A heterogeneous airspace distributed aircraft cluster cooperative navigation optimization method

Abstract

The application discloses a kind of aircraft cluster cooperative navigation optimization methods of different space distribution, according to the different three-dimensional space relative position distribution in cluster each aircraft, different space distribution aircraft cluster is divided, first, low altitude aircraft in different configuration under satellite denial area outside middle, low altitude aircraft in satellite denial area in the positioning accuracy of auxiliary area, determine the optimized middle, low altitude aircraft cluster configuration, keep its configuration unchanged in flight process, analyze the cooperative positioning performance of high altitude aircraft cluster in different configuration to middle air layer aircraft, obtain the final optimization configuration of different space distribution aircraft cluster, on this basis, construct cooperative navigation model, and obtain the final cooperative positioning result of solution.Compared with the cooperative positioning method without considering the aircraft different space distribution and configuration optimization, the positioning accuracy of the aircraft to be assisted in the application is more optimal, and more in line with the actual application scenario.

Description

Technical Field

[0001] This invention relates to the field of positioning and navigation technology, and in particular to an optimization method for cooperative navigation of aircraft swarms distributed in different airspaces. Background Technology

[0002] Aircraft swarms possess numerous advantages, including a wide operating range, high reliability, and high overall efficiency, making them suitable for a wide range of applications. However, aircraft swarms typically consist of multiple aircraft of different functions and types flying in formation. The varying navigation performance between these aircraft can cause some with less accurate onboard navigation equipment to be unable to autonomously complete navigation tasks, thus affecting the overall operation of the aircraft swarm.

[0003] Furthermore, to address the negative impact of satellite denial environments on the navigation and positioning accuracy of aircraft, they need to rely on other aircraft as navigation and positioning benchmarks to obtain relative navigation data information among aircraft for collaborative navigation and positioning. Therefore, researching navigation optimization theories for aircraft swarms and expanding the application scenarios of collaborative navigation technology for aircraft swarms is an important trend in the future development of aircraft swarm navigation technology. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide an optimized method for cooperative navigation of aircraft swarms distributed in different airspaces. This method can overcome the problem of increased aircraft positioning errors caused by the decrease in satellite navigation accuracy in satellite-denied areas. Furthermore, it optimizes the configuration of aircraft swarms in different airspaces to improve the practicality of cooperative navigation and positioning algorithms for swarm aircraft in different scenarios and enhance positioning accuracy. This allows for better navigation and positioning services even when some aircraft in the swarm enter satellite-denied areas.

[0005] Technical solution: The aircraft swarm cooperative navigation optimization method of the present invention includes the following steps:

[0006] S1: Obtain the latitude, longitude, and altitude coordinates of each aircraft in a cluster of aircraft distributed in different airspaces, as well as their position coordinates, speed, and the accuracy of their own onboard navigation equipment in the ECEF coordinate system.

[0007] S2. Based on the relative positional relationships of the aircraft clusters distributed in different airspaces and the functions and types of the aircraft in the clusters, the aircraft clusters distributed in different airspaces are divided, the number of aircraft in each cluster and their distribution airspace are determined, the satellite denial area and the coordinates of the sampling points in the satellite denial area are determined, and the initial longitude, latitude and altitude coordinate range of the sampling points in each defined airspace and satellite denial area are transformed to the ECEF coordinate system.

[0008] S3, based on satellite denial zone Z targetThe objective function of the internal TD-GDOP value design is the optimization criterion. It comprehensively optimizes the configuration of the mid- and low-altitude vehicle clusters outside the satellite denial area, keeps the configuration of the mid- and low-altitude vehicle clusters unchanged during flight, and provides navigation assistance for low-altitude vehicles entering the satellite denial area.

[0009] S4. Based on step S3, the objective function designed based on the TD-GDOP value in the airspace where the mid-altitude vehicle cluster is distributed is used as the optimization criterion to obtain the optimized configuration of the high-altitude vehicle cluster, thereby obtaining the final optimized configuration of the heterogeneous airspace distributed vehicle cluster.

[0010] S5: Obtain the position information and relative distance data of aircraft in different airspaces, select the primary and secondary reference aircraft respectively, establish a relative coordinate system with the primary reference aircraft as the coordinate origin, and construct a cooperative navigation model based on the TDOA principle;

[0011] S6. Using a cooperative positioning algorithm based on spherical interpolation, the cooperative navigation model based on the TDOA principle is solved to obtain the position coordinates of the aircraft to be assisted in the middle and low altitude layers in the relative coordinate system.

[0012] S7. Based on the position coordinates of the aircraft to be assisted in the relative coordinate system calculated in step S6, convert them to the three-dimensional Earth coordinate system and convert them into longitude, latitude and altitude data. Establish a filtering equation to correct the airborne position coordinates of the aircraft to be assisted in the middle and low altitude layers.

[0013] S8, determine whether the aircraft's navigation position coordinates have been corrected. If corrected, navigation ends; otherwise, repeat step S2. In step S2, determine the number of aircraft in each cluster and their distribution airspace, determine the satellite denial area and the coordinates of sampling points in the satellite denial area; transform the initial longitude, latitude, and altitude coordinate ranges of the sampling points in each defined airspace and satellite denial area to the ECEF coordinate system. The detailed implementation steps are as follows:

[0014] S21. Based on the relative positional relationship of the aircraft clusters in different airspaces, the airspace where the aircraft are distributed is divided into the altitude direction and the forward direction of the aircraft clusters. Based on the three relative altitude relationships of high, medium and low altitudes and the two relative positional relationships of front and rear, six relative positional relationships between aircraft clusters are obtained. The high, medium and low altitude layers where the aircraft clusters are located correspond to the subscripts A, B and C, respectively. The front and rear relationships between aircraft clusters are represented by the superscript k. The larger the value of k, the further back the relative position of the aircraft cluster is.

[0015] S22 defines a cluster of high-altitude aircraft. The number of medium-sized aircraft is The corresponding airspace for the aircraft cluster distribution is

[0016]

[0017] Wherein, λ, L, and H represent the longitude, latitude, and altitude coordinates of the aircraft cluster, respectively; These represent the minimum and maximum longitude coordinates of the high-altitude aircraft cluster, respectively. These represent the minimum and maximum latitudinal coordinates of the high-altitude aircraft cluster, respectively. These represent the minimum and maximum altitude coordinates of the high-altitude spacecraft cluster, respectively; the high-altitude spacecraft cluster It utilizes its own high-precision airborne navigation equipment for inertial / satellite combined navigation and provides cooperative navigation assistance for mid-altitude spacecraft clusters;

[0018] S23, defines mid-altitude spacecraft clusters The number of medium-sized aircraft is The corresponding airspace for the aircraft cluster distribution is

[0019]

[0020] These represent the minimum and maximum longitude coordinates of the mid-altitude spacecraft cluster, respectively. These represent the minimum and maximum latitudinal coordinates of the mid-level spacecraft cluster, respectively. These represent the minimum and maximum altitude coordinates of the atrium spacecraft cluster, respectively; the atrium spacecraft cluster It utilizes its own airborne navigation equipment to conduct cooperative navigation with high-altitude aircraft clusters and provides cooperative navigation assistance to low-altitude aircraft clusters.

