Three-dimensional positioning method and device for binary stationary radiation sources based on passive synthetic aperture

Abstract

The present invention provides a method and device for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture, relating to the field of space electronic reconnaissance technology. The method comprises: performing passive synthetic aperture processing on radiation source signals received by a first satellite and a second satellite from a target radiation source to determine the instantaneous position vector, instantaneous velocity vector, and range distance of the first and second satellites at their respective azimuth moments; constructing equations for a first plane and a second plane on which the target radiation source is located based on the instantaneous position vector and the instantaneous velocity vector; constructing equations for a first curved surface and a second curved surface on which the target radiation source is located based on the instantaneous position vector and the range distance; and solving the equations for the first plane, the second plane, the first curved surface, and the second curved surface to form a nonlinear system of equations, which are then solved to obtain the position coordinates of the target radiation source. This method can improve the positioning accuracy of radiation sources.

Description

Technical Field

[0001] The present invention relates to the technical field of space electronic reconnaissance, and in particular to a three-dimensional positioning method and device for a binary stationary radiation source based on passive synthetic aperture. Background Art

[0002] In space electronic reconnaissance, traditional methods for locating radiation sources include frequency measurement, direction finding, time difference, and time-frequency difference. While these methods are relatively mature, they often suffer from low positioning accuracy and high satellite payload requirements. Positioning accuracy is typically only on the order of kilometers. To address this low positioning accuracy, researchers have recently proposed a passive synthetic aperture radiation source localization method. This method converts the radiation source's position relative to the satellite into range and azimuth parameters, and achieves accurate estimation of both range and azimuth distances through coherent accumulation.

[0003] Traditional passive synthetic aperture radiation source positioning methods generally need to assume that the radiation source is located on the surface of the earth and that the earth's surface satisfies the ellipsoid model. However, in reality, since the earth's surface contains elevation information, assuming that the radiation source is located on the earth's surface and ignoring the elevation information will affect the radiation source positioning accuracy, resulting in low radiation source positioning accuracy. Summary of the Invention

[0004] The present invention provides a method, device and computer program product for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture, which are used to solve the defect of low radiation source positioning accuracy in the prior art and improve the radiation source positioning accuracy.

[0005] In a first aspect, the present invention provides a method for three-dimensional positioning of a binary stationary radiation source based on passive synthetic aperture, comprising the following steps:

[0006] performing passive synthetic aperture processing on radiation source signals from a target radiation source received by a first satellite and a second satellite, respectively, to determine an instantaneous position vector, an instantaneous velocity vector, and a range distance of the first satellite and the second satellite, respectively, at respective azimuth moments corresponding to the target radiation source;

[0007] Constructing an equation of a first plane and an equation of a second plane in which the target radiation source is located based on the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite, respectively;

[0008] Constructing an equation of a first curved surface and an equation of a second curved surface on which the target radiation source is located based on the instantaneous position vector and the range direction distance of the first satellite and the second satellite respectively;

[0009] The equation of the first plane, the equation of the second plane, the equation of the first curved surface, and the equation of the second curved surface are combined to form a nonlinear equation group, and the position coordinate value of the target radiation source is obtained by solving the nonlinear equation group.

[0010] According to a method for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture provided by the present invention, passive synthetic aperture processing is performed on radiation source signals received by a first satellite and a second satellite from a target radiation source, respectively, to determine the instantaneous position vector, instantaneous velocity vector, and range distance of the first satellite and the second satellite at respective azimuth moments corresponding to the target radiation source, including:

[0011] performing passive synthetic aperture processing on the radiation source signals from the target radiation source received by the first satellite and the second satellite, respectively, to obtain the azimuth time and Doppler slope of the first satellite and the second satellite corresponding to the target radiation source, respectively;

[0012] Determine, based on the navigation positioning information of the first satellite and the second satellite, the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite at the respective azimuth moments;

[0013] Determine the range distances between the first satellite and the second satellite and the target radiation source respectively based on the instantaneous velocity vector and the Doppler slope of the first satellite and the second satellite respectively.

[0014] According to a method for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture provided by the present invention, determining the distance between the first satellite and the second satellite and the target radiation source respectively based on the instantaneous velocity vector and the Doppler slope of the first satellite and the second satellite, including:

[0015] Determine, based on the instantaneous velocity vectors of the first satellite and the second satellite, the instantaneous velocity values of the first satellite and the second satellite at the respective azimuth moments;

[0016] determining a carrier frequency of the target radiation source based on the radiation source signals received by the first satellite and the second satellite;

[0017] Determine the distances between the first satellite and the second satellite and the target radiation source respectively based on the instantaneous velocity values and the Doppler slopes of the first satellite and the second satellite, the carrier frequency and the speed of light of the target radiation source.

[0018] According to a method for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture provided by the present invention, constructing an equation of a first plane and an equation of a second plane in which the target radiation source is located based on the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite, respectively, includes:

[0019] Constructing a first position vector of the target radiation source relative to the first satellite and a second position vector of the target radiation source relative to the second satellite, respectively, according to differences between the position coordinate variable of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite;

[0020] constructing an equation of a first plane in which the target radiation source is located according to the first position vector and the instantaneous velocity vector of the first satellite;

[0021] An equation of a second plane in which the target radiation source is located is constructed according to the second position vector and the instantaneous velocity vector of the second satellite.

