Space-based passive radar positioning method considering ionospheric correction

Abstract

The application discloses a space-based passive radar positioning method considering ionospheric correction, and the ionospheric single-layer piercing point longitude and latitude coordinates corresponding to each satellite-borne receiver are obtained based on the coordinates of a radiation source target without ionospheric correction; then, the estimation of the ionospheric delay theoretical value corresponding to each satellite-borne receiver is calculated by combining the calculated ionospheric TEC distribution map; the estimation of the distance coordinate offset caused by the ionosphere is obtained according to the estimation of the ionospheric delay theoretical value corresponding to all satellite-borne receivers; and the estimated coordinates of the radiation source target after the ionospheric correction are obtained according to the estimation of the distance coordinate offset and the coordinates of the radiation source target without ionospheric correction. When the satellite is used as a receiver to perform passive positioning, the ionospheric error existing in the propagation path of the received ground signal is considered, the insufficient research on the ionosphere in the propagation process of the space-based passive positioning is made up, and the positioning result has higher precision.

Description

TECHNICAL FIELD

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

[0002] Space-based radio signal source positioning, also known as space-based passive positioning, does not emit electromagnetic signals by itself, generally uses the electromagnetic signals already existing in space, and determines the position of the radiation source by intercepting and receiving the signals of the radiation source through one or more observation stations (spaceborne receivers) and measuring the signal parameters.

[0003] The ionosphere is an ionized region of 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, causing air molecules and atoms to ionize, forming charged particles. These charged particles cause signals passing through them to be delayed, dispersed, absorbed, and Faraday rotated, which is an important factor affecting the propagation process of satellite positioning.

[0004] In the field of space-based passive positioning, the error caused by ionospheric delay in the propagation process of satellite passive positioning of ground targets is rarely studied. As the requirement for positioning accuracy gradually increases, there is an urgent need for high-precision space-based passive positioning. SUMMARY

[0005] The present application provides a space-based passive radar positioning method considering ionospheric correction to make up for the lack of research on the ionosphere in the propagation process of space-based passive positioning. The influence of the ionosphere on the propagation path of the satellite receiving ground observation station can be calculated using IGS ionospheric observation data.

[0006] The above object of the present application is achieved by the following scheme:

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

[0008] Step 1: Select one of the plurality of spaceborne receivers as the main spaceborne receiver, and the remaining spaceborne receivers as the auxiliary spaceborne receivers;

[0009] The radiation source target simultaneously emits radiation source signals to each satellite-borne receiver, each satellite-borne receiver sends time point information of receiving the radiation source signal to the main satellite-borne receiver; the main satellite-borne receiver obtains coordinates of the radiation source target without ionospheric correction by using time points of receiving the radiation source signal by each satellite-borne receiver and a time difference of arrival TDOA positioning method; the coordinates of the radiation source target without ionospheric correction are sent to each satellite-borne receiver;

[0010] Obtaining the calculated ionospheric TEC distribution map;

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

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

[0013] An ionospheric delay correction formula is constructed based on that the estimated value of the ionospheric delay theoretical value is approximately equal to a positioning observation distance change caused by the ionosphere; the main satellite-borne receiver solves the ionospheric delay correction formula by using the estimated values of the corresponding ionospheric delay theoretical values of all satellite-borne receivers, obtains an estimated value of a distance coordinate offset caused by the ionosphere, and corrects the coordinates of the radiation source target without ionospheric correction by using the estimated value of the distance coordinate offset, to obtain estimated coordinates of the radiation source target after ionospheric correction.

