spaceborne receivers serve as secondary monitoring spaceborne receivers; each secondary monitoring spaceborne receiver sends the time point information of the corresponding received radiation source signal to the main monitoring spaceborne receiver; the main monitoring spaceborne receiver uses the time points of the corresponding received radiation source signals of each monitoring spaceborne receiver and the time difference of arrival (TDOA) positioning method to obtain the coordinates of the radiation source target without ionospheric correction.

[0010] Step 2: Select W reference stations within a region with a preset radius length centered on the coordinates of the radiation source target without ionospheric correction; each of the M navigation spaceborne transceivers sends signals to the W reference stations respectively.

[0011] Among the M navigation spaceborne transceivers, 1 navigation spaceborne transceiver serves as the main navigation spaceborne transceiver, and the remaining navigation spaceborne transceivers serve as secondary navigation spaceborne transceivers; among the W reference stations, 1 reference station serves as the main reference station, and the remaining reference stations all serve as secondary reference stations.

[0012] The reference stations send the pseudorange between the corresponding navigation spaceborne transceiver and the reference station, the true distance between the navigation spaceborne transceiver and the reference station, and the actual coordinates of the reference station to the ground control station.

[0013] The ground control station calculates the double-difference ionospheric delay corresponding to each secondary reference station for each secondary navigation spaceborne transceiver based on the double-difference equation considering only the ionospheric influence; linearly interpolates the approximate coordinates of the virtual observation station V using the actual coordinates of all reference stations; for each secondary navigation spaceborne transceiver, linearly interpolates the approximate coordinates of the virtual observation station V, the actual coordinates of each secondary reference station, and the double-difference ionospheric delay corresponding to each secondary reference station to obtain the double-difference ionospheric delay of the secondary navigation spaceborne transceiver corresponding to the virtual observation station V; then, the ground control station sends the double-difference ionospheric delays of all secondary navigation spaceborne transceivers corresponding to the virtual observation station V to the main monitoring spaceborne receiver through the radar.

[0014] The main monitoring spaceborne receiver performs short-baseline solution on the double-difference ionospheric delays of all secondary navigation spaceborne transceivers corresponding to the virtual observation station V and the coordinates of the radiation source target without ionospheric correction to complete differential positioning and obtain the coordinates of the radiation source target after eliminating the ionospheric delay.

[0015] In step 1 above, the main monitoring satellite receiver uses the time points at which each monitoring satellite receiver receives the radiation source signal and the arrival time difference TDOA positioning method to obtain the coordinates of the radiation source target without ionospheric correction, including the following steps:

[0016] According to the time point when the radiation source signal arrives at the secondary monitoring satellite receiver and the time point when the radiation source signal arrives at the primary monitoring satellite receiver, the arrival time difference corresponding to each secondary monitoring satellite receiver is calculated, where the arrival time difference corresponding to the secondary monitoring satellite receiver with sequence number j is It is equal to the difference between the time point when the radiation source signal reaches the secondary monitoring satellite receiver with sequence number j and the time point when the radiation source signal reaches the primary monitoring satellite receiver;

[0017] The observed value of the distance difference between the radiation source signal reaching the secondary monitoring satellite receiver and the radiation source signal reaching the primary monitoring satellite receiver is obtained according to the following formula:

[0018] ,

[0019] in, is the propagation speed of the radiation source signal, which is equal to the propagation speed of the electromagnetic wave; is the distance difference observation value between the radiation source signal reaching the secondary monitoring satellite receiver with sequence number j and the radiation source signal reaching the primary monitoring satellite receiver with sequence number 1, recorded as the distance difference observation value ; Serial number of the secondary monitoring satellite receiver , To monitor the total number of onboard receivers; Indicates the arrival time difference corresponding to the secondary monitoring satellite receiver with sequence number j;

[0020] Actual value via distance difference Observed value of distance difference The coordinates of the radiation source target without ionospheric correction are calculated based on the relationship ;in, The actual distance difference between the radiation source signal to the secondary monitoring satellite receiver with serial number j and the radiation source signal to the primary monitoring satellite receiver with serial number 1 is recorded as the actual distance difference value .

[0021] In step 1 as described above, the actual value of the distance difference Observed value of distance difference The coordinates of the radiation source target without ionospheric correction are calculated based on the relationship , specifically including the following steps:

[0022] Solve the following formula to calculate the coordinates of the radiation source target without ionospheric correction :

[0023] ,

[0024] Among them, is the distance difference observation value matrix, ; is the actual value matrix of the distance difference, ; is the measurement error matrix of the time difference of arrival, ; is the measurement error of the distance difference between the radiation source target and the slave monitoring satellite receiver with serial number j and the distance between the radiation source target and the master monitoring satellite receiver with serial number 1; represents transpose;

[0025] Among them,

[0026] ,

[0027] ,

[0028] ,

[0029] is the actual distance from the radiation source target to the slave monitoring satellite receiver with serial number j, is the actual distance from the radiation source target to the master monitoring satellite receiver with serial number 1; is the actual coordinate of the slave monitoring satellite receiver with serial number j; is the actual coordinate of the master monitoring satellite receiver; the coordinate of the radiation source target without ionospheric correction , respectively represent the north component, east component and vertical component of the coordinate of the radiation source target without ionospheric correction; is the distance operator;

[0030] Measurement error matrix of time difference of arrival obeys a Gaussian distribution with zero mean and covariance matrix :

[0031] ,

[0032] is the root mean square matrix of the error of the time difference measurement, = .