[0022] According to a method for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture provided by the present invention, constructing an equation of a first curved surface and an equation of a second curved surface on which the target radiation source is located based on the instantaneous position vector and the range distance of the first satellite and the second satellite, respectively, includes:

[0023] Constructing a first position vector of the target radiation source relative to the first satellite and a second position vector of the target radiation source relative to the second satellite, respectively, according to differences between the position coordinate variable of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite;

[0024] Constructing an equation of a first curved surface on which the target radiation source is located according to the first position vector and the range distance of the first satellite;

[0025] An equation of a second curved surface on which the target radiation source is located is constructed according to the second position vector and the range distance of the second satellite.

[0026] According to a three-dimensional positioning method for a binary stationary radiation source based on passive synthetic aperture provided by the present invention, solving the nonlinear equation group to obtain the position coordinate value of the target radiation source includes:

[0027] Constructing Newton's equations according to the nonlinear equations;

[0028] Obtaining an initial predicted position coordinate value, and using the initial predicted position coordinate value as the predicted position coordinate value in the first round of iteration;

[0029] In each round of iteration, the predicted position coordinate values of the current round of iteration are substituted into the Newton equations to obtain the position coordinate adjustment values of the current round of iteration;

[0030] Determining the predicted position coordinate value for the next iteration according to the position coordinate adjustment value of the current iteration and the predicted position coordinate value of the current iteration;

[0031] Returning to the step of substituting the predicted position coordinate values of the current iteration into the Newton equations to solve and obtain the position coordinate adjustment values of the current iteration, so as to enter the next iteration, until the iteration stop condition is satisfied;

[0032] After the iteration is stopped, the predicted position coordinate value obtained in the last round of iteration is determined as the position coordinate value of the target radiation source.

[0033] In a second aspect, the present invention provides a three-dimensional positioning device for a dual-satellite stationary radiation source based on passive synthetic aperture, comprising the following modules:

[0034] a data processing module, configured to perform passive synthetic aperture processing on the radiation source signals received by the first satellite and the second satellite from the target radiation source, respectively, to determine the instantaneous position vector, instantaneous velocity vector, and range distance of the first satellite and the second satellite at respective azimuth moments corresponding to the target radiation source;

[0035] an equation construction module, configured to construct an equation of a first plane and an equation of a second plane in which the target radiation source is located based on the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite, respectively; and construct an equation of a first curved surface and an equation of a second curved surface in which the target radiation source is located based on the instantaneous position vector and the range distance of the first satellite and the second satellite, respectively;

[0036] A position solving module is used to jointly solve the equation of the first plane, the equation of the second plane, the equation of the first curved surface and the equation of the second curved surface to form a nonlinear equation group, and solve the nonlinear equation group to obtain the position coordinate value of the target radiation source.

[0037] According to a dual-satellite stationary radiation source three-dimensional positioning device based on passive synthetic aperture provided by the present invention, the data processing module is further used to perform passive synthetic aperture processing on the radiation source signals from the target radiation source received by the first satellite and the second satellite, respectively, to obtain the azimuth time and Doppler slope of the first satellite and the second satellite corresponding to the target radiation source respectively; based on the navigation positioning information of the first satellite and the second satellite, determine the instantaneous position vector and instantaneous velocity vector of the first satellite and the second satellite at their respective azimuth times; based on the instantaneous velocity vector and the Doppler slope of the first satellite and the second satellite, determine the distance between the first satellite and the second satellite and the target radiation source respectively.

[0038] According to a three-dimensional positioning device for a binary stationary radiation source based on passive synthetic aperture provided by the present invention, the position solving module is further used to construct a Newton equation group based on the nonlinear equation group; obtain an initial predicted position coordinate value, and use the initial predicted position coordinate value as the predicted position coordinate value in the first round of iteration; in each round of iteration, substitute the predicted position coordinate value of the current round of iteration into the Newton equation group, and solve to obtain the position coordinate adjustment value of the current round of iteration; determine the predicted position coordinate value of the next round of iteration based on the position coordinate adjustment value of the current round of iteration and the predicted position coordinate value of the current round of iteration; return to execute the step of substituting the predicted position coordinate value of the current round of iteration into the Newton equation group, and solve to obtain the position coordinate adjustment value of the current round of iteration, so as to enter the next round of iteration until the iteration stopping condition is met; after stopping the iteration, determine the predicted position coordinate value obtained in the last round of iteration as the position coordinate value of the target radiation source.

[0039] In a third aspect, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements any of the above-described methods for three-dimensional positioning of binary stationary radiation sources based on passive synthetic aperture.

[0040] The present invention provides a method, device and computer program product for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture. By performing passive synthetic aperture processing on radiation source signals from the same target radiation source received by two satellites respectively, and then constructing a nonlinear equation group for solution, the method avoids the problem of being unable to obtain elevation information by using only a single satellite for passive synthetic aperture processing. The method can accurately determine the position coordinate value of the target radiation source including the elevation information, realize three-dimensional positioning and improve the radiation source positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the present invention or the prior art, a brief introduction is given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0042] Figure 1 This is one of the flow charts of the three-dimensional positioning method of a binary stationary radiation source based on passive synthetic aperture provided by the present invention.

[0043] Figure 2 It is a schematic diagram of the geometric model of the three-dimensional positioning method of a binary stationary radiation source based on passive synthetic aperture provided by the present invention.

[0044] FIG3( a ) and FIG3 ( b ) are schematic diagrams of passive synthetic aperture processing results in the passive synthetic aperture-based three-dimensional positioning method for a dual-satellite stationary radiation source provided by the present invention.

[0045] Figure 4 This is a schematic diagram of the relationship between the number of iterations and positioning error in the three-dimensional positioning method for a binary stationary radiation source based on passive synthetic aperture provided by the present invention.