[0021] S24 defines a low-altitude aircraft cluster. The number of medium-sized aircraft is The corresponding airspace for the aircraft cluster distribution is

[0022]

[0023] These represent the minimum and maximum longitude coordinates of the low-altitude aircraft cluster, respectively. These represent the minimum and maximum latitudinal coordinates of the low-altitude aircraft cluster, respectively. These represent the minimum and maximum altitude coordinates of a low-altitude aircraft cluster, respectively; low-altitude aircraft cluster It utilizes its own airborne navigation equipment to conduct cooperative navigation with the mid-altitude spacecraft cluster, and provides cooperative navigation assistance to the low-altitude spacecraft cluster that has entered the satellite denial zone ahead;

[0024] S25, low-altitude aircraft cluster In The aircraft entered the satellite denial zone Z during flight. target At that time, its satellite navigation system was unavailable, and it needed to use the adjacent mid-altitude spacecraft cluster. low-altitude aircraft cluster The spacecraft in the region provides cooperative navigation assistance, and the satellite denial zone Z target Let it be a semi-ellipsoid, defined as follows:

[0025]

[0026] Where, (λ target ,L target H target Z is the satellite denial zone. target The coordinates of any point within the interior, including latitude, longitude, and altitude, are represented by the axis. λ axis L axis H Satellite Denial Zone Z target Axial length in the directions of longitude, latitude, and altitude;

[0027] S26 will define the airspace and satellite denial zone Z target The initial latitude, longitude, and altitude coordinates are transformed to the ECEF coordinate system to obtain the airspace distribution area of ​​the heterogeneous airspace vehicle cluster in the ECEF coordinate system:

[0028]

[0029] Satellite denial zone Z target Equal-interval sampling is performed along the longitude, latitude, and altitude directions to obtain N. target Latitude, longitude, and altitude coordinates of each target sampling point Where i = 1, 2, ..., N target Satellite denial zone Z target Sampling point coordinates Perform a coordinate transformation to obtain the satellite rejection region Z in the ECEF coordinate system. target The coordinates of the i-th target sampling point

[0030]

[0031] Among them, R N Let f be the radius of curvature of the Earth's zonal orbit and f be the Earth's oblateness.

[0032] Furthermore, in step S3, based on the satellite denial region Z... targetThe objective function for designing the internal TD-GDOP value is the optimization criterion. The detailed implementation steps for comprehensively optimizing the configuration of mid- and low-altitude spacecraft clusters outside the satellite denial zone are as follows:

[0033] S31, Initialize the mid-altitude spacecraft cluster low-altitude aircraft cluster The aircraft configuration in the diagram uses the initialized mid- and low-altitude aircraft cluster as the reference aircraft cluster for cooperative navigation. One of the mid-altitude spacecraft is used as the primary reference spacecraft, and the remaining mid- and low-altitude spacecraft are used as secondary reference spacecraft. The relationship between the primary and secondary reference spacecraft and the satellite rejection zone Z is obtained. target Coordinates of the i-th target sampling point within Geometric distance difference for:

[0034]

[0035] Measuring pseudorange for:

[0036]

[0037] in, The geometric distance from the primary reference spacecraft to the i-th target sampling point is denoted as . Let be the geometric distance from the j-th sub-reference spacecraft to the i-th target sampling point. The pseudorange measured from the primary reference aircraft to the i-th target sampling point. The pseudorange measured from the j-th sub-reference spacecraft to the i-th target sampling point is... (x1, y1, z1) represent the position coordinates of the primary reference spacecraft in the ECEF coordinate system within the mid-atmosphere; (x j ,y j ,z j (This refers to the middle and lower atmosphere) Position coordinates of the secondary reference aircraft in the ECEF coordinate system; The clock error between the primary reference aircraft and the i-th target sampling point. Let c be the clock error between the j-th sub-reference spacecraft and the i-th target sampling point; c is the speed of light;

[0038] For the j-th sub-reference aircraft, the following relationship holds:

[0039]

[0040] in, Satellite Denial Zone Z target The direction cosine from the i-th target sampling point within the spacecraft to the main reference spacecraft. Satellite Denial Zone Z target The direction cosine (δx) from the i-th target sampling point to the j-th sub-reference spacecraft i ,δy i ,δz i ) represents the position error of the i-th target sampling point within the satellite rejection area, δu i This is a ranging error caused by clock error;

[0041] S32, regarding the geometric distance difference in step S31 and measurement pseudorange difference A matrix description is performed to obtain the geometric distance difference matrix between the target sampling point within the satellite rejection area and the primary and secondary reference spacecraft:

[0042]

[0043] And the measurement pseudorange difference matrix between the target sampling point within the satellite denial area and the primary and secondary reference spacecraft:

[0044]

[0045] Considering the difference in the standard deviation of the pseudorange measurement between the i-th target sampling point and different primary and secondary reference aircraft, we introduce... dimensional noise ε i The ranging error matrix is ​​obtained. as follows:

[0046] in,

[0047] S33, using a weight transformation matrix For the ranging error matrix β i After normalization, we get:

[0048] D i β i =D i H i ·X i +D i ε i

[0049] in, for The standard deviation of the ranging error between the secondary reference aircraft and the i-th target sampling point; noise matrix D i ε i D follows a standard normal distribution i ε i ~N(0,1);

[0050] The normalized range error equations satisfy the ordinary least squares condition, yielding the weighted least squares solution for the position error of the i-th target sampling point within the satellite rejection region:

[0051]

[0052] in,

[0053] Therefore, the position error of the i-th target sampling point within the satellite rejection area is:

[0054]

[0055] Its corresponding positioning error covariance matrix is:

[0056]

[0057] S34, based on the positioning error covariance matrix cov(δX) of the i-th target sampling point within the satellite rejection area derived in step S33. i Let matrix G i for:

[0058]

[0059] TD-GDOP at the i-th target sampling point under different primary and secondary reference aircraft configurations i Define it as follows:

[0060]

[0061] Where, trace() represents the trace of the matrix, G i (1,1), G i (2,2), G i (3,3) represent matrix G. i The main diagonal element.

[0062] S35, regarding satellite denial zone Z target Inside N target TD-GDOP at each sampling point i Numerical calculations are performed to define the weighted time difference geometric precision factor (WTD-GDOP) within the satellite denial area. target as follows:

[0063]

[0064] Where, ω i Satellite Denial Zone Z target The weight of the i-th target sampling point within the region; based on entering the satellite rejection zone Z. target Low-altitude aircraft altitude layer For weight ω i Define:

[0065]

[0066] Therefore, the mid-altitude spacecraft cluster was calculated. low-altitude aircraft cluster Objective functions for optimizing the configurations of the primary and secondary reference aircraft:

[0067]

[0068] in, For those participating in collaborative navigation The position coordinates of the reference aircraft in the middle and lower altitudes are arranged in one dimension in the ECEF coordinate system;

[0069] S36, based on the mid- and low-altitude vehicle cluster proposed in step (2) and Distribution space and Randomly generate a population of M1 individuals and initialize the individuals. The initial position coordinates and velocity of each reference spacecraft in the ECEF coordinate system are used to calculate the fitness of each individual based on the objective function f1(θ). The velocity v and position x of each individual are then updated according to the following optimization algorithm:

[0070]

[0071] Where n represents the nth iteration number, m represents the mth particle, ω represents the inertia weight; c1 and c2 represent learning factors, which are non-negative constants used to adjust the maximum step size between the individual optimal position p and the population optimal position g; r1 and r2 are random numbers in the range [0,1].