[0033] As described in step 2 above, the ground control station calculates the double-difference ionospheric delay corresponding to each sub-reference station for each sub-navigation satellite transceiver based on the double-difference equation considering only the ionospheric influence, which specifically includes the following steps:

[0034] The double-difference equation for each sub-navigation spaceborne transceiver is as follows:

[0035] ,

[0036] where denotes the pseudo-range after double-differencing corresponding to the sub-reference station with serial number and the sub-navigation spaceborne transceiver with serial number , denoted as the pseudo-range after double-differencing ; where , intermediate quantity = , intermediate quantity = ; denotes the pseudo-range between the sub-reference station with serial number and the sub-navigation spaceborne transceiver with serial number ; denotes the pseudo-range between the sub-reference station with serial number and the main-navigation spaceborne transceiver with serial number ; denotes the pseudo-range between the main-reference station with serial number and the sub-navigation spaceborne transceiver with serial number ; denotes the pseudo-range between the main-reference station with serial number and the main-navigation spaceborne transceiver with serial number ;

[0037] denotes the true distance after double-differencing corresponding to the sub-reference station with serial number and the sub-navigation spaceborne transceiver with serial number , denoted as the true distance after double-differencing ; where , intermediate quantity = , intermediate quantity = ; is the true distance between the sub-reference station with serial number and the sub-navigation spaceborne transceiver with serial number , is the true distance between the sub-reference station with serial number and the main-navigation spaceborne transceiver with serial number 1; denotes the true distance between the main-reference station with serial number and the sub-navigation spaceborne transceiver with serial number , denotes the true distance between the main-reference station with serial number and the main-navigation spaceborne transceiver with serial number The true distance between the main navigation spaceborne transceivers;

[0038] Indicates the serial number The double-difference ionospheric delay of the secondary reference station corresponding to the secondary navigation spaceborne transceiver with the serial number is denoted as the double-difference ionospheric delay ;

[0039] Double-difference ionospheric delay The pseudorange after double-differencing and the true distance after double-differencing are calculated;

[0040] is the serial number of the secondary reference station; is the serial number of the secondary navigation spaceborne transceiver.

[0041] The total number of monitoring spaceborne receivers as described above ≥4; The total number of reference stations W≥4.

[0042] In step 2 as described above, for each secondary navigation spaceborne transceiver, the approximate coordinates of the virtual observation station V, the actual coordinates of each secondary reference station, and the double-difference ionospheric delay corresponding to each secondary reference station are linearly interpolated to obtain the double-difference ionospheric delay of the secondary navigation spaceborne transceiver corresponding to the virtual observation station V, which specifically includes the following steps:

[0043] The double-difference ionospheric delay of the virtual observation station V is obtained through the following formula:

[0044] ,

[0045] where represents the double-difference ionospheric delay of the secondary navigation spaceborne transceiver with the serial number i corresponding to the virtual observation station V;

[0046] are respectively the north component, east component, and vertical component of the approximate coordinates of the virtual observation station V;

[0047] are respectively the north component, east component, and vertical component of the actual coordinates of the main reference station with the serial number

[0048] are respectively the north component, east component, and vertical component of the actual coordinates of the secondary reference station with the serial number

[0049] are respectively the north component, east component, and vertical component of the actual coordinates of the secondary reference station with the serial number

[0050] They are respectively the north component, east component and vertical component of the actual coordinates of the secondary reference station with the serial number .

[0051] Indicates the double-difference ionospheric delay of the secondary reference station corresponding to the secondary navigation spaceborne transceiver with the serial number i and the serial number .

[0052] Indicates the double-difference ionospheric delay of the secondary reference station corresponding to the secondary navigation spaceborne transceiver with the serial number i and the serial number .

[0053] Indicates the double-difference ionospheric delay of the secondary reference station corresponding to the secondary navigation spaceborne transceiver with the serial number i and the serial number .

[0054] The advantages and beneficial effects of the present invention are as follows:

[0055] When calculating the passive positioning of the monitoring spaceborne receiver, the present invention uses the VRS method model to eliminate the influence of the ionosphere.

[0056] (1) High precision. The method of using VRS to eliminate ionospheric delay proposed by the present invention has higher positioning accuracy compared with the research results of ignoring ionospheric delay or simply weakening ionospheric delay by using the model method in the prior art.