[0046] Figure 5 It is a structural schematic diagram of a three-dimensional positioning device for a binary stationary radiation source based on passive synthetic aperture provided by the present invention. DETAILED DESCRIPTION

[0047] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0048] The following combination Figure 1-Figure 5 The present invention provides a method, device and computer program product for three-dimensional positioning of a binary stationary radiation source based on passive synthetic aperture.

[0049] In one embodiment, the three-dimensional positioning method of a dual-satellite stationary radiation source based on passive synthetic aperture provided by the present invention can be executed by an electronic device. The electronic device can receive the radiation source signals from the target radiation source respectively sent by the first satellite and the second satellite, and then execute the three-dimensional positioning method of a dual-satellite stationary radiation source based on passive synthetic aperture in each embodiment of the present invention.

[0050] In another embodiment, the method for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture provided by the present invention can be executed by a first satellite or a second satellite. The first satellite can receive a radiation source signal from a target radiation source sent by a second satellite and received by the second satellite. The first satellite can execute the method for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture in each embodiment of the present invention based on the radiation source signal from the target radiation source received by itself and the radiation source signal from the target radiation source received by the second satellite. Alternatively, the second satellite can receive a radiation source signal from a target radiation source sent by a first satellite and received by the first satellite. The second satellite can execute the method for three-dimensional positioning of a dual-satellite stationary radiation source based on passive synthetic aperture in each embodiment of the present invention based on the radiation source signal from the target radiation source received by itself and the radiation source signal from the target radiation source received by the first satellite.

[0051] Figure 1 This is one of the flow charts of the three-dimensional positioning method of a binary stationary radiation source based on passive synthetic aperture provided by the present invention, such as Figure 1 As shown, the method includes the following:

[0052] Step 102 : Passive synthetic aperture processing is performed on the radiation source signals received by the first satellite and the second satellite from the target radiation source, respectively, to determine the instantaneous position vector, instantaneous velocity vector, and range distance of the first satellite and the second satellite at the respective azimuth moments corresponding to the target radiation source.

[0053] The target emitter is stationary. Passive synthetic aperture processing utilizes the temporal correlation of the signal, combining continuously measured short arrays into a virtual long array through phase compensation and spatial position compensation, thereby achieving azimuth resolution of the target. The azimuth time is the time when the satellite is closest to the emitter. The range distance is the straight-line distance between the satellite and the target emitter.

[0054] The geometric model used in the present invention is as follows Figure 2 As shown, the moment when the low-orbit satellite A (the first satellite) is closest to the target radiation source is the azimuth moment The moment when the low-orbit satellite B (the second satellite) is closest to the target radiation source is the azimuth moment . Low-orbit satellite A is at the azimuth time The instantaneous position vector under , the instantaneous velocity vector is . Low-orbit satellite B is at the azimuth time The instantaneous position vector under , the instantaneous velocity vector .

[0055] In one embodiment, passive synthetic aperture processing is performed on the radiation source signals received by the first satellite and the second satellite from the target radiation source to obtain the azimuth time and Doppler slope of the first satellite and the second satellite, respectively, corresponding to the target radiation source. Then, based on the azimuth time and Doppler slope of the first satellite and the second satellite, the instantaneous position vector, instantaneous velocity vector, and range distance of the first satellite and the second satellite at the azimuth time corresponding to the target radiation source are determined, respectively. The Doppler slope represents the rate at which the signal frequency of the radiation source signal received by the satellite changes over time.

[0056] Step 104 : constructing an equation of a first plane and an equation of a second plane where the target radiation source is located based on the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite, respectively.

[0057] Specifically, an equation of a first plane where the target radiation source is located is constructed based on the instantaneous position vector and instantaneous velocity vector of the first satellite. An equation of a second plane where the target radiation source is located is constructed based on the instantaneous position vector and instantaneous velocity vector of the second satellite.

[0058] The first plane is perpendicular to the instantaneous velocity vector of the first satellite; and the second plane is perpendicular to the instantaneous velocity vector of the second satellite.

[0059] Step 106 : constructing an equation of a first curved surface and an equation of a second curved surface where the target radiation source is located based on the instantaneous position vectors and range distances of the first satellite and the second satellite, respectively.

[0060] Specifically, an equation of a first curved surface where the target radiation source is located is constructed based on the instantaneous position vector and the range distance of the first satellite. An equation of a second curved surface where the target radiation source is located is constructed based on the instantaneous position vector and the range distance of the second satellite.

[0061] The distance between any point on the first curved surface and the first satellite is equal to the range distance of the first satellite. The distance between any point on the second curved surface and the second satellite is equal to the range distance of the second satellite.

[0062] Step 108 : The equation of the first plane, the equation of the second plane, the equation of the first curved surface, and the equation of the second curved surface are combined to form a nonlinear equation group, and the nonlinear equation group is solved to obtain the position coordinate value of the target radiation source.

[0063] In one embodiment, a Newtonian equation group is constructed based on a nonlinear equation group, an initial predicted position coordinate value is set, and the Newtonian equation group is iteratively solved until the iteration is stopped, and the predicted position coordinate value obtained in the last round of iteration is determined as the position coordinate value of the target radiation source.

[0064] The above-mentioned passive synthetic aperture-based dual-satellite stationary emitter three-dimensional positioning method performs passive synthetic aperture processing on the emitter signals received by two satellites from the same target emitter, and then constructs a set of nonlinear equations for solution. This avoids the problem of using only a single satellite for passive synthetic aperture processing and failing to obtain elevation information. It can accurately determine the position coordinates of the target emitter, including elevation information, to achieve three-dimensional positioning and improve the emitter positioning accuracy. In addition, compared with traditional methods such as frequency measurement positioning, direction finding positioning, time difference positioning, and time-frequency difference positioning, the use of passive synthetic aperture processing not only improves positioning accuracy, but also replaces the array antenna with a single antenna, reducing the size and thus reducing the requirements for satellite payload.

