A fast and high-precision calculation method for satellite earth observation overpass time

Abstract

The invention discloses a method for quickly and accurately calculating the satellite's overpass time for earth observation. The method calculates the satellite orbit elements and the ground distances between the sub-satellite point and the target point at multiple time points; compares the ground distances between the sub-satellite point and the target point at adjacent time points to obtain all intervals with minimum ground distance points; uses a one-dimensional search algorithm in each interval to solve the minimum ground distance between the sub-satellite point and the target point and the corresponding time; if the minimum ground distance in a certain interval is less than or equal to the equivalent width of the satellite's earth observation, the corresponding time is the overpass time of the satellite's observation target; sorts all the overpass times in chronological order to obtain all the overpass times of the satellite's observation of the ground target in a specified time period; the invention first searches for possible intervals of the overpass time, uses a one-dimensional search algorithm to accurately obtain the overpass time in a smaller interval, avoids repeated large-scale search and calculation of the overpass time, and has the advantages of fast calculation speed, high calculation accuracy and wide adaptability.

Description

Technical Field

[0001] The invention belongs to the technical field of aerospace navigation, and in particular relates to a method for quickly and accurately calculating the time when a satellite observes the earth. Background Art

[0002] When planning a satellite earth observation mission, it is necessary to calculate the visible arc of the satellite to the ground target, so as to determine in which arc the satellite can observe a specific ground target. In the visible arc, the satellite passes the ground target at the time when the distance between the satellite and the target is the shortest, and the observation effect is the best. In the usual multi-satellite multi-ground target observation mission planning, the time of passing the top must be calculated for any satellite and any ground target, and the number of combinations of satellites and ground targets is often in the order of thousands, which makes the efficiency of the calculation of the top time crucial; on the other hand, because the satellite moves very fast, the best observation time for a ground target is fleeting, which makes the calculation accuracy of the top time equally important. The existing satellite earth observation top time calculation methods either use a high-precision orbit extrapolation model to search from a large step size to a small step size, which has high accuracy but slow calculation speed; or use an analytical model for calculation, but the deviation from the actual orbit of the satellite is too large, and the accuracy is not enough for real observation mission planning, and the result can only be used as a reference in the initial design stage of the satellite orbit. Summary of the invention

[0003] The purpose of the present invention is to provide a method for quickly and accurately calculating the time when a satellite observes the earth, so as to overcome the problem in the prior art that it is difficult to strike a balance between calculation efficiency and calculation accuracy, and to ensure high accuracy while quickly completing the calculation of the time when the satellite passes the earth.

[0004] The technical solution adopted by the present invention is a method for quickly and accurately calculating the time when a satellite observes the earth, which is specifically implemented in the following steps:

[0005] Step 1: Note that the calculation time interval is [t0,t f ], calculate and record t0-60s, from t0 to t f The time points with intervals of Δt and t f The satellite orbit epoch root number E at +60s i And the ground distance L between the subsatellite point and the target point i , i=1,2,L,n;

[0006] Step 2, select k = 2, 3, L, n-1, if L k-1 >L k <L k+1 , record the interval where L has a minimum value [E k-1 ,E k+1 ], if t k-1 <t0, use Ek Replace E k-1 , if t k+1 >t f , use E k Replace E k+1 ; Select k = 3, 4, L, n-1, if L k-1 =L k And L k-1 ≤L k-2 And L k ≤L k+1 , record the interval where L has a minimum value [E k-1 ,E k ]; all the above intervals are recorded as i=1,2,L,m;

[0007] Step 3, select i = 1, 2, L, m, and is the initial number of orbital elements. The ground distance between the sub-satellite point and the target point is only related to time. A one-dimensional search algorithm is used to solve and record the interval Minimum ground distance between the inner subsatellite point and the target point and the corresponding time

[0008] Step 4, select i = 1, 2, L, m, if Less than or equal to the equivalent half width W of satellite earth observation eq , then the time is the passing time of the satellite observable target, and all observable passing times are recorded as j=1,2,L,s;

[0009] Step 5: sort by time j=1,2,L,s are sorted to obtain the satellite observation over-the-top time of the ground target sorted by time k=1,2,L,s.