[0057] (2) Universality. The core idea of the method of using VRS to eliminate ionospheric delay in the present invention is to eliminate the influence of the ionosphere by taking the difference in the propagation path, which is applicable to the reference stations near the radiation source.

[0058] (3) Practicality. The method of using VRS to eliminate ionospheric delay proposed by the present invention makes up for the lack of research on the ionosphere in the propagation process of the positioning of spaceborne radar radiation sources. Brief Description of the Drawings

[0059] Figure 1 It is a schematic diagram of the model for eliminating ionospheric delay using VRS. Detailed Embodiment

[0060] In order to facilitate the understanding and implementation of the present invention by those of ordinary skill in the art, the present invention will be further described in detail below with reference to examples and drawings. The embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0061] The monitoring spaceborne receiver in the spaceborne radar receives the radiation source signal (such as communication L-band) emitted by the radiation source target. Using the Time Difference of Arrival (TDOA) positioning method, the coordinates of the radiation source target without ionospheric correction can be calculated. However, during the propagation of the radiation source signal, it is affected by ionospheric refraction and other factors, and the ionospheric delay error cannot be ignored. A spaceborne radar radiation source positioning method considering ionospheric correction according to the present invention has the following specific implementation steps:

[0062] Step 1: The radiation source signals simultaneously emitted by the radiation source target reach each monitoring spaceborne receiver; among them, one monitoring spaceborne receiver is used as the main monitoring spaceborne receiver, and the remaining monitoring spaceborne receivers are used as secondary monitoring spaceborne receivers; each secondary monitoring spaceborne receiver sends the time point information of the corresponding received radiation source signal to the main monitoring spaceborne receiver; the main monitoring spaceborne receiver uses the time points of the corresponding received radiation source signals of each monitoring spaceborne receiver and the TDOA positioning method to obtain the coordinates of the radiation source target without ionospheric correction.

[0063] In the scenario of three-dimensional positioning in this embodiment, five monitoring spaceborne receivers simultaneously receive the radiation source signals of the radiation source target. One of the five monitoring spaceborne receivers is selected as the main monitoring spaceborne receiver, and the remaining monitoring spaceborne receivers are used as secondary monitoring spaceborne receivers. Let the actual coordinates of the monitoring spaceborne receiver with the serial number be , the serial number of the monitoring spaceborne receiver , is the total number of monitoring spaceborne receivers (in this embodiment, the serial number of the monitoring spaceborne receiver = 1, 2, 3, 4, 5, and the monitoring spaceborne receiver with the serial number = 1 is the main monitoring spaceborne receiver) respectively represent the north component, east component, and vertical component of the actual coordinates of the monitoring spaceborne receiver with the serial number . The coordinates of the radiation source target without ionospheric correction are set as , respectively represent the north component, east component, and vertical component of the coordinates of the radiation source target without ionospheric correction.

[0064] According to the time point when the radiation source signal reaches the secondary monitoring spaceborne receiver and the time point when the radiation source signal reaches the main monitoring spaceborne receiver, calculate the time difference of arrival TDOA. The time difference of arrival TDOA is a set of the time differences of arrival corresponding to each secondary monitoring spaceborne receiver. Among them, the time difference of arrival corresponding to the secondary monitoring spaceborne receiver with the serial number is equal to the time when the radiation source signal reaches the serial number The difference between the time point of the secondary monitoring spaceborne receiver and the time point when the radiation source signal arrives at the primary monitoring spaceborne receiver; the serial number of the secondary monitoring spaceborne receiver ;

[0065] Wherein, the distance from the radiation source target to the monitoring spaceborne receiver and the propagation time of the radiation source signal from the radiation source target to the monitoring spaceborne receiver satisfy the following relationship:

[0066] ,

[0067] In the formula, is the propagation speed of the radiation source signal, and the propagation speed of the radiation source signal is equal to the propagation speed of electromagnetic waves; is the distance between the monitoring spaceborne receiver with serial number and the radiation source target, is the propagation time of the radiation source signal from the radiation source target to the monitoring spaceborne receiver with serial number . In this embodiment, the arrival time difference corresponding to the secondary monitoring spaceborne receiver with serial number , the serial number of the secondary monitoring spaceborne receiver , is the propagation time of the radiation source signal from the radiation source target to the secondary monitoring spaceborne receiver with serial number ; is the propagation time of the radiation source signal from the radiation source target to the primary monitoring spaceborne receiver with serial number .

[0068] From the relationship between the distance from the radiation source target to the monitoring spaceborne receiver and the propagation time of the radiation source signal from the radiation source target to the monitoring spaceborne receiver, the difference RDOA (Range Difference of Arrival) between the distance at which the radiation source signal arrives at each secondary monitoring spaceborne receiver and the distance at which the radiation source signal arrives at the primary monitoring spaceborne receiver can be calculated based on the arrival time difference corresponding to each secondary monitoring spaceborne receiver, that is, the distance difference observation value at which the radiation source signal arrives at the secondary monitoring spaceborne receiver and the radiation source signal arrives at the primary monitoring spaceborne receiver is obtained according to the following formula:

[0069] ,

[0070] Wherein, is the distance difference observation value at which the radiation source signal arrives at the secondary monitoring spaceborne receiver with serial number j and the radiation source signal arrives at the primary monitoring spaceborne receiver with serial number 1, denoted as the distance difference observation value ; represents the arrival time difference corresponding to the secondary monitoring spaceborne receiver with serial number j.

