Coverage evaluation method taking into account sensor pointing for a given height segment target

Abstract

The application discloses a coverage evaluation method considering sensor pointing for a space given height section target, and belongs to the field of aerospace. The application realizes the method as follows: in a target coordinate system, a space target is equivalent to a double height section spherical layer, and the coverage zenith angle interval of a discrete unit center line is taken as an evaluation index in the azimuth and distance dimensions; a mapping relationship between a sensor coverage area and the azimuth and the corresponding coverage zenith angle is established in an observation coordinate system; the observation coordinate system and the target coordinate system are combined, all nodes existing between the field of view boundary and the discrete unit center line are defined, the nodes are sorted according to the zenith angle and are read in sequence to switch the coverage, and the coverage zenith angle interval of the target area under the field of view of any sensor is obtained; two evaluation index systems, a coverage volume coverage score and a weighted score considering the target distribution density, are constructed for two working conditions of the maximum coverage area and the maximum intersection probability, and efficient and high-precision coverage evaluation is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to a coverage evaluation method considering sensor pointing for a given altitude segment target, in particular to an evaluation method considering altitude density for a large number of concentrated distribution targets, and belongs to the field of aerospace. BACKGROUND

[0002] Space-based optical observation has become a feasible and effective method for space target observation due to its advantages of no weather influence, high maneuverability, all-weather working, etc. In recent years, the increasing number of space targets has attracted the attention of the world, among which the distribution density of LEO orbit is the largest, and about 75.2% of the cataloged space targets are distributed in this area. The present application considers the different orbit altitude distribution characteristics of space targets and approximates them as center lines with different weights for calculation, and also discusses the coverage area of sensors with different field of view constraints and pointing.

[0003] The existing space-based coverage research is divided into two categories according to the research object: target-oriented and sensor-oriented. The target-oriented research mainly considers the visibility of specific moving targets. The first technology [1] (see Detectable Model Based on Medium and Low Earth Orbit Constellation for Ballistic Missile Surveillance [J] Shanghai Aerospace, Zhao Yin, Yi Dongyun, Zhang Qian, Li Zhenjie, 2010, 27(2): 1-8+33) comprehensively considers the constraints of earth blocking, earth shadow, earth thermal radiation, natural celestial body reflected light and load field of view angle, etc. However, this part of the research is only suitable for the coverage determination of a small number of specific targets, and when considering the observation task of a large number of space targets, the calculation complexity increases with the number of targets and observation satellites.

[0004] The research on sensors mainly considers the coverage of a given target area. Since existing coverage analysis is mainly developed for ground targets, the given target area is generally set as a sphere with the same radius as the earth and the origin located at the center of the earth. Prior art [2] (see Research on Graphical Display Algorithm of Instantaneous Coverage Area of Reconnaissance Satellite [J] Journal of Equipment Command and Technology College, Zhang Zhan Yue, 2006 (3): 40-44) studies the coverage area of a conical field of view sensor on the earth considering the yaw angle. Prior art [3] (see Above the Horizon Satellite Coverage with Dual-Altitude Band Constraints [J] Journal of Spacecraft and Rockets, Marchand B G, Kobel C J, 2009, 46 (4): 845-857) extends the target area to a target segment with dual-altitude constraints and studies the planar coverage area of an omnidirectional sensor considering the effective range of the load. However, the research in this part is mainly developed based on graphical visualization, and the graphical algorithm tool needs to be used for quantitative calculation of the coverage area. Meanwhile, prior arts [2] and [3] are both developed for two-dimensional coverage, and further analysis and transformation are needed for the three-dimensional space height segment target coverage problem considered in the present application. SUMMARY

[0005] The main purpose of the present application is to provide a coverage evaluation method for a given height segment target in space considering the pointing of a sensor, which is equivalent to a double-height segment spherical layer determined by the target distribution height in the target coordinate system, is discretized in the azimuth and distance dimensions, and takes the coverage zenith angle interval of the center line of the discrete unit as the evaluation index. The mapping relationship between the coverage area of the sensor and the azimuth and the corresponding coverage zenith angle is established in the observation coordinate system, which is applied to the visualization and quantitative calculation of the coverage area of a conical sensor with any constraint and pointing. The observation coordinate system and the target coordinate system are combined, all the nodes existing between the field of view boundary and the center line of the discrete unit are defined, the nodes are sorted according to the zenith angle and read in sequence to switch the coverage, and the coverage zenith angle interval of the target area under the field of view of any sensor is obtained. Two evaluation index systems, the coverage volume coverage score and the weighted score considering the target distribution density, are constructed for the two working conditions of maximum coverage area and maximum intersection probability, and the coverage evaluation for a given height segment target considering the pointing of a sensor is realized through the two evaluation index systems.

[0006] The purpose of the present application is realized through the following technical solutions.

[0007] The coverage evaluation method for a given height segment target considering the pointing of a sensor disclosed in the present application comprises the following steps:

[0008] Step 1: In the geocentric inertial frame E XYZ Below, the target coordinate system, the observation coordinate system, and the sensor pointing are defined. The observation coordinate system is established based on three dimensions: zenith angle, azimuth angle, and distance. The sensor pointing includes pitch and yaw.