[0065] In one embodiment, passive synthetic aperture processing is performed on radiation source signals received by a first satellite and a second satellite from a target radiation source, respectively, to determine instantaneous position vectors, instantaneous velocity vectors, and range distances of the first satellite and the second satellite at respective azimuth moments corresponding to the target radiation source, including: performing passive synthetic aperture processing on radiation source signals received by the first satellite and the second satellite from the target radiation source, respectively, to obtain azimuth moments and Doppler slopes of the first satellite and the second satellite corresponding to the target radiation source, respectively; determining instantaneous position vectors and instantaneous velocity vectors of the first satellite and the second satellite at respective azimuth moments based on navigation positioning information of the first satellite and the second satellite; and determining range distances between the first satellite and the second satellite and the target radiation source, respectively, based on the instantaneous velocity vectors and Doppler slopes of the first satellite and the second satellite.

[0066] For example, passive synthetic aperture processing is performed on the radiation source signals received by the first satellite A and the second satellite B from the target radiation source, and the azimuth time of the first satellite A corresponding to the target radiation source is obtained. and Doppler slope , and the azimuth time corresponding to the second satellite B and Doppler slope According to the navigation positioning information of the first satellite A, determine the first satellite A at the azimuth time The instantaneous position vector under and the instantaneous velocity vector According to the navigation positioning information of the second satellite B, determine the azimuth time of the second satellite B The instantaneous position vector under and the instantaneous velocity vector .

[0067] In one embodiment, the navigation positioning information may be GNSS (Global Navigation Satellite System) information of a satellite.

[0068] In one embodiment, the instantaneous velocity values of the first and second satellites at their respective azimuth moments can be determined based on their instantaneous velocity vectors. Then, the range-direction distances between the first and second satellites and the target radiation source can be determined based on the instantaneous velocity values and Doppler slopes of the first and second satellites. The range-direction distance of the first satellite is proportional to the square of the instantaneous velocity value of the first satellite. The range-direction distance of the second satellite is proportional to the square of the instantaneous velocity value of the second satellite. The range-direction distance of the first satellite is inversely proportional to the absolute value of the Doppler slope of the first satellite. The range-direction distance of the second satellite is inversely proportional to the absolute value of the Doppler slope of the second satellite. The instantaneous velocity value is the modulus of the instantaneous velocity vector.

[0069] In the above embodiment, passive synthetic aperture processing is performed on the radiation source signal to obtain the azimuth time and Doppler slope. Then, based on the navigation positioning information of the satellite, the instantaneous position vector and instantaneous velocity vector at the azimuth time can be accurately and efficiently determined. Based on the instantaneous velocity vector and the Doppler slope, the range distance can be accurately and efficiently determined.

[0070] In one embodiment, the distances between the first satellite and the second satellite and the target radiation source are determined based on the instantaneous velocity vectors and Doppler slopes of the first satellite and the second satellite, respectively, including: determining the instantaneous velocity values of the first satellite and the second satellite at their respective azimuth moments based on the instantaneous velocity vectors of the first satellite and the second satellite, respectively; determining the carrier frequency of the target radiation source based on the radiation source signals received by the first satellite and the second satellite; and determining the distances between the first satellite and the second satellite and the target radiation source based on the instantaneous velocity values and Doppler slopes of the first satellite and the second satellite, the carrier frequency of the target radiation source, and the speed of light.

[0071] In one embodiment, the range distance is proportional to the carrier frequency of the target radiation source. The range distance is proportional to the square of the instantaneous velocity value. The range distance is inversely proportional to the speed of light. The range distance is inversely proportional to the absolute value of the Doppler slope.

[0072] In one embodiment, the distances between the first satellite and the second satellite and the target radiation source may be determined according to the following formula:

[0073]

[0074]

[0075] in, represents the distance between the first satellite A and the target radiation source. represents the distance between the second satellite B and the target radiation source. Indicates the carrier frequency of the target radiation source. Represents the speed of light. Represents the instantaneous velocity value of the first satellite A. Indicates the instantaneous velocity value of the second satellite B. represents the Doppler slope of the first satellite A. represents the Doppler slope of the second satellite B.

[0076] In the above embodiment, the distances between the first satellite and the second satellite and the target radiation source can be accurately determined based on the instantaneous velocity values and Doppler slopes of the first satellite and the second satellite, the carrier frequency and the speed of light of the target radiation source.

[0077] In one embodiment, the equation of the first plane and the equation of the second plane in which the target radiation source is located are constructed based on the instantaneous position vector and instantaneous velocity vector of the first satellite and the second satellite, respectively, including: constructing the first position vector and the second position vector of the target radiation source relative to the first satellite and the second satellite respectively based on the difference between the position coordinate variable of the target radiation source and the instantaneous position vector of the first satellite and the second satellite; constructing the equation of the first plane in which the target radiation source is located based on the first position vector and the instantaneous velocity vector of the first satellite; constructing the equation of the second plane in which the target radiation source is located based on the second position vector and the instantaneous velocity vector of the second satellite.

[0078] In one embodiment, an equation for a first plane in which the target radiation source is located may be constructed based on a dot product between a first position vector and an instantaneous velocity vector of a first satellite being equal to zero. An equation for a second plane in which the target radiation source is located may be constructed based on a dot product between a second position vector and an instantaneous velocity vector of a second satellite being equal to zero.