[0072] In addition, based on the clusters of mid- and low-altitude aircraft and Distribution space and Definition, for an individual For each position coordinate in the data, when At that time, there were:

[0073]

[0074] when At that time, there were:

[0075]

[0076] At the same time, the distance between mid-altitude spacecraft clusters is maintained at the minimum spacing. With maximum spacing between:

[0077]

[0078] in

[0079] The individual θ with the smallest objective function f1(θ) obtained within the specified number of iterations is the mid-level spacecraft cluster. low-altitude aircraft cluster The optimal configuration is obtained by combining the comprehensive parameters, and the optimized configuration of the mid-altitude spacecraft is as follows:

[0080]

[0081] 4. The method for optimizing cooperative navigation of aircraft clusters with different airspace distributions according to claim 3, characterized in that, in step S4, the objective function designed based on the TD-GDOP values ​​in the airspace where the mid-altitude aircraft cluster is distributed is used as the optimization criterion, and the following steps are taken to obtain the optimized configuration of the high-altitude aircraft cluster:

[0082] High-altitude aircraft cluster In Taking aircraft as the target, and focusing on mid-altitude aircraft clusters Distribution airspace Equal-interval sampling is performed along the longitude, latitude, and altitude directions to obtain... Target sampling points; combined with the optimized configuration of the mid-altitude spacecraft obtained in step S3. In the configuration-optimized mid-altitude spacecraft cluster The position coordinates of the aircraft are extended equidistantly in the x, y, and z directions to obtain... Where s represents the total cumulative number of expansions of the i-th mid-level spacecraft's position coordinates in a certain direction, and (Δx, Δy, Δz) represents the distance of a single equidistant expansion in the x, y, and z directions; thus, we can obtain An extended set of coordinates for the position of a mid-level spacecraft; for the extended set of coordinates for the i-th mid-level spacecraft, the number of coordinate points in the x, y, and z directions is 2s+1, thus yielding a total of An extended set of coordinates for the location of a cluster of mid-altitude spacecraft;

[0083] calculate High-altitude aircraft in specific configurations for Inside Target sampling points and The TD-GDOP values ​​of the extended mid-altitude spacecraft position coordinates are obtained and weighted to obtain the weighted time difference geometric precision factor.

[0084]

[0085] in, This calculation yields the high-altitude aircraft cluster. Objective function for optimizing the configuration of a medium-scale aircraft:

[0086]

[0087] in, For those participating in collaborative positioning The position coordinates of the reference aircraft at the elevated altitude are arranged in one dimension in the ECEF coordinate system;

[0088] Based on the optimization algorithm in step S36, individuals are initialized in the upper-level airspace. The initial position coordinates and velocities of each primary and secondary reference aircraft in the ECEF coordinate system are used to calculate the fitness of each individual based on the objective function f2(θ), and the individual velocity v and position x are updated; and the specific inertial weight ω and learning factors c1 and c2 are reset when optimizing the configuration of the high-altitude aircraft.

[0089] In addition, according to the high-altitude aircraft cluster Distribution airspace The definition, for individuals For each position coordinate in the data, when At that time, there were:

[0090]

[0091] At the same time, a minimum distance is set between high-altitude aircraft clusters. The optimized spacing between high-altitude aircraft is not less than

[0092]

[0093] in,

[0094] The individual with the smallest objective function f2(θ) value obtained within the specified number of iterations is the high-altitude vehicle cluster. middle The optimal configuration for an aircraft;

[0095] Furthermore, the position coordinates of the upper-level reference vehicle in the optimized ECEF coordinate system With the center of the circle, It hovers within a radius to provide cooperative navigation assistance to mid-altitude spacecraft swarms, among which...

[0096] Furthermore, in step S5, using the position information and relative distance data of aircraft in different airspaces, primary and secondary reference aircraft are selected respectively, and a relative coordinate system with the primary reference aircraft as the origin is established. The steps for constructing a cooperative navigation model based on the TDOA principle are as follows:

[0097] S51, respectively in the mid-altitude reference aircraft cluster Low-altitude reference vehicle cluster and high-altitude reference vehicle cluster The process involves identifying the primary and secondary reference aircraft, obtaining the relative distance d1 between the aircraft to be assisted and the corresponding primary reference aircraft, and the distance d1 between the aircraft to be assisted and the corresponding j-th reference aircraft. s The relative distance between the sub-reference aircraft

[0098] S52, with the main reference aircraft as the origin of the coordinate system, establishes a relative coordinate system. The three-dimensional coordinate axes of the relative coordinate system are parallel to the coordinate axes of the ECEF coordinate system. The Z-axis is parallel to the direction of the Earth's rotation axis. The X-axis intersects the zero meridian in the equatorial plane. The Y-axis, X-axis, and Z-axis form a right-handed rectangular coordinate system.

[0099] S53, based on the relative distances between the aircraft to be assisted and the primary and secondary reference aircraft in S51, construct the distance difference between the aircraft to be assisted and the primary and secondary reference aircraft. Where j s =2,3,...,N s N s To determine the number of reference aircraft participating in cooperative positioning, a cooperative navigation model based on the TDOA principle is established in a relative coordinate system:

[0100] Among them, (x r ,y r ,z r ( ) represents the position coordinates of the aircraft to be assisted in the relative coordinate system. The position coordinates of the primary reference aircraft in the relative coordinate system. This represents the coordinate position of the secondary reference aircraft in the relative coordinate system.

[0101] Compared with the prior art, the significant advantages of this invention are as follows:

[0102] 1. This invention addresses the issue of aircraft swarms distributed across different airspaces in practical application scenarios. Based on the relative positional relationships between swarms, it divides the swarms into altitude and forward directions, resulting in three relative altitude relationships (high, medium, and low) and two relative positional relationships (front and rear). Prioritizing navigation assistance for swarms entering satellite-denied zones in the low-altitude layer, the invention first optimizes the configurations of aircraft providing cooperative navigation assistance in the medium and low-altitude layers, and then optimizes the configurations of aircraft in the high-altitude layer, resulting in the final optimized configuration of the swarms across different airspaces. Compared to methods that do not consider the swarm distribution across different airspaces, this invention has stronger practical significance and is more in line with actual application scenarios.

[0103] 2. This invention takes into account the different cooperative navigation assistance performance of different aircraft configurations for specific target areas such as satellite denial zones. It designs corresponding objective functions for the TD-GDOP numerical calculation results of different aircraft configurations within different aircraft clusters for specific target areas. Based on these functions, it sequentially optimizes different aircraft cluster configurations with heterogeneous spatial distributions, resulting in optimized aircraft configurations with better cooperative navigation performance for specific target areas. This provides better cooperative navigation assistance for aircraft entering satellite denial zones within the cluster. Compared with methods that do not consider the optimization of aircraft cluster configurations with heterogeneous spatial distributions, this invention provides better cooperative navigation assistance performance for aircraft within specific target areas. Attached Figure Description

[0104] Figure 1 This is a schematic diagram illustrating the principle and flow of the method of the present invention;

[0105] Figure 2(a) shows the objective function variation curves in the configuration optimization of the benchmark aircraft in the middle and low altitude layers.

[0106] Figure 2(b) shows the curve of the objective function variation in the configuration optimization of the high-altitude reference aircraft;

[0107] Figure 3 A schematic diagram of the configuration of the spacecraft in different airspaces before and after configuration optimization, and the satellite denial zone;

[0108] Figure 4 A schematic diagram of the orbital trajectory of an aircraft in a different airspace after configuration optimization and the satellite denial zone;

[0109] Figure 5(a) shows the curves of the overall positioning accuracy of the No. 1 low-altitude auxiliary aircraft before and after configuration optimization as a function of time.

[0110] Figure 5(b) shows the curves of the overall positioning accuracy of the No. 2 low-altitude auxiliary aircraft before and after configuration optimization as a function of time.