[0071] Define is the actual value of the distance difference between the radiation source signal reaching the slave monitoring satellite receiver with serial number j and the radiation source signal reaching the master monitoring satellite receiver with serial number 1 (denoted as the actual distance difference ), and the coordinates of the radiation source target without ionospheric correction are calculated through the relationship between the actual distance difference and the observed distance difference , and the specific steps are as follows:

[0072] For each slave monitoring satellite receiver, the actual distance difference relative to the observed distance difference has the following relationship:

[0073] ,

[0074] In this embodiment, the serial number j of the slave monitoring satellite receiver , is the measurement error of the distance difference between the distance from the radiation source target to the slave monitoring satellite receiver with serial number j and the distance from the radiation source target to the master monitoring satellite receiver with serial number 1;

[0075] For the actual distance difference there is:

[0076] ,

[0077] ,

[0078] ,

[0079] is the actual distance from the radiation source target to the slave monitoring satellite receiver with serial number j, is the actual distance from the radiation source target to the master monitoring satellite receiver with serial number 1, is the actual coordinate of the slave monitoring satellite receiver with serial number j, is a known quantity; is the actual coordinate of the master monitoring satellite receiver, is a known quantity; the coordinates of the radiation source target without ionospheric correction is the quantity to be solved; is the distance operator. To facilitate solving the coordinates of the radiation source target without ionospheric correction in three-dimensional space , the total number of monitoring satellite receivers ≥4.

[0080] Then, combining the relationship formula between the actual distance difference and the observed distance difference , the coordinates of the radiation source target without ionospheric correction are calculated by solving the following formula :

[0081] ,

[0082] is the matrix of range difference observation values, ; is the matrix of actual range difference values, ; is the measurement error matrix of time difference of arrival, ; In this embodiment, , , ; denotes transpose;

[0083] The measurement error matrix of time difference of arrival follows a Gaussian distribution with zero mean and covariance matrix :

[0084] ,

[0085] wherein, is the root mean square matrix of the error of time difference measurement, is the propagation speed of the radiation source signal, = .

[0086] Step 2: Use the VRS method to eliminate the ionospheric delay generated by the influence of the ionosphere on the propagation path of the satellite receiving the ground signal.

[0087] After step 1, the coordinates of the radiation source target without ionospheric correction can be obtained. In step 2, the VRS method is used to eliminate the ionospheric delay. As Figure 1 shown, the VRS method uses a continuously operating GPS multi-reference station system, which includes multiple reference stations. One reference station is selected as the main reference station, and the remaining reference stations are used as secondary reference stations. In this embodiment, it includes reference stations , , , and , and the reference station is used as the main reference station, and the reference stations , reference station , and reference station are used as secondary reference stations.

[0088] The method for eliminating the ionospheric delay using the VRS method is:

[0089] Select W reference stations within a region centered on the coordinates of the radiation source target without ionospheric correction, with a preset radius length as the radius; each of the M navigation spaceborne transceivers in the navigation spaceborne transceivers sends signals to the W reference stations; the navigation spaceborne transceiver is a signal receiving and transmitting device on the satellite in the navigation positioning system, and the navigation positioning system is the GPS of the United States or the Beidou satellite navigation system of China or the Galileo satellite positioning system of Europe or GLONASS of Russia and related navigation positioning systems, etc.;

[0090] Among the M navigation spaceborne transceivers, 1 navigation spaceborne transceiver is used as the main navigation spaceborne transceiver, and the remaining navigation spaceborne transceivers are used as sub-navigation spaceborne transceivers; among the W reference stations (the total number of reference stations W≥4), 1 reference station is the main reference station, and the remaining reference stations are all used as sub-reference stations;

[0091] The reference station sends the pseudorange between the corresponding navigation spaceborne transceiver and the reference station, the true distance between the navigation spaceborne transceiver and the reference station, and the actual coordinates of the reference station to the ground control station;

[0092] The ground control station calculates the double-difference ionospheric delay of each sub-navigation spaceborne transceiver corresponding to each sub-reference station based on the double-difference equation considering only the ionospheric influence; linearly interpolates the approximate coordinates of the virtual observation station V using the actual coordinates of all reference stations; for each sub-navigation spaceborne transceiver, linearly interpolates the approximate coordinates of the virtual observation station V, the actual coordinates of each sub-reference station, and the double-difference ionospheric delay of each sub-reference station to obtain the double-difference ionospheric delay of the sub-navigation spaceborne transceiver corresponding to the virtual observation station V; then, the ground control station sends the double-difference ionospheric delay of all sub-navigation spaceborne transceivers corresponding to the virtual observation station V to the main monitoring spaceborne receiver through radar;

[0093] The main monitoring spaceborne receiver performs short-baseline solution on the double-difference ionospheric delay of all sub-navigation spaceborne transceivers corresponding to the virtual observation station V and the coordinates of the radiation source target without ionospheric correction to complete differential positioning and obtain the coordinates of the radiation source target after eliminating the ionospheric delay.

