A dual-satellite joint passive localization method based on direction-finding error weights

Abstract

This invention relates to a dual-satellite joint passive positioning method based on direction-finding error weighting, comprising: acquiring the positioning results P1(x) of the two satellites for the same target at the same time. p1 ,y p1 ,z p1 ) and P2(x p2 ,y p2 ,z p2 The system calculates the positions of the two satellites, S1(x1,y1,z1) and S2(x2,y2,z2), and obtains their positions at that time. Based on the positioning results and the positions of the two satellites, it obtains the direction cosines of the direction-finding lines S1P1 and S2P2 of the two satellites relative to the target. Based on the direction cosines and the positions of the two satellites, it constructs the direction-finding lines of the two satellites relative to the target and calculates the endpoint P of the shortest distance segment of the two direction-finding lines. l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 The method involves obtaining the direction-finding errors α1 and α2 of the two satellites after ground testing or on-orbit testing; obtaining the direction-finding error weights based on the direction-finding errors and the endpoints; and finally determining the position of the target. This invention achieves high-precision passive positioning of targets, including those in the air, within the shared field of view of two satellites without adding any onboard equipment.

Description

Technical Field

[0001] This invention relates to the field of passive radio positioning technology, and in particular to a dual-satellite joint passive positioning method based on direction finding error weights. Background Technology

[0002] Space-based passive positioning has attracted much attention and research due to its advantages of all-day, all-weather, and global detection capabilities. Space-based passive positioning systems mainly employ single-satellite direction-finding positioning, dual-satellite time-difference-of-use (TDO) and frequency-difference-of-use (FDO) positioning, and multi-satellite TDO positioning. Among these systems, single-satellite direction-finding passive positioning is the least technically complex and least costly. However, the positioning accuracy of single-satellite direction-finding passive positioning systems increases with the distance between the target and the nadir point, and high-precision positioning is limited to a certain range from the satellite's nadir point.

[0003] In single-satellite passive positioning systems, the target is assumed to be a sea or ground target in the absence of prior information. When the target is an aerial target, the assumption of the target as a ground target will lead to an error in the elevation assumption. As the target moves far from the nadir point, the positioning accuracy of the single-satellite passive positioning system for aerial targets will further deteriorate.

[0004] With the continuous development of satellite systems, the opportunities and conditions for multiple satellites to simultaneously detect the same area or target have increased, providing a technical foundation for improving positioning accuracy by using dual-satellite direction finding and joint positioning technology. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to provide a dual-satellite joint passive positioning method based on direction finding error weights, which can achieve high-precision passive positioning of targets in the common field of view of the two satellites without adding any on-board equipment.

[0006] To achieve the above-mentioned objectives, the technical solution of this invention is as follows:

[0007] This invention provides a dual-satellite joint passive localization method based on direction-finding error weights, comprising:

[0008] Obtain the positioning results P1(x) of two satellites for the same target at the same time. p1 ,y p1 ,z p1 ) and P2(x p2 ,y p2 ,z p2 ), and obtain the positions of the two satellites at this time: S1(x1,y1,z1) and S2(x2,y2,z2);

[0009] Based on the positioning results and the positions of the two satellites, the direction cosines of the direction finding lines S1P1 and S2P2 of the two satellites relative to the target are obtained.

[0010] Based on the direction cosine and the positions of the two satellites, construct the direction-finding lines for the target from the two satellites, and calculate the endpoint P of the shortest distance segment between these two direction-finding lines. l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 );

[0011] Obtain the direction-finding errors α1 and α2 of the two satellites after they have passed ground testing or in-orbit testing;

[0012] Based on the direction finding error and the endpoint, the direction finding error weight is obtained, and the position of the target is finally determined.

[0013] According to one aspect of the present invention, obtaining the direction cosines of the direction-finding lines S1P1 and S2P2 of the two satellites relative to the target based on the positioning result and the positions of the two satellites includes:

[0014] Based on the positioning results and the positions of the two satellites, the direction cosines of the direction-finding lines S1P1 and S2P2 of the two satellites relative to the target are obtained according to the following formulas, respectively: (a x a y a z ) and (b x b y b z ):

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] According to one aspect of the invention, the method involves constructing direction-finding lines for the target from the two satellites based on the direction cosine and the positions of the two satellites, and calculating the endpoint P of the shortest distance segment between the two direction-finding lines. l1 (x l1 ,yl1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 ),include:

[0022] Based on the direction cosine and the positions of the two satellites, direction-finding lines for the target are constructed according to the following formulas, with the lengths of direction-finding lines S1P1 and S2P2 defined as l1 and l2, respectively.