[0079] It can be understood that, since the first position vector of the target radiation source relative to the first satellite is perpendicular to the instantaneous velocity vector of the first satellite, the equation of the first plane can be constructed by constraining the dot product between the first position vector and the instantaneous velocity vector of the first satellite to be equal to zero. Since the second position vector of the target radiation source relative to the second satellite is perpendicular to the instantaneous velocity vector of the second satellite, the equation of the second plane can be constructed by constraining the dot product between the second position vector and the instantaneous velocity vector of the second satellite to be equal to zero.

[0080] In one embodiment, the equation of the first plane is as follows:

[0081]

[0082] in, represents the instantaneous velocity vector of the first satellite A. represents the instantaneous position vector of the first satellite A. The position coordinate variable representing the target radiation source. represents the first position vector of the target radiation source relative to the first satellite. T represents transpose.

[0083] In one embodiment, the equation of the second plane is as follows:

[0084]

[0085] in, represents the instantaneous velocity vector of the second satellite B. represents the instantaneous position vector of the second satellite B. The position coordinate variable representing the target radiation source. represents the second position vector of the target radiation source relative to the second satellite. T represents transpose.

[0086] In the above embodiment, the equation of the first plane in which the target radiation source is located is constructed based on the first position vector and the instantaneous velocity vector of the first satellite; the equation of the second plane in which the target radiation source is located is constructed based on the second position vector and the instantaneous velocity vector of the second satellite, so that the equation of the first plane and the equation of the second plane in which the target radiation source is located can be accurately obtained.

[0087] In one embodiment, an equation of a first curved surface and an equation of a second curved surface where a target radiation source is located are constructed based on the instantaneous position vectors and range distances of the first satellite and the second satellite, respectively, including: constructing a first position vector of the target radiation source relative to the first satellite and a second position vector of the target radiation source relative to the second satellite based on the differences between the position coordinate variables of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite, respectively; constructing an equation of the first curved surface where the target radiation source is located based on the first position vector and the range distance of the first satellite; and constructing an equation of the second curved surface where the target radiation source is located based on the second position vector and the range distance of the second satellite.

[0088] In one embodiment, an equation for a first curved surface where the target radiation source is located can be constructed based on the dot product of the first position vector and itself being equal to the square of the distance in the range direction of the first satellite. An equation for a second curved surface where the target radiation source is located can be constructed based on the dot product of the second position vector and itself being equal to the square of the distance in the range direction of the second satellite.

[0089] In one embodiment, the equation of the first surface is as follows:

[0090]

[0091] in, represents the instantaneous position vector of the first satellite A. The position coordinate variable representing the target radiation source. A first position vector representing the target radiation source relative to the first satellite. represents the distance between the first satellite A and the target radiation source. T represents the transpose.

[0092] In one embodiment, the equation of the second surface is as follows:

[0093]

[0094] in, represents the instantaneous position vector of the second satellite B. The position coordinate variable representing the target radiation source. A second position vector representing the target radiation source relative to the second satellite. represents the distance between the second satellite B and the target radiation source. T represents the transpose.

[0095] In the above embodiment, the equation of the first surface where the target radiation source is located is constructed based on the first position vector and the distance in the range direction of the first satellite, and the equation of the second surface where the target radiation source is located is constructed based on the second position vector and the distance in the range direction of the second satellite. The equations of the first surface and the second surface where the target radiation source is located can be accurately constructed.

[0096] In one embodiment, solving a nonlinear equation group to obtain the position coordinate value of the target radiation source includes: constructing a Newton equation group based on the nonlinear equation group; obtaining an initial predicted position coordinate value, and using the initial predicted position coordinate value as the predicted position coordinate value in the first round of iteration; in each round of iteration, substituting the predicted position coordinate value of the current round of iteration into the Newton equation group, and solving to obtain the position coordinate adjustment value of the current round of iteration; determining the predicted position coordinate value of the next round of iteration based on the position coordinate adjustment value of the current round of iteration and the predicted position coordinate value of the current round of iteration; returning to execute the step of substituting the predicted position coordinate value of the current round of iteration into the Newton equation group, and solving to obtain the position coordinate adjustment value of the current round of iteration, so as to enter the next round of iteration until the iteration stopping condition is met; after stopping the iteration, determining the predicted position coordinate value obtained in the last round of iteration as the position coordinate value of the target radiation source.

[0097] In one embodiment, in each round of iteration, the predicted position coordinate value of the next round of iteration may be determined according to the sum of the position coordinate adjustment value of the current round of iteration and the predicted position coordinate value of the current round of iteration.

[0098] In one embodiment, the nonlinear system of equations is as follows:

[0099]

[0100] The nonlinear equations are converted into vector form as follows:

[0101]

[0102] in, The position coordinate variable representing the target radiation source.

[0103] Then you can ask The derivative matrix of . The derivative matrix can be a Jacobi matrix, etc.

[0104] Obtain The Jacobian matrix as follows:

[0105]

[0106] according to and Construct Newton's equations:

[0107]

[0108] Where k represents the iteration round number. Represents the predicted position coordinate value of the kth iteration. Indicates the position coordinate adjustment value of the kth iteration.

[0109] Get the initial predicted position coordinates ,Will As the predicted position coordinate value in the first round of iteration, substitute it into Newton's equations:

[0110]

[0111] Solve the Newton equations to get the position coordinate adjustment value of the first round:

[0112] Then, based on the predicted position coordinate values in the first round of iteration Adjusted position coordinates compared to the first iteration The sum of the predicted position coordinates in the next iteration is determined :

[0113]

[0114] Iterate the above steps of solving Newton's equations to obtain the position coordinate adjustment value, and then obtain the predicted position coordinate value in the next round of iteration until the iteration stop condition is met, and the predicted position coordinate value obtained in the last round of iteration is Determine the position coordinate value of the target radiation source.