[0014] As described above in step 1, the main satellite-borne receiver obtains the coordinates of the radiation source target without ionospheric correction by using time points of receiving the radiation source signal by each satellite-borne receiver and a time difference of arrival TDOA positioning method, including the following steps:

[0015] According to the time point of the radiation source signal arriving at the satellite-borne receiver and the time point of the radiation source signal arriving at the main satellite-borne receiver, the corresponding time difference of arrival of each satellite-borne receiver is calculated, wherein the time difference of arrival of the satellite-borne receiver with the serial number i is ΔT i which is equal to the difference between the time point of the radiation source signal arriving at the satellite-borne receiver with the serial number i and the time point of the radiation source signal arriving at the main satellite-borne receiver;

[0016] The distance difference observation value of the radiation source signal arriving at the satellite-borne receiver and the radiation source signal arriving at the main satellite-borne receiver is obtained according to the following formula:

[0017] R i1 = ΔT i * c

[0018] Where c is the propagation speed of the radiation source signal, which is equal to the propagation speed of electromagnetic waves; R i1 Let R be the observed distance difference between the arrival of the radiation source signal at the secondary satellite receiver with sequence number i and the arrival of the radiation source signal at the primary satellite receiver with sequence number 1. i1 The serial numbers of the secondary satellite receivers are i∈{2,3,…,M}, where M is the total number of satellite receivers; ΔT i This represents the time difference of arrival for the secondary satellite receiver with serial number i.

[0019] definition Let be the actual distance difference between the radiation source signal reaching the secondary satellite receiver (number i) and the radiation source signal reaching the primary satellite receiver (number 1), denoted as _actual distance difference_. Actual value of distance difference The distance difference observation value R i1 Calculate the coordinates u of the radiation source target without ionospheric correction. 0 .

[0020] As described in step 1 above, the actual value of the distance difference is used. The distance difference observation value R i1 Calculate the coordinates u of a radiation source target without ionospheric correction. 0 Specifically, it 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] Where R is the distance difference observation matrix, R T =(R 21 ,R 31 ,…,R i1 ,…,R M1 ); R 0 This is the matrix of actual distance differences. σ is the measurement error matrix for the distance difference of arrival. T =(σ 21 ,σ 31 ,…,σ i1 ,…,σ M1 );σ i1 The measurement error is the difference between the distance from the radiation source target to the secondary satellite receiver with serial number i and the distance from the radiation source target to the primary satellite receiver with serial number 1; T represents transpose;

[0024] in,

[0025]

[0026] is the actual distance from the radiation source target to the i-th sub-space-borne receiver, is the actual distance from the radiation source target to the 1st main-space-borne receiver; S i is the actual coordinate of the i-th sub-space-borne receiver; S1 is the actual coordinate of the main-space-borne receiver; u is the coordinate 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 distance difference satisfies the Gaussian distribution with zero mean and covariance matrix Q:

[0028]

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

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

[0031] As described in step 2 above, each space-borne receiver obtains the longitude and latitude coordinates of the corresponding ionospheric single layer penetration point based on the coordinate of the radiation source target without ionospheric correction, which specifically includes 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; the longitude component and the latitude component of the coordinate of the radiation source target without ionospheric correction are obtained from the north component x u and the east component y u of the coordinate of the radiation source target without ionospheric correction λ u , respectively, and the longitude and latitude coordinates of the ionospheric single layer penetration point corresponding to the m-th space-borne receiver are calculated by the following formula

[0033]

[0034] wherein, 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; γ m is the azimuth angle of the spaceborne receiver with serial number m relative to the radiation source target; ω m is the included angle between the line from the radiation source target to the center of the earth and the line from the spaceborne receiver with serial number m to the center of the earth; the serial number m of the spaceborne receiver is in {1, 2, 3, …, M}; and M is the total number of the spaceborne receivers.

[0035] As described above in step 2, each spaceborne receiver calculates the estimated value of the corresponding ionospheric delay theoretical value based on the longitude and latitude coordinates of the corresponding ionospheric single layer piercing point and the calculated ionospheric TEC distribution, specifically including the following steps:

[0036] The estimated value of the ionospheric delay theoretical value corresponding to each spaceborne receiver is calculated by the following formula:

[0037]

[0038] wherein, I′ m is the estimated value of the ionospheric delay theoretical value of the mth spaceborne receiver, f is the frequency of the radiation source signal; ΔTEC m is the ionospheric electron content of the piercing point corresponding to the mth spaceborne receiver, which is obtained by spatial interpolation and mapping calculation based on the ionospheric TEC distribution calculated in step 1 and the longitude and latitude coordinates of the ionospheric single layer piercing point .