[0094] (1) Establish the reference station observation equation, obtain the double-difference equation from the reference station observation equation; obtain the double-difference ionospheric delay of each sub-navigation spaceborne transceiver corresponding to each sub-reference station using the double-difference equation

[0095] Suppose that in the signal propagation path, only the influence of the ionosphere is considered for environmental factors, then the reference station observation equation is:

[0096] ,

[0097] In the formula, represents the reference station with serial number and the serial number The true distance between the navigation spaceborne transceiver, denotes the serial number of the reference station and the pseudorange between the navigation spaceborne transceiver with the serial number ; refers to the receiver clock error of the reference station with the serial number ; refers to the receiver clock error of the navigation spaceborne transceiver with the serial number ; refers to the ionospheric delay during the process that the reference station with the serial number receives the signal transmitted by the navigation spaceborne transceiver with the serial number , denoted as ionospheric delay , the serial number of the navigation spaceborne transceiver , is the total number of navigation spaceborne transceivers; in this embodiment, the serial number of the reference station = , , , respectively represent reference station , reference station , reference station , and reference station . Then , , , respectively represent the true distances between each reference station and the navigation spaceborne transceiver with the serial number ; , , , respectively represent the ionospheric delays during the process that each reference station receives the signal transmitted by the navigation spaceborne transceiver with the serial number ; , , , respectively denote the pseudoranges between each reference station and the navigation spaceborne transceiver with the serial number ; , , , respectively represent the receiver clock errors of each reference station in this embodiment. Then the reference station , , , and corresponding reference station observation equations are respectively:

[0098] ,

[0099] ,

[0100] ,

[0101] ,

[0102] Among them, , refers to the actual coordinates of the reference station with serial number , are respectively the north component, east component and vertical component of the actual coordinates of the reference station with serial number ; respectively represent the north component, east component and vertical component of the actual coordinates of the navigation spaceborne transceiver with serial number , and the actual coordinates of the navigation spaceborne transceiver with serial number are .

[0103] The above reference stations , , , and the corresponding error information of the reference station observation equation includes the receiver clock error of the navigation spaceborne transceiver with serial number , the receiver clock error of the reference station with serial number , and the ionospheric delay . For the same reference station, first select the reference station observation equation corresponding to the main navigation spaceborne transceiver as the reference equation (that is, the reference station , , , and in the corresponding reference station observation equation uses the reference station observation equation with as the reference equation), and subtract the reference station observation equation corresponding to the secondary navigation spaceborne transceiver from the reference equation corresponding to the secondary navigation spaceborne transceiver to obtain the single-difference equation, thereby eliminating the receiver clock errors of each reference station. A total of 16 single-difference equations are obtained in this embodiment:

[0104] ,

[0105] Among them, the intermediate quantity = , represents the pseudorange between the reference station with serial number and the secondary navigation spaceborne transceiver with serial number , represents the pseudorange between the reference station with serial number and the main navigation spaceborne transceiver with serial number 1. The serial number of the secondary navigation spaceborne transceiver .

[0106] Intermediate quantity = , represents the true distance between the reference station with serial number and the sub-navigation satellite transceiver with serial number ; is the true distance between the reference station with serial number and the main navigation satellite transceiver with serial number ;

[0107] Intermediate quantity , is the receiver clock error of the sub-navigation satellite transceiver with serial number ; is the receiver clock error of the main navigation satellite transceiver with serial number ;

[0108] Intermediate quantity , is the ionospheric delay during the process that the reference station with serial number receives the signal transmitted by the sub-navigation satellite transceiver with serial number ; is the ionospheric delay during the process that the reference station with serial number receives the signal transmitted by the main navigation satellite transceiver with serial number 1;

[0109] In this embodiment, the serial number of the sub-navigation satellite transceiver ; the serial number of the reference station .