[0010] The present invention is also characterized in that:

[0011] Wherein, the range of Δt is 0<Δt≤P / 2, P is the satellite orbit period, for a high-precision dynamic model, preferably, in order to reduce the time consumption of orbit extrapolation in subsequent local optimization, preferably, Δt is taken as 1 minute, for a simplified dynamic model, the orbit extrapolation consumes very little time, in order to reduce the number of time points, preferably, Δt is taken as P / 2;

[0012] In step 1, t0-60s and t0 to t f The time points with intervals of Δt and t f The specific process of the satellite orbit elements at +60s and the ground distance between the sub-satellite point and the target point is as follows:

[0013] A high-precision dynamic model is used to calculate the number of satellite orbit elements at each time point, as shown in formula (1):

[0014]

[0015] In the formula, r is the satellite radius vector, μ is the earth's gravitational constant, and a perturbed is the total perturbation acceleration including the non-spherical perturbation of the Earth, the atmospheric drag perturbation, the third body gravitational perturbation and the light pressure perturbation;

[0016] The ground distance calculation method between the satellite sub-satellite point and the target point is shown in formula (6):

[0017]

[0018] Where L is the ground distance between the satellite sub-satellite point and the target, R e is the radius of the Earth, r satellite is the radius vector from the center of the Earth to the satellite, r target is the radius vector from the center of the earth to the target point;

[0019] When calculating the satellite orbit elements at each time point in step 1, if the accuracy requirement is moderate, in order to obtain faster calculation speed, the average orbit motion model that only considers the J2 perturbation is used, as shown in formula (2):

[0020]

[0021] Where a is the semi-major axis of the orbit, e is the eccentricity, incl is the orbit inclination, Ω is the right ascension of the ascending node, ω is the argument of perigee, M is the mean anomaly, t is the time, t0 is the initial time, According to formula (3), According to formula (4), Calculate according to formula (5):

[0022]

[0023]

[0024]

[0025] The one-dimensional search algorithm in step 3 is the golden section method, and the dynamic model used for satellite orbit extrapolation is the same as that in step 1;

[0026] The calculation process of the equivalent half-width of satellite earth observation in step 4 is as follows:

[0027]

[0028] Where W sensoris the sensor width of the satellite when there is no lateral swing, θ swath is the geocentric angle corresponding to the half width of the satellite sensor, r is the distance from the center of the earth, R e is the radius of the earth, c is the distance from the satellite to the ground boundary of the sensor width, β swath is the semi-conical angle corresponding to the field of view of the satellite sensor, is the maximum roll angle of the satellite, β is the equivalent field of view semi-cone angle after considering the roll of the satellite, W eq is the equivalent half-width of satellite earth observation.

[0029] The beneficial effects of the present invention are:

[0030] The invention discloses a method for quickly and accurately calculating the time when a satellite observes the earth, which is applicable to the problem of quickly and accurately calculating the time when a satellite observes the earth. The method first calculates the ground distance between the satellite sub-satellite point and the target point at equally spaced time points, and then determines a series of shorter time intervals that may contain the minimum distance value by comparing the ground distances between the sub-satellite point and the target point corresponding to adjacent time points, and finally solves the time when the satellite passes by a one-dimensional search algorithm in each time interval. The method first searches for the possible interval of the time when the satellite passes, and then uses a one-dimensional search algorithm to accurately obtain the time when the satellite passes in a smaller possible interval, thereby avoiding repeated large-scale search and calculation of the time when the satellite passes. The method has no restrictions on the satellite motion model, and can be used in dynamic models of different precisions for orbital extrapolation calculations. The method has the advantages of fast calculation speed, high calculation precision and wide adaptability, and solves the problem that the traditional satellite earth observation time when the satellite passes algorithm is difficult to balance the calculation efficiency and calculation precision, and has poor adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 The present invention is a flow chart of a method for quickly and accurately calculating the time when a satellite observes the earth. DETAILED DESCRIPTION

[0032] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] A method for quickly and accurately calculating the time when a satellite observes the earth is provided. Figure 1 As shown, the specific calculation process includes the following steps:

[0034] Step 1: Note that the calculation time interval is [t0,t f ], calculate and record t0-60s, from t0 to t f Time points with intervals of Δt (0<Δt≤P / 2, P is the satellite orbit period, and the last interval can be less than Δt) and t f Satellite orbit element number E at +60s i (including orbital epoch t i) and the ground distance L between the subsatellite point and the target point i , i=1,2,L,n;

[0035] A high-precision dynamic model is used to calculate the number of satellite orbit elements at each time point, as shown in formula (1):

[0036]

[0037] In the formula, r is the satellite radius vector, μ is the earth's gravitational constant, and a perturbed is the total perturbation acceleration including the non-spherical perturbation of the Earth, the atmospheric drag perturbation, the third body gravitational perturbation and the light pressure perturbation;

[0038] For occasions with moderate accuracy requirements, in order to obtain faster calculation speed, the average orbit motion model that only considers the J2 perturbation can also be used: as shown in formula (2):

[0039]

[0040] Where a is the semi-major axis of the orbit, e is the eccentricity, incl is the orbit inclination, Ω is the right ascension of the ascending node, ω is the argument of perigee, M is the mean anomaly, t is the time, t0 is the initial time, According to formula (3), According to formula (4), Calculate according to formula