Space-based passive radar positioning method considering ionosphere correction

Abstract

The invention discloses a space-based passive radar positioning method considering ionosphere correction. The method comprises the following steps: acquiring latitude and longitude coordinates of an ionosphere single-layer puncture point corresponding to each spaceborne receiver based on coordinates of a radiation source target without ionosphere correction; calculating an estimated value of an ionized layer delay theoretical value corresponding to each spaceborne receiver by combining the calculated ionized layer TEC distribution diagram; obtaining an estimated value of distance coordinate offset caused by the ionosphere according to the estimated values of the ionosphere delay theoretical values corresponding to all satellite-borne receivers; and according to the estimated value of the distance coordinate offset and the coordinates of the radiation source target without ionospheric correction, obtaining estimated coordinates of the radiation source target after ionospheric correction. According to the method, when the satellite is used as the receiver for passive positioning, the ionosphere error existing in the propagation path for receiving the ground signal is considered, the defect of research on the ionosphere in the space-based passive positioning propagation process is overcome, and the positioning result has higher precision.

Description

Technical Field

[0001] The present invention belongs to the field of satellite radio navigation, and particularly relates to a space-based passive radar positioning method considering ionospheric correction. Background Art

[0002] Space-based radio signal source positioning, also known as space-based passive positioning, 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 and measures their signal parameters through one or more observation stations (spaceborne receivers) to determine the position of the radiation source. Space-based passive positioning has the advantages of strong survivability, good concealment, anti-stealth, strong radiation ability, low cost, etc. It can make up for the deficiencies of active detection. Compared with ground-based and airborne passive positioning systems, this method can monitor non-cooperative targets that emit radio signals in most parts of the world. For sparsely populated areas such as the open sea and polar regions, satellite detection is the only realistic and feasible method.

[0003] The ionosphere is an ionized region in the Earth's atmosphere, located at an altitude of about 60 to 2000 kilometers from the ground. This region is strongly affected by solar radiation (especially ultraviolet and X-rays) and cosmic rays, which ionize air molecules and atoms to form charged particles. These charged particles will cause delays, dispersions, absorptions, and Faraday rotations in the signals passing through them, and are an important link affecting the satellite positioning propagation process.

[0004] In the field of space-based passive positioning, few people have studied the errors brought by ionospheric delay to the propagation process of satellite passive positioning of ground targets. With the increasing requirement for positioning accuracy, there is an urgent need for high-precision space-based passive positioning. Summary of the Invention

[0005] In order to make up for the lack of research on the ionosphere in the propagation process of space-based passive positioning, the present invention provides a space-based passive radar positioning method considering ionospheric correction, which can calculate the influence of the ionosphere on the propagation path of the satellite receiving the ground observation station by using IGS ionospheric observation data.

[0006] The above object of the present invention is achieved by the following solutions:

[0007] A space-based passive radar positioning method considering ionospheric correction includes the following steps:

[0008] Step 1: Select one spaceborne receiver as the main spaceborne receiver from multiple spaceborne receivers, and the remaining spaceborne receivers as the secondary spaceborne receivers;

[0009] The radiation source signals simultaneously emitted by the radiation source target reach each spaceborne receiver. Each sub-spaceborne receiver sends the time point information of the received radiation source signal to the main spaceborne receiver; the main spaceborne receiver uses the time points when each 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; the coordinates of the radiation source target without ionospheric correction are sent to each sub-spaceborne receiver;

[0010] Obtain the calculated ionospheric Total Electron Content (TEC) distribution map;

[0011] Step 2: Each spaceborne receiver obtains the longitude and latitude coordinates of the corresponding single-layer ionospheric piercing point based on the coordinates of the radiation source target without ionospheric correction;

[0012] Each spaceborne receiver calculates the estimated value of the corresponding theoretical ionospheric delay based on the longitude and latitude coordinates of the corresponding single-layer ionospheric piercing point and the calculated ionospheric TEC distribution map; each sub-spaceborne receiver sends the estimated value of the corresponding theoretical ionospheric delay to the main spaceborne receiver;

[0013] Based on the fact that the estimated value of the theoretical ionospheric delay is approximately equal to the change in the positioning observation distance caused by the ionosphere, construct an ionospheric delay correction formula; the main spaceborne receiver uses the estimated values of the theoretical ionospheric delays corresponding to all spaceborne receivers to solve the ionospheric delay correction formula to obtain the estimated value of the distance coordinate offset caused by the ionosphere; and uses the estimated value of the distance coordinate offset to correct the coordinates of the radiation source target without ionospheric correction to obtain the estimated coordinates of the radiation source target after ionospheric correction.

