Optical single-satellite and double-satellite combined on-board positioning method and system for aerial moving targets

Abstract

The present invention provides an optical single-star and double-star combined on-board positioning method and system for aerial moving targets, comprising: solving a target viewing direction sequence with high time resolution of a local satellite, storing the target viewing direction sequence and the corresponding time and local satellite position; receiving a target viewing direction sequence with low time resolution, time and other satellite position from another satellite, and matching the target viewing direction sequence of the other satellite to the target viewing direction sequence of the local satellite in time and space; solving the three-dimensional position of the target by using the dual-star position and viewing direction matched in time and space, and converting it into the longitude, latitude and elevation of a geodetic coordinate system; interpolating the low-time resolution elevation result obtained by solving the dual-star solution to the time corresponding to the target viewing direction sequence with high time resolution of the local satellite of the same target; solving the three-dimensional position of the target by using the target viewing direction sequence with high time resolution of the local satellite, the local satellite position and the target elevation information, and converting it into the longitude, latitude and elevation of the geodetic coordinate system.

Description

Technical Field

[0001] The present invention relates to the field of target positioning technology, and in particular to an optical single-star and double-star combined on-board positioning method and system for an aerial moving target. Background Art

[0002] With the rapid development of space technology and remote sensing applications, the use of satellites for space-based observation and positioning and tracking of aerial moving targets has become a hot topic in the field of reconnaissance. Compared with ground-based, sea-based and aircraft observations, satellite observation has the advantage of fewer restrictions. As the most widely used technology in the field of remote sensing reconnaissance, optical observation can achieve high spatial resolution, high temporal resolution and wide spectral range observation. For aerial moving targets, the use of optical satellites can achieve target detection on the satellite, and to further track aerial moving targets, it is necessary to accurately locate the targets in three dimensions on the satellite.

[0003] A single optical satellite can only obtain the relative angle information of the target in the sky, but not the distance information, so it is impossible to perform accurate stereo positioning. Through the observation of optical dual-satellite network, the three-dimensional spatial position of the target can be analyzed. The real-time positioning of the target on the satellite is limited by the data transmission capacity between the dual-satellites, so there will be a situation where the time resolution of the target obtained on the local satellite is high but there are few opportunities for dual-satellite positioning.

[0004] Reference 1 (Lin Xueyuan, A Positioning Solution Method for a Dual-Satellite Positioning System, Journal of Wuhan University·Information Science Edition, Vol. 34, No. 5, 2009) discloses an active positioning algorithm, in which the distances from the user to satellites 1 and 2 are obtained by dual-satellite measurement. For the dual-satellite navigation and positioning system, an accurate model of the third observation quantity related to the user's elevation is constructed, and then the dynamic navigation solution positioning algorithm of the system is studied.

[0005] Reference 2 (Lin Xueyuan, Analysis and Research on Baggage Error in Dual-Star Positioning System, Journal of Harbin Institute of Technology, Vol. 41, No. 5, 2009) discloses an active positioning method, in which the user position is solved at the ground control center. Based on the mathematical model of dual-star positioning system, the influence of various measurement errors on the positioning accuracy of the system is analyzed, and the positioning error model of the system under the differential positioning system is derived. The focus is on studying the influence of ephemeris error on its positioning accuracy.

[0006] Reference 3 (Yang Hong, Target Positioning Error Analysis of Binary Star Optical Observation System, Chinese Optics, Vol. 9, No. 4, 2016) discloses a binary star optical observation platform. By modeling the satellite and the optoelectronic observation platform, an observation vector model between the platform and the target in the Earth-inertial system is constructed. Using the geometric positioning algorithm, the target positioning model and positioning error model in the Earth-inertial system are derived, and the positioning error distribution is obtained using the Monte Carlo method. The positioning model is a target positioning method for binary star optical tracking in the Earth-inertial system.

[0007] Reference 4 (Ding Wenzhe, Target Positioning Accuracy Analysis Based on Binary Star Optical Tracking, Acta Astronomica Sinica, Vol. 58, No. 4, 2017) discloses a binary star optical tracking detection system equipped with a two-axis two-frame optoelectronic tracker, and uses the line of sight vector of the satellite-borne observation platform as an intermediate variable to derive the system's positioning model and positioning error model. The positioning model is a target positioning method for binary star optical tracking in the Earth-inertial system.

[0008] Patent document CN108226978A (application number: 201810033790.1) discloses a dual-satellite positioning method based on the WGS-84 model. The invention proposes a closed-form solution method for dual-satellite direction-finding positioning based on the WGS-84 model. By pseudo-linearizing the angle measurement equation and integrating the constraints of the WGS-84 earth ellipsoid model, a closed-form solution method for dual-satellite direction-finding positioning is provided. The positioning solution is realized for the surface target radiation source, and the weighted least squares analytical solution of the target under the constraints of the earth ellipsoid model is provided. The simulation shows that the algorithm can approach the Cramer-Rao lower bound (CRLB) of the positioning error when the system direction-finding error is not particularly large.