[0115] In one embodiment, the iteration stopping condition may be that the difference between the predicted position coordinate value in the current iteration and the predicted position coordinate value in the previous iteration is less than a preset threshold.

[0116] In one embodiment, the iteration stopping condition may be as follows:

[0117]

[0118] in, Indicates the predicted position coordinate value in the current round iteration. Indicates the predicted position coordinate value in the previous iteration. Indicates the preset threshold. The dimension representing the coordinate values of the predicted location. Represents the value of the i-th position in the predicted position coordinate value in the current round iteration. Indicates the value of the i-th position in the predicted position coordinate value in the previous iteration.

[0119] In the above embodiment, a Newton equation group is constructed based on a nonlinear equation group, and then the Newton equation group is iteratively solved. The predicted position coordinate value obtained in the last round of iteration is determined as the position coordinate value of the target radiation source. The position coordinate value of the target radiation source can be accurately determined, thereby improving the positioning accuracy of the radiation source.

[0120] The efficiency of the present invention is verified by simulation data. In this simulation experiment, the position coordinates of the radiation source in the ECEF coordinate system (Earth-Centered, Earth-Fixed) are [-2164952.31, 4394341.81, 4099970.57], the carrier frequency of the radiation source is 1.6 GHz, the sampling rate of the baseband signal is 96 kHz, the reception time of the low-orbit satellite A (the first satellite) and the low-orbit satellite B (the second satellite) during the overhead period is 6 seconds, the instantaneous speed values of the low-orbit satellite A and the low-orbit satellite B are 7258.96 m / s and 7383.64 m / s, and the azimuth time is 1.6 GHz. and They are 1.3141s and 1.4471s respectively, and the distance to distance and The passive synthetic aperture processing time is 0.69s for both the received radiation source signals of low-orbit satellite A and low-orbit satellite B. Passive synthetic aperture processing is performed on the received radiation source signals of low-orbit satellite A and low-orbit satellite B, and the Doppler slope-azimuth time processing result diagrams are shown in Figure 3 (a) and Figure 3 (b). Figure 3 (a) is the Doppler slope-azimuth time processing result diagram of low-orbit satellite A, and Figure 3 (b) is the Doppler slope-azimuth time processing result diagram of low-orbit satellite B. According to Figures 3 (a) and 3 (b), the azimuth time and Doppler slope estimated by passive synthetic aperture processing are respectively 、 、 、 The distance to distance is calculated as 、 . Given the initial predicted position coordinate value , to obtain for:

[0121]

[0122] Obtain The Jacobi matrix is:

[0123]

[0124] Will and Substituting into Newton's equations and solving them we get:

[0125]

[0126] Further we get:

[0127]

[0128] Iterate the above steps until the iteration stop condition is met, and the output position coordinate value of the target radiation source is [-2165170.48, 4394692.05, 4100205.73], with an estimated error of 474.95m. The change of positioning estimation error with the number of iterations is shown in the figure below. Figure 4 shown.

[0129] The following describes the three-dimensional positioning device for a dual-satellite stationary radiation source based on passive synthetic aperture provided by the present invention. The three-dimensional positioning device for a dual-satellite stationary radiation source based on passive synthetic aperture described below and the three-dimensional positioning method for a dual-satellite stationary radiation source based on passive synthetic aperture described above can be referenced to each other.

[0130] like Figure 5 As shown, the present invention provides a three-dimensional positioning device 500 for a dual-satellite stationary radiation source based on passive synthetic aperture, comprising the following modules:

[0131] The data processing module 502 is configured to perform passive synthetic aperture processing on the radiation source signals received by the first satellite and the second satellite from the target radiation source, respectively, to determine the instantaneous position vector, instantaneous velocity vector, and range distance of the first satellite and the second satellite at the respective azimuth moments corresponding to the target radiation source.

[0132] The equation construction module 504 is used to construct the equation of the first plane and the equation of the second plane where the target radiation source is located based on the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite respectively; and to construct the equation of the first curved surface and the equation of the second curved surface where the target radiation source is located based on the instantaneous position vector and the range distance of the first satellite and the second satellite respectively.

[0133] The position solving module 506 is used to solve the nonlinear equation group formed by combining the equation of the first plane, the equation of the second plane, the equation of the first curved surface and the equation of the second curved surface to obtain the position coordinate value of the target radiation source.

[0134] In one embodiment, the data processing module 502 is further used to perform passive synthetic aperture processing on the radiation source signals received by the first satellite and the second satellite from the target radiation source, respectively, to obtain the azimuth time and Doppler slope of the first satellite and the second satellite corresponding to the target radiation source, respectively; determine the instantaneous position vector and instantaneous velocity vector of the first satellite and the second satellite at their respective azimuth time according to the navigation positioning information of the first satellite and the second satellite; and determine the distance between the first satellite and the second satellite and the target radiation source, respectively, based on the instantaneous velocity vector and the Doppler slope of the first satellite and the second satellite.

[0135] In one embodiment, the data processing module 502 is further used to determine the instantaneous velocity values of the first satellite and the second satellite at their respective azimuth moments based on the instantaneous velocity vectors of the first satellite and the second satellite respectively; determine the carrier frequency of the target radiation source based on the radiation source signals received by the first satellite and the second satellite; and determine the distance between the first satellite and the second satellite and the target radiation source respectively based on the instantaneous velocity values and Doppler slopes of the first satellite and the second satellite, and the carrier frequency and speed of light of the target radiation source.