[0009] The geocentric inertial frame of reference is composed of E XYZ Indicated by E, where E represents the Earth's center. The observation coordinate system fixed to the satellite is defined by S. o Indicated, where o represents the center of the satellite, z o Axis along satellite position vector r Sat And x is positive if it is away from the Earth's center. o The axis is located within the orbital plane and intersects with the z-axis. o The axes are orthogonal and point positive in the direction of satellite motion, y o The axes are obtained using the right-hand rule. The origin of the target coordinate system S is located at the Earth's center, and the three axes point in the same direction as the observation coordinate system.

[0010] The sensor is specified to be fixed to the satellite and pointed at l v Initial and observation coordinate system z o When the axes coincide, the sensor pointing vector in spherical coordinates is represented as... Where the zenith angle θ v Simultaneously, the corresponding sensor's pitch angle and azimuth angle The corresponding yaw angle of the sensor. Considering the sensor's pointing modulus r... v This invention does not contain relevant valid information regarding coverage, and since the field of view of a conical load does not need to consider the sensor's roll angle ψ, it does not include such information. v , pointing to simplified

[0011] Step Two: In the target coordinate system defined in Step One, approximate a large number of spatial targets at a given altitude range as a unified three-dimensional sphere, avoiding point-to-point simulation calculations of a large number of actual spatial targets. This is achieved by using distance r and azimuth angle... The three-dimensional spherical layer T is discretized at equal intervals in two dimensions, and the discretized dual-height segment spherical layer is analyzed in the zenith angle θ dimension to obtain the discrete unit T. ij And with the center line C of the discrete unit ij The line coverage interval is used as an evaluation index for equivalently determining the coverage of the entire discrete unit. This facilitates subsequent steps using two-dimensional discretization and one-dimensional analytical line coverage evaluation methods. Compared with the traditional three-dimensional discrete point coverage calculation method, it can effectively reduce the amount of computation and improve the approximate accuracy of the target discrete model.

[0012] Because of the characteristic of spatial targets with concentrated distribution of orbital height, the spatial targets are equivalent to double-height three-dimensional spherical layer by setting the lower limit of target height LTAS and the upper limit of target height UTAS, avoiding the point-to-point simulation calculation of a large number of actual spatial targets. In the target spherical coordinate system defined in step one, the target region T is expressed as:

[0013]

[0014] where r L and r U are the radii of LTAS and UTAS respectively. By equidistantly dispersing the three-dimensional spherical layer T in the distance r and azimuth two dimensions, and analyzing the dispersed double-height spherical layer in the zenith angle dimension, the dispersed unit T ij is obtained, expressed as:

[0015]

[0016] where r i and represent the dispersed nodes, and Δr = r i -r i-1 , obtained:

[0017] r0 = r L , r I = r U ,

[0018] Taking the line coverage interval of the center line C ij of the dispersed unit as the evaluation index for equivalent determination of the coverage of the entire dispersed unit, expressed as:

[0019]

[0020] When I and J are large enough, the coverage of C ij is taken as the coverage determination of the entire dispersed spherical layer T ij , expressed as:

[0021]

[0022] where Θ Cov(ij) is the coverage zenith angle of the center line C ij . By calculating the coverage zenith angle of I x J center lines, the effective coverage of the sensor for the double-height target spherical layer is obtained, which facilitates the subsequent step of two-dimensional dispersion and one-dimensional analysis of the line coverage evaluation method, compared with the traditional three-dimensional dispersed point coverage calculation method, which can effectively reduce the calculation amount and improve the approximation accuracy of the target dispersed model.

[0023] Step three: for conic field of view sensors, calculate the azimuth angle coverage range determined by different sensor half-cone angles and pointing directions and the corresponding coverage zenith angle range in the observation coordinate system defined in step one. First, for the effective azimuth angle Φ Cov of the sensor field of view, the coverage range of the azimuth angle is calculated by the discrete calculation in step two. Since the target coordinate system S is the observation coordinate system S o , the coverage range of the zenith angle is calculated by the discrete calculation in step two. Since the target coordinate system S is the observation coordinate system S o , the coverage range of the zenith angle is calculated by the discrete calculation in step two. Since the target coordinate system S is the observation coordinate system S , the coverage range of the zenith angle is calculated by the discrete calculation in step two. Since the target coordinate system S is the observation coordinate system S , the coverage range of the zenith angle is calculated by the discrete calculation in step two. Since the target coordinate system S is the observation coordinate system S , the coverage range of the zenith angle is calculated by the discrete calculation in step two. Since the target coordinate system S is the observation coordinate system S

[0024] In the observation spherical coordinate system, any direction vector i is represented by two variables θ o and :

[0025]

[0026] Set the field of view half-cone angle to α v , and the sensor pointing direction to Any unit vector located in the field of view is subject to the following conditions:

[0027]

[0028] Formula (1) is equivalent to:

[0029]

[0030] Simplify to:

[0031]

[0032] Where b = cos θ v and δ = arctan (b / a).