[0009] In order to solve the problem of high-time-resolution target positioning on satellite with limited resources, the present invention proposes an optical single-star and double-star combined on-satellite positioning method for aerial moving targets, which obtains high-time-resolution target three-dimensional positioning information by fusing the low-time-resolution target sight direction information obtained by other satellites with the high-time-resolution sight direction information of the local satellite. Summary of the invention

[0010] In view of the defects in the prior art, the object of the present invention is to provide an optical single-star and double-star combined on-board positioning method and system for aerial moving targets.

[0011] According to the present invention, an optical single-star and double-star combined on-board positioning method for an aerial moving target comprises:

[0012] Step S1: Calculate the target viewing sequence of the local satellite with high time resolution, and store the target viewing sequence and the corresponding time and local satellite position;

[0013] Step S2: receiving a low-time-resolution target viewing sequence, time, and position of another satellite from another satellite, and matching the target viewing sequence of another satellite to the target viewing sequence of the local satellite in terms of time and space;

[0014] Step S3: Calculate the three-dimensional position of the target using the binary satellite positions and viewing directions matched in time and space, and convert them into longitude, latitude and elevation of the geodetic coordinate system;

[0015] Step S4: interpolating the low-time-resolution elevation result obtained by binary satellite solution to the time corresponding to the target viewing sequence of the same target local satellite with high time resolution;

[0016] Step S5: Utilize the high temporal resolution target sight sequence of the local satellite, the local satellite position and the target elevation information to calculate the three-dimensional position of the target and convert it into the longitude, latitude and elevation of the geodetic coordinate system.

[0017] Preferably, in step S2, the time matching method is threshold matching, and the exposure time t1 corresponding to the viewing direction of the local star and the exposure time t2 corresponding to the viewing direction of the other star satisfy |t1-t2|≤T time , then the time is considered to match; otherwise, the time is considered to not match; where T time Indicates the set threshold.

[0018] Preferably, in step S2, the spatial matching method is the sameness judgment of the surface inclination difference method, and the local star sight direction that meets the time matching condition is Position of this star Its star direction Its star position When satisfied When , it is considered that both time and space match; where × represents the vector cross multiplication operation, · represents the vector inner product operation, and f norm represents the vector normalization function; T space Indicates the set threshold.

[0019] Preferably, the step S3 adopts: when the positions of the binary stars matched in time and space are The binary star target sight directions are The exposure times corresponding to the binary star viewing directions are t1 and t2 respectively, then the three-dimensional position of the target in the Earth-centered Earth-fixed coordinate system is And the time t corresponding to the current position is calculated by the following formula:

[0020]

[0021] Among them, the distances d1 and d2 satisfy:

[0022]

[0023] Preferably, the longitude, latitude and elevation converted into the geodetic coordinate system adopts: Bowring improved algorithm, with a preset number of iterations, and the conversion relationship is recorded as f Bowing , in, represents latitude; λ represents longitude; h represents altitude; Represents a three-dimensional position in an Earth-centered, Earth-fixed coordinate system.

[0024] Preferably, the step S5 adopts:

[0025] Step S5.1: Based on the location View direction Determine the point on the line closest to the center of the earth

[0026]

[0027] Step S5.2: Calculate the current point elevation h using the Bowring improved algorithm y , when h y >h, it is considered that there is no solution, the no-solution flag is returned and the solution is terminated, otherwise step S5.3 is triggered;

[0028] Step S5.3: Calculate parameters When the parameter C ≥ 0, the viewing direction intersects with the earth ellipse model, and the intersection is taken as the starting point. Otherwise, the nearest point As a starting point starting point satisfy

[0029]

[0030] Among them, the distance d satisfies

[0031]

[0032] Among them, the vector With vector Represents vectors and Element-wise division by vector The result is, a is the major axis of the earth ellipsoid model, b is the minor axis of the earth ellipsoid model, f divide A function that divides corresponding elements of vectors of the same dimension;

[0033]

[0034] Step S5.4: Calculate the first back-off distance D;

[0035]

[0036] in, express The unit external normal at the point;

[0037]

[0038] Step S5.5: Calculate the point after backing off

[0039]

[0040] Step S5.6: Calculate using Bowring's improved algorithm The corresponding longitude λ1, latitude Height h1, when h1-h>T h If the number of iterations is less than or equal to the preset value, step S5.7 is triggered, otherwise the iteration is stopped and the current three-dimensional position is output. And longitude λ1, latitude Height h1, where T h Indicates the elevation threshold;

[0041] Step S5.7: Calculation The external normal of the point corresponding to the earth intersection Update the backoff distance D and the point after backoff After that, repeat the steps S5.5 to S5.6 until the iteration stops and the current three-dimensional position is output. And longitude λ1, latitude Height h1

[0042]

[0043]

[0044] An optical single-star and double-star combined on-board positioning system for aerial moving targets provided by the present invention comprises:

[0045] Module M1: solves the target viewing sequence of the local satellite with high time resolution, and stores the target viewing sequence and the corresponding time and local satellite position;

[0046] Module M2: Receives low-time-resolution target sight sequence, time, and position of other satellites from other satellites, and matches the target sight sequence of other satellites to the target sight sequence of the local satellite in terms of time and space;

[0047] Module M3: Calculate the three-dimensional position of the target using the binary satellite positions and viewing directions matched in time and space, and convert them into longitude, latitude and elevation of the geodetic coordinate system;

[0048] Module M4: interpolate the low-time-resolution elevation results obtained by binary satellite solution to the time corresponding to the target viewing sequence of the same target satellite with high time resolution;

[0049] Module M5: Utilize the high-temporal-resolution target sight sequence, the satellite position and the target elevation information to calculate the target's three-dimensional position and convert it into the longitude, latitude and elevation of the geodetic coordinate system.

[0050] Preferably, the module M2 adopts: the time matching method is threshold matching, and the exposure time t1 corresponding to the viewing direction of the local star and the exposure time t2 corresponding to the viewing direction of the other star satisfy |t1-t2|≤T time , then the time is considered to match; otherwise, the time is considered to not match; where T time Indicates the set threshold;

[0051] The module M2 adopts: the spatial matching method is the surface inclination difference method identity judgment, and the local star line of sight that meets the time matching conditions Position of this star Its star direction Its star position When satisfied When , it is considered that both time and space match; where × represents the vector cross multiplication operation, · represents the vector inner product operation, and f norm represents the vector normalization function; T space Indicates the set threshold.

[0052] Preferably, the module M3 adopts: when the positions of the binary satellites matched in time and space are The binary star target sight directions are The exposure times corresponding to the binary star viewing directions are t1 and t2 respectively, then the three-dimensional position of the target in the Earth-centered Earth-fixed coordinate system is And the time t corresponding to the current position is calculated by the following formula:

[0053]

[0054] Among them, the distances d1 and d2 satisfy:

[0055]

[0056] The longitude, latitude and elevation converted to the geodetic coordinate system adopts: Bowring improved algorithm, with a preset number of iterations, and the conversion relationship is recorded as f Bowing , in, represents latitude; λ represents longitude; h represents altitude; Represents a three-dimensional position in an Earth-centered, Earth-fixed coordinate system.

[0057] Preferably, the module M5 adopts:

[0058] Module M5.1: By location View direction Determine the point on the line closest to the center of the earth

[0059]

[0060] Module M5.2: Calculate the current point elevation h using the Bowring improved algorithm y , when h y >h, it is considered that there is no solution, the no-solution flag is returned and the solution is terminated, otherwise module M5.3 is triggered;

[0061] Module M5.3: Calculation parameters When the parameter C ≥ 0, the viewing direction intersects with the earth ellipse model, and the intersection is taken as the starting point. Otherwise, the nearest point As a starting point starting point satisfy

[0062]

[0063] Among them, the distance d satisfies

[0064]

[0065] Among them, the vector With vector Represents vectors and Element-wise division by vector The result is, a is the major axis of the earth ellipsoid model, b is the minor axis of the earth ellipsoid model, f divide A function that divides corresponding elements of vectors of the same dimension;

[0066]

[0067] Module M5.4: Calculate the first retreat distance D;

[0068]

[0069] in, express The unit external normal at the point;

[0070]

[0071] Module M5.5: Calculate the point after fallback

[0072]

[0073] Module M5.6: Using Bowring to improve algorithm calculation The corresponding longitude λ1, latitude Height h1, when h1-h>T h If the number of iterations is less than or equal to the preset value, module M5.7 is triggered, otherwise the iteration is stopped and the current three-dimensional position is output. And longitude λ1, latitude Height h1, where T h Indicates the elevation threshold;

[0074] Module M5.7: Computing The external normal of the point corresponding to the earth intersection Update the backoff distance D and the point after backoff After that, repeatedly trigger module M5.5 to module M5.6 until the iteration stops and the current three-dimensional position is output. And longitude λ1, latitude Height h1

[0075]

[0076]

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] The present invention can use the high time resolution target sight sequence of the own satellite and the low time resolution target sight sequence of other satellites to match the target and accurately locate the target with high time resolution, which is suitable for on-board real-time processing. The method of the present invention is reasonable, simple in calculation and easy in implementation, and can be widely used in the on-board positioning of optical single-star and double-star combined targets in the air. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0080] Figure 1 It is a flow chart of the present invention.

[0081] Figure 2 It is a schematic diagram of the algorithm iteration principle of the present invention.

[0082] Figure 3 It is the distance between the target three-dimensional position calculated by the method of the present invention and the known real three-dimensional position of the target when there is no error in the input data source.