[0039] As described above in step 2, the ionospheric delay correction formula is constructed based on that the estimated value of the ionospheric delay theoretical value is approximately equal to the positioning observation distance change caused by the ionosphere; the master spaceborne receiver uses the estimated values of the ionospheric delay theoretical values 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 the estimated coordinates of the radiation source target without ionospheric correction are corrected by using the estimated value of the distance coordinate offset, to obtain the estimated coordinates of the radiation source target after ionospheric correction, specifically including the following steps:

[0040] The ionospheric delay correction formula in the form of a matrix is constructed as follows:

[0041] L = AX + δε

[0042] wherein, L is a vector composed of the estimated values of the ionospheric delay theoretical values, L = (I′1, I′2, …, I′ m , …, I′ M )T X is the distance coordinate offset, X = (Δx, Δy, Δz) T Δx, Δy, and Δz are the north, east, and vertical components of the distance coordinate offset, respectively; δε is the linear error vector, δε = (Δε1, Δε2, ..., Δε m ,…,Δε M ) T ,Δε m It is the difference in the linear error of the positioning observation distance before and after ionospheric correction for the m-th satellite-borne receiver;

[0043] A is a matrix of constant terms:

[0044]

[0045] θ m α is the elevation angle between the radiation source target and the m-th satellite-borne receiver. m It is the azimuth angle between the radiation source target and the m-th satellite-borne receiver;

[0046] Based on the least squares principle, the estimated value of the distance coordinate offset X′=(A) is calculated. T A) -1 A T L defines the estimated distance coordinate offset X′=(Δx′,Δy′,Δz′). T , where Δx′ is the north component of the estimated distance coordinate offset, Δy′ is the east component of the estimated distance coordinate offset, and Δz′ is the vertical component of the estimated 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 mentioned above, the total number of satellite receivers M ≥ 4.

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

[0050] This invention considers the ionospheric error in the propagation path of the ground signal received by the satellite when calculating passive positioning as a receiver, thus compensating for the lack of research on the ionosphere in the propagation process of space-based passive positioning.

[0051] Compared with previous research results that ignored ionospheric delay or simply reduced ionospheric delay using model methods, this invention has higher accuracy in positioning results. Attached Figure Description

[0052] Figure 1This is a schematic diagram of a single-layer ionosphere 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 Z′ represents the angle between the line connecting the radiation source target to the Earth's center and the line connecting the satellite receiver (numbered m) to the Earth's center; Z′ represents the angle of the puncture point, which is the angle between the line segment from the puncture point to the satellite receiver and the straight line from the Earth's center to the puncture point. The puncture point is the point on the ionosphere that the radiation source signal passes through during its propagation to the satellite receiver.

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

[0054] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to examples and accompanying drawings. The embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0055] like Figure 1 As shown, the spaceborne receiver receives the radiation source signal (e.g., L-band communication) 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, resulting in a non-negligible ionospheric delay error. This invention provides a space-based passive radar positioning method that takes ionospheric correction into account. The specific implementation steps are as follows:

[0056] Step 1: Select one of the multiple satellite-borne receivers as the primary satellite-borne receiver, and the rest as secondary satellite-borne receivers. The radiation source target simultaneously emits radiation source signals to each of the satellite-borne receivers. Each secondary satellite-borne receiver sends the time point information of the received radiation source signals to the primary satellite-borne receiver. The primary satellite-borne receiver uses the time points of the received radiation source signals from each satellite-borne receiver 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 secondary satellite-borne receiver. The calculated ionospheric TEC distribution map is also obtained.