[0014] In Step 1 as described above, the main spaceborne receiver uses the time points when each spaceborne receiver receives the radiation source signal and the TDOA positioning method to obtain the coordinates of the radiation source target without ionospheric correction, including the following steps:

[0015] According to the time point when the radiation source signal reaches the sub-spaceborne receiver and the time point when the radiation source signal reaches the main spaceborne receiver, calculate the corresponding time difference of arrival for each sub-spaceborne receiver. Among them, the time difference of arrival ΔT i corresponding to the i-th sub-spaceborne receiver is equal to the difference between the time point when the radiation source signal reaches the i-th sub-spaceborne receiver and the time point when the radiation source signal reaches the main spaceborne receiver;

[0016] Obtain the observed value of the distance difference between the radiation source signal reaching the sub-spaceborne receiver and the radiation source signal reaching the main spaceborne receiver according to the following formula:

[0017] R i1 =ΔT i *c

[0018] Among them, c 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; R i1 is the observed value of the distance difference between the radiation source signal reaching the slave satellite receiver with serial number i and the radiation source signal reaching the master satellite receiver with serial number 1, denoted as the observed distance difference R i1 ; the serial number i of the slave satellite receiver belongs to {2, 3, …, M}, and M is the total number of satellite receivers; ΔT i represents the arrival time difference corresponding to the slave satellite receiver with serial number i;

[0019] Define as the actual value of the distance difference between the radiation source signal reaching the slave satellite receiver with serial number i and the radiation source signal reaching the master satellite receiver with serial number 1, denoted as the actual distance difference Through the actual distance difference and the observed distance difference R i1 , calculate the coordinates u of the radiation source target without ionospheric correction 0 .

[0020] As described in step 1 above, through the actual distance difference and the observed distance difference R i1 , calculate the coordinates u of the radiation source target without ionospheric correction 0 , which specifically includes the following steps:

[0021] Solve the following formula to calculate the coordinates u of the radiation source target without ionospheric correction 0 :

[0022] R = R 0 + σ

[0023] Among them, R is the observed distance difference matrix, R T =(R 21 , R 31 , …, R i1 , …, R M1 ); R 0 is the actual distance difference matrix, σ is the measurement error matrix of the arrival distance difference, σ T =(σ 21 , σ 31 , …, σ i1 , …, σ M1 ); σ i1 is the measurement error of the distance difference between the distance from the radiation source target to the slave satellite receiver with serial number i and the distance from the radiation source target to the master satellite receiver with serial number 1; T represents the transpose;

[0024] Among them,

[0025]

[0026] is the actual distance from the radiation source target to the slave satellite-borne receiver with serial number i, is the actual distance from the radiation source target to the master satellite-borne receiver with serial number 1; S i is the actual coordinate of the slave satellite-borne receiver with serial number i; S 1 is the actual coordinate of the master satellite-borne receiver; the coordinate u of the radiation source target without ionospheric correction 0 =(x u , y u , z u ), x u , y u , z u 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;

[0027] The measurement error matrix σ of the arrival distance difference follows a Gaussian distribution with zero mean and covariance matrix Q:

[0028]

[0029] σ′ is the root mean square matrix of the error of the time difference measurement, and σ′ = σ / c.

[0030] As described in step 1 above, the solved ionospheric TEC distribution map is sourced from the International GPS Service Center.

[0031] As described in step 2 above, each satellite-borne receiver obtains the longitude and latitude coordinates of the corresponding ionospheric single-layer piercing point based on the coordinate of the radiation source target without ionospheric correction, specifically including the following steps:

[0032] The coordinate of the radiation source target without ionospheric correction obtained in step 1 is denoted as u 0 =(x u , y u , z u ), x u , y u , z u respectively represent the north component, east component, and vertical component of the coordinate of the radiation source target without ionospheric correction; from the north component x u and the east component y u of the coordinate of the radiation source target without ionospheric correction, the longitude and latitude coordinates of the radiation source target without ionospheric correction are obtained λ u , are respectively the longitude component and latitude component of the longitude and latitude coordinates of the radiation source target without ionospheric correction, and the longitude and latitude coordinates of the ionospheric single-layer piercing point corresponding to the satellite-borne receiver with serial number m are calculated through the following formula

[0033]

[0034] where λ m and are the longitude component and the latitude component of the longitude and latitude coordinates of the ionospheric single-layer piercing point corresponding to the spaceborne receiver with serial number m, respectively; γ m is the azimuth angle of the spaceborne receiver with serial number m relative to the radiation source target; ω m is the angle between the line connecting the radiation source target to the earth's center and the line connecting the spaceborne receiver with serial number m to the earth's center; the serial number m of the spaceborne receiver belongs to {1, 2, 3, …, M}; M is the total number of spaceborne receivers.