[0111] Figure 5(c) shows the curves of the overall positioning accuracy of the No. 3 low-altitude auxiliary aircraft before and after configuration optimization as a function of time. Detailed Implementation

[0112] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0113] This invention proposes an optimization method for cooperative navigation of aircraft swarms distributed across different airspaces, applicable when the swarms are distributed over a large airspace area and the types of aircraft and the accuracy of onboard navigation equipment vary. Based on the relative positional relationships between the swarms, the swarms are divided along the altitude and forward direction, resulting in high, medium, and low relative altitude relationships and forward and backward relative positional relationships, and satellite rejection zones are determined. On this basis, different strategies are applied to optimize the configurations of different swarms distributed across different airspaces, resulting in the final optimized configuration. Then, primary and secondary reference aircraft are selected from different swarms to determine the aircraft to be assisted. Based on the relative distance information between the aircraft, a cooperative navigation model based on the TDOA principle is constructed, and the coordinates of the aircraft to be assisted are calculated using a spherical interpolation algorithm. Finally, filtering is used to correct the position information of the aircraft to be assisted, thereby improving navigation performance using swarm cooperative navigation technology. Compared with cooperative navigation methods that do not consider the spatial distribution and configuration optimization of aircraft, the present invention has a better cooperative navigation assistance effect on aircraft to be assisted within a specific target area, and is more in line with actual application scenarios.

[0114] like Figure 1 As shown, a collaborative navigation optimization method for aircraft swarms distributed in different airspace includes the following steps:

[0115] Step (1): Obtain the latitude, longitude, and altitude coordinates of each aircraft in the aircraft cluster distributed in different airspaces, as well as its position coordinates, velocity, and the accuracy of its own airborne navigation equipment in the ECEF coordinate system.

[0116] Step (2): Based on the relative positional relationship of the aircraft clusters distributed in different airspaces and the functions and types of the aircraft in the clusters, divide the aircraft clusters distributed in different airspaces, determine the number of aircraft in each cluster and their distribution airspace, determine the satellite denial area and the coordinates of the sampling points in the satellite denial area, and convert the initial longitude, latitude and altitude coordinate range of each defined airspace and satellite denial area sampling point to the ECEF coordinate system.

[0117] Step (3), based on the satellite denial region Z targetThe objective function for designing the internal TD-GDOP (Time Difference-Geometric Dilution of Precision) value is the optimization criterion. It comprehensively optimizes the configuration of mid- and low-altitude spacecraft clusters outside the satellite denial area, keeps the configuration of mid- and low-altitude spacecraft clusters unchanged during flight, and provides navigation assistance for low-altitude spacecraft entering the satellite denial area.

[0118] Step (4): Based on step (3), the objective function designed based on the TD-GDOP value of the airspace where the mid-altitude aircraft cluster is distributed is used as the optimization criterion to obtain the optimized configuration of the high-altitude aircraft cluster, thereby obtaining the final optimized configuration of the heterogeneous airspace distributed aircraft cluster.

[0119] Step (5): Obtain the position information and relative distance data of aircraft in different airspaces, select references respectively, select primary and secondary reference aircraft, establish a relative coordinate system with the primary reference aircraft as the origin, and construct a cooperative navigation model based on the TDOA (Time Difference of Arrival) principle.

[0120] Step (6): Using the cooperative positioning algorithm based on spherical interpolation, the cooperative navigation model based on the TDOA principle established in step (5) is solved to obtain the position coordinates of the aircraft to be assisted in the middle and low altitude layers in the relative coordinate system.

[0121] Step (7): Based on the position coordinates of the aircraft to be assisted in the relative coordinate system calculated in step (6), convert them to the three-dimensional Earth coordinate system and convert them into longitude, latitude and altitude data. Establish a filtering equation to correct the airborne position coordinates of the aircraft to be assisted in the middle and low altitude layers.

[0122] Step (8): Determine whether the aircraft's navigation position coordinates have been corrected. If they have been corrected, navigation ends; otherwise, repeat steps (3) to (7).

[0123] Step (2) includes the following specific steps:

[0124] Step (2-1): Based on the relative positional relationship of the aircraft clusters in different airspaces, the airspace where the aircraft are distributed is divided into the altitude direction and the forward direction of the aircraft clusters. Based on the three relative altitude relationships of high, medium and low altitudes and the two relative positional relationships of front and back, six relative positional relationships between aircraft clusters are obtained. The high, medium and low altitude layers where the aircraft clusters are located correspond to the subscripts A, B and C, respectively. The front and back relationships between aircraft clusters are represented by the superscript k. The larger the value of k, the further back the relative position of the aircraft cluster is.

[0125] Step (2-2), define the high-altitude vehicle cluster. The number of medium-sized aircraft is The corresponding airspace for the aircraft cluster distribution is as follows:

[0126]

[0127] Wherein, λ, L, and H represent the longitude, latitude, and altitude coordinates of the aircraft cluster, respectively; These represent the minimum and maximum longitude coordinates of the high-altitude aircraft cluster, respectively. These represent the minimum and maximum latitudinal coordinates of the high-altitude aircraft cluster, respectively. These represent the minimum and maximum altitude coordinates of the upper-level spacecraft cluster, respectively; upper-level spacecraft cluster It utilizes its own high-precision airborne navigation equipment for inertial / satellite combined navigation and provides cooperative navigation assistance for mid-altitude spacecraft clusters.

[0128] Steps (2-3) define the mid-altitude spacecraft cluster. The number of medium-sized aircraft is The corresponding airspace for the aircraft cluster distribution is as follows:

[0129]

[0130] These represent the minimum and maximum longitude coordinates of the mid-altitude spacecraft cluster, respectively. These represent the minimum and maximum latitudinal coordinates of the mid-level spacecraft cluster, respectively. These represent the minimum and maximum altitude coordinates of the atrium swarm; atrium swarm It utilizes its own airborne navigation equipment to conduct collaborative navigation with high-altitude aircraft clusters and provides collaborative navigation assistance to low-altitude aircraft clusters.

[0131] Steps (2-4) define the low-altitude vehicle cluster. The number of medium-sized aircraft is The corresponding airspace for the aircraft cluster distribution is as follows:

[0132]

[0133] These represent the minimum and maximum longitude coordinates of the low-altitude aircraft cluster, respectively. These represent the minimum and maximum latitudinal coordinates of the low-altitude aircraft cluster, respectively. These represent the minimum and maximum altitude coordinates of a low-altitude aircraft cluster, respectively; low-altitude aircraft cluster During flight, it is susceptible to satellite denial zones. It uses its own onboard navigation equipment to conduct cooperative navigation with mid-level spacecraft clusters and provides cooperative navigation assistance to low-level spacecraft clusters that have already entered satellite denial zones.

[0134] Steps (2-5) involve considering low-altitude vehicle clusters that are vulnerable to satellite denial zones. In The aircraft entered the satellite denial zone Z during flight. target Its satellite navigation system is unavailable, and it needs to use the adjacent mid-altitude spacecraft cluster. Low-altitude aircraft cluster The spacecraft in the region provides cooperative navigation assistance, and the satellite denial area Z target For a semi-ellipsoid, it has the following definition:

[0135]

[0136] Where, (λ target ,L target H target Z is the satellite denial zone. target The coordinates of any point within the interior, including latitude, longitude, and altitude, are represented by the axis. λ axis L axis H Satellite Denial Zone Z target The axial length in the longitude, latitude, and altitude directions.