[0083] Figure 4It is the distance between the target three-dimensional position calculated by the method of the present invention when the input data source contains errors and the known real three-dimensional position of the target. DETAILED DESCRIPTION

[0084] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0085] Example 1

[0086] The technical problem to be solved by the present invention is to provide an optical single-star and double-star combined on-board positioning method for aerial moving targets, which can fully utilize the double-star observation data to perform three-dimensional positioning of the target with high time resolution.

[0087] The flow chart of the optical single-star and double-star combined on-board positioning method for aerial moving targets of the present invention is as follows: Figure 1 As shown. After the optical single satellite detects and identifies the target, the relative angle information of the target at the exposure time can be obtained. First, the high-time resolution target viewing sequence of the local satellite is solved on the satellite, and the target viewing sequence and the corresponding time and local satellite position are stored; at the same time, the low-time resolution target viewing sequence, time, and other satellite position from other satellites are received. The viewing sequence and satellite position are defined in the Earth-centered Earth-fixed coordinate system, and the viewing directions are all normalized unit vectors.

[0088] The targets processed by the two stars are independent in time and space, so it is necessary to match the target sequence of the other star to the target sequence of this star in time and space.

[0089] The present invention provides an optical single-star and double-star combined on-board positioning method for an aerial moving target, comprising the following steps:

[0090] Step 1: Calculate the high-time resolution target sight sequence of the local satellite, store the target sight sequence and the corresponding time and local satellite position; and receive the low-time resolution target sight sequence, time and other satellite position from other satellites. The sight sequence and satellite position are defined in the Earth-centered Earth-fixed coordinate system, and the sight direction is a normalized unit vector.

[0091] Step 2: Match the target sequence of other stars to the target sequence of this star in time and space.

[0092] Step 3: Use the time and space matching binary satellite positions and viewing directions to solve the three-dimensional position of the target and convert it into the longitude, latitude, and elevation of the geodetic coordinate system.

[0093] Step 4: interpolate the low-time-resolution elevation results obtained by binary satellite solution to the time corresponding to the target viewing sequence of the same target satellite with high resolution.

[0094] Step 5: Use the high-temporal-resolution target viewing sequence of the local satellite, the local satellite position and the target elevation information to calculate the three-dimensional position of the target and convert it into the longitude, latitude and elevation of the geodetic coordinate system.

[0095] Specifically, the time matching method in step 2 is threshold matching, that is, the exposure time t corresponding to the local star’s viewing direction is I The exposure time t corresponding to the star's viewing direction II If satisfied

[0096] |t I -t II |≤T time (Formula 1)

[0097] The time is considered to match. time is the threshold value set, without loss of generality, we can take T time Equal to half of the nominal exposure interval of the optical camera of this star.

[0098] Specifically, the spatial matching method in step 2 is the identity judgment of the surface inclination difference method, that is, the local star line of sight that meets the time matching condition is Position of this star Its star direction Its star position If satisfied

[0099]

[0100] It is considered that both time and space are matched. Where × represents the vector cross multiplication operation, · represents the vector inner product operation, and f norm is the vector normalization function, T space is the threshold value set, without loss of generality, we can take T space =Δ 2 / 2, Δ is the nominal pointing accuracy of a single star.

[0101] Specifically, in step 3, if the binary star positions that match in time and space are The binary star target sight directions are The exposure times corresponding to the binary star viewing directions are t I ,t II , then the three-dimensional position of the target in the Earth-centered Earth-fixed coordinate system is And the time t corresponding to this position is calculated by the following formula:

[0102]

[0103] Among them, the distance d I ,d II satisfy

[0104]

[0105] Specifically, in step 3 and step 5, the three-dimensional position of the Earth-centered Earth-fixed coordinate system is (a vector containing three elements, each element is in meters) converted to the longitude λ (unit: radians, ranging from -π to π) and latitude of the geodetic coordinate system The method of calculating the height h (unit: radian, value range -π / 2~π / 2) and the height h (unit: m) is the Bowring improved algorithm, and the maximum number of iterations is set to 3. The conversion relationship is recorded as f Bowing ,Right now

[0106] The low-time-resolution elevation results obtained by solving the binary satellite solution are interpolated to the time corresponding to the target viewing sequence of the same target star with high resolution, thereby making up for the defect that single-star observation lacks distance information and is insufficient for three-dimensional positioning.

[0107] Specifically, in step 5, the high-time-resolution target viewing sequence of the local star is Position of this star The three-dimensional position of the target is calculated by combining the target elevation information h, which is essentially the distance information of the target. The method includes the following steps:

[0108] The target sight sequence, the position of the satellite and the target elevation information with high temporal resolution are difficult to obtain through analytical expression of distance solution. Therefore, an iterative approximation solution is adopted. First, a starting point is constructed, and then the target elevation is gradually approached, such as Figure 2 shown.