[0035] In step 2 as described above, each spaceborne receiver calculates an estimated value of the corresponding theoretical ionospheric delay based on the longitude and latitude coordinates of the corresponding ionospheric single-layer piercing point and the calculated ionospheric TEC distribution map, which specifically includes the following steps:

[0036] Calculate the estimated value of the corresponding theoretical ionospheric delay for each spaceborne receiver through the following formula:

[0037]

[0038] where I′ m is the estimated value of the theoretical ionospheric delay of the m-th spaceborne receiver, f is the radiation source signal frequency; ΔTEC m is the ionospheric electron content at the piercing point corresponding to the m-th spaceborne receiver, and is obtained by spatial interpolation and mapping through the ionospheric TEC distribution map solved in step 1 and the longitude and latitude coordinates of the ionospheric single-layer piercing point as well as the longitude and latitude coordinates of the ionospheric single-layer piercing point.

[0039] In step 2 as described above, construct an ionospheric delay correction formula based on the fact that the estimated value of the theoretical ionospheric delay is approximately equal to the change in the positioning observation distance caused by the ionosphere; the main spaceborne receiver uses the estimated values of the theoretical ionospheric delays corresponding to all spaceborne receivers to solve the ionospheric delay correction formula to obtain an estimated value of the distance coordinate offset caused by the ionosphere; and uses the estimated value of the distance coordinate offset to correct the coordinates of the radiation source target without ionospheric correction to obtain an estimated coordinate of the radiation source target after ionospheric correction, which specifically includes the following steps:

[0040] Construct an ionospheric delay correction formula in matrix form:

[0041] L = AX + δε

[0042] where L is a vector composed of the estimated values of the theoretical ionospheric delays, L = (I′ 1 , I′ 2,…,I′ m ,…,I′ M ) T ; X is the distance coordinate offset, X = (Δx, Δy, Δz) T , where Δx, Δy, and Δz are the north, east, and vertical components of the distance coordinate offset respectively; δε is the linear error vector, δε = (Δε 1 , Δε 2 ,…, Δε m ,…, Δε M ) T , and Δε m is the difference in the linear error of the positioning observation distance before and after ionospheric correction corresponding to the m-th spaceborne receiver;

[0043] A is the constant term matrix:

[0044]

[0045] θ m is the elevation angle between the radiation source target and the m-th spaceborne receiver, and α m is the azimuth angle between the radiation source target and the m-th spaceborne receiver;

[0046] According to the least squares principle, the estimated value of the distance coordinate offset X′ = (A T A) -1 A T L. Define the estimated value of the distance coordinate offset X′ = (Δx′, Δy′, Δz′) T , where Δx′ is the north component of the estimated value of the distance coordinate offset, Δy′ is the east component of the estimated value of the distance coordinate offset, and Δz′ is the vertical component of the estimated value of the distance coordinate offset;

[0047] The estimated coordinates of the radiation source target after ionospheric correction are (x u + Δx′, y u + Δy′, z u + Δz′).

[0048] As described above, the total number M of spaceborne receivers is M ≥ 4.

[0049] The advantages and beneficial effects of the present invention are as follows:

[0050] When calculating the passive positioning of a satellite as a receiver, the present invention takes into account the ionospheric error existing in the propagation path of the ground signal received by the satellite, making up for the lack of research on the ionosphere in the propagation process of space-based passive positioning.

[0051] Compared with the previous research results that ignored ionospheric delay or simply weakened ionospheric delay using the model method, the present invention has higher accuracy for the positioning result. Description of the Drawings

[0052] Figure 1 It is a schematic diagram of the ionospheric single-layer model. Z″ is the elevation angle of the radiation source target relative to the spaceborne receiver; H represents the distance between the single-layer ionosphere and the Earth's surface; R is the distance from the Earth's surface to the Earth's center; O represents the Earth's center; ω m is the angle between the line connecting the radiation source target to the Earth's center and the line connecting the spaceborne receiver numbered m to the Earth's center; Z′ represents the angle of the piercing point, that is, the angle between the line segment from the piercing point to the spaceborne receiver and the straight line in the direction from the Earth's center to the piercing point. The piercing point is the point on the ionosphere through which the radiation source signal passes during the propagation process to reach the spaceborne receiver;

[0053] Figure 2 It is a schematic diagram of the ionospheric delay correction model. D m is the positioning observation distance without ionospheric correction, and D′ m is the positioning observation distance after ionospheric correction. Detailed Implementation Manner

[0054] 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 in conjunction with examples and drawings. The implementation examples described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0055] As Figure 1 shown, the spaceborne receiver 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 process of the radiation source signal, it is affected by the refraction of the ionosphere, etc., and the ionospheric delay error cannot be ignored. A space-based passive radar positioning method considering ionospheric correction according to the present invention has the following specific implementation steps:

[0056] Step 1: Select one spaceborne receiver as the main spaceborne receiver from multiple spaceborne receivers, and the remaining spaceborne receivers as secondary spaceborne receivers; the radiation source signals simultaneously emitted by the radiation source target reach each spaceborne receiver, and each secondary spaceborne receiver sends the time point information of receiving the radiation source signal to the main spaceborne receiver; the main spaceborne receiver uses the time points of each spaceborne receiver receiving the radiation source signal and the TDOA positioning method to obtain the coordinates of the radiation source target without ionospheric correction; the coordinates of the radiation source target without ionospheric correction are sent to each secondary spaceborne receiver; and the ionospheric TEC distribution map obtained by the solution is acquired.