[0033] When , sin (θ o + δ) = 1. At this time, the coverage zenith angle range degenerates to a point. When and only when is located at the boundary of the azimuth angle coverage area , it degenerates to a point. ​

[0034] Thus, the azimuthal coverage boundary is obtained is expressed as:

[0035]

[0036] When θ v < α v , formula (2) is not valid. Because z o axis is contained in the coverage field of view, the coverage area cannot be continuously expressed in the effective interval of the zenith angle, and the coverage azimuthal angle interval is set as

[0037] Thus, is expressed as:

[0038]

[0039] After obtaining , for any , the corresponding coverage zenith angle range is calculated. After is uniquely determined, the coverage zenith angle is expressed as The boundary calculation formula is:

[0040]

[0041] Step four: obtain the coverage azimuth in the observation spherical coordinate system by step three and the corresponding , the effective azimuth Φ Cov of the sensor field of view in the target spherical coordinate system is the same azimuth. Then, for any azimuthal plane coverage problem in the target spherical coordinate system, the coverage zenith angle interval of the target area under any sensor field of view is obtained by defining all the nodes existing in the field of view boundary in step three and the center line of the discrete unit in step two, sorting the nodes according to the zenith angle and reading them in sequence to switch the coverage.

[0042] Rotate the x-axis of the S system around the z-axis by to obtain the k-axis, and set the azimuthal plane as the kz plane. The coverage in the kz plane is expressed as the coverage zenith angle range of the disc determined by the field of view range and the effective distance r Sen , and a plurality of target arcs C i-1 with r = (r i + r ij ) / 2.

[0043] In the azimuthal plane, set the straight line where the field of view boundary determined by is located as lmin , and The straight line where the field of view boundary is located is l max . The center of the earth and l min are perpendicular to point F, and l max is perpendicular to point G, and the distances are respectively:

[0044]

[0045] C ij is the intersection of l min and l max , and G1, G2 are the intersection of l ij and z-axis. The intersection of the omnidirectional sensor and the positive direction of the k-axis is H, and the intersection with the positive direction of the z-axis is P. The zenith angles of the above six points in the target coordinate system are:

[0046]

[0047]

[0048]

[0049] By defining the field of view boundary in step three and all nodes existing in the center line of the discrete unit in step two, the six points in formula (6) are sorted in ascending order according to the value of the zenith angle, and the original sequence is obtained:

[0050] Γ Ori = {θ1, θ2, …, θ P , …, θ H , …}

[0051] Where θ P is the nth element of the original sequence Γ Ori .

[0052] Let θ P be the starting point of calculation, and rewrite it as Where the superscript + indicates the coverage starting point, and the superscript - indicates the coverage end point. At this time, there are two cases: when r = r Sat , the P point is covered, and is set to When r ≠ r Sat , the P point is not covered, and is set to Then, read the nodes in turn, and perform a coverage switching operation every time a node is read. Finally, the coverage sequence is obtained Take r ≠ r Sat as an example, and obtain:

[0053]

[0054] Where the continuous Each represents a single covering interval (s∈{1,2,…,S}). Θ Cov(ij) The union of all coverage intervals yields the coverage zenith angle interval of the target area under any sensor's field of view.

[0055] Step 5: Construct two different coverage evaluation methods for the two operating conditions: maximizing the coverage area and maximizing the intersection probability. For the coverage area maximization condition, construct a coverage volume score (V) evaluation index system; for the intersection probability maximization condition, construct a weighted score (W) evaluation index system considering target distribution density. By constructing different evaluation index systems for the above two operating conditions based on the overall three-dimensional target sphere layer defined in Step 2, the coverage evaluation efficiency of sensor pointing can be improved in a targeted manner. In Step 2, the centerline C of the discrete unit for the given target height segment I×J is obtained. ij Then, the coverage zenith angle Θ of the center lines of all discrete units is obtained through step four. Cov(ij) The one-dimensional coverage interval is converted into corresponding discrete unit T according to the different evaluation index systems constructed above. ij The coverage score is a coverage evaluation that takes into account the sensor pointing direction for a target at a given altitude in space.

[0056] Under the condition of maximizing the coverage area, the zenith angle interval Θ is covered by the discrete cell centerline obtained in step four. Cov(ij) As the coverage criterion, the corresponding discrete unit T in step two ij The covering volume is expressed in spherical coordinates as:

[0057]

[0058] The coverage volume score of a single satellite for the entire dual-altitude range of targets is then expressed as:

[0059]

[0060] According to the evaluation index system, deployment based on maximizing the coverage volume of a single satellite can be achieved.

[0061] Under the condition of maximizing the rendezvous probability, since the space targets are concentrated in the LEO orbit segment and have a strong high concentration distribution characteristic, according to the distance discrete segment [r] in step two... i-1 ,r i The target distribution density in ] is set by r = (r i-1 +r i C determined by ) / 2 ij Coverage weight ω i .

[0062] In spherical coordinates, the zenith angle interval Θ is covered by the centerline of the discrete unit obtained in step four. Cov(ij)As the coverage determination criterion, the distribution weighted score of the discrete unit T ij is expressed as:

[0063]

[0064] The weighted parameter ω i in formula (9) is used instead of the volume parameter This is easy to understand in concept, when the target in space is uniformly distributed, the density is consistent with the trend of volume change.

[0065] The coverage score of a single star for the entire double-height segment target considering the distribution characteristics is expressed as:

[0066]

[0067] According to formula (8) and formula (10), the coverage of the entire double-height segment target is determined, and by setting the equivalent number of actual space targets of the entire double-height segment target sphere, the coverage evaluation of the given height segment target considering the sensor pointing is realized by one calculation.