[0110] For each sub-navigation satellite transceiver, the single-difference equations corresponding to the sub-reference stations 、 、 are respectively subtracted from the single-difference equations corresponding to the main reference station to obtain the corresponding double-difference equations, thereby eliminating the clock error of the navigation satellite transceiver with serial number m, and the specific formula is as follows:

[0111] ,

[0112] Among them, represents the pseudo-range after double-differencing corresponding to the sub-reference station with serial number and the sub-navigation satellite transceiver with serial number , denoted as the pseudo-range after double-differencing ; among them, , intermediate quantity = , intermediate quantity = ; Indicates the pseudorange between the secondary reference station numbered and the secondary navigation spaceborne transceiver numbered , which belongs to the reference station observation value; Indicates the pseudorange between the secondary reference station numbered and the primary navigation spaceborne transceiver numbered , which belongs to the reference station observation value; Indicates the pseudorange between the primary reference station numbered and the secondary navigation spaceborne transceiver numbered , which belongs to the reference station observation value; Indicates the pseudorange between the primary reference station numbered and the primary navigation spaceborne transceiver numbered , which belongs to the reference station observation value;

[0113] Indicates the true distance after double differencing corresponding to the secondary navigation spaceborne transceiver numbered and the secondary reference station numbered , denoted as the true distance after double differencing ; Among them, , intermediate quantity = , intermediate quantity = ; is the true distance between the secondary reference station numbered and the secondary navigation spaceborne transceiver numbered , is the true distance between the secondary reference station numbered and the primary navigation spaceborne transceiver numbered 1; Indicates the true distance between the primary reference station numbered and the secondary navigation spaceborne transceiver numbered , Indicates the true distance between the primary reference station numbered and the primary navigation spaceborne transceiver numbered ; The true distance after double differencing can be calculated through the actual coordinates of the known secondary navigation spaceborne transceiver and the actual coordinates of the secondary reference station;

[0114] Indicates the double-differenced ionospheric delay corresponding to the secondary navigation spaceborne transceiver numbered and the secondary reference station numbered , denoted as the double-differenced ionospheric delay ; Among them, , intermediate quantity , intermediate quantity , is the ionospheric delay in the process of the deputy reference station with serial number receiving the signal transmitted by the deputy navigation satellite transceiver with serial number ; is the ionospheric delay in the process of the deputy reference station with serial number receiving the signal transmitted by the main navigation satellite transceiver with serial number ; is the ionospheric delay in the process of the main reference station with serial number receiving the signal transmitted by the deputy navigation satellite transceiver with serial number ; is the ionospheric delay in the process of the main reference station with serial number receiving the signal transmitted by the main navigation satellite transceiver with serial number ; double-difference ionospheric delay The double-difference ionospheric delay can be obtained by the pseudo-range after double-difference and the true distance after double-difference;

[0115] In this embodiment, the serial number of the deputy reference station is .

[0116] (2) Obtain the double-difference ionospheric delay of the deputy navigation satellite transceiver corresponding to the virtual observation station V

[0117] The approximate coordinates of the virtual observation station V are obtained by linear interpolation of the actual coordinates of all reference stations , which are the north component, east component and vertical component of the approximate coordinates of the virtual observation station V respectively;

[0118] For each deputy navigation satellite transceiver, according to the approximate coordinates of the virtual observation station V, the actual coordinates of each deputy reference station and the double-difference ionospheric delay corresponding to each deputy reference station (in this embodiment: double-difference ionospheric delay , , ) linear interpolation is used to obtain the double-difference ionospheric delay corresponding to the virtual observation station V, that is:

[0119] ,

[0120] wherein, represents the double-difference ionospheric delay of the deputy navigation satellite transceiver with serial number i corresponding to the virtual observation station V;

[0121] The serial number is the actual coordinates of the main reference station are , which are the serial numbers respectively The north component, east component, and vertical component of the actual coordinates of the main reference station;

[0122] The serial number is The actual coordinates of the secondary reference station numbered , are respectively the north component, east component, and vertical component of the actual coordinates of the secondary reference station numbered ;

[0123] The serial number is The actual coordinates of the secondary reference station numbered , are respectively the north component, east component, and vertical component of the actual coordinates of the secondary reference station numbered ;

[0124] The serial number is The actual coordinates of the secondary reference station numbered , are respectively the north component, east component, and vertical component of the actual coordinates of the secondary reference station numbered .

[0125] Indicates the double-difference ionospheric delay of the secondary navigation spaceborne transceiver numbered i corresponding to the secondary reference station numbered ;

[0126] Indicates the double-difference ionospheric delay of the secondary navigation spaceborne transceiver numbered i corresponding to the secondary reference station numbered ;

[0127] Indicates the double-difference ionospheric delay of the secondary navigation spaceborne transceiver numbered i corresponding to the secondary reference station numbered .

[0128] (3) Obtain the coordinates of the radiation source target after eliminating the ionospheric delay

[0129] Because the distance between the virtual observation station V and the radiation source target is relatively close, the ionospheric delay of the navigation spaceborne transceiver in the signal propagation direction for the virtual observation station V is regarded as the same as the ionospheric delay of the navigation spaceborne transceiver in the signal propagation direction for the radiation source target. Then, the ionospheric delay of all secondary navigation spaceborne transceivers corresponding to the virtual observation station V and the coordinates of the radiation source target without ionospheric correction are used for short-baseline solution to complete differential positioning, and the coordinates of the radiation source target after eliminating the ionospheric delay are obtained, thereby realizing positioning of the radiation source target considering ionospheric correction.