[0023]

[0024]

[0025] Among them, the direction cosines of the direction-finding lines S1P1 and S2P2 are respectively (a x a y a z ) and (b x b y b z );

[0026] The distance between any points on the direction-finding lines S1P1 and S2P2 can be expressed as follows:

[0027] f(k1,k2)=(x1+a x k1-x2-b x k2) 2 +(y1+a y k1-y2-b y k2) 2 +(z1+a z k1-z2-b z k2) 2 ;

[0028] Differentiating the distance f(k1,k2) between any points on the direction-finding lines S1P1 and S2P2, the derivative is as follows:

[0029]

[0030] in,

[0031] Let the parametric equation values ​​of the two endpoints of the shortest distance segments of the direction-finding lines S1P1 and S2P2 be denoted as k1′ and k2′, respectively, and satisfy the following system of equations:

[0032]

[0033] After rearranging the system of equations, we get:

[0034] X×K=Y,

[0035] in, Solving the system of equations yields K = X. -1 Y, k1′, and k2′ are used to finally obtain the two endpoints P of the shortest distance line segments of the direction-finding lines S1P1 and S2P2. l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 ).

[0036] According to one aspect of the present invention, obtaining the direction-finding error weight based on the direction-finding error and the endpoint includes:

[0037] Based on the two endpoints P of the shortest distance line segment between the direction finding lines S1P1 and S2P2 l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 Given the positions of the two satellites, calculate the distances from each satellite to the endpoints of the shortest distance line segment using the following formula:

[0038]

[0039]

[0040] Based on the direction-finding errors α1 and α2 of the two satellites, the satellite's position at point P is calculated using the following formula. l1 and P l2 The direction finding error weight w at the location l1 and w l2 for:

[0041] w l1 =|S1P l1 |tanα1,

[0042] w l2 =|S2P l2 |tanα2.

[0043] According to one aspect of the present invention, determining the location of the target includes:

[0044] Based on the direction-finding error weights, the position P of the target is determined on the shortest distance segment of the two direction-finding lines according to the following formula. wfor:

[0045]

[0046] Among them, P w Represented as P w (x w ,y w ,z w ).

[0047] Compared with the prior art, the present invention has the following advantages:

[0048] According to the scheme of the present invention, the joint positioning of the target by two satellites with common vision and direction finding results of two satellites is performed, which increases the area of ​​high-precision satellite positioning. The positioning point of the target is selected on the common perpendicular line of the direction finding line of the two satellites according to the direction finding error weight of the two satellites. This effectively overcomes the defect of large positioning error of single satellites with far-away points, improves the joint direction finding positioning accuracy of two satellites, and realizes high-precision positioning of targets including air targets.

[0049] The method of this invention, without adding any onboard equipment, only requires processing and calculating the satellite's ground data using an analytical algorithm. This reduces the computational load, minimizes modifications to existing systems, and facilitates widespread application.

[0050] The positioning method of this invention is not constrained by the Earth's surface equation and can directly locate the target without assuming its height. Therefore, this method can not only locate traditional sea and ground targets, but also has the ability to identify and locate aerial targets. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0052] Figure 1 This schematic diagram illustrates a flowchart of a dual-satellite joint passive localization method based on direction-finding error weights provided in an embodiment of the present invention.

[0053] Figure 2 This diagram illustrates the decomposition of the elevation and azimuth angles of the geostationary coordinate system and the direction-finding line formed by the two satellites and the positioning target in the geostationary coordinate system provided in the embodiments of the present invention.

[0054] Figure 3 This schematic diagram illustrates the interstellar spacing of a binary system provided in an embodiment of the present invention.

[0055] Figure 4 This diagram illustrates the target positioning error decomposition provided in an embodiment of the present invention.

[0056] Figure 5 This diagram illustrates the target positioning error results provided in an embodiment of the present invention.

[0057] Figure 6 This diagram illustrates the target elevation positioning error results provided in an embodiment of the present invention.

[0058] Figure 7 This diagram illustrates the target tangent positioning error results provided in an embodiment of the present invention. Detailed Implementation

[0059] The description of the embodiments in this specification should be taken in conjunction with the accompanying drawings, which should form part of the complete specification. In the drawings, the shape or thickness of the embodiments may be exaggerated and may be indicated in a simplified or convenient manner. Furthermore, parts of the various structures in the drawings will be described separately; it is worth noting that elements not shown in the figures or not described in words are in a form known to those skilled in the art.