[0068] It also includes step six: according to the coverage evaluation result of the given height segment target in space considering the sensor pointing obtained in step five, the corresponding optimal satellite orbit height and sensor pointing are applied to the single star deployment of the actual space target observation task, which can realize the two different task requirements of maximizing the number of observation targets or maximizing the number of observations.

[0069] It also includes step seven: according to the single star deployment strategy obtained in step six, the effective optimization parameter initial value of constellation design is provided to speed up the optimization process, and then the application range of the present application is expanded to the preliminary optimization of the observation constellation of the given height segment target.

[0070] Advantages:

[0071] 1、The coverage evaluation method for given height segment targets considering sensor pointing disclosed in the present application approximates a large number of space targets in a given height segment to an overall three-dimensional spherical layer, avoiding point-to-point simulation calculation of a large number of actual space targets. By equally spacing the three-dimensional spherical layer in the distance and azimuth dimensions, and analyzing the discrete double-height segment spherical layer in the zenith dimension, discrete units are obtained, and the line coverage interval of the center line of the discrete units is used as an evaluation index for equivalent determination of the coverage of the entire discrete unit. Compared with the traditional three-dimensional discrete point coverage calculation method, the calculation amount can be effectively reduced and the approximation accuracy of the target discrete model can be improved.

[0072] 2. The application discloses a coverage evaluation method for a given height stage target considering sensor pointing, which can be applied to visualization and quantitative calculation of coverage areas of conical sensors with any constraints and pointing by establishing a mapping relationship between the coverage areas and the azimuth and corresponding coverage zenith in an observation coordinate system, and does not need to rely on a graphic algorithm tool for quantitative calculation of the coverage areas relative to a traditional coverage area projection method.

[0073] 3. The application discloses a coverage evaluation method for a given height stage target considering sensor pointing, which obtains coverage zenith intervals of a target region under any sensor field of view by defining all nodes existing between a field of view boundary and a discrete unit center line, sorting the nodes according to the zenith and reading the nodes in sequence for coverage switching.

[0074] 4. The application discloses a coverage evaluation method for a given height stage target considering sensor pointing, which constructs two different coverage evaluation modes for two working conditions of maximum coverage area and maximum intersection probability, and can improve the coverage evaluation efficiency of the sensor pointing in a targeted manner. BRIEF DESCRIPTION OF DRAWINGS

[0075] Figure 1 It is a flowchart of the coverage evaluation method for a given height stage target considering sensor pointing.

[0076] Figure 2 It is a target coordinate system and an observation coordinate system diagram of step one of the application.

[0077] Figure 3 It is a sensor pointing diagram in an observation spherical coordinate system of step one of the application.

[0078] Figure 4 It is a three-dimensional space target equidistant discrete unit and a center line diagram of step two of the application.

[0079] Figure 5 It is a conical field of view coverage range diagram in an observation spherical coordinate system of step three of the application.

[0080] Figure 6 It is an azimuth plane coverage diagram in a target spherical coordinate system of step four of the application.

[0081] Figure 7 It is a coverage zenith diagram in the azimuth plane of step four of the application.

[0082] Figure 8 This is a field-of-view diagram of the conic section in the observation spherical coordinate system of this invention. The diagram shows two conic pointing scenarios, scenario one with the sensor half-cone angle α. v =18°, pitch angle θ v =10°, yaw angle Case 2: Sensor half-cone angle α v =18°, pitch angle θ v =105°, yaw angle The yellow part in the picture is due to The determined field of view boundary, green as the basis The determined field of view boundary, with the red asterisk indicating the sensor pointing to l. v .

[0083] Figure 9 This figure shows the conical field-of-view coverage volume score under the influence of different altitudes and pitch angles in an example of this invention. The red line in the figure represents the optimal pitch angle that maximizes the coverage volume for each orbital altitude.

[0084] Figure 10 This describes the semi-major axis distribution characteristics of 19,103 actual space targets at orbital altitudes of 300-1600 km in this invention example.

[0085] Figure 11 This is a conical field-of-view coverage weighted score considering the target distribution density under different altitudes and pitch angles, as described in this invention example. The red line in the figure represents the optimal pitch angle that maximizes the coverage weighted score for each orbital altitude. Detailed Implementation

[0086] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0087] Example 1:

[0088] To verify the feasibility of the method, a three-dimensional target region is given, and for a spaceborne sensor with known effective distance and field of view, the region is traversed within a given orbital altitude and pitch angle range. The coverage scores of the two evaluation methods are calculated. The task parameters are shown in the table below:

[0089] Table 1. Parameters for the Task and Discrete Method

[0090]

[0091] like Figure 1 As shown in the figure, this embodiment discloses a coverage evaluation method for a target at a given altitude range that takes into account sensor pointing. The specific implementation steps are as follows:

[0092] Step 1: Define target coordinate system and observation coordinate system (zenith angle, azimuth angle, distance) and sensor pointing (pitch, yaw) in geocentric inertial system.

[0093] The geocentric inertial system is represented by E XYZ , where E represents the geocenter. The observation coordinate system fixed to the satellite is represented by S o , where o represents the center of the satellite, z o axis is along the satellite position vector r Sat and is positive away from the geocenter, x o axis is in the orbital plane and orthogonal to z o axis and is positive pointing to the satellite motion direction, y o axis is obtained by the right-hand rule. The origin of the target coordinate system S is at the geocenter, and the three axes are the same as the observation coordinate system.