[0109] Step 5.1, considering that there may be non-ideal factors such as false detection in the on-board calculation, we first determine the existence of the solution before solving it, and calculate the position View direction The closest point to the center of the earth Right now

[0110]

[0111] Step 5.2: Calculate the elevation h of the point using the Bowring improved algorithm y , if h y >h, it is considered that there is no solution, the no-solution flag is returned and the solution is terminated; otherwise, execute step 5.3.

[0112] Step 5.3, when the viewing direction intersects with the earth ellipsoid model, the starting point can be selected as the intersection point as the starting point Otherwise, the closest point to the center of the earth is the straight line determined by the satellite position and the target line of sight. As a starting point Whether the target viewing direction intersects with the earth ellipsoid model is determined by calculating the parameters If the parameter C ≥ 0, the viewing direction intersects with the earth ellipsoid model, and the intersection is taken as the starting point. Otherwise, the nearest point As a starting point Starting point satisfy

[0113]

[0114] Among them, the distance d satisfies

[0115]

[0116] vector With vector Respectively, vector and Element-wise division by vector The result is, a is the major axis of the earth ellipsoid model, b is the minor axis of the earth ellipsoid model, f divide is a function that divides corresponding elements of vectors of the same dimension.

[0117]

[0118] Step 5.4, such as Figure 2 As shown, when the viewing direction intersects the earth ellipsoid model, the first retreat distance D is calculated.

[0119] When the viewing direction has no intersection with the Earth ellipsoid, select the maximum possible distance As the first retreat distance.

[0120]

[0121] in for The unit external normal at the point,

[0122]

[0123] Step 5.5, calculate the point after retreat

[0124]

[0125] Step 5.6, use Bowring's improved algorithm to calculate The corresponding longitude λ1, latitude Height h1, the point after the first retreat The corresponding elevation is greater than or equal to h, when h1-h≤T h (T h is the elevation threshold, which can be set to 10 -8 ) can be considered that the point That is the target position point, stop iteration, and output the current three-dimensional position And longitude λ1, latitude Height h1;

[0126] Step 5.7, when h1-h>T h When , the retreat distance D needs to be updated to approach the target elevation. Figure 2 As shown, calculation The external normal of the point corresponding to the earth intersection

[0127]

[0128] Step 5.8, update the backoff distance D and the point after backoff Then repeat steps 5.5 to 5.6.

[0129]

[0130] Update according to (Formula 11) Then the elevation is recalculated and compared with the threshold. The maximum number of iterations is set to 5 based on the actual convergence speed and to avoid repeated cycles during on-board calculations.

[0131] The method proposed in the present invention is verified in conjunction with the STK simulation scenario. In the simulation, the high-time-resolution view of the local satellite is updated at 10 Hz, while the data of other satellites is updated at 1 Hz. Two groups of aerial target (aircraft) positioning are simulated respectively. The first group of optical star view and position are error-free, which is used to verify the error introduced by the method. In the second group of simulations, error terms are added to the target view and satellite position obtained by the local satellite and other satellites to simulate the actual situation and verify the adaptability of the algorithm to the real scene. The Euclidean distance between the target three-dimensional position calculated by the method of the present invention and the known real three-dimensional position of the target is used as an evaluation index. When the first group of view and position are error-free, the Euclidean distance between the calculated position and the real position is as shown in the attached figure. Figure 3 As shown, the error is better than 10 -5 The second group adds a random error of 70 μrad to the direction of the local star and other stars, and a random error of 50m to the position of the local star and other stars. The distance between the target three-dimensional position updated at 10Hz and the actual position is shown in the attached figure. Figure 4 The results show that the positioning error introduced by the method of the present invention itself is extremely small, and the error of the final positioning result mainly comes from the error of the input data source. The method of the present invention can be applied to the optical single-star and double-star combined on-board positioning of aerial moving targets.

[0132] The present invention provides an optical single-star and double-star combined on-board positioning system for aerial moving targets, comprising:

[0133] Module 1 solves the high-time-resolution target sight sequence of the local satellite, stores the target sight sequence and the corresponding time and local satellite position; and receives the low-time-resolution target sight sequence, time and other satellite position from other satellites. The sight sequence and satellite position are defined in the Earth-centered Earth-fixed coordinate system, and the sight direction is a normalized unit vector.

[0134] Module 2 matches the target sequence of other stars to the target sequence of this star in time and space.

[0135] Module 3 uses the time and space matching binary satellite positions and viewing directions to solve the three-dimensional position of the target and convert it into the longitude, latitude and elevation of the geodetic coordinate system.

[0136] Module 4 interpolates the low-time-resolution elevation results obtained by binary satellite solution to the time corresponding to the target viewing sequence of the same target satellite with high resolution.

[0137] Module 5 uses the high-temporal-resolution target viewing sequence of the local satellite, the local satellite position and the target elevation information to calculate the three-dimensional position of the target and convert it into the longitude, latitude and elevation of the geodetic coordinate system.