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

[0058] In the scene of three-dimensional positioning, five satellite receivers simultaneously receive the radiation source signals of the radiation source target, one of the five satellite receivers is selected as a main satellite receiver, and the rest of the satellite receivers are selected as auxiliary satellite receivers, the actual coordinates of the satellite receiver with the serial number m are S m =(x m ,y m ,z m ), the serial number m of the satellite receiver is included in the set {1, 2, 3, …, M}, and M is the total number of satellite receivers (in this embodiment, the serial number m of the satellite receiver is 1, 2, 3, 4, and 5, and the satellite receiver with the serial number m = 1 is the main satellite receiver) m , y m , and z m respectively represent the north component, the east component, and the vertical component of the actual coordinates of the satellite receiver with the serial number m, and the coordinates of the radiation source target without ionospheric correction are set as u 0 =(x u ,y u ,z u ), x u , y u , and z u respectively represent the north component, the east component, and the vertical component of the coordinates of the radiation source target without ionospheric correction.

[0059] According to the time point at which the radiation source signal reaches the auxiliary satellite receiver and the time point at which the radiation source signal reaches the main satellite receiver, the time difference of arrival TDOA is calculated, and the time difference of arrival TDOA is a set of time differences of arrival corresponding to each auxiliary satellite receiver, wherein the time difference of arrival ΔT i corresponding to the auxiliary satellite receiver with the serial number i is equal to the difference between the time point at which the radiation source signal reaches the auxiliary satellite receiver with the serial number i and the time point at which the radiation source signal reaches the main satellite receiver; the serial number i of the auxiliary satellite receiver is included in the set {2, 3, …, M};

[0060] wherein the distance between the radiation source target and the satellite receiver and the propagation time of the radiation source signal from the radiation source target to the satellite receiver satisfy the following relationship:

[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 satellite receiver with the 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 satellite receiver with the serial number m. In this embodiment, the time difference of arrival ΔT i corresponding to the auxiliary satellite receiver with the serial number i is Δti - Δti, the order number of the secondary spaceborne receiver, i ∈ {2, 3, 4, 5}, Δt i is the propagation time of the radiation source signal from the radiation source target to the secondary spaceborne receiver with order number i; Δt1is the propagation time of the radiation source signal from the radiation source target to the primary spaceborne receiver with order number 1.

[0063] According to 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, the distance of the radiation source signal to each secondary spaceborne receiver and the difference RDOA (Range Difference of Arrival) between the distance of the radiation source signal to the primary spaceborne receiver can be calculated according to the time difference of arrival corresponding to each secondary spaceborne receiver, that is, the distance difference observation value of the radiation source signal to the secondary spaceborne receiver and the radiation source signal to the primary spaceborne receiver is obtained according to the following formula:

[0064] R i1 = ΔT i * c

[0065] Wherein, R i1 is the distance difference observation value of the radiation source signal to the secondary spaceborne receiver with order number i and the radiation source signal to the primary spaceborne receiver with order number 1, recorded as distance difference observation value R i1 ; ΔT i represents the time difference of arrival corresponding to the secondary spaceborne receiver with order number i.

[0066] Definition is the distance difference actual value of the radiation source signal to the secondary spaceborne receiver with order number i and the radiation source signal to the primary spaceborne receiver with order number 1 (recorded as distance difference actual value R ), the coordinates of the radiation source target without ionosphere correction are calculated through the relationship between the distance difference actual value R and the distance difference observation value R i1 , and specifically include the following steps:

[0067] For each secondary spaceborne receiver, the distance difference actual value R has the following relationship with the distance difference observation value R i1 :

[0068]

[0069] In this embodiment, the order number of the secondary spaceborne receiver i ∈ {2, 3, 4, 5}, σ i1 is the measurement error of the distance from the radiation source target to the secondary spaceborne receiver with order number i and the distance difference from the radiation source target to the primary spaceborne receiver with order number 1;

[0070] For the distance difference actual value R , there is:

[0071]

[0072] is the actual distance from the radiation source target to the i-th secondary spaceborne receiver, is the actual distance from the radiation source target to the 1st primary spaceborne receiver, S i is the actual coordinate of the i-th secondary spaceborne receiver, S i is a known quantity; S1 is the actual coordinate of the primary spaceborne receiver, S1 is a known quantity; u is the coordinate of the radiation source target without ionosphere correction 0 is a quantity to be solved; ‖.‖ is a distance operator. In order to facilitate the solution of the coordinate u of the radiation source target without ionosphere correction in three-dimensional space, 0 the total number of spaceborne receivers M≥4.