[0094] The sensor is fixed to the satellite and points in the direction l v , which is initially coincident with the observation coordinate system z o axis, at this time the sensor pointing vector is represented in spherical coordinate system as where the zenith angle θ v corresponds to the pitch angle of the sensor, the azimuth angle corresponds to the yaw angle of the sensor. Considering the modulus r v of the sensor pointing, it does not contain the coverage-related effective information, and the present application considers that the conical load field of view does not need to consider the roll angle ψ v of the sensor, and the pointing is simplified as

[0095] Step 2: In the target coordinate system defined in step 1, a large number of space targets in a given height range are approximated as three-dimensional spherical layers, and are scattered in the distance and azimuth angle dimensions.

[0096] Due to the characteristic of the orbital height of space targets being concentratedly distributed, by setting LTAS and UTAS, it is assumed to be a double-height three-dimensional spherical layer. In the target spherical coordinate system defined in step 1, the target region T is represented as:

[0097]

[0098] where r L and r U are the radii of LTAS and UTAS, respectively. By scattering the three-dimensional spherical layer T in the distance r and azimuth angle two dimensions, the discrete unit T ij is obtained, which is represented as:

[0099]

[0100] where r i and Representing discrete nodes, the parameter Δr = r in Table 1. i -r i-1 , get:

[0101] r0 = r L ,r I =r U ,

[0102] C, the centerline of the discrete region spherical layer ij Represented as:

[0103]

[0104] When I and J are large enough, use C. ij The coverage of the entire discrete spherical layer T ij The coverage determination is expressed as:

[0105]

[0106] Where Θ Cov(ij) C is the centerline of the discrete element. ij The coverage zenith angle is calculated. By calculating the coverage zenith angles of I×J centerlines, the effective coverage of the sensor for the target sphere in the dual-height range is obtained.

[0107] Step 3: For the conical field-of-view sensor, calculate the azimuth coverage range determined by the semi-cone angle and direction of different sensors, and the coverage zenith angle range corresponding to different azimuth angles, in the observation coordinate system defined in Step 1.

[0108] In the observation spherical coordinate system, any direction vector i is determined by two variables θ. o and Represented as:

[0109]

[0110] Let the field of view half-cone angle be α v The sensor points to arbitrary unit vector The conditions for being within the field of view are:

[0111]

[0112] Equivalent to:

[0113]

[0114] Simplified to:

[0115]

[0116] where b = cos θ v and δ = arctan(b / a).

[0117] When sin(θ o + δ) = 1. At this time, the zenith angle range degenerates to a point. When and only when is located at the boundary of the azimuth angle coverage area degenerates to a point. Therefore, the azimuth angle coverage boundary

[0118] is expressed as:

[0119]

[0120]

[0121] When θ v < α v , the above formula is not established. Because the z o axis is contained in the coverage field of view, the coverage area cannot be continuously represented in the effective interval of the zenith angle, at this time, the coverage azimuth angle interval is set as

[0122] Therefore, is expressed as:

[0123]

[0124] After obtaining , for any the corresponding coverage zenith angle range is calculated. After is uniquely determined, the coverage zenith angle is expressed as The boundary calculation formula is:

[0125]

[0126] Figure 8 is the range diagram of the conical field of view in the observation spherical coordinate system in the present example. Two kinds of conical pointing situations are shown in the figure, situation one sensor half-cone angle α v = 18°, pitch angle θ v = 10°, yaw angle situation two sensor half-cone angle α v = 18°, pitch angle θ v = 105°, yaw angle The yellow in the figure is the field of view boundary determined by , and the green is the field of view boundary determined by ​The determined field of view boundary, with the red asterisk indicating the sensor pointing to l. v Step 4: Obtain the coverage azimuth in the observation spherical coordinate system through Step 3. and corresponding Then, for any target sphere coordinate system The analysis focuses on the azimuth plane coverage problem.

[0127] Rotate the x-axis about the z-axis in the S-frame. Once the k-axis is obtained, the azimuth plane is defined as the kz plane. The coverage within the kz plane is represented by the discretization method in step two, based on the field of view. and effective distance r Sen The determined disk and multiple r = (r i-1 +r i ) / 2 target arc C ij zenith angle coverage

[0128] Within the azimuth plane, set by The line containing the determined field of view boundary is l min ,Depend on The line containing the determined field of view boundary is l max Earth's center and l min Perpendicular to point F, and l max Perpendicular to point G, the distances are as follows:

[0129]

[0130] C ij With l min The intersection points are F1 and F2 respectively, and l max The intersection points are G1 and G2 respectively. The omnidirectional sensor and C... ij The intersection point with the positive k-axis is H, and the intersection point with the positive z-axis is P. The zenith angles of these six points in the target coordinate system are:

[0131]

[0132]

[0133]

[0134] Then, sort the six points according to their zenith angle values ​​from smallest to largest to obtain the original sequence:

[0135] Γ Ori ={θ1,θ2,…,θ P ,…,θ H ,…}

[0136] Where θP For the original sequence Γ Ori The nth element.