[0060] The descriptions of the embodiments herein, including any references to directions and orientations, are for ease of description only and should not be construed as limiting the scope of the invention. The following description of preferred embodiments involves combinations of features, which may exist independently or in combination; the invention is not particularly limited to the preferred embodiments. The scope of the invention is defined by the claims.

[0061] like Figure 1 As shown in the figure, an embodiment of the present invention discloses a dual-satellite joint passive localization method based on direction-finding error weights, which includes the following steps:

[0062] First, obtain the positioning results P1(x) of the two satellites for the same target at the same time. p1 ,y p1 ,z p1 ) and P2(x p2 ,y p2 ,z p2 ), and obtain the positions of the two satellites at this time: S1(x1,y1,z1) and S2(x2,y2,z2).

[0063] Secondly, based on the positioning results and the positions of the two satellites, the direction cosines of the direction-finding lines S1P1 and S2P2 of the two satellites relative to the target are obtained.

[0064] In some embodiments, the specific implementation process of obtaining the direction cosines of the direction-finding lines S1P1 and S2P2 of the two satellites relative to the target based on the positioning result and the positions of the two satellites includes:

[0065] Based on the positioning results and the positions of the two satellites, the direction cosines of the direction-finding lines S1P1 and S2P2 of the two satellites relative to the target are obtained according to the following formulas, respectively: (a x a y a z ) and (b x b y b z ):

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Next, based on the direction cosine and the positions of the two satellites, direction-finding lines for the target are constructed for both satellites, and the endpoints of the shortest distance segments of these two direction-finding lines are calculated. and P l2 (x l2 ,y l2 ,z l2 ).

[0073] In some embodiments, this step involves constructing direction-finding lines for the target from the two satellites based on the direction cosine and the positions of the two satellites, and calculating the endpoint P of the shortest distance segment between the two direction-finding lines. l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 The specific implementation process includes:

[0074] Based on the direction cosine and the positions of the two satellites, direction-finding lines for the target are constructed according to the following formulas. The lengths of direction-finding lines S1P1 and S2P2 are defined as l1 and l2, respectively, which can also be called direction-finding lines l1 and l2.

[0075]

[0076]

[0077] Among them, (a x a y a z ) and (b x b y b z ) represent the direction cosines of the direction-finding lines S1P1 and S2P2, respectively;

[0078] The distance between any points on the direction-finding lines S1P1 and S2P2 can be expressed as follows:

[0079] f(k1,k2)=(x1+a x k1-x2-b x k2) 2 +(y1+a y k1-y2-b y k2) 2 +(z1+a z k1-z2-b z k2) 2 ;

[0080] Considering that the two stars will not coincide and that their direction finding has errors, the two straight lines used for direction finding are not parallel in most cases. Therefore, the shortest distance between the two direction finding lines can be obtained by differentiating f(k1,k2). So, next, we differentiate the distance f(k1,k2) between any points on the direction finding lines S1P1 and S2P2, and obtain the derivative result:

[0081]

[0082] in,

[0083] Let the parametric equation values ​​of the two endpoints of the shortest distance segments of the direction-finding lines S1P1 and S2P2 be denoted as k1′ and k2′, respectively, and satisfy the following system of equations:

[0084]

[0085] After rearranging the system of equations, we get:

[0086] X×K=Y,

[0087] in, Solving the system of equations yields K = X. -1Y is calculated, and k1′ and k2′ are obtained. Finally, the two endpoints P of the shortest distance line segments of the direction-finding lines S1P1 and S2P2 are obtained. l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 ).

[0088] Then, the direction finding errors α1 and α2 of the two satellites after ground testing or on-orbit testing are obtained.

[0089] Finally, based on the direction finding error and the endpoint, the direction finding error weight is obtained, and the position of the target is finally determined.

[0090] In some embodiments, the specific implementation process of obtaining the direction-finding error weight based on the direction-finding error and the endpoint in this step includes:

[0091] Based on the two endpoints P of the shortest distance line segment between the direction finding lines S1P1 and S2P2 l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 Given the positions of the two satellites, calculate the distances from each satellite to the endpoints of the shortest distance line segment using the following formula:

[0092]

[0093]

[0094] Based on the direction-finding errors α1 and α2 of the two satellites, the satellite's position at point P is calculated using the following formula. l1 and P l2 The direction finding error weight w at the location l1 and w l2 for:

[0095] w l1 =|S1P l1 |tanα1,

[0096] w l2 =|S2P l| |tanα2.