[0138] Specifically, the time matching method in module 2 is threshold matching, that is, the exposure time t corresponding to the local star’s viewing direction I The exposure time t corresponding to the star's viewing direction II If satisfied

[0139] |t I -t II |≤T time (Formula 1)

[0140] The time is considered to match. time is the threshold value set, without loss of generality, we can take T time Equal to half of the nominal exposure interval of the optical camera of this star.

[0141] Specifically, the spatial matching method in module 2 is the identity judgment of the surface inclination difference method, that is, the viewing direction of the local star that meets the time matching conditions is Position of this star Its star direction Its star position If satisfied

[0142]

[0143] It is considered that both time and space are matched. Where × represents the vector cross multiplication operation, · represents the vector inner product operation, and f norm is the vector normalization function, T space is the threshold value set, without loss of generality, we can take T space =Δ 2 / 2, Δ is the nominal pointing accuracy of a single star.

[0144] Specifically, in module 3, if the binary star positions that match in time and space are The binary star target sight directions are The exposure times corresponding to the binary star viewing directions are t I ,t II , then the three-dimensional position of the target in the Earth-centered Earth-fixed coordinate system is And the time t corresponding to this position is calculated by the following formula:

[0145]

[0146] Among them, the distance d I ,d II satisfy

[0147]

[0148] Specifically, in the modules 3 and 5, the three-dimensional position of the Earth-centered Earth-fixed coordinate system is (a vector containing three elements, each element is in meters) converted to the longitude λ (unit: radians, ranging from -π to π) and latitude of the geodetic coordinate system The method of calculating the height h (unit: radian, value range -π / 2~π / 2) and the height h (unit: m) is the Bowring improved algorithm, and the maximum number of iterations is set to 3. The conversion relationship is recorded as f Bowing ,Right now

[0149] The low-time-resolution elevation results obtained by solving the binary satellite solution are interpolated to the time corresponding to the target viewing sequence of the same target star with high resolution, thereby making up for the defect that single-star observation lacks distance information and is insufficient for three-dimensional positioning.

[0150] Specifically, in module 5, the high-time-resolution target viewing sequence of the local satellite is Position of this star The three-dimensional position of the target is calculated with the target elevation information h, which is essentially the distance information of the target. The method includes the following modules:

[0151] The target sight sequence, the position of the satellite and the target elevation information with high temporal resolution are difficult to obtain through analytical expression of distance solution. Therefore, an iterative approximation solution is adopted. First, a starting point is constructed, and then the target elevation is gradually approached, such as Figure 2 shown.

[0152] Module 5.1, considering the possible non-ideal factors such as false detection in satellite calculations, we first determine the existence of the solution before solving it, and calculate the position View direction The closest point to the center of the earth Right now

[0153]

[0154] Module 5.2, use Bowring's improved algorithm to calculate the elevation h of the point y , if h y >h, it is considered that there is no solution, the no-solution flag is returned and the solution is terminated, otherwise, module 5.3 is executed.

[0155] Module 5.3, when the viewing direction intersects with the earth ellipsoid model, the starting point can be selected as the intersection point as the starting point Otherwise, the closest point to the center of the earth is the straight line determined by the satellite position and the target line of sight. As a starting point Whether the target viewing direction intersects with the earth ellipsoid model is determined by calculating the parameters If the parameter C ≥ 0, the viewing direction intersects with the earth ellipsoid model, and the intersection is taken as the starting point. Otherwise, the nearest point As a starting point Starting point satisfy

[0156]

[0157] Among them, the distance d satisfies

[0158]

[0159] vector With vector Respectively, vector and Element-wise division by vector The result is, a is the major axis of the earth ellipsoid model, b is the minor axis of the earth ellipsoid model, f divide is a function that divides corresponding elements of vectors of the same dimension.

[0160]

[0161] Module 5.4, such as Figure 2As shown, when the viewing direction intersects the earth ellipsoid model, the first retreat distance D is calculated.

[0162] When the viewing direction has no intersection with the Earth ellipsoid, select the maximum possible distance As the first retreat distance.

[0163]

[0164] in for The unit external normal at the point,

[0165]

[0166] Module 5.5, Calculate the point after fallback

[0167]

[0168] Module 5.6, using Bowring to improve the algorithm calculation The corresponding longitude λ1, latitude Height h1, the point after the first retreat The corresponding elevation is greater than or equal to h, when h1-h≤T h (T h is the elevation threshold, which can be set to 10 -8 ) can be considered that the point That is the target position point, stop iteration, and output the current three-dimensional position And longitude λ1, latitude Height h1;

[0169] Module 5.7, when h1-h>T h When , the retreat distance D needs to be updated to approach the target elevation. Figure 2 As shown, calculation The external normal of the point corresponding to the earth intersection

[0170]

[0171] Module 5.8, update the backoff distance D and the point after backoff Then repeat module 5.5 to module 5.6.

[0172]

[0173] Update according to (Formula 11) Then the elevation is recalculated and compared with the threshold. The maximum number of iterations is set to 5 based on the actual convergence speed and to avoid repeated cycles during on-board calculations.