[0137] Set θ P To calculate the starting point, rewrite as follows: The superscript + indicates the starting point of the cover, and the superscript - indicates the ending point. There are two cases: when r = r Sat When point P is covered, it is set as When r≠r Sat At that time, point P was not covered and was set as Then, nodes are read sequentially, and a coverage switch operation is performed after each node is read. Finally, the coverage sequence is obtained. With r≠r Sat For example, we get:

[0138]

[0139] Among them continuous Each represents a single covering interval (s∈{1,2,…,S}). Θ Cov(ij) The union of all coverage intervals yields the coverage zenith angle interval of the target area under any sensor's field of view.

[0140] Step 5: Obtain the center line C of the discrete element for the given target height segment I×J through Step 4. ij The coverage zenith angle Θ Cov(ij) Then, it is converted into the corresponding discrete unit T. ij The coverage score is calculated. Two evaluation methods are considered: one is the coverage volume score V, and the other is the weighted score W that takes into account the target distribution density.

[0141] In spherical coordinates, with Θ Cov(ij) Discrete unit T as the criterion for coverage determination ij The coverage volume is expressed as:

[0142]

[0143] The coverage volume score of a single satellite for the entire dual-altitude range of targets is then expressed as:

[0144]

[0145] This evaluation system enables deployment designs that maximize the coverage volume of a single satellite.

[0146] Step Six: Based on the coverage evaluation results obtained in Step Five for targets at a given altitude in space, considering sensor pointing, the corresponding optimal satellite orbital altitude and sensor pointing are applied to the single-satellite deployment for actual space target observation missions. This can achieve two different mission requirements: maximizing the number of observed targets or maximizing the number of observations.

[0147] Step 7: Based on the single-satellite deployment strategy obtained in Step 6, provide effective initial values ​​of optimized constellation design parameters to accelerate the optimization process, thereby extending the application scope of this embodiment to the preliminary optimization of observation constellations for targets at a given altitude range.

[0148] Figure 9 This figure shows the conical field-of-view coverage volume score under different altitudes and elevation angles in this invention example. The red line in the figure represents the optimal elevation angle that maximizes the coverage volume for each orbital altitude. The optimal elevation angle for the conical field of view is concentrated in the range of [92°, 105.5°] and increases with increasing orbital altitude. However, when the elevation angle exceeds a certain value, the observation quality is affected by the Earth's thermal background, and the effective observation volume decreases accordingly.

[0149] Furthermore, since space targets are concentrated in the LEO orbit segment and exhibit a strong high-concentration distribution characteristic, based on the distance discrete segment [r] in step two... i-1 ,r i The target distribution density in ] is set by r = (r i-1 +r i C determined by ) / 2 ij Coverage weight ω i .

[0150] Figure 10 This describes the semi-major axis distribution characteristics of 19,103 actual space targets at orbital altitudes of 300-1600 km in this invention example.

[0151] In spherical coordinates, with Θ Cov(ij) Discrete unit T as the criterion for coverage determination ij The weighted score distribution is represented as:

[0152]

[0153] Using weighted parameter ω i Alternate volume parameters This is conceptually easy to understand: when targets are uniformly distributed in space, their density and volume change in the same direction.

[0154] The coverage score of a single satellite for the entire dual-altitude range of targets, considering distribution characteristics, is expressed as:

[0155]

[0156] Figure 11 is the conical field of view coverage weighted score considering target distribution density in the examples of the present application under the influence of different altitudes and elevation angles. The red line in the figure is the optimal elevation angle corresponding to each orbital altitude that maximizes the coverage weighted score. The optimal elevation angle of the conical field of view is concentrated in the interval [94°, 110°], slightly larger than the optimal elevation angle of the volume score and increases with the increase of orbital altitude.

[0157] For the 19103 space targets of the mission target segment given in Table 1, 10 satellites evenly distributed in a single orbit carrying a conical field of view are used for 2 hours of observation. The initial epoch time is selected as 2022-03-21 00:00:00, and the observation step is 10s. The conical field of view is deployed at an orbital altitude of 500-1200km, the yaw angle is fixed at 60°, and the elevation angle is set according to the volume score optimization and the distribution score optimization. Table 2 gives the number of visible targets corresponding to different orbital altitudes and elevation angles, the average number of observations of visible targets, and the number of observations of all targets.

[0158] Table 2 Space target observation

[0159]

[0160] As can be seen from Table 2, the constellation deployed based on the coverage volume maximization strategy is mostly superior to the conjunction probability maximization constellation in terms of the number of visible targets; the constellation deployed based on the conjunction probability maximization strategy is always superior to the coverage volume maximization constellation in terms of the total number of observations.