[0097] Determining the position of the target accordingly specifically includes: determining the position P of the target on the shortest distance segment of the two direction-finding lines according to the direction-finding error weight and the following formula. w for:

[0098]

[0099] Among them, P w Represented as P w (x w ,y w ,z w At this point, the execution flow of the dual-satellite joint passive positioning method based on direction-finding error weighting is complete, and the positioning result of the target is obtained. The above-described positioning method does not employ the Earth's spherical constraint equations; that is, the positioning method in this embodiment of the invention can also be applied to other targets, including aerial targets.

[0100] The above-described dual-satellite joint passive positioning method in this embodiment, without adding any on-board equipment, only requires processing and calculating the ground data of the satellites, selecting the target's positioning point on the common perpendicular line of the two satellites' direction-finding lines according to the direction-finding error weights of the two satellites, and realizing high-precision passive positioning of targets, including aerial targets, within the common field of view of the two satellites.

[0101] The following section analyzes and verifies the error of the dual-satellite joint positioning method for aerial targets provided in this embodiment.

[0102] To facilitate the analysis of positioning errors, without loss of generality, it is assumed that the two stars are located in the +Z direction of the Earth-fixed coordinate system. The calculation process for positioning error analysis is as follows:

[0103] (1) Based on the satellite's altitude, set the target to be within the common line of sight of the two satellites;

[0104] (2) The XOY plane of the Earth-fixed coordinate system is divided into grids. Each grid node is projected onto the height of the aerial target to obtain multiple target points. The Z coordinate is calculated based on the XY coordinates (x, y) and height h of each aerial target point:

[0105] Where h is the altitude of the target in the air, and R is the Earth's radius;

[0106] Then, for each aerial target point, perform the following steps to obtain the positioning error of each grid node, including GDOP and GDOP. 高程 GDOP 切线 :

[0107] (3) Based on the positioning results of the two satellites for the target, and the following formula, calculate the elevation angle ε of the straight line formed by the two satellites and the positioning target in the Earth-fixed coordinate system. i and azimuth φ i , i represents the number of satellites, i = 1, 2:

[0108]

[0109] (4) The errors of two satellites in azimuth and elevation angles relative to the target (including the direction-finding errors of the satellite payload and the satellite attitude) are randomly generated according to a normal distribution and denoted as dφ respectively. i and dε i The error is then added to the actual target's elevation and azimuth angles of the binary stars to simulate the direction-finding line obtained for the binary stars and target positioning. i represents the number of satellites, i = 1, 2.

[0110] (5) Based on the azimuth and elevation angles with added errors, calculate the direction cosines of the direction finding lines between the satellite and the positioning target, i.e. (cos(φ1+dφ1)cos(ε1+dε1), cos(φ1+dφ1)sin(ε1+dε1), sin(φ1+dφ1)) and (cos(φ2+dφ2)cos(ε2+dε2), cos(φ2+dφ2)sin(ε2+dε2), sin(φ2+dφ2)).

[0111] (6) Randomly generate the position errors of two satellites according to a normal distribution, respectively [dx] i dy i dz i The error is then added to the actual satellite position to simulate the obtained position of the two satellites, where i represents the number of satellites, i = 1, 2.

[0112] (7) Using the positioning method provided in the embodiments of the present invention, the position P of the target is calculated. w (x w ,y w ,z w The target single positioning error is obtained by comparing it with the true value.

[0113] (8) Repeat steps 5-7 above to obtain N samples at the target location; calculate GDOP and GDOP. 高程 GDOP 切线 :

[0114] The GDOP positioning error is defined as:

[0115] Where (x) wi ,y wi ,z wi (x, y, z) represents the calculated target position, i represents the number of random calculations, and (x, y, z) represents the actual target position.

[0116] like Figure 2 and Figure 4As shown, positioning errors are generally decomposed into elevation errors and horizontal errors. Where r represents the elevation direction from the geocenter to the target, P′ is the true value, and P... wi This is the positioning result of the positioning method in this embodiment. h represents the target height.