[0057] (1) Obtain the coordinates of the radiation source target without ionospheric correction

[0058] In the scenario of three-dimensional positioning, five spaceborne receivers simultaneously receive the radiation source signals of the radiation source target. One of the five spaceborne receivers is selected as the main spaceborne receiver, and the remaining spaceborne receivers are used as secondary spaceborne receivers. Let the actual coordinates of the spaceborne receiver with serial number m be S m =(x m , y m , z m ), where the serial number m of the spaceborne receiver belongs to {1, 2, 3, …, M}, and M is the total number of spaceborne receivers (in this embodiment, the serial numbers of the spaceborne receivers are m = 1, 2, 3, 4, 5, and the spaceborne receiver with serial number m = 1 is the main spaceborne receiver). x m , y m , z m respectively represent the north component, east component, and vertical component of the actual coordinates of the spaceborne receiver with serial number m. The coordinates of the radiation source target without ionospheric correction are set as u 0 =(x u , y u , z u ), and x u , y u , z u respectively represent the north component, east component, and vertical component of the coordinates of the radiation source target without ionospheric correction.

[0059] According to the time points when the radiation source signal arrives at the secondary spaceborne receivers and the time point when the radiation source signal arrives at the main spaceborne receiver, calculate the time difference of arrival TDOA. The time difference of arrival TDOA is a set of time differences of arrival corresponding to each secondary spaceborne receiver. Among them, the time difference of arrival ΔT i corresponding to the secondary spaceborne receiver with serial number i is equal to the difference between the time point when the radiation source signal arrives at the secondary spaceborne receiver with serial number i and the time point when the radiation source signal arrives at the main spaceborne receiver; the serial number i of the secondary spaceborne receiver belongs to {2, 3, …, M};

[0060] Among them, the relationship between the distance from the radiation source target to the spaceborne receiver and the propagation time of the radiation source signal from the radiation source target to the spaceborne receiver is as follows:

[0061] r m =c*Δt m

[0062] In the formula, c 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; r m is the distance between the spaceborne receiver with serial number m and the radiation source target, and Δt m is the propagation time of the radiation source signal from the radiation source target to the spaceborne receiver with serial number m. In this embodiment, the time difference of arrival ΔT i corresponding to the secondary spaceborne receiver with serial number i is Δti -Δt 1 , where the serial number i of the slave satellite receiver belongs to {2, 3, 4, 5}, and Δt i is the propagation time of the radiation source signal from the radiation source target to the slave satellite receiver with serial number i; Δt 1 is the propagation time of the radiation source signal from the radiation source target to the master satellite receiver with serial number 1.

[0063] From the relationship between the distance from the above radiation source target to the satellite receiver and the propagation time of the radiation source signal from the radiation source target to the satellite receiver, the distance difference RDOA (Range Difference of Arrival) between the distance of the radiation source signal reaching each slave satellite receiver and the distance of the radiation source signal reaching the master satellite receiver can be calculated according to the time difference of arrival corresponding to each slave satellite receiver, that is, the distance difference observation value of the radiation source signal reaching the slave satellite receiver and the radiation source signal reaching the master satellite receiver is obtained according to the following formula:

[0064] R i1 = ΔT i *c

[0065] where R i1 is the distance difference observation value of the radiation source signal reaching the slave satellite receiver with serial number i and the radiation source signal reaching the master satellite receiver with serial number 1, denoted as the distance difference observation value R i1 ; ΔT i represents the time difference of arrival corresponding to the slave satellite receiver with serial number i.