[0073] then the relationship between the actual value of the distance difference and the observed value of the distance difference R i1 is combined, and the coordinate u of the radiation source target without ionosphere correction is calculated by solving the following formula: 0

[0074] R=R 0 +σ

[0075] R is a distance difference observation value matrix, R T =(R 21 ,R 31 ,…,R i1 ,…,R M1 ); R 0 is a distance difference actual value matrix, σ is a measurement error matrix of the 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 transposition;

[0076] The measurement error matrix σ of the distance difference obeys a Gaussian distribution with zero mean and a covariance matrix Q:

[0077] ​

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

[0079] (2) Obtain the calculated TEC distribution map of the ionosphere.

[0080] The calculated TEC distribution map of the ionosphere was obtained using the International GPS Service (IGS).

[0081] Step 2: Construction of the ionospheric delay estimation model:

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

[0083] Each satellite-borne receiver calculates an estimated theoretical value of ionospheric delay based on the latitude and longitude coordinates of the corresponding ionospheric single-layer puncture point and the calculated ionospheric TEC distribution map; each secondary satellite-borne receiver sends the estimated theoretical value of ionospheric delay to the primary satellite-borne receiver.

[0084] The estimated value of ionospheric delay is approximately equal to the change in positioning observation distance caused by the ionosphere, and an ionospheric delay correction formula is constructed accordingly.

[0085] The main satellite receiver uses the estimated theoretical values ​​of ionospheric delay corresponding to all satellite receivers to solve the ionospheric delay correction formula, and obtains the estimated value of the range coordinate offset caused by the ionosphere; and uses the estimated value of the range coordinate offset to correct the coordinates of the radiation source target without ionospheric correction, and obtains the estimated coordinates of the radiation source target after ionospheric correction.

[0086] (1) Obtain the latitude and longitude coordinates of the ionospheric single-layer puncture point corresponding to each satellite receiver.

[0087] Assuming the ionosphere is a monolayer model, meaning that free electrons are densely distributed in an infinitely thin layer at a height H above the ground:

[0088] For each onboard receiver, define ω m It is the angle between the line connecting the radiation source target to the Earth's center and the line connecting the satellite receiver with serial number m to the Earth's center (i.e., Figure 1 The angle between the two red dashed lines (Z″) is the elevation angle of the radiation source target relative to the spaceborne receiver. The coordinates u of the radiation source target without ionospheric correction obtained in step 1 are... 0 =(x u ,y u ,z u The north component x of the coordinates of the radiation source target without ionospheric correction. uAnd East weight y u The latitude and longitude coordinates of the radiation source target without ionospheric correction are obtained as follows: λ u , These are the longitude and latitude components of the latitude and longitude coordinates of the radiation source target without ionospheric correction. The following formula is used to calculate the latitude and longitude coordinates of the radiation source target without ionospheric correction. The latitude and longitude coordinates of the ionospheric single-layer puncture point corresponding to the satellite receiver with serial number m are calculated as follows:

[0089]

[0090] Where, λ m and These are the longitude and latitude components of the ionospheric monolayer puncture point corresponding to the satellite-borne receiver with serial number m; γ m denoted by m, the azimuth angle of the satellite-borne receiver relative to the radiation source target. In this embodiment, there are five satellite-borne receivers, obtaining the latitude and longitude coordinates of five ionospheric single-layer puncture points.

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

[0092] like Figure 2 As 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 fewer than three spaceborne receivers. The coordinates of the radiation source target without ionospheric correction are (x... u ,y u ,z u The coordinates of the uncorrected radiation source target can be calculated using step 1. Let the coordinates of the ionospherically corrected radiation source target be (x...). u +Δx,y u +Δy,z u +Δz), where Δx, Δy, and Δz are the north, east, and vertical components of the distance coordinate offset, respectively, and the positional shift of the radiation source target is caused by ionospheric delay.