[0117] The elevation positioning error GDOP 高程 Calculate using the following formula:

[0118]

[0119] Tangent error GDOP 切线 Calculate using the following formula:

[0120]

[0121] The distance between the two satellites is as follows Figure 3 As shown, assume that both satellites are at an altitude of 500km, the angle θ between them and the Earth's center is 20 degrees, the positioning error of each satellite is 10 meters, and the direction finding errors in azimuth and elevation are both 0.1 degrees. Assume the target is an aerial target at an altitude of 10 kilometers. Calculate 300 times (N=300) for the same grid node, and calculate the positioning error, elevation positioning error, and tangential positioning error according to the relevant formulas mentioned above, as follows: Figure 5 , Figure 6 and Figure 7 As shown in the figure, the dual-satellite joint passive positioning method based on direction-finding error weighting provided by this embodiment of the invention has high target positioning accuracy, can effectively identify aerial targets, and has the capability to locate and identify targets including aerial targets.

[0122] The sequence numbers of the various steps involved in the method of the present invention do not imply the order of execution of the method. The execution order of each step should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0123] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for passive location based on direction finding error weight of double satellites, comprising: Obtain positioning results P1(x p1 ,y p1 ,z p1 ) and P2(x p2 ,y p2 ,z p2 ) of two satellites on the same target at the same time, and obtain positions S1(x1,y1,z1) and S2(x2,y2,z2) of the two satellites at the same time; obtaining direction cosines of direction finding straight lines S1P1 and S2P2 of the target by two satellites according to the location result and positions of the two satellites; According to the direction cosine and the positions of the two satellites, a direction-finding straight line of the target by the two satellites is respectively constructed, and the end point P of the shortest distance line segment of the two direction-finding straight lines is calculated l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 ); obtaining direction finding errors a1 and a2 of the two satellites after ground test or on-orbit test; obtaining a direction finding error weight according to the direction finding error and the end point, and finally determining the position of the target; the step of obtaining the direction cosines of the direction finding straight lines S1P1 and S2P2 of the target by the two satellites according to the location result and the positions of the two satellites comprises: According to the positioning result and the positions of the two satellites, the direction cosines of the straight lines S1P1 and S2P2 of the target, respectively, are obtained according to the following formulas (a x ,a y ,a z ) and (b x ,b y ,b z ): The direction cosine and the position of two satellites are used to construct two direction-finding straight lines of the target by the two satellites respectively, and the end points P of the shortest distance line segment of the two direction-finding straight lines are calculated l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 ) are calculated, including: constructing the direction finding straight lines of the target by the two satellites according to the following formula according to the direction cosines and the positions of the two satellites, defining lengths of the direction finding straight lines S1P1 and S2P2 as l1 and l2 respectively, Among them, the direction cosines of the direction-finding lines S1P1 and S2P2 are respectively (a x ,a y ,a z ) and (b x ,b y ,b z ); expressing distances between any points on the direction finding straight lines S1P1 and S2P2 as the following formula: f(k1, k2) = (x1 + a x k1 - x2 - b x k2) 2 +(y1 + a y k1 - y2 - b y k2) 2 +(z1 + a z k1 - z2 - b z k2) 2 ; deriving the distances f(k1, k2) between any points on the direction finding straight lines S1P1 and S2P2 to obtain a derivation result, wherein recording parameter equation values of two end points of the shortest distance line segment of the direction finding straight lines S1P1 and S2P2 as k1' and k2' respectively, and satisfying the following equation group: obtaining the following equation after arranging the equation group: X x K = Y, wherein, and solving the system of equations gives K = X -1 Y, k1' and k2', and finally the two end points P l1 (x l1 ,y l1 ,z l1 ) and P l2 (x l2 ,y l2 ,z l2 ).

2. The method of claim 1, wherein, the step of obtaining the direction finding error weight according to the direction finding error and the end point comprises: According to the two end points P l1 (x l1 ,y l1 ,z l1 ) of the shortest distance line segment of the direction finding straight lines S1P1 and S2P2 l2 (x l2 ,y l2 ,z l2 ), and the positions of the two satellites, the distances of the satellites to the end points of the shortest distance line segment are respectively calculated according to the following formula: From the direction finding errors α1 and α2 of the two satellites, the direction finding error weights w l1 and w l2 of the satellites at P l1 and P l2 are calculated according to the following equations: w l1 = α1 / (α1 + α2) w l2 = α2 / (α1 + α2) w l1 = |S1P l1 |tanα1, w l2 = |S2P l2 |tanα2.

3. The method of claim 2, wherein, the step of determining the position of the target comprises: According to the direction-finding error weight, the position P of the target is determined on the shortest distance line segment of the two direction-finding straight lines as follows w is: where P w is expressed as P w (x w ,y w ,z w ).

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