[0137] Steps (2-6) will define the airspace. and satellite denial zone Z target The initial latitude, longitude, and altitude coordinates are transformed to the ECEF coordinate system to obtain the airspace distribution area of ​​the heterogeneous airspace vehicle cluster in the ECEF coordinate system:

[0138]

[0139] Satellite denial zone Z target Equal-interval sampling is performed along the longitude, latitude, and altitude directions to obtain N. target Latitude, longitude, and altitude coordinates of each target sampling point Where i = 1, 2, ..., N target Satellite denial zone Z target Sampling point coordinates Perform a coordinate transformation to obtain the satellite rejection region Z in the ECEF coordinate system. target The coordinates of the i-th target sampling point

[0140]

[0141] Among them, R N Let f be the radius of curvature of the Earth's zonal orbit and f be the Earth's oblateness.

[0142] Step (3) includes the following specific steps:

[0143] Step (3-1), initialize the mid-altitude spacecraft cluster low-altitude aircraft cluster The aircraft configuration in the middle atmosphere will be the initial configuration of the mid-altitude aircraft cluster. low-altitude aircraft cluster As a benchmark aircraft swarm in cooperative navigation, select One of the mid-altitude spacecraft is used as the primary reference spacecraft, and the remaining mid- and low-altitude spacecraft are used as secondary reference spacecraft. This yields the satellite rejection region Z between the primary and secondary reference spacecraft in the reference spacecraft cluster. target Coordinates of the i-th target sampling point within Geometric distance difference for:

[0144]

[0145] in, The geometric distance from the primary reference spacecraft to the i-th target sampling point is denoted as . Let be the geometric distance from the j-th sub-reference spacecraft to the i-th target sampling point. (x1, y1, z1) represents the position coordinates of the primary reference spacecraft in the ECEF coordinate system within the mid-atmosphere. j ,y j ,z j (This refers to the middle and lower atmosphere) The position coordinates of the secondary reference aircraft in the ECEF coordinate system.

[0146] make The pseudorange measured from the primary reference aircraft to the i-th target sampling point. The pseudorange difference is obtained by measuring the pseudorange from the j-th sub-reference spacecraft to the i-th target sampling point. for:

[0147]

[0148] in, The clock error between the primary reference aircraft and the i-th target sampling point. Let be the clock error between the j-th sub-reference spacecraft and the i-th target sampling point, and c be the speed of light.

[0149] For the j-th sub-reference aircraft, the following relationship holds:

[0150]

[0151] in, Satellite Denial Zone Z target The direction cosine from the i-th target sampling point within the spacecraft to the main reference spacecraft. Satellite Denial Zone Z target The direction cosine (δx) from the i-th target sampling point to the j-th sub-reference spacecraft i ,δy i ,δz i ) represents the position error of the i-th target sampling point within the satellite rejection area, δu i This is a ranging error caused by clock error.

[0152] Step (3-2) involves performing a matrix description of formulas (7) and (8) from step (3-1) to obtain the satellite rejection region Z. target The geometric distance difference matrix R between the i-th target sampling point and the primary and secondary reference aircraft i :

[0153]

[0154] and satellite denial zone Z target The measurement pseudorange difference matrix P between the i-th target sampling point and the primary and secondary reference aircraft i :

[0155]

[0156] Furthermore, considering the difference in the standard deviation of the pseudorange measurement between the i-th target sampling point and different primary and secondary reference aircraft, a method is introduced... dimensional noise ε i The ranging error matrix can be obtained. as follows:

[0157] β i =R i -P i =H i ·X i +ε i (12)

[0158] in,

[0159] Step (3-3), use the weight transformation matrix Normalizing equation (12) yields:

[0160] D i β i =D i H i ·Xi +D i ε i (13)

[0161] in, for The standard deviation of the ranging error between the reference aircraft and the i-th target sampling point. This results in the noise matrix D. i ε i D follows a standard normal distribution i ε i ~N(0,1). The above normalized ranging error equations satisfy the ordinary least squares condition, and the satellite rejection region Z can be obtained by solving for it. target The weighted least squares solution for the position error of the i-th target sampling point within the range:

[0162]

[0163] in, This leads to the satellite denial region Z. target The position error of the i-th target sampling point is:

[0164]

[0165] Its corresponding positioning error covariance matrix is:

[0166]

[0167] Step (3-4) is based on the satellite denial region Z derived in step (3-3). target The localization error covariance matrix of the i-th target sampling point is cov(δX). i Let matrix G i for:

[0168]

[0169] This allows the TD-GDOP to sample the i-th target point under different primary and secondary reference aircraft configurations. i Define it as follows:

[0170]

[0171] Where, trace() represents the trace of the matrix, G i (1,1), G i (2,2), G i (3,3) represent matrix G. i The main diagonal element.

[0172] Steps (3-5) involve the satellite denial zone Z. target Inside N targetTD-GDOP at each sampling point i Numerical calculations are performed to define the weighted time difference geometric precision factor (WTD-GDOP) within the satellite denial area. target as follows:

[0173]

[0174] Where, ω i Satellite Denial Zone Z target The weight of the i-th target sampling point within the region. Based on entering the satellite rejection zone Z. target Low-altitude aircraft altitude layer For weight ω i Define:

[0175]

[0176] From this, the mid-altitude spacecraft cluster can be calculated. low-altitude aircraft cluster Objective functions for optimizing the configurations of the primary and secondary reference aircraft:

[0177]

[0178] in, For those participating in collaborative navigation The position coordinates of the reference aircraft in the middle and lower altitude layers are arranged in one dimension in the ECEF coordinate system, which is the independent variable in the configuration optimization process of the reference aircraft.

[0179] Steps (3-6) are based on the mid- and low-altitude vehicle clusters proposed in step (2). and Distribution space and Randomly generate a population of M1 individuals and initialize the individuals. The initial position coordinates and velocity of each reference aircraft in the ECEF coordinate system are used to calculate the fitness of each individual according to the objective function f1(θ). The velocity v and position x of each individual are then updated according to formula (22):

[0180]

[0181] Where n represents the nth iteration number, m represents the mth particle, ω represents the inertial weight; c1 and c2 represent learning factors, which are non-negative constants used to adjust the maximum step size between the individual optimal position p and the population optimal position g; r1 and r2 are random numbers in the range [0,1].

[0182] In addition, according to the mid-altitude spacecraft cluster low-altitude aircraft cluster Distribution space and Definition, for an individual For each position coordinate in the data, when At that time, there were:

[0183]

[0184] when At that time, there were:

[0185]

[0186] Meanwhile, to avoid excessively dense or sparse spacing between aircraft in actual application scenarios, the distance between mid-altitude aircraft clusters is set to maintain a minimum. With maximum spacing Between, that is:

[0187]

[0188] in

[0189] The individual θ with the smallest objective function f1(θ) value obtained within the specified number of iterations is the mid-level spacecraft cluster. low-altitude aircraft cluster The optimal configuration is obtained by combining the comprehensive parameters; among which, the optimized configuration of the mid-level spacecraft is as follows:

[0190]

[0191] The difference between step (4) and step (3) is:

[0192] Step (4) uses a cluster of high-altitude aircraft In Taking aircraft as the target, and focusing on mid-altitude aircraft clusters Distribution airspace Equal-interval sampling is performed along the longitude, latitude, and altitude directions to obtain... One target sampling point. Combined with the optimized configuration of the mid-level spacecraft obtained in step (3). In the configuration-optimized mid-altitude spacecraft cluster The position coordinates of the aircraft are extended equidistantly in the x, y, and z directions to obtain... Where s represents the total cumulative number of expansions of the i-th mid-level spacecraft's position coordinates in a certain direction, and (Δx, Δy, Δz) represents the distance of a single equidistant expansion in the x, y, and z directions. Therefore, we can obtain... An extended set of coordinates for the position of a mid-level spacecraft. For the extended set of coordinates for the i-th mid-level spacecraft, the number of coordinate points in the x, y, and z directions is 2s+1. Therefore, a total of... An extended set of location coordinates for a cluster of mid-altitude spacecraft.