[0066] Define as the actual value of the distance difference between the radiation source signal reaching the slave satellite receiver with serial number i and the radiation source signal reaching the master satellite receiver with serial number 1 (denoted as the actual value of the distance difference ), and the coordinates of the radiation source target without ionospheric correction are calculated through the relationship between the actual value of the distance difference and the distance difference observation value R i1 , which specifically includes the following steps:

[0067] For each slave satellite receiver, the actual value of the distance difference has the following relationship with respect to the distance difference observation value R i1 :

[0068]

[0069] In this embodiment, the serial number i of the slave satellite receiver belongs to {2, 3, 4, 5}, and σ i1 is the measurement error of the distance difference between the distance from the radiation source target to the slave satellite receiver with serial number i and the distance from the radiation source target to the master satellite receiver with serial number 1;

[0070] For the actual value of the distance difference There is:

[0071]

[0072] is the actual distance from the radiation source target to the slave satellite receiver with serial number i, is the actual distance from the radiation source target to the master satellite receiver with serial number 1, S i is the actual coordinate of the slave satellite receiver with serial number i, S i is a known quantity; S 1 is the actual coordinate of the master satellite receiver, S 1 is a known quantity; the coordinate u of the radiation source target without ionospheric correction 0 is the quantity to be solved; ‖.‖ is the distance operator. To facilitate solving for the coordinate u of the radiation source target without ionospheric correction in three-dimensional space 0 , the total number M of satellite receivers ≥ 4.

[0073] Then, combining the actual value of the distance difference with the observed value R of the distance difference i1 of the relationship, by solving the following formula, calculate the coordinate u of the radiation source target without ionospheric correction 0 :

[0074] R = R 0 + σ

[0075] R is the matrix of observed values of the distance difference, R T =(R 21 , R 31 ,…, R i1 ,…, R M1 ); R 0 is the matrix of actual values of the distance difference, σ is the measurement error matrix of the arrival distance difference, σ T =(σ 21 , σ 31 ,…, σ i1 ,…, σ M1 ); In this embodiment, R T =(R 21 , R 31 , R 41 , R 51 ), σ T =(σ 21 , σ 31 , σ 41 , σ 51 ); T represents the transpose;

[0076] The measurement error matrix σ of the difference in arrival distances follows a Gaussian distribution with zero mean and covariance matrix Q:

[0077]

[0078] where σ′ is the root mean square matrix of the error in time difference measurement, c is the propagation speed of the radiation source signal, and σ′ = σ / c.

[0079] (2) Obtain the solved ionospheric TEC distribution map

[0080] Use the international GPS service (IGS) to obtain the solved ionospheric TEC distribution map.

[0081] Step 2: Construct the ionospheric delay estimation model:

[0082] Each spaceborne receiver obtains the longitude and latitude coordinates of the corresponding single-layer ionospheric piercing point based on the coordinates of the radiation source target without ionospheric correction;

[0083] Each spaceborne receiver calculates the estimated value of the corresponding theoretical ionospheric delay value based on the longitude and latitude coordinates of the corresponding single-layer ionospheric piercing point and the solved ionospheric TEC distribution map; each secondary spaceborne receiver sends the estimated value of the corresponding theoretical ionospheric delay value to the primary spaceborne receiver;

[0084] Based on the fact that the estimated value of the theoretical ionospheric delay value is approximately equal to the change in the positioning observation distance caused by the ionosphere, construct the ionospheric delay correction formula;

[0085] The primary spaceborne receiver uses the estimated values of the corresponding theoretical ionospheric delay values of all spaceborne receivers to solve the ionospheric delay correction formula to obtain the estimated value of the distance coordinate offset caused by the ionosphere; and uses the estimated value of the distance coordinate offset to correct the coordinates of the radiation source target without ionospheric correction to obtain the estimated coordinates of the radiation source target after ionospheric correction.

[0086] (1) Obtain the longitude and latitude coordinates of the corresponding single-layer ionospheric piercing point for each spaceborne receiver

[0087] Assume that the ionosphere is a single-layer model, that is, free electrons are densely distributed on an infinite thin layer at a height H from the ground:

[0088] For each spaceborne receiver, define ω m as the angle between the line connecting the radiation source target to the center of the earth and the line connecting the m-th spaceborne receiver to the center of the earth (i.e., Figure 1 the angle between the two red dashed lines in), and Z″ is the elevation angle of the radiation source target relative to the spaceborne receiver. The coordinates u 0 =(xu , y u , z u The north component x of the coordinates of the radiation source target without ionospheric correction u and the east component y u , the longitude and latitude coordinates of the radiation source target without ionospheric correction are obtained as λ u , are the longitude component and latitude component of the longitude and latitude coordinates of the radiation source target without ionospheric correction respectively. Through the following formula, from the longitude and latitude coordinates of the radiation source target without ionospheric correction the longitude and latitude coordinates of the single-layer ionospheric piercing point corresponding to the spaceborne receiver with serial number m are calculated as

[0089]

[0090] where λ m and are the longitude component and latitude component of the longitude and latitude coordinates of the single-layer ionospheric piercing point corresponding to the spaceborne receiver with serial number m respectively; γ m is the azimuth angle of the spaceborne receiver with serial number m relative to the radiation source target. In this embodiment, there are five spaceborne receivers, and the longitude and latitude coordinates of 5 single-layer ionospheric piercing points are obtained in total.