[0093] The uncorrected positioning observation distance 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] wherein 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 mth spaceborne receiver, a m is the azimuth angle between the radiation source target and the mth 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] The positioning observation distance change caused by the ionosphere is:

[0101] D' m - D m = Δx sin θ m cos a m + Δy sin θ m sin a m + Δz cos θ m + Δε m ,

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

[0103] The difference value of the linear error of the positioning observation distance before and after ionospheric correction corresponding to the mth spaceborne receiver is Δε m = ε' m - ε m , Δε m is regarded as a very small random quantity; the positioning observation distance change caused by the ionosphere is wherein I m is the theoretical value of the ionospheric delay of the mth spaceborne receiver, I' m is the estimation value of the theoretical value of the ionospheric delay of the mth spaceborne receiver, approximately equal to; then the ionospheric delay correction formula is constructed as:

[0104] I' m = Δx sin θ m cos a m + Δy sin θ m sin a m + Δz cos θ m+ Δε m

[0105] wherein the estimation of the ionospheric delay theoretical value of the mth spaceborne receiver I' m According to the following ionospheric delay expression:

[0106]

[0107] wherein f is the signal frequency of the radiation source; ΔTEC m is the ionospheric electron content of the mth spaceborne receiver corresponding to the piercing point, denoted as ionospheric electron content ΔTEC m , ionospheric electron content ΔTEC m The ionospheric TEC distribution and the longitude and latitude coordinates of the ionospheric single-layer piercing point solved in step 1 are calculated through spatial interpolation and mapping.

[0108] The ionospheric delay correction formula of all spaceborne receivers is arranged into a matrix form of ionospheric delay correction formula:

[0109] L = AX + δε

[0110] wherein L is a vector composed of the estimations of the ionospheric delay theoretical value, L = (I'1, I'2, …, I' m , …, I' M ) T ; X is the distance coordinate offset, X = (Δx, Δy, Δz) T , δε is a linear error vector, δε = (Δε1, Δε2, …, Δε m , …, Δε M ) T , Δε m is the difference of the linear positioning observation distance error of the mth spaceborne receiver before and after the ionospheric correction, which is considered as a very small random quantity, the serial number of the spaceborne receiver m ∈ {1, 2, 3, …, M}, M is the total number of spaceborne receivers, in this embodiment M = 5,

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

[0112]

[0113] In the above formula, the vector L and the constant term matrix A are known, in order to solve the estimation value X' of the distance coordinate offset X caused by the ionosphere, according to the least square principle, the estimation value X' of the distance coordinate offset can be calculated X' = (A T A) -1 A TL, which is the correction amount needed on the basis of the coordinates of the radiation source target obtained in step 1 without ionospheric correction, defines an estimate X' = (Δx', Δy', Δz') of the distance coordinate offset T where Δx' is the north component of the estimate of the distance coordinate offset, Δy' is the east component of the estimate of the distance coordinate offset, and Δz' is the vertical component of the estimate of the distance coordinate offset; and 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 application. Various modifications or changes in addition or substitution to the described specific embodiments can be made by those skilled in the art without departing from the spirit of the application or exceeding the scope of the appended claims.

Claims

1. A space-based passive radar positioning method that takes into account ionospheric correction, characterized in that, Includes the following steps: Step 1: Select one satellite receiver from among the multiple satellite receivers as the primary satellite receiver, and the remaining satellite receivers as secondary satellite receivers; The radiation source target simultaneously emits radiation source signals to each onboard receiver. Each secondary onboard receiver sends the time information of the received radiation source signals to the primary onboard receiver. The primary onboard receiver uses the time points of the radiation source signals received by each onboard receiver 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 then sent to each secondary onboard receiver. Obtain the calculated TEC distribution map of the ionosphere; Step 2: Each spaceborne receiver obtains the latitude and longitude 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 an estimated theoretical value of ionospheric delay based on the latitude and longitude coordinates of the corresponding ionospheric single-layer puncture point and the solved ionospheric TEC distribution map; Each secondary satellite receiver sends its estimated theoretical value of the ionospheric delay to the primary satellite receiver. based on Construct an ionospheric delay correction formula, where I′ m D′ is an estimate of the theoretical ionospheric delay for the m-th satellite-borne receiver. m -D m D represents the change in positioning observation distance caused by the ionosphere. m This is the positioning observation distance without ionospheric correction, D′ m This is the ionospheric-corrected positioning observation distance. This means approximately equal to; the main satellite receiver uses the estimated theoretical values ​​of ionospheric delay corresponding to all satellite receivers to solve the ionospheric delay correction formula, and obtains the estimated value of the range coordinate offset caused by the ionosphere; and uses the estimated value of the range coordinate offset to correct the coordinates of the radiation source target without ionospheric correction, and obtains the estimated coordinates of the radiation source target after ionospheric correction.