[0161] The above specific description further describes the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only a specific embodiment of the present application and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A coverage evaluation method taking into account sensor pointing for a given height segment target, characterized in that: Comprising the following steps: Step one: Define the target coordinate system and the observation coordinate system and sensor pointing in the Earth-Centered Inertial (ECI) frame E XYZ Next, define the target coordinate system and the observation coordinate system and sensor pointing; The observation coordinate system is established on the basis of three dimensions of zenith angle, azimuth angle and distance; the sensor pointing direction comprises pitch and yaw; Step two: In the target coordinate system defined in step one, a large number of space targets in a given height section are approximated as a whole three-dimensional spherical layer to avoid point-to-point simulation calculation of a large number of actual space targets; the three-dimensional spherical layer T is discretized at equal intervals in two dimensions, and the discrete double-height-section spherical layer is analyzed in the zenith angle θ dimension to obtain discrete units T ij , and the line coverage interval of the center line C ij of the discrete unit is used as an evaluation index for equivalent determination of the coverage of the whole discrete unit.​ Step 3: For the conical field-of-view sensor, calculate the azimuth coverage range determined by different sensor half-cone angles and pointing directions, and the corresponding coverage zenith angle range under the observation coordinate system defined in Step 1; first, for the effective azimuth angle Φ of the sensor's field of view... Cov Perform calculations to reduce the computational overhead of discrete calculations in step two; since the target coordinate system S is the observation coordinate system S... o Along z o By axial translation, the azimuth angle of any direction vector i is the same in both coordinate systems. The effective coverage range of the sensor is expressed as the coverage azimuth angle in the observation spherical coordinate system. and corresponding It can be represented; by establishing a mapping relationship between the sensor coverage area and the azimuth angle and the corresponding coverage zenith angle in the observation coordinate system, it can be applied to the visualization and quantitative calculation of the coverage area of ​​a conical sensor with arbitrary constraints and orientation. Step 4: Obtain the coverage azimuth in the observation spherical coordinate system through Step 3. and corresponding Then, the effective azimuth angle Φ of the sensor's field of view in the target spherical coordinate system. Cov For the same azimuth angle; subsequently, for any target sphere coordinate system... The azimuth plane coverage problem is calculated by defining the field of view boundary in step three and all nodes existing in the discrete unit centerline in step two. The nodes are sorted according to their zenith angles and read sequentially to switch coverage, thus obtaining the coverage zenith angle range of the target area under any sensor field of view. Step five: two different coverage evaluation methods are constructed for the two working conditions of maximum coverage area and maximum intersection probability: in the working condition of maximum coverage area, the coverage volume coverage score V evaluation index system is constructed; in the working condition of maximum intersection probability, the weighted score W evaluation index system considering target distribution density is constructed; by defining the overall three-dimensional target sphere layer in step two, different evaluation index systems for the above two working conditions are constructed, which can improve the coverage evaluation efficiency of sensor pointing; in step two, the given target height section I×J discrete unit center line C ij is obtained Cov(ij) , and then the coverage zenith angle Θ of all discrete unit center lines is obtained through step four Cov(ij) . The one-dimensional coverage interval is converted into the coverage score of the corresponding discrete unit T ij according to the different evaluation index systems constructed above, that is, the coverage evaluation considering sensor pointing for the space given height section target is realized.

2. The method for coverage evaluation considering sensor pointing towards a given height segment target according to claim 1, characterized in that: Step six is further included, and the single-satellite deployment corresponding to the optimal satellite orbit height and sensor pointing direction is applied to the actual space target observation task according to the coverage evaluation result considering the sensor pointing direction of the space given height segment target obtained in step five, so that the two different task requirements of maximum number of observation targets or maximum number of observation times can be realized.

3. The method for coverage evaluation considering sensor pointing towards a given height segment target as claimed in claim 2, wherein: Step seven is further included, and the optimization parameter initial value of the effective constellation design is provided according to the single-satellite deployment strategy obtained in step six to speed up the optimization process, and then the coverage evaluation method is applied to the preliminary optimization of the observation constellation of the given height segment target.

4. The coverage evaluation method for a given height segment target taking into account sensor pointing of claim 1, 2 or 3, characterized in that: The implementation method of step one is, The geocentric inertial system is denoted by E XYZ , where E denotes the geocenter; the observation coordinate system fixed to the satellite is denoted by S o , where o denotes the center of the satellite, the z o -axis is along the satellite position vector r Sat and is positive away from the geocenter, the x o -axis is in the orbital plane and orthogonal to the z o -axis and is positive in the direction of satellite motion, and the y o -axis is obtained by the right-hand rule; the origin of the target coordinate system S is at the geocenter, and the three axes are in the same direction as the observation coordinate system. The sensor is rigidly attached to the satellite and points in the direction of l v Initial and observed coordinate systems z o The axes coincide, and the sensor pointing vector is represented in the spherical coordinate system as where the zenith angle θ v Also corresponds to the sensor's pitch angle, azimuth angle Corresponds to the sensor's yaw angle; the modulus r v Does not contain the coverage-related valid information, and the sensor's roll angle ψ v The pointing simplifies to 5. The method for coverage evaluation considering sensor pointing towards a given height segment target as claimed in claim 4, wherein: The implementation method of step two is, Due to the characteristic of the concentrated distribution of the orbit height of the space target, the space target is equivalent to a double-height three-dimensional spherical layer by setting the lower limit LTAS and the upper limit UTAS of the target height, so that the point-to-point simulation calculation of a large number of actual space targets is avoided; in the target spherical coordinate system defined in step one, the target region T is represented as: where r L and r U are the radii of the LTAS and UTAS, respectively; and r is the distance from the center of the sphere to the point of intersection of the LTAS and UTAS. ij The three-dimensional spherical shell T is equidistantly scattered in two dimensions, and the discrete two-height spherical shell is analyzed in the zenith angle dimension, to obtain the discrete unit T ij , which is expressed as: where r i and represent discrete nodes, and Δr = r i -r i-1 , results in: r0＝r L ,r I ＝r U , The center line C of the discrete unit ij The line coverage interval of the center line C of the discrete unit is used as an evaluation index for equivalent determination of the coverage of the entire discrete unit, and is expressed as: When I and J are large enough, the coverage of C ij is used as the coverage criterion of the entire discrete sphere layer T ij is expressed as: where Θ Cov(ij) is the coverage zenith angle of the centerline C ij of the discrete unit; by calculating the coverage zenith angle for I x J centerlines, the effective coverage of the sensor for the target spherical layer of double height sections is obtained, which facilitates the subsequent steps of two-dimensional discrete and one-dimensional analytical line coverage evaluation method, compared with the traditional three-dimensional discrete point coverage calculation method, which can effectively reduce the calculation amount and improve the approximation accuracy of the target discrete model.