[0091] (2) Construct an ionospheric delay correction model to obtain the distance coordinate offset of the position deviation of the radiation source target caused by ionospheric delay

[0092] As Figure 2 shown, the actual coordinates of the spaceborne receiver are (x m , y m , z m ) (in this embodiment, m = 1, 2, 3, 4, 5). Generally, there are no less than three spaceborne receivers. The coordinates of the radiation source target without ionospheric correction are (x u , y u , z u ), and the coordinates of the radiation source target without ionospheric correction can be calculated through step 1. Let the coordinates of the radiation source target after ionospheric correction be set as (x u +Δx, y u +Δy, z u +Δz), where Δx, Δy, and Δz are the north component, east component, and vertical component of the distance coordinate offset respectively, and the position of the radiation source target is offset due to ionospheric delay.

[0093] The positioning observation distance without ionospheric correction is:

[0094]

[0095] (In this embodiment, m = 1, 2, 3, 4, 5)

[0096] The positioning observation distance after ionospheric correction is:

[0097]

[0098] (In this embodiment, m = 1, 2, 3, 4, 5)

[0099] Where D m is the positioning observation distance without ionospheric correction, D' m is the positioning observation distance after ionospheric correction, θ m is the elevation angle between the radiation source target and the m-th spaceborne receiver, α m is the azimuth angle between the radiation source target and the m-th spaceborne receiver, ε m is the linear error of the positioning observation distance without ionospheric correction, ε' m is the linear error of the positioning observation distance after ionospheric correction;

[0100] Then the change in the positioning observation distance caused by the ionosphere is:

[0101] D' m - D m = Δx sinθ m cosα m + Δy sinθ m sinα m + Δz cosθ m + Δε m ,

[0102] (m = 1, 2, 3, 4, 5)

[0103] The difference Δε in the linear errors of the positioning observation distances before and after ionospheric correction corresponding to the m-th spaceborne receiver m = ε' m - ε m , Δε m is regarded as a very small random quantity; The change in the positioning observation distance caused by the ionosphere Where I m is the theoretical value of the ionospheric delay of the m-th spaceborne receiver, I' m is the estimated value of the theoretical value of the ionospheric delay of the m-th spaceborne receiver, denotes approximately equal to; Then the ionospheric delay correction formula is constructed as:

[0104] I' m = Δx sinθ m cosαm +Δysinθ m sinα m +Δz cosθ m +Δε m

[0105] Among them, the estimated value I′ of the theoretical value of the ionospheric delay of the m-th spaceborne receiver m is calculated according to the following ionospheric delay expression:

[0106]

[0107] where f is the radiation source signal frequency; ΔTEC m is the ionospheric electron content at the piercing point corresponding to the m-th spaceborne receiver, denoted as the ionospheric electron content ΔTEC m , and the ionospheric electron content ΔTEC m is obtained by spatial interpolation and mapping calculation from the ionospheric TEC distribution map solved in step 1 and the longitude and latitude coordinates of the ionospheric single-layer piercing point The ionospheric delay correction formulas of all spaceborne receivers are sorted into the ionospheric delay correction formula in matrix form:

[0108] L = AX + δε

[0109] where L is the vector composed of the estimated values of the theoretical values of the ionospheric delay, L = (I′

[0110] , I′ 1 , I′ 2 , …, I′ m , …, I′ M ) T ; X is the distance coordinate offset, X = (Δx, Δy, Δz) T , δε is the linear error vector, δε = (Δε 1 , Δε 2 , …, Δε m , …, Δε M ) T , and Δε m is the difference between the linear errors of the positioning observations before and after the ionospheric correction corresponding to the m-th spaceborne receiver, regarded as a very small random quantity, and the serial number m of the spaceborne receiver belongs to {1, 2, 3, …, M}, where M is the total number of spaceborne receivers. In this embodiment, M = 5

[0111] The constant term matrix A about θ m and α m :

[0112]

[0113] In the above formula, the vector L and the constant term matrix A are both known. To solve for the estimated value X' of the distance coordinate offset X caused by the ionosphere, the estimated value of the distance coordinate offset X' = (A T A) -1 A T L can be calculated according to the least squares principle. This is the correction amount required based on the coordinates of the radiation source target without ionospheric correction obtained in Step 1. Define the estimated value of the distance coordinate offset X' = (Δx', Δy', Δz')[[]] T , where Δx' is the north component of the estimated value of the distance coordinate offset, Δy' is the east component of the estimated value of the distance coordinate offset, and Δz' is the vertical component of the estimated value of the distance coordinate offset; the estimated coordinates of the radiation source target after ionospheric correction are (x u + Δx', y u + Δy', z u + Δz').