2. The space-based passive radar positioning method considering ionospheric correction according to claim 1, characterized in that, In step 1, the main satellite receiver uses the time points at which each satellite 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: Based on the arrival times of the radiation source signal at the secondary satellite receiver and the arrival times of the radiation source signal at the primary satellite receiver, the arrival time difference for each secondary satellite receiver is calculated. The arrival time difference ΔT for the secondary satellite receiver with sequence number i is calculated as follows: i It is equal to the difference between the time when the radiation source signal arrives at the secondary satellite receiver with sequence number i and the time when the radiation source signal arrives at the primary satellite receiver; The distance difference between the radiation source signal reaching the secondary satellite receiver and the distance between the radiation source signal reaching the primary satellite receiver is obtained using 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 electromagnetic waves; R i1 Let R be the observed distance difference between the arrival of the radiation source signal at the secondary satellite receiver with sequence number i and the arrival of the radiation source signal at the primary satellite receiver with sequence number 1. i1 The serial numbers of the secondary satellite receivers are i∈{2,3,…,M}, where M is the total number of satellite receivers; ΔT i This represents the time difference of arrival for the secondary satellite receiver with serial number i. definition Let be the actual distance difference between the radiation source signal reaching the secondary satellite receiver (number i) and the radiation source signal reaching the primary satellite receiver (number 1), denoted as _actual distance difference_. Actual value of distance difference The distance difference observation value R i1 Calculate the coordinates u of the radiation source target without ionospheric correction. 0 .

3. The space-based passive radar positioning method considering ionospheric correction according to claim 2, characterized in that, In step 1, the actual value of the distance difference is used. The distance difference observation value R i1 Calculate the coordinates u of the radiation source target without ionospheric correction. 0 Specifically, it includes 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 Where R is the distance difference observation matrix, R T =(R 21 ,R 31 ,…,R i1 ,…,R M1 ); R 0 This is the matrix of actual distance differences. σ is the measurement error matrix for the distance difference of arrival. T =(σ 21 ,σ 31 ,…,σ i1 ,…,σ M1 );σ i1 The measurement error is the difference between the distance from the radiation source target to the secondary satellite receiver with serial number i and the distance from the radiation source target to the primary satellite receiver with serial number 1; T represents transpose; in, It is the actual distance from the radiation source target to the secondary satellite-borne receiver with serial number i. It is the actual distance from the radiation source target to the primary satellite-borne receiver with serial number 1; S i S1 is the actual coordinate of the secondary satellite receiver with serial number i; S1 is the actual coordinate of the primary satellite receiver; and u is the coordinate of the radiation source target without ionospheric correction. 0 =(x u ,y u ,z u ), x u y u z u These represent the north, east, and vertical components of the coordinates of a radiation source target without ionospheric correction, respectively; ‖.‖ is the distance operator; The measurement error matrix σ of the distance difference follows a Gaussian distribution with zero mean and covariance matrix Q. σ ′ Let σ be the root mean square matrix of the time difference measurement error. ′ =σ / c.