[0174] The method proposed in the present invention is verified in conjunction with the STK simulation scenario. In the simulation, the high-time-resolution view of the local satellite is updated at 10 Hz, while the data of other satellites is updated at 1 Hz. Two groups of aerial target (aircraft) positioning are simulated respectively. The first group of optical star view and position are error-free, which is used to verify the error introduced by the method. In the second group of simulations, error terms are added to the target view and satellite position obtained by the local satellite and other satellites to simulate the actual situation and verify the adaptability of the algorithm to the real scene. The Euclidean distance between the target three-dimensional position calculated by the method of the present invention and the known real three-dimensional position of the target is used as an evaluation index. When the first group of view and position are error-free, the Euclidean distance between the calculated position and the real position is as shown in the attached figure. Figure 3 As shown, the error is better than 10 -5 The second group adds a random error of 70 μrad to the direction of the local star and other stars, and a random error of 50m to the position of the local star and other stars. The distance between the target three-dimensional position updated at 10Hz and the actual position is shown in the attached figure. Figure 4 The results show that the positioning error introduced by the method of the present invention itself is extremely small, and the error of the final positioning result mainly comes from the error of the input data source. The method of the present invention can be applied to the optical single-star and double-star combined on-board positioning of aerial moving targets.

[0175] Those skilled in the art know that, in addition to implementing the system, device and its various modules provided by the present invention in a purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps. Therefore, the system, device and its various modules provided by the present invention can be considered as a hardware component, and the modules included therein for implementing various programs can also be considered as structures within the hardware component; the modules for implementing various functions can also be considered as both software programs for implementing the method and structures within the hardware component.

[0176] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. An optical single-star and double-star combined on-board positioning method for aerial moving targets, characterized in that: include: Step S1: Calculate the target viewing sequence of the local satellite with high time resolution, and store the target viewing sequence and the corresponding time and local satellite position; Step S2: receiving a low-time-resolution target viewing sequence, time, and position of another satellite from another satellite, and matching the target viewing sequence of another satellite to the target viewing sequence of the local satellite in terms of time and space; Step S3: Calculate the three-dimensional position of the target using the binary satellite positions and viewing directions matched in time and space, and convert them into longitude, latitude and elevation of the geodetic coordinate system; Step S4: interpolating the low-time-resolution elevation result obtained by binary satellite solution to the time corresponding to the target viewing sequence of the same target local satellite with high time resolution; Step S5: Calculate the three-dimensional position of the target using the high-temporal-resolution target viewing sequence of the local satellite, the local satellite position and the target elevation information, and convert it into the longitude, latitude and elevation of the geodetic coordinate system; The step S5 adopts: Step S5.1: Based on the location View direction Determine the point on the line closest to the center of the earth Step S5.2: Calculate the current point elevation h using the Bowring improved algorithm y , when h y >h, it is considered that there is no solution, the no-solution flag is returned and the solution is terminated, otherwise step S5.3 is triggered; Step S5.3: Calculate parameters When the parameter C ≥ 0, the viewing direction intersects with the earth ellipse model, and the intersection is taken as the starting point. Otherwise, the nearest point As a starting point starting point satisfy Among them, the distance d satisfies Among them, the vector With vector Represents vectors and Element-wise division by vector The result is, a is the major axis of the earth ellipsoid model, b is the minor axis of the earth ellipsoid model, f divide A function that divides corresponding elements of vectors of the same dimension; Step S5.4: Calculate the first back-off distance D; in, express The unit external normal at the point; Step S5.5: Calculate the point after backing off Step S5.6: Calculate using Bowring's improved algorithm The corresponding longitude λ1, latitude Height h1, when h1-h>T h If the number of iterations is less than or equal to the preset value, step S5.7 is triggered, otherwise the iteration is stopped and the current three-dimensional position is output. And longitude λ1, latitude Height h1, where T h Indicates the elevation threshold; Step S5.7: Calculation The external normal of the point corresponding to the earth intersection Update the backoff distance D and the point after backoff After that, repeat the steps S5.5 to S5.6 until the iteration stops and the current three-dimensional position is output. And longitude λ1, latitude Height h1 2. The optical single-star and double-star combined on-board positioning method for aerial moving targets according to claim 1 is characterized in that: In step S2, the time matching method is threshold matching, and the exposure time t1 corresponding to the viewing direction of the local star and the exposure time t2 corresponding to the viewing direction of the other star satisfy |t1-t2|≤T time , then the time is considered to match; otherwise, the time is considered to not match; where T time Indicates the set threshold.

3. The optical single-star and double-star combined on-board positioning method for aerial moving targets according to claim 1 is characterized in that: In step S2, the spatial matching method is the same as the surface inclination difference method, and the local star sight direction that meets the time matching condition is Position of this star Its star direction Its star position When satisfied When , it is considered that both time and space match; where × represents the vector cross multiplication operation, · represents the vector inner product operation, and f norm represents the vector normalization function; T space Indicates the set threshold.