[0130] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Those skilled in the art to which the present invention pertains may make various modifications or supplements to the described specific embodiments or use similar means for substitution, but will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A method for locating spaceborne radar radiation sources considering ionospheric correction, characterized in that, It includes the following steps: Step 1: The radiation source signals simultaneously emitted by the radiation source target reach each monitoring spaceborne receiver; among them, 1 monitoring spaceborne receiver serves as the main monitoring spaceborne receiver, and the remaining monitoring spaceborne receivers serve as secondary monitoring spaceborne receivers; each secondary monitoring spaceborne receiver sends the time point information of the corresponding received radiation source signal to the main monitoring spaceborne receiver; the main monitoring spaceborne receiver uses the time points when each monitoring spaceborne receiver receives the radiation source signal and the Time Difference of Arrival (TDOA) positioning method to obtain the coordinates of the radiation source target without ionospheric correction; Step 2: Select W reference stations within a region centered at the coordinates of the radiation source target without ionospheric correction and with a preset radius length; each of the M navigation spaceborne transceivers among the M navigation spaceborne transceivers sends signals to the W reference stations respectively; Among the M navigation spaceborne transceivers, 1 navigation spaceborne transceiver serves as the main navigation spaceborne transceiver, and the remaining navigation spaceborne transceivers serve as secondary navigation spaceborne transceivers; among the W reference stations, 1 reference station serves as the main reference station, and the remaining reference stations all serve as secondary reference stations; The reference stations send the pseudo-range between the corresponding navigation spaceborne transceiver and the reference station, the true distance between the navigation spaceborne transceiver and the reference station, and the actual coordinates of the reference station to the ground control station; The ground control station calculates the double-difference ionospheric delay for each secondary reference station corresponding to each secondary navigation spaceborne transceiver based on the double-difference equation considering only the ionospheric influence; linearly interpolates the approximate coordinates of the virtual observation station V using the actual coordinates of all reference stations; for each secondary navigation spaceborne transceiver, linearly interpolates the approximate coordinates of the virtual observation station V, the actual coordinates of each secondary reference station, and the double-difference ionospheric delay corresponding to each secondary reference station to obtain the double-difference ionospheric delay of the secondary navigation spaceborne transceiver corresponding to the virtual observation station V; then, the ground control station sends the double-difference ionospheric delay of all secondary navigation spaceborne transceivers corresponding to the virtual observation station V to the main monitoring spaceborne receiver through radar; The main monitoring spaceborne receiver performs short baseline solution on the double-difference ionospheric delay of all secondary navigation spaceborne transceivers corresponding to the virtual observation station V and the coordinates of the radiation source target without ionospheric correction to complete differential positioning and obtain the coordinates of the radiation source target after eliminating the ionospheric delay; 2. The spaceborne radar radiation source positioning method considering ionospheric correction according to claim 1, characterized in that In the said Step 1, the main monitoring spaceborne receiver uses the time points when each monitoring spaceborne receiver receives the radiation source signal and the Time Difference of Arrival (TDOA) positioning method to obtain the coordinates of the radiation source target without ionospheric correction, including the following steps: According to the time point when the radiation source signal arrives at the slave monitoring spaceborne receiver and the time point when the radiation source signal arrives at the master monitoring spaceborne receiver, calculate the arrival time difference corresponding to each slave monitoring spaceborne receiver, where the arrival time difference corresponding to the slave monitoring spaceborne receiver with serial number j is equal to the difference between the time point when the radiation source signal arrives at the slave monitoring spaceborne receiver with serial number j and the time point when the radiation source signal arrives at the master monitoring spaceborne receiver; Obtain the range difference observation value of the radiation source signal reaching the secondary monitoring spaceborne receiver and the radiation source signal reaching the main monitoring spaceborne receiver according to the following formula: ， Among them, is the propagation speed of the radiation source signal, and the propagation speed of the radiation source signal is equal to the propagation speed of the electromagnetic wave; is the observed value of the distance difference between the radiation source signal reaching the slave monitoring satellite-borne receiver with serial number j and the radiation source signal reaching the master monitoring satellite-borne receiver with serial number 1, denoted as the observed value of the distance difference ; the serial number of the slave monitoring satellite-borne receiver , is the total number of the monitoring satellite-borne receivers; represents the arrival time difference corresponding to the slave monitoring satellite-borne receiver with serial number j; By the actual value of the distance difference and the observed value of the distance difference to calculate the coordinates of the radiation source target without ionospheric correction ; where is the actual value of the distance difference between the radiation source signal reaching the slave monitoring satellite receiver numbered j and the radiation source signal reaching the master monitoring satellite receiver numbered 1, denoted as the actual value of the distance difference .