6. The method for coverage evaluation considering sensor pointing towards a given height segment target as claimed in claim 5, wherein: The implementation method of step three is, In the spherical coordinate system, an arbitrary direction vector i is represented by two variables θ o and as: The field of view half-cone angle is set as α v The sensor pointing is Any unit vector The condition for being located in the field of view is: Formula (1) is equivalent to: Simplified as: wherein b = cos θ v and δ = arctan(b / a); when When, sin(θ) o +δ)=1; at this time, the coverage area is the zenith angle range. Degenerates into a point if and only if Located in the azimuth coverage area When the boundary Degenerates into a point; therefore, the azimuth coverage boundary is obtained. Represented as: When θ v < α v , formula (2) is not valid; because z o axis is contained within the covered field of view, the covered azimuthal angular interval cannot be continuously represented over the valid interval of zenith angle, and the covered azimuthal angular interval is set to Thus, is represented as: After obtaining for any The corresponding coverage zenith angle range is calculated; from After uniquely determining δ, the coverage zenith angle is expressed as The boundary calculation formula is:

7. The method for coverage evaluation considering sensor pointing towards a given height segment target as claimed in claim 6, wherein: The implementation method of step four is, Rotate the x-axis about the z-axis in the S-frame. Once the k-axis is obtained, the azimuth plane is defined as the kz plane; the coverage within the kz plane is represented by the discretization method in step two, based on the field of view. and effective distance r Sen The determined disk and multiple r = (r i-1 +r i ) / 2 target arc C ij zenith angle coverage In the azimuth plane, set the straight line l on which the field of view boundary determined by min is located is l max ; the center of the earth and l min are perpendicular to point F, and l max is perpendicular to point G, the distances are respectively: C ij The intersection of l min The intersection of l max The intersection of l ij The intersection of l The intersection of l The intersection of l By defining all the nodes existing between the field of view boundary in step three and the center line of the discrete unit in step two, the six points in formula (6) are sorted in ascending order according to the value of the zenith angle, and the original sequence is obtained: Γ Ori = {θ1, θ2,..., θ P ,..., θ H ,...} where θ P is the nth element of the original sequence Γ Ori . Set θ P For the calculation of the starting point, rewrite as Where the superscript + represents the coverage starting point, and the superscript - represents the coverage termination point; at this time, there are two cases: when r = r Sat , the P point is covered, and is set as When r ≠ r Sat , the P point is not covered, and is set as Then, read the nodes in turn backward, and perform a coverage switching operation for each read node; finally, the coverage sequence is obtained Take r ≠ r Sat as an example, and obtain: wherein consecutive all represent a single coverage interval (s e {1,2,...,S}); Θ Cov(ij) is the union of all coverage intervals, resulting in the coverage zenith angle interval of the target region under any sensor field of view.

8. The method for coverage evaluation considering sensor pointing towards a given height segment target as claimed in claim 7, wherein: The implementation method of step five is, In the maximum coverage area working condition, the discrete unit center line obtained in step four covers the zenith angle interval Θ Cov(ij) As the coverage criterion, the corresponding discrete unit T ij The coverage volume of T is expressed in spherical coordinates as: The coverage volume score of the single satellite for the entire double-height segment target is represented as: According to the evaluation index system, the deployment based on the maximum coverage volume of the single satellite can be realized; In the maximum encounter probability condition, the space targets are distributed in the LEO orbit segment, and have strong height concentration distribution characteristics. According to the target distribution density in the distance discrete segment [r i-1 , i ] in step two, the C ij overweight ω i is determined by r = (r i-1 + r i ) / 2; In spherical coordinates, the centerline of the discrete cell obtained in Step Four covers the zenith angle interval Θ Cov(ij) As the coverage criterion, the discrete cell T ij The distribution weighted score is expressed as: The weighted parameter ω in formula (9) i Instead of the volume parameter in formula (7) This is easy to understand in concept, when the target in space is uniformly distributed, its density is consistent with the trend of volume change; The coverage score of the single satellite for the entire double-height segment target considering the distribution characteristics is represented as: According to formula (8) and formula (10), the coverage of the entire double-height segment target is determined, a large number of actual space targets are equivalent to the entire double-height segment target spherical layer, and the coverage evaluation considering the sensor pointing direction of the given height segment target is realized by one calculation.

Images