[0114] 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 can make various modifications or supplements to the described specific embodiments or use similar ways to substitute, but will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A space-based passive radar positioning method taking into account ionospheric correction, characterized in that: The steps include: Step 1: Select one satellite receiver from multiple satellite receivers as the main satellite receiver, and the remaining satellite receivers as secondary satellite receivers; The radiation source target simultaneously sends the radiation source signal to each satellite receiver, and each secondary satellite receiver sends the time point information of receiving the radiation source signal to the main satellite receiver; the main satellite receiver uses the time point of receiving the radiation source signal by each satellite receiver and the arrival time difference TDOA positioning method to obtain the coordinates of the radiation source target without ionospheric correction; the coordinates of the radiation source target without ionospheric correction are sent to each secondary satellite receiver; Obtain the solved ionospheric TEC distribution map; Step 2: Each satellite receiver obtains the longitude and latitude coordinates of the corresponding ionospheric single layer puncture point based on the coordinates of the radiation source target without ionospheric correction; Each satellite receiver calculates the corresponding ionospheric delay theoretical value estimate based on the latitude and longitude coordinates of the corresponding ionospheric single layer puncture point and the solved ionospheric TEC distribution map; Each secondary onboard receiver sends an estimate of the corresponding theoretical value of ionospheric delay to the primary onboard receiver; An ionospheric delay correction formula is constructed based on the assumption that the estimated theoretical value of ionospheric delay is approximately equal to the change in positioning observation distance caused by the ionosphere. The main satellite receiver uses the estimated theoretical value of ionospheric delay corresponding to all satellite receivers to solve the ionospheric delay correction formula and obtain the estimated value of the distance coordinate offset caused by the ionosphere. The estimated value of the distance coordinate offset is used to correct the coordinates of the radiation source target without ionospheric correction to obtain the estimated coordinates of the radiation source target after ionospheric correction.

2. A space-based passive radar positioning method taking into account ionospheric correction according to claim 1, characterized in that: In step 1, the main satellite receiver uses the time point at which each 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: According to the time point when the radiation source signal arrives at the secondary satellite receiver and the time point when the radiation source signal arrives at the primary satellite receiver, the arrival time difference corresponding to each secondary satellite receiver is calculated, where the arrival time difference ΔT corresponding to the secondary satellite receiver with sequence number i is i is equal to the difference between the time point when the radiation source signal reaches the secondary satellite receiver with sequence number i and the time point when the radiation source signal reaches the primary satellite receiver; The observed value of the distance difference between the radiation source signal reaching the secondary satellite receiver and the radiation source signal reaching the primary satellite receiver is obtained according to the following formula: R i1 =ΔT i *c Where c is the propagation speed of the radiation source signal, which is equal to the propagation speed of the electromagnetic wave; R i1 is the distance difference observation value between the radiation source signal reaching the secondary satellite receiver with serial number i and the radiation source signal reaching the primary satellite receiver with serial number 1, denoted as the distance difference observation value R i1 ; The serial number of the secondary satellite receiver i∈{2,3,…,M}, M is the total number of satellite receivers; ΔT i Indicates the arrival time difference corresponding to the secondary satellite receiver with serial number i; definition The actual distance difference between the radiation source signal to the secondary satellite receiver with serial number i and the radiation source signal to the primary satellite receiver with serial number 1 is recorded as the actual distance difference Actual value via distance difference The observed value of the distance difference R i1 The coordinates u of the radiation source target without ionospheric correction are calculated based on the relationship 0 .

3. The space-based passive radar positioning method taking into account ionospheric correction according to claim 2, characterized in that: In step 1, the actual value of the distance difference The observed value of the distance difference R i1 The coordinates u of the radiation source target without ionospheric correction are calculated based on the relationship 0 , specifically including the following steps: Solve the following formula to calculate the coordinates u of the radiation source target without ionospheric correction: 0 : R=R 0 +s Among them, R is the distance difference observation matrix, R T =(R 21 ,R 31 ,…,R i1 ,…,R M1 );R 0 is the distance difference actual value matrix, σ is the measurement error matrix of the arrival distance difference, σ T =(σ 21 ,σ 31 ,…,σ i1 ,…,σ M1 );σ i1 is the measurement error of the distance difference between the radiation source target and the secondary satellite receiver with serial number i and the distance difference between the radiation source target and the primary satellite receiver with serial number 1; T represents transposition; in, is the actual distance from the radiation source target to the secondary satellite receiver with serial number i, is the actual distance from the radiation source target to the primary satellite receiver with serial number 1; S i is the actual coordinate of the secondary satellite receiver with serial number i; S1 is the actual coordinate of the primary satellite receiver; the coordinate of the radiation source target without ionospheric correction u 0 =(x u ,y u ,z u ), x u ,y u 、z u 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; The measurement error matrix σ of the arrival distance difference obeys zero mean, and the covariance matrix is ​​a Gaussian distribution of Q: σ′ is the root mean square error matrix of the time difference measurement, σ′=σ / c.