[0193] calculate High-altitude aircraft in specific configurations for Inside Target sampling points and The TD-GDOP values ​​of the extended mid-altitude spacecraft position coordinates are obtained and weighted to obtain the weighted time difference geometric precision factor. as follows:

[0194]

[0195] in, This calculation yields the high-altitude aircraft cluster. Objective function for optimizing the configuration of a medium-scale aircraft:

[0196]

[0197] in, For those participating in collaborative positioning The position coordinates of the high-altitude reference aircraft in the ECEF coordinate system are arranged in one dimension, which is the independent variable in the configuration optimization process of the high-altitude reference aircraft. According to the optimization algorithm of formula (22) in step (3-6), in the airspace Internal initialization individuals The initial position coordinates and velocity of each reference aircraft in the ECEF coordinate system are used to calculate the fitness of each individual according to the objective function f2(θ), and the individual velocity v and position x are updated. The specific inertial weight ω and learning factors c1 and c2 can be reset when optimizing the configuration of the high-altitude aircraft.

[0198] In addition, it is necessary to consider the high-altitude aircraft cluster. Distribution airspace The definition, for individuals For each position coordinate in the data, when At that time, there were:

[0199]

[0200] Meanwhile, considering the relatively dispersed distribution of high-altitude aircraft clusters during flight, a minimum distance between high-altitude aircraft clusters is set. The optimized spacing between high-altitude aircraft is not less than Right now:

[0201]

[0202] in The individual with the smallest objective function f2(θ) value obtained within the specified number of iterations is the high-altitude vehicle cluster. middle The optimal configuration of the aircraft. Furthermore, the position coordinates of the high-altitude reference aircraft in the optimized ECEF coordinate system. With the center of the circle, It hovers within a radius to provide cooperative navigation assistance to mid-altitude spacecraft swarms, among which...

[0203] Step (5) includes the following specific steps:

[0204] Step (5-1) involves the formation of a cluster of reference spacecraft in the mid-atmosphere. Low-altitude reference vehicle cluster and high-altitude reference vehicle cluster The process involves identifying the primary and secondary reference aircraft, obtaining the relative distance d1 between the aircraft to be assisted and the corresponding primary reference aircraft, and the distance d1 between the aircraft to be assisted and the corresponding j-th reference aircraft. s The relative distance between the sub-reference aircraft

[0205] Step (5-2): Using the main reference spacecraft as the origin of the coordinate system, establish a relative coordinate system. The three-dimensional coordinate axes of the relative coordinate system are parallel to the coordinate axes of the ECEF coordinate system. The Z-axis is parallel to the direction of the Earth's rotation axis. The X-axis intersects the zero meridian in the equatorial plane. The Y-axis forms a right-hand rectangular coordinate system with the X-axis and Z-axis.

[0206] Step (5-3): Based on the relative distances between the aircraft to be assisted and the primary and secondary reference aircraft in step (5-1), construct the distance difference between the aircraft to be assisted and the primary and secondary reference aircraft. Where j s =2,3,...,N s N s To determine the number of reference aircraft participating in cooperative positioning, a cooperative navigation model based on the TDOA principle is established in a relative coordinate system:

[0207]

[0208] Among them, (x r ,y r ,z r ( ) represents the position coordinates of the aircraft to be assisted in the relative coordinate system. The position coordinates of the primary reference aircraft in the relative coordinate system. This represents the coordinate position of the secondary reference aircraft in the relative coordinate system.

[0209] To verify the effectiveness of the proposed collaborative navigation optimization technology for aircraft swarms with heterogeneous airspace distribution, simulation analysis was conducted. The simulation designed 13 aircraft flying in formation, maintaining consistent flight direction and trajectory across high, medium, and low altitudes. The number of aircraft in the cluster were 4, 3, 3, and 3 respectively. The low-altitude aircraft cluster... Three of the aircraft entered a satellite denial zone during flight, rendering satellite navigation signals unavailable. Cooperative navigation assistance from a reference aircraft swarm is required. A mid-to-low altitude aircraft swarm is used. and The cooperative navigation information provided by the mid-level spacecraft corrects the inertial navigation information of the low-altitude spacecraft requiring assistance within the satellite-denied zone, thus achieving cooperative navigation assistance for the cluster of low-altitude spacecraft requiring assistance within the satellite-denied zone. An optimization algorithm is first used to optimize the mid- and low-altitude spacecraft clusters. and The cluster configuration of mid-altitude aircraft is optimized, and then the high-altitude aircraft cluster is analyzed based on the optimized mid-altitude aircraft cluster distribution airspace. The cluster configuration of the medium-sized aircraft is optimized, and the objective function change curve during the optimization process is shown in the figure. Figure 2(a) , 2(b) As shown. Figure 3 This is a schematic diagram showing the configuration of the spacecraft in different airspaces before and after configuration optimization, as well as the satellite denial zone. Figure 4 Based on the obtained optimized configuration of the heterogeneous airspace swarm, the flight trajectories of the swarm and the satellite rejection zones in each airspace are illustrated in the simulation. Figures 5(a), 5(b), and 5(c) are curves showing the changes in the overall positioning error of the three low-altitude assisted aircraft entering the satellite rejection zone before and after applying the method of this invention, as a function of time. It can be seen that the heterogeneous airspace distributed swarm cooperative navigation optimization technology designed in this invention can effectively improve the navigation and positioning accuracy of the assisted aircraft swarm when some aircraft enter the satellite rejection zone.

[0210] The above description is merely an optimized embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing cooperative navigation of aircraft swarms with heterogeneous spatial distribution, characterized in that, Includes the following steps: S1: Obtain the latitude, longitude, and altitude coordinates of each aircraft in a cluster of aircraft distributed in different airspaces, as well as their position coordinates, speed, and the accuracy of their own onboard navigation equipment in the ECEF coordinate system. S2. Based on the relative positional relationships of the aircraft clusters distributed in different airspaces and the functions and types of the aircraft in the clusters, the aircraft clusters distributed in different airspaces are divided, the number of aircraft in each cluster and their distribution airspace are determined, the satellite denial area and the coordinates of the sampling points in the satellite denial area are determined, and the initial longitude, latitude and altitude coordinate range of the sampling points in each defined airspace and satellite denial area are transformed to the ECEF coordinate system. S3, based on satellite denial zone Z target The objective function of the internal TD-GDOP value design is the optimization criterion. It comprehensively optimizes the configuration of the mid- and low-altitude vehicle clusters outside the satellite denial area, keeps the configuration of the mid- and low-altitude vehicle clusters unchanged during flight, and provides navigation assistance for low-altitude vehicles entering the satellite denial area. S4. Based on step S3, the objective function designed based on the TD-GDOP value in the airspace where the mid-altitude vehicle cluster is distributed is used as the optimization criterion to obtain the optimized configuration of the high-altitude vehicle cluster, thereby obtaining the final optimized configuration of the heterogeneous airspace distributed vehicle cluster. S5: Obtain the position information and relative distance data of aircraft in different airspaces, select the primary and secondary reference aircraft respectively, establish a relative coordinate system with the primary reference aircraft as the coordinate origin, and construct a cooperative navigation model based on the TDOA principle; S6. Using a cooperative positioning algorithm based on spherical interpolation, the cooperative navigation model based on the TDOA principle is solved to obtain the position coordinates of the aircraft to be assisted in the middle and low altitude layers in the relative coordinate system. S7. Based on the position coordinates of the aircraft to be assisted in the relative coordinate system calculated in step S6, convert them to the three-dimensional Earth coordinate system and convert them into longitude, latitude and altitude data. Establish a filtering equation to correct the airborne position coordinates of the aircraft to be assisted in the middle and low altitude layers. S8, determine whether the aircraft's navigation position coordinates have been corrected; if corrected, navigation ends. Otherwise, repeat steps S3-S7.