4. The optical single-star and double-star combined on-board positioning method for aerial moving targets according to claim 1 is characterized in that: The step S3 adopts: when the positions of the binary stars matching in time and space are The binary star target sight directions are The exposure times corresponding to the binary star viewing directions are t1 and t2 respectively, then the three-dimensional position of the target in the Earth-centered Earth-fixed coordinate system is And the time t corresponding to the current position is calculated by the following formula: Among them, the distances d1 and d2 satisfy:

5. The optical single-star and double-star combined on-board positioning method for aerial moving targets according to claim 1, characterized in that: The longitude, latitude and elevation converted to the geodetic coordinate system adopts: Bowring improved algorithm, preset number of iterations, and the conversion relationship is recorded as f Bowing , in, represents latitude; λ represents longitude; h represents altitude; Represents a three-dimensional position in an Earth-centered, Earth-fixed coordinate system.

6. An optical single-star and double-star combined on-board positioning system for aerial moving targets, characterized in that: include: Module M1: solves the target viewing sequence of the local satellite with high time resolution, and stores the target viewing sequence and the corresponding time and local satellite position; Module M2: Receives low-time-resolution target sight sequence, time, and position of other satellites from other satellites, and matches the target sight sequence of other satellites to the target sight sequence of the local satellite in terms of time and space; Module M3: Calculate the three-dimensional position of the target using the binary satellite positions and viewing directions matched in time and space, and convert them into longitude, latitude and elevation of the geodetic coordinate system; Module M4: interpolate the low-time-resolution elevation results obtained by binary satellite solution to the time corresponding to the target viewing sequence of the same target satellite with high time resolution; Module M5: Utilize the high-temporal-resolution target sight sequence, the position of the satellite and the target elevation information to calculate the three-dimensional position of the target and convert it into the longitude, latitude and elevation of the geodetic coordinate system; The module M5 adopts: Module M5.1: By location View direction Determine the point on the line closest to the center of the earth Module M5.2: Calculate the current point elevation h using the Bowring improved algorithm y , when h y >h, it is considered that there is no solution, the no-solution flag is returned and the solution is terminated, otherwise module M5.3 is triggered; Module M5.3: Calculation parameters When the parameter C ≥ 0, the viewing direction intersects with the earth ellipse model, and the intersection is taken as the starting point. Otherwise, the nearest point As a starting point starting point satisfy Among them, the distance d satisfies Among them, the vector With vector Represents vectors and Element-wise division by vector The result is, a is the major axis of the earth ellipsoid model, b is the minor axis of the earth ellipsoid model, f divide A function that divides corresponding elements of vectors of the same dimension; Module M5.4: Calculate the first retreat distance D; in, express The unit external normal at the point; Module M5.5: Calculating the point after fallback Module M5.6: Using Bowring to improve algorithm calculation The corresponding longitude λ1, latitude Height h1, when h1-h>T h If the number of iterations is less than or equal to the preset value, module M5.7 is triggered, otherwise the iteration is stopped and the current three-dimensional position is output. And longitude λ1, latitude Height h1, where T h Indicates the elevation threshold; Module M5.7: Computing The external normal of the point corresponding to the earth intersection Update the backoff distance D and the point after backoff After that, repeatedly trigger module M5.5 to module M5.6 until the iteration stops and the current three-dimensional position is output. And longitude λ1, latitude Height h1 7. The optical single-star and double-star combined on-board positioning system for aerial moving targets according to claim 6, characterized in that: The module M2 adopts: the time matching method is threshold matching, and the exposure time t1 corresponding to the viewing direction of the local star and the exposure time t2 corresponding to the viewing direction of the other star satisfy |t1-t2|≤T time , then the time is considered to match; otherwise, the time is considered to not match; where T time Indicates the set threshold; The module M2 adopts: the spatial matching method is the surface inclination difference method identity judgment, and the local star line of sight that meets the time matching conditions Position of this star Its star direction Its star position When satisfied When , it is considered that both time and space match; where × represents the vector cross multiplication operation, · represents the vector inner product operation, and f norm represents the vector normalization function; T space Indicates the set threshold.

8. The optical single-star and double-star combined on-board positioning system for aerial moving targets according to claim 6, characterized in that: The module M3 adopts: when the time and space matching binary star positions are The binary star target sight directions are The exposure times corresponding to the binary star viewing directions are t1 and t2 respectively, then the three-dimensional position of the target in the Earth-centered Earth-fixed coordinate system is And the time t corresponding to the current position is calculated by the following formula: Among them, the distances d1 and d2 satisfy: The longitude, latitude and elevation converted to the geodetic coordinate system adopts: Bowring improved algorithm, with a preset number of iterations, and the conversion relationship is recorded as f Bowing , in, represents latitude; λ represents longitude; h represents altitude; Represents a three-dimensional position in an Earth-centered, Earth-fixed coordinate system.

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