3. The method for positioning a spaceborne radar radiation source considering ionospheric correction according to claim 2, wherein In the said step 1, the coordinates of the radiation source target without ionospheric correction are calculated based on the relationship between the actual value of the distance difference and the observed value of the distance difference , and the specific steps are as follows: Solve the following formula to calculate the coordinates of the radiation source target without ionospheric correction : ， Among them, is the distance difference observation value matrix, ; is the actual value matrix of the distance difference, ; is the measurement error matrix of the time difference of arrival, ; is the measurement error of the distance difference between the radiation source target and the slave monitoring satellite receiver with serial number j and the distance between the radiation source target and the master monitoring satellite receiver with serial number 1; represents transpose; Where, ， ， ， is the actual distance from the radiation source target to the slave monitoring satellite receiver with serial number j, and is the actual distance from the radiation source target to the master monitoring satellite receiver with serial number 1; is the actual coordinate of the slave monitoring satellite receiver with serial number j; is the actual coordinate of the master monitoring satellite receiver; the coordinates of the radiation source target without ionospheric correction , respectively represent the north component, east component and vertical component of the coordinates of the radiation source target without ionospheric correction; is the distance operator; Measurement error matrix of time difference of arrival Subject to a Gaussian distribution with zero mean and covariance matrix : ， The root mean square error matrix for time difference measurement, = .

4. A spaceborne radar radiation source positioning method considering ionospheric correction according to claim 1, characterized in that, In the said Step 2, the ground control station calculates the double-difference ionospheric delay for each secondary reference station corresponding to each secondary navigation spaceborne transceiver based on the double-difference equation considering only the ionospheric influence, specifically including the following steps: The double-difference equation for each secondary navigation spaceborne transceiver is: ， Among them, represents the double-differenced pseudorange corresponding to the secondary reference station with serial number and the secondary navigation spaceborne transceiver with serial number , denoted as the double-differenced pseudorange ; among them, , intermediate quantity = , intermediate quantity = ; represents the pseudorange between the secondary reference station with serial number and the secondary navigation spaceborne transceiver with serial number ; represents the pseudorange between the secondary reference station with serial number and the primary navigation spaceborne transceiver with serial number ; represents the pseudorange between the primary reference station with serial number and the secondary navigation spaceborne transceiver with serial number ; represents the pseudorange between the primary reference station with serial number and the primary navigation spaceborne transceiver with serial number ; Indicates the true distance after double differencing corresponding to the secondary reference station with serial number and the secondary navigation spaceborne transceiver with serial number , denoted as the true distance after double differencing ; where , intermediate quantity = , intermediate quantity = ; is the true distance between the secondary reference station with serial number and the secondary navigation spaceborne transceiver with serial number ; is the true distance between the secondary reference station with serial number and the primary navigation spaceborne transceiver with serial number 1; Indicates the true distance between the primary reference station with serial number and the secondary navigation spaceborne transceiver with serial number ; Indicates the true distance between the primary reference station with serial number and the primary navigation spaceborne transceiver with serial number ; Indicates that the serial number is of the sub-navigation satellite transceiver corresponds to the serial number of the sub-reference station's double-differenced ionospheric delay, denoted as the double-differenced ionospheric delay ; Double-difference ionospheric delay Pseudorange after double-differencing And the true distance after double-differencing Calculated is the serial number of the secondary reference station; is the serial number of the secondary navigation satellite transceiver.

5. A spaceborne radar radiation source positioning method considering ionospheric correction according to claim 3, characterized in that, The total number of the monitored spaceborne receivers ≥4; the total number W of the reference stations ≥4.

6. The spaceborne radar radiation source positioning method considering ionospheric correction according to claim 5, characterized in that, In step 2, for each sub-navigation spaceborne transceiver, linear interpolation is performed on the approximate coordinates of the virtual observatory V, the actual coordinates of each sub-reference station, and the double-differenced ionospheric delay corresponding to each sub-reference station to obtain the double-differenced ionospheric delay of the sub-navigation spaceborne transceiver corresponding to the virtual observatory V. The specific steps are as follows: The double-differenced ionospheric delay of the virtual observatory V is obtained through the following formula: ， Among them, represents the double-difference ionospheric delay of the virtual observation station V corresponding to the sub-navigation satellite transceiver with serial number i; They are respectively the north component, east component and vertical component of the approximate coordinates of the virtual observation station V; are respectively the north component, east component and vertical component of the actual coordinates of the main reference station with the serial number ; are respectively the north component, east component, and vertical component of the actual coordinates of the secondary reference stations with serial numbers ; are respectively the north component, east component and vertical component of the actual coordinates of the deputy reference stations with serial numbers ; are respectively the north component, east component and vertical component of the actual coordinates of the secondary reference stations with serial numbers ; Indicates the double-difference ionospheric delay of the sub-reference station corresponding to the sub-navigation satellite transceiver with serial number i; ​ Indicates the double-difference ionospheric delay of the sub-reference station corresponding to the sub-navigation satellite transceiver with serial number i; ​ Indicates the double-difference ionospheric delay of the sub-reference station corresponding to the sub-navigation satellite transceiver with serial number i and serial number

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