2. The method for optimizing cooperative navigation of aircraft swarms with heterogeneous airspace distribution according to claim 1, characterized in that, In step S2, the number of aircraft in each cluster and their distribution airspace are determined, and the satellite denial area and the coordinates of the sampling points within the satellite denial area are determined. The initial latitude, longitude, and altitude coordinates of the sampling points in each defined airspace and satellite denial area are transformed to the ECEF coordinate system. The detailed implementation steps are as follows: S21. Based on the relative positional relationship of the aircraft clusters in different airspaces, the airspace where the aircraft are distributed is divided into the altitude direction and the forward direction of the aircraft clusters. Based on the three relative altitude relationships of high, medium and low altitudes and the two relative positional relationships of front and rear, six relative positional relationships between aircraft clusters are obtained. The high, medium and low altitude layers where the aircraft clusters are located correspond to the subscripts A, B and C, respectively. The front and rear relationships between aircraft clusters are represented by the superscript k. The larger the value of k, the further back the relative position of the aircraft cluster is. S22 defines a cluster of high-altitude aircraft. The number of medium-sized aircraft is The corresponding airspace for the aircraft cluster distribution is Wherein, λ, L, and H represent the longitude, latitude, and altitude coordinates of the aircraft cluster, respectively; These represent the minimum and maximum longitude coordinates of the high-altitude aircraft cluster, respectively. These represent the minimum and maximum latitudinal coordinates of the high-altitude aircraft cluster, respectively. These represent the minimum and maximum altitude coordinates of the high-altitude spacecraft cluster, respectively; the high-altitude spacecraft cluster It utilizes its own high-precision airborne navigation equipment for inertial / satellite combined navigation and provides cooperative navigation assistance for mid-altitude spacecraft clusters; S23, defines mid-altitude spacecraft clusters The number of medium-sized aircraft is The corresponding airspace for the aircraft cluster distribution is These represent the minimum and maximum longitude coordinates of the mid-altitude spacecraft cluster, respectively. These represent the minimum and maximum latitudinal coordinates of the mid-level spacecraft cluster, respectively. These represent the minimum and maximum altitude coordinates of the atrium spacecraft cluster, respectively; the atrium spacecraft cluster It utilizes its own airborne navigation equipment to conduct cooperative navigation with high-altitude aircraft clusters and provides cooperative navigation assistance to low-altitude aircraft clusters. S24 defines a low-altitude aircraft cluster. The number of medium-sized aircraft is The corresponding airspace for the aircraft cluster distribution is These represent the minimum and maximum longitude coordinates of the low-altitude aircraft cluster, respectively. These represent the minimum and maximum latitudinal coordinates of the low-altitude aircraft cluster, respectively. These represent the minimum and maximum altitude coordinates of a low-altitude aircraft cluster, respectively; low-altitude aircraft cluster It utilizes its own airborne navigation equipment to conduct cooperative navigation with the mid-altitude spacecraft cluster, and provides cooperative navigation assistance to the low-altitude spacecraft cluster that has entered the satellite denial zone ahead; S25, low-altitude aircraft cluster In The aircraft entered the satellite denial zone Z during flight. target At that time, its satellite navigation system was unavailable, and it needed to use the adjacent mid-altitude spacecraft cluster. low-altitude aircraft cluster The spacecraft in the region provides cooperative navigation assistance, and the satellite denial zone Z target It is a semi-ellipsoid, defined as follows: Wherein, (λ target ,L target H target Z is the satellite denial zone. target The coordinates of any point within the axis are latitude, longitude, and altitude. λ axis L axis H Satellite Denial Zone Z target The axial length in the longitude, latitude, and altitude directions; S26 will define the airspace and satellite denial zone Z target The initial latitude, longitude, and altitude coordinates are transformed to the ECEF coordinate system to obtain the airspace distribution area of ​​the heterogeneous airspace vehicle cluster in the ECEF coordinate system: Satellite denial zone Z target Equal-interval sampling is performed along the longitude, latitude, and altitude directions to obtain N. target Latitude, longitude, and altitude coordinates of each target sampling point Where i = 1, 2, ..., N target ; Satellite denial zone Z target Sampling point coordinates Perform a coordinate transformation to obtain the satellite rejection region Z in the ECEF coordinate system. target The coordinates of the i-th target sampling point Among them, R N Let f be the radius of curvature of the Earth's zonal orbit and f be the Earth's oblateness.