4. The space-based passive radar positioning method taking into account ionospheric correction according to claim 1, characterized in that: In the step 1, the calculated ionospheric TEC distribution map originates from the International GPS Service Center.

5. The space-based passive radar positioning method taking into account ionospheric correction according to claim 1, characterized in that: In step 2, each satellite receiver obtains the longitude and latitude coordinates of the corresponding ionospheric single layer puncture point based on the coordinates of the radiation source target without ionospheric correction, which specifically includes the following steps: The coordinates of the radiation source target obtained in step 1 without ionospheric correction are marked as u 0 =(x u ,y u ,z u ), x u ,y u 、z u They represent the north component, east component and vertical component of the coordinates of the radiation source target without ionospheric correction; the north component x of the coordinates of the radiation source target without ionospheric correction u and the east component y u , get the latitude and longitude coordinates of the radiation source target without ionospheric correction λ u , The longitude and latitude components of the latitude and longitude coordinates of the radiation source target without ionospheric correction are respectively used. The longitude and latitude coordinates of the ionospheric single layer puncture point corresponding to the satellite receiver with serial number m are calculated by the following formula Among them, λ m and are respectively the longitude and latitude components of the latitude and longitude coordinates of the ionospheric single layer puncture point corresponding to the satellite receiver with serial number m; γ m is the azimuth of the satellite receiver with serial number m relative to the radiation source target; ω m It is the angle between the line from the radiation source target to the center of the earth and the line from the satellite receiver with serial number m to the center of the earth; the serial number of the satellite receiver m∈{1,2,3,…,M}; M is the total number of satellite receivers.

6. A space-based passive radar positioning method taking into account ionospheric correction according to claim 5, characterized in that: In step 2, each satellite receiver calculates an estimate of the corresponding ionospheric delay theoretical value based on the latitude and longitude coordinates of the corresponding ionospheric single layer puncture point and the solved ionospheric TEC distribution map, which specifically includes the following steps: The estimated theoretical value of ionospheric delay for each satellite receiver is calculated using the following formula: Among them, I′ m is the estimated value of the theoretical ionospheric delay of the mth satellite receiver, f is the frequency of the radiation source signal; ΔTEC m is the ionospheric electron content of the mth satellite receiver corresponding to the puncture point, which is obtained from the ionospheric TEC distribution map solved in step 1 and the longitude and latitude coordinates of the ionospheric single layer puncture point Calculated through spatial interpolation and mapping.

7. A space-based passive radar positioning method taking into account ionospheric correction according to claim 6, characterized in that: In the step 2, an ionospheric delay correction formula is constructed based on that the estimated value of the theoretical ionospheric delay is approximately equal to the change in the positioning observation distance caused by the ionosphere; the main satellite receiver uses the estimated value of the theoretical ionospheric delay corresponding to all satellite receivers to solve the ionospheric delay correction formula to obtain an estimated value of the distance coordinate offset caused by the ionosphere; and the estimated value of the distance coordinate offset is used to correct the coordinates of the radiation source target without ionospheric correction to obtain the estimated coordinates of the radiation source target after ionospheric correction, which specifically includes the following steps: Construct the ionospheric delay correction formula in matrix form: L=AX+δε Where L is a vector of estimates of the theoretical value of ionospheric delay, L = (I′1, I′2, …, I′ m ,…,I′ M ) T ; X is the distance coordinate offset, X = (Δx, Δy, Δz) T , Δx, Δy, Δz are the north component, east component and vertical component of the distance coordinate offset respectively; δε is the linear error vector, δε=(Δε1,Δε2,…,Δε m ,…,Δε M ) T , Δε m is the difference in linear error of the positioning observation distance before and after ionospheric correction corresponding to the mth satellite receiver; A is the constant term matrix: θ m is the elevation angle between the radiation source target and the mth satellite receiver, α m is the azimuth angle between the radiation source target and the mth satellite receiver; According to the least squares principle, the estimated value of the distance coordinate offset is calculated as X′=(A T A) -1 A T L, defines the estimated value of the distance coordinate offset X′=(Δx′,Δy′,Δz′) T , where Δx′ is the north component of the estimated value of the distance coordinate offset, Δy′ is the east component of the estimated value of the distance coordinate offset, and Δz′ is the vertical component of the estimated value of the distance coordinate offset; The estimated coordinates of the radiation source target after ionospheric correction are (x u +Δx′,y u +Δy′,z u +Δz′).

8. A space-based passive radar positioning method taking into account ionospheric correction according to claim 3, characterized in that: The total number of satellite-borne receivers M≥4.

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