[0136] In one embodiment, the equation construction module 504 is also used to construct a first position vector of the target radiation source relative to the first satellite and a second position vector relative to the second satellite based on the difference between the position coordinate variable of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite respectively; construct an equation of the first plane in which the target radiation source is located based on the first position vector and the instantaneous velocity vector of the first satellite; and construct an equation of the second plane in which the target radiation source is located based on the second position vector and the instantaneous velocity vector of the second satellite.

[0137] In one embodiment, the equation construction module 504 is also used to construct a first position vector of the target radiation source relative to the first satellite and a second position vector relative to the second satellite based on the difference between the position coordinate variable of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite respectively; construct an equation of the first surface on which the target radiation source is located based on the first position vector and the distance in the range direction of the first satellite; and construct an equation of the second surface on which the target radiation source is located based on the second position vector and the distance in the range direction of the second satellite.

[0138] In one embodiment, the position solving module 506 is also used to construct a Newton equation group based on the nonlinear equation group; obtain the initial predicted position coordinate value, and use the initial predicted position coordinate value as the predicted position coordinate value in the first round of iteration; in each round of iteration, substitute the predicted position coordinate value of the current round of iteration into the Newton equation group, and solve to obtain the position coordinate adjustment value of the current round of iteration; determine the predicted position coordinate value of the next round of iteration based on the position coordinate adjustment value of the current round of iteration and the predicted position coordinate value of the current round of iteration; return to execute the step of substituting the predicted position coordinate value of the current round of iteration into the Newton equation group, and solve to obtain the position coordinate adjustment value of the current round of iteration, so as to enter the next round of iteration until the iteration stop condition is met; after stopping the iteration, determine the predicted position coordinate value obtained in the last round of iteration as the position coordinate value of the target radiation source.

[0139] On the other hand, the present invention also provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the three-dimensional positioning method of a dual-satellite stationary radiation source based on passive synthetic aperture provided by the above methods. The method includes: performing passive synthetic aperture processing on the radiation source signals from the target radiation source received by the first satellite and the second satellite, respectively, to determine the instantaneous position vector, instantaneous velocity vector and range distance of the first satellite and the second satellite at the azimuth moments corresponding to the target radiation source; constructing the equation of the first plane and the equation of the second plane in which the target radiation source is located based on the instantaneous position vector and instantaneous velocity vector of the first satellite and the second satellite, respectively; constructing the equation of the first curved surface and the equation of the second curved surface in which the target radiation source is located based on the instantaneous position vector and the range distance of the first satellite and the second satellite, respectively; combining the equations of the first plane, the second plane, the first curved surface and the second curved surface to form a nonlinear equation group, and solving the nonlinear equation group to obtain the position coordinate value of the target radiation source.

[0140] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0141] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0142] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A three-dimensional positioning method for binary stationary radiation sources based on passive synthetic aperture, characterized in that: include: performing passive synthetic aperture processing on radiation source signals from a target radiation source received by a first satellite and a second satellite, respectively, to determine an instantaneous position vector, an instantaneous velocity vector, and a range distance of the first satellite and the second satellite, respectively, at respective azimuth moments corresponding to the target radiation source; Constructing an equation of a first plane and an equation of a second plane in which the target radiation source is located based on the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite, respectively, where the first plane is perpendicular to the instantaneous velocity vector of the first satellite, and the second plane is perpendicular to the instantaneous velocity vector of the second satellite; Constructing an equation of a first curved surface and an equation of a second curved surface on which the target radiation source is located based on the instantaneous position vectors and the range distances of the first satellite and the second satellite, respectively, where the distance between any point on the first curved surface and the first satellite is equal to the range distance of the first satellite, and the distance between any point on the second curved surface and the second satellite is equal to the range distance of the second satellite; The equation of the first plane, the equation of the second plane, the equation of the first curved surface, and the equation of the second curved surface are combined to form a nonlinear equation group, and the position coordinate value of the target radiation source is obtained by solving the nonlinear equation group.

2. The method for three-dimensional positioning of a binary stationary radiation source based on passive synthetic aperture according to claim 1, characterized in that: The performing passive synthetic aperture processing on the radiation source signals received by the first satellite and the second satellite from the target radiation source, respectively, to determine the instantaneous position vector, instantaneous velocity vector, and range distance of the first satellite and the second satellite at respective azimuth moments corresponding to the target radiation source, includes: performing passive synthetic aperture processing on the radiation source signals from the target radiation source received by the first satellite and the second satellite, respectively, to obtain the azimuth time and Doppler slope of the first satellite and the second satellite corresponding to the target radiation source, respectively; Determine, based on the navigation positioning information of the first satellite and the second satellite, the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite at the respective azimuth moments; Determine the range distances between the first satellite and the second satellite and the target radiation source respectively based on the instantaneous velocity vector and the Doppler slope of the first satellite and the second satellite respectively.

3. The method for three-dimensional positioning of a binary stationary radiation source based on passive synthetic aperture according to claim 2, characterized in that: The determining, based on the instantaneous velocity vector and the Doppler slope of the first satellite and the second satellite, respectively, the range distances between the first satellite and the second satellite and the target radiation source, includes: Determine, based on the instantaneous velocity vectors of the first satellite and the second satellite, the instantaneous velocity values of the first satellite and the second satellite at the respective azimuth moments; determining a carrier frequency of the target radiation source based on the radiation source signals received by the first satellite and the second satellite; Determine the distances between the first satellite and the second satellite and the target radiation source respectively based on the instantaneous velocity values and the Doppler slopes of the first satellite and the second satellite, the carrier frequency and the speed of light of the target radiation source.