3. The method for optimizing cooperative navigation of aircraft swarms with heterogeneous airspace distribution according to claim 1, characterized in that, In step S3, based on the satellite denial region Z target The objective function for designing the internal TD-GDOP value is the optimization criterion. The detailed implementation steps for comprehensively optimizing the configuration of mid- and low-altitude spacecraft clusters outside the satellite denial zone are as follows: S31, Initialize the mid-altitude spacecraft cluster low-altitude aircraft cluster The aircraft configuration in the diagram uses the initialized mid- and low-altitude aircraft cluster as the reference aircraft cluster for cooperative navigation. One of the mid-altitude spacecraft is used as the primary reference spacecraft, and the remaining mid- and low-altitude spacecraft are used as secondary reference spacecraft. The relationship between the primary and secondary reference spacecraft and the satellite rejection zone Z is obtained. target Coordinates of the i-th target sampling point within Geometric distance difference for: Measuring pseudorange for: in, The geometric distance from the primary reference spacecraft to the i-th target sampling point is denoted as . Let be the geometric distance from the j-th sub-reference spacecraft to the i-th target sampling point. The pseudorange measured from the primary reference aircraft to the i-th target sampling point. The pseudorange measured from the j-th sub-reference spacecraft to the i-th target sampling point is... (x1, y1, z1) represent the position coordinates of the primary reference spacecraft in the ECEF coordinate system within the mid-atmosphere; (x j ,y j ,z j (This refers to the middle and lower atmosphere) Position coordinates of the secondary reference aircraft in the ECEF coordinate system; The clock error between the primary reference aircraft and the i-th target sampling point is... Let c be the clock error between the j-th sub-reference spacecraft and the i-th target sampling point; c is the speed of light; For the j-th sub-reference aircraft, the following relationship holds: in, Satellite Denial Zone Z target The direction cosine from the i-th target sampling point within the spacecraft to the main reference spacecraft. Satellite Denial Zone Z target The direction cosine (δx) from the i-th target sampling point to the j-th sub-reference spacecraft i ,δy i ,δz i ) represents the position error of the i-th target sampling point within the satellite rejection area, δu i This is a ranging error caused by clock error; S32, regarding the geometric distance difference in step S31 and measuring pseudorange difference A matrix description is performed to obtain the geometric distance difference matrix between the target sampling point within the satellite rejection area and the primary and secondary reference spacecraft: And the measurement pseudorange difference matrix between the target sampling point within the satellite denial area and the primary and secondary reference spacecraft: Considering the difference in the standard deviation of the pseudorange measurement between the i-th target sampling point and different primary and secondary reference aircraft, we introduce... dimensional noise ε i The ranging error matrix is ​​obtained. as follows: in, S33, using a weight transformation matrix For the ranging error matrix β i After normalization, we get: D i b i =D i H i ·X i +D i e i in, for The standard deviation of the ranging error between the secondary reference aircraft and the i-th target sampling point; noise matrix D i ε i D follows a standard normal distribution i ε i ~N(0,1); The normalized range error equations satisfy the ordinary least squares condition, yielding the weighted least squares solution for the position error of the i-th target sampling point within the satellite rejection region: in, Therefore, the position error of the i-th target sampling point within the satellite rejection area is: Its corresponding positioning error covariance matrix is: S34, based on the positioning error covariance matrix cov(δX) of the i-th target sampling point within the satellite rejection area derived in step S33. i Let matrix G i for: TD-GDOP at the i-th target sampling point under different primary and secondary reference aircraft configurations i Define it as follows: Where, trace() represents the trace of the matrix, G i (1,1), G i (2,2), G i (3,3) represent matrix G. i The main diagonal elements; S35, regarding satellite denial zone Z target Inside N target TD-GDOP at each sampling point i Numerical calculations are performed to define the weighted time difference geometric precision factor (WTD-GDOP) within the satellite denial area. target as follows: Where, ω i Satellite Denial Zone Z target The weight of the i-th target sampling point within the region; based on entering the satellite rejection zone Z. target Low-altitude aircraft altitude layer For weight ω i Define: Therefore, the mid-altitude spacecraft cluster was calculated. low-altitude aircraft cluster Objective functions for optimizing the configurations of the primary and secondary reference aircraft: in, For those participating in collaborative navigation The position coordinates of the reference aircraft in the middle and lower altitudes are arranged in one dimension in the ECEF coordinate system; S36, based on the mid- and low-altitude vehicle cluster proposed in step (2) and Distribution space and Randomly generate a population of M1 individuals and initialize the individuals. The initial position coordinates and velocity of each reference spacecraft in the ECEF coordinate system are used to calculate the fitness of each individual based on the objective function f1(θ). The velocity v and position x of each individual are then updated according to the following optimization algorithm: Where n represents the nth iteration number, m represents the mth particle, ω represents the inertia weight; c1 and c2 represent learning factors, which are non-negative constants used to adjust the maximum step size between the individual optimal position p and the population optimal position g; r1 and r2 are random numbers in the range [0,1]. In addition, based on the clusters of mid- and low-altitude aircraft and Distribution space and Definition, for an individual For each position coordinate in the array, when j1 = 1, 2, ..., At that time, there were: when At that time, there were: At the same time, the distance between mid-altitude spacecraft clusters is maintained at the minimum spacing. With maximum spacing between: Where j2 = 1, 2, ..., The individual θ with the smallest objective function f1(θ) obtained within the specified number of iterations is the mid-level spacecraft cluster. low-altitude aircraft cluster The optimal configuration is obtained by combining the comprehensive parameters, and the optimized configuration of the mid-altitude spacecraft is as follows:

4. The method for optimizing cooperative navigation of aircraft swarms with heterogeneous airspace distribution according to claim 3, characterized in that, In step S4, using the objective function designed based on the TD-GDOP values ​​within the airspace where the mid-altitude aircraft cluster is distributed as the optimization criterion, the following steps are taken to obtain the optimized configuration of the high-altitude aircraft cluster: High-altitude aircraft cluster In Taking aircraft as the target, and focusing on mid-altitude aircraft clusters Distribution airspace Equal-interval sampling is performed along the longitude, latitude, and altitude directions to obtain... Target sampling points; combined with the optimized configuration of the mid-altitude spacecraft obtained in step S3. In the configuration-optimized mid-altitude spacecraft cluster The position coordinates of the aircraft are extended equidistantly in the x, y, and z directions to obtain... Where s represents the total cumulative number of expansions of the i-th mid-level spacecraft's position coordinates in a certain direction, and (Δx, Δy, Δz) represents the distance of a single equidistant expansion in the x, y, and z directions; thus, we can obtain An extended set of coordinates for the position of a mid-level spacecraft; for the extended set of coordinates for the i-th mid-level spacecraft, the number of coordinate points in the x, y, and z directions is 2s+1, thus yielding a total of An extended set of coordinates for the location of a cluster of mid-altitude spacecraft; calculate High-altitude aircraft, under specific configurations, for Inside Target sampling points and The TD-GDOP values ​​of the extended mid-altitude spacecraft position coordinates are obtained and weighted to obtain the weighted time difference geometric precision factor. in, This calculation yields the high-altitude aircraft cluster. Objective function for optimizing the configuration of a medium-scale aircraft: in, For those participating in collaborative positioning The position coordinates of the reference aircraft at the elevated altitude are arranged in one dimension in the ECEF coordinate system; Based on the optimization algorithm in step S36, individuals are initialized in the upper-level airspace. The initial position coordinates and velocities of each primary and secondary reference aircraft in the ECEF coordinate system are used to calculate the fitness of each individual based on the objective function f2(θ), and the individual velocity v and position x are updated; and the specific inertial weight ω and learning factors c1 and c2 are reset when optimizing the configuration of the high-altitude aircraft. In addition, according to the high-altitude aircraft cluster Distribution airspace The definition, for individuals For each position coordinate in the array, when j3 = 1, 2, ..., At that time, there were: At the same time, a minimum distance is set between high-altitude aircraft clusters. The optimized spacing between high-altitude aircraft is not less than Where j4 = 1, 2, ..., The individual with the smallest objective function f2(θ) value obtained within the specified number of iterations is the high-altitude vehicle cluster. middle The optimal configuration for an aircraft; Furthermore, the position coordinates of the upper-level reference vehicle in the optimized ECEF coordinate system With the center of the circle, It hovers within a radius to provide cooperative navigation assistance to a mid-altitude spacecraft cluster, where j3 = 1, 2, ...

5. The method for optimizing cooperative navigation of aircraft swarms with heterogeneous airspace distribution according to claim 1, characterized in that, In step S5, using the position information and relative distance data of aircraft in different airspaces, primary and secondary reference aircraft are selected respectively, and a relative coordinate system with the primary reference aircraft as the origin is established. The steps for constructing a cooperative navigation model based on the TDOA principle are as follows: S51, respectively in the mid-altitude reference aircraft cluster Low-altitude reference vehicle cluster and high-altitude reference vehicle cluster The process involves identifying the primary and secondary reference aircraft, obtaining the relative distance d1 between the aircraft to be assisted and the corresponding primary reference aircraft, and the distance d1 between the aircraft to be assisted and the corresponding j-th reference aircraft. s The relative distance between the sub-reference aircraft S52, with the main reference aircraft as the origin of the coordinate system, establishes a relative coordinate system. The three-dimensional coordinate axes of the relative coordinate system are parallel to the coordinate axes of the ECEF coordinate system. The Z-axis is parallel to the direction of the Earth's rotation axis. The X-axis intersects the zero meridian in the equatorial plane. The Y-axis, X-axis, and Z-axis form a right-handed rectangular coordinate system. S53, based on the relative distances between the aircraft to be assisted and the primary and secondary reference aircraft in S51, construct the distance difference between the aircraft to be assisted and the primary and secondary reference aircraft. Where j s =2,3,...,N s N s To determine the number of reference aircraft participating in cooperative positioning, a cooperative navigation model based on the TDOA principle is established in a relative coordinate system: Among them, (x r ,y r ,z r ( ) represents the position coordinates of the aircraft to be assisted in the relative coordinate system. The position coordinates of the primary reference aircraft in the relative coordinate system. This represents the coordinate position of the secondary reference aircraft in the relative coordinate system.

Images