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

5. The space-based passive radar positioning method considering ionospheric correction according to claim 1, characterized in that, In step 2, each spaceborne receiver obtains the latitude and longitude coordinates of the corresponding ionospheric single-layer puncture point based on the coordinates of the radiation source target without ionospheric correction. Specifically, this includes the following steps: The coordinates of the radiation source target without ionospheric correction obtained in step 1 are denoted as u. 0 =(x u ,y u ,z u ), x u y u z u Let x represent the north component, east component, and vertical component of the coordinates of the un-ionospherically corrected radiation source target; x represent the north component of the coordinates of the un-ionospherically corrected radiation source target. u And East weight y u The latitude and longitude coordinates of the radiation source target without ionospheric correction were obtained. λ u , Let the longitude and latitude components of the latitude and longitude coordinates of the radiation source target without ionospheric correction be given. The latitude and longitude coordinates of the ionospheric single-layer puncture point corresponding to the spaceborne receiver with serial number m be calculated using the following formula. Where, λ m and These are the longitude and latitude components of the ionospheric monolayer puncture point corresponding to the satellite-borne receiver with serial number m; γ m ω is the azimuth angle of the satellite receiver with serial number m relative to the radiation source target; m It is the angle between the line connecting the radiation source target to the Earth's center and the line connecting the satellite receiver with the serial number m to the Earth's center; the serial number m of the satellite receiver is {1,2,3,…,M}; M is the total number of satellite receivers.

6. The space-based passive radar positioning method considering ionospheric correction according to claim 5, characterized in that, In step 2, each spaceborne receiver calculates an estimated theoretical value of the ionospheric delay based on the latitude and longitude coordinates of the corresponding ionospheric monolayer puncture point and the solved ionospheric TEC distribution map. This specifically includes the following steps: The estimated theoretical value of the ionospheric delay for each satellite-borne receiver is calculated using the following formula: Among them, I′ m This is an estimate of the theoretical ionospheric delay for the m-th satellite-borne receiver, where f is the frequency of the radiation source signal; ΔTEC m The ionospheric electron content at the puncture point corresponding to the m-th satellite receiver is determined by the ionospheric TEC distribution map calculated in step 1 and the latitude and longitude coordinates of the ionospheric monolayer puncture point. It is obtained through spatial interpolation and mapping calculation.

7. The space-based passive radar positioning method considering ionospheric correction according to claim 6, characterized in that, In step 2, based on Construct an ionospheric delay correction formula, where I′ m D′ is an estimate of the theoretical ionospheric delay for the m-th satellite-borne receiver. m -D m D represents the change in positioning observation distance caused by the ionosphere. m This is the positioning observation distance without ionospheric correction, D′ m This is the ionospheric-corrected positioning observation distance. This means approximately equal to; the main satellite receiver uses the estimated theoretical values ​​of ionospheric delay corresponding to all satellite receivers to solve the ionospheric delay correction formula, obtaining an estimated value of the range coordinate offset caused by the ionosphere; and uses the estimated value of the range coordinate offset to correct the coordinates of the radiation source target without ionospheric correction, obtaining the estimated coordinates of the radiation source target after ionospheric correction. Specifically, this includes the following steps: Construct a matrix form for the ionospheric delay correction formula: L=AX+δε Where L is a vector composed of estimates of the theoretical values ​​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, and Δz are the north, east, and vertical components of the distance coordinate offset, respectively; δε is the linear error vector, δε = (Δε1, Δε2, ..., Δε m ,…,Δε M ) T ,Δε m It is the difference in the linear error of the positioning observation distance before and after ionospheric correction for the m-th satellite-borne receiver; A is a matrix of constant terms: θ m α is the elevation angle between the radiation source target and the m-th satellite-borne receiver. m It is the azimuth angle between the radiation source target and the m-th satellite-borne receiver; The estimated value of the distance coordinate offset X is calculated based on the least squares principle. ′ =(A T A) -1 A T L defines the estimated distance coordinate offset X. ′ =(Δx′,Δy′,Δz′) T , where Δx′ is the north component of the estimated distance coordinate offset, Δy′ is the east component of the estimated distance coordinate offset, and Δz′ is the vertical component of the estimated 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 considering ionospheric correction according to claim 3, characterized in that, The total number of satellite-borne receivers, M, is greater than or equal to 4.

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