4. The method for three-dimensional positioning of a binary stationary radiation source based on passive synthetic aperture according to claim 1, characterized in that: The constructing an equation of a first plane and an equation of a second plane in which the target radiation source is located according to the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite, respectively, comprises: Constructing a first position vector of the target radiation source relative to the first satellite and a second position vector of the target radiation source relative to the second satellite, respectively, according to differences between the position coordinate variable of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite; constructing an equation of a first plane in which the target radiation source is located according to the first position vector and the instantaneous velocity vector of the first satellite; An equation of a second plane in which the target radiation source is located is constructed according to the second position vector and the instantaneous velocity vector of the second satellite.

5. The method for three-dimensional positioning of a binary stationary radiation source based on passive synthetic aperture according to claim 1, characterized in that: The constructing an equation of a first curved surface and an equation of a second curved surface on which the target radiation source is located according to the instantaneous position vector and the range direction distance of the first satellite and the second satellite, respectively, comprises: Constructing a first position vector of the target radiation source relative to the first satellite and a second position vector of the target radiation source relative to the second satellite, respectively, according to differences between the position coordinate variable of the target radiation source and the instantaneous position vectors of the first satellite and the second satellite; Constructing an equation of a first curved surface on which the target radiation source is located according to the first position vector and the range distance of the first satellite; An equation of a second curved surface on which the target radiation source is located is constructed according to the second position vector and the range distance of the second satellite.

6. The method for three-dimensional positioning of a binary stationary radiation source based on passive synthetic aperture according to any one of claims 1 to 5, characterized in that: Solving the nonlinear equation group to obtain the position coordinate value of the target radiation source includes: Constructing Newton's equations according to the nonlinear equations; Obtaining an initial predicted position coordinate value, and using the initial predicted position coordinate value as the predicted position coordinate value in the first round of iteration; In each round of iteration, the predicted position coordinate values of the current round of iteration are substituted into the Newton equations to obtain the position coordinate adjustment values of the current round of iteration; Determining the predicted position coordinate value for the next iteration according to the position coordinate adjustment value of the current iteration and the predicted position coordinate value of the current iteration; Returning to the step of substituting the predicted position coordinate values of the current iteration into the Newton equations to solve and obtain the position coordinate adjustment values of the current iteration, so as to enter the next iteration, until the iteration stop condition is satisfied; After the iteration is stopped, the predicted position coordinate value obtained in the last round of iteration is determined as the position coordinate value of the target radiation source.

7. A three-dimensional positioning device for a binary stationary radiation source based on passive synthetic aperture, characterized in that: include: a data processing module, configured to perform passive synthetic aperture processing on the radiation source signals received by the first satellite and the second satellite from the target radiation source, respectively, to determine the instantaneous position vector, instantaneous velocity vector, and range distance of the first satellite and the second satellite at respective azimuth moments corresponding to the target radiation source; an equation construction module, configured to construct an equation of a first plane and an equation of a second plane in which the target radiation source is located based on the instantaneous position vector and the instantaneous velocity vector of the first satellite and the second satellite, respectively, where the first plane is perpendicular to the instantaneous velocity vector of the first satellite, and the second plane is perpendicular to the instantaneous velocity vector of the second satellite; Constructing an equation of a first curved surface and an equation of a second curved surface on which the target radiation source is located based on the instantaneous position vectors and the range distances of the first satellite and the second satellite, respectively, where the distance between any point on the first curved surface and the first satellite is equal to the range distance of the first satellite, and the distance between any point on the second curved surface and the second satellite is equal to the range distance of the second satellite; A position solving module is used to jointly solve the equation of the first plane, the equation of the second plane, the equation of the first curved surface and the equation of the second curved surface to form a nonlinear equation group, and solve the nonlinear equation group to obtain the position coordinate value of the target radiation source.

8. The three-dimensional positioning device for a dual-satellite stationary radiation source based on passive synthetic aperture according to claim 7, characterized in that: The data processing module is further used to perform passive synthetic aperture processing on the radiation source signals from the target radiation source received by the first satellite and the second satellite, respectively, to obtain the azimuth time and Doppler slope of the first satellite and the second satellite corresponding to the target radiation source, respectively; determine the instantaneous position vector and instantaneous velocity vector of the first satellite and the second satellite at their respective azimuth time according to the navigation positioning information of the first satellite and the second satellite, respectively; and determine the distance between the first satellite and the second satellite and the target radiation source, respectively, based on the instantaneous velocity vector and the Doppler slope of the first satellite and the second satellite, respectively.

9. The three-dimensional positioning device for a dual-satellite stationary radiation source based on passive synthetic aperture according to claim 7, characterized in that: The position solving module is further configured to construct a Newtonian equation system based on the nonlinear equation system; obtain an initial predicted position coordinate value, and use the initial predicted position coordinate value as the predicted position coordinate value in the first iteration; in each iteration, substitute the predicted position coordinate value of the current iteration into the Newtonian equation system to solve and obtain the position coordinate adjustment value of the current iteration; and determine the predicted position coordinate value of the next iteration based on the position coordinate adjustment value of the current iteration and the predicted position coordinate value of the current iteration; Return to the step of substituting the predicted position coordinate value of the current round of iteration into the Newton equations to solve the position coordinate adjustment value of the current round of iteration to enter the next round of iteration until the iteration stop condition is met; after stopping the iteration, the predicted position coordinate value obtained in the last round of iteration is determined as the position coordinate value of the target radiation source.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the three-dimensional positioning method for a binary stationary radiation source based on passive synthetic aperture as claimed in any one of claims 1 to 6 is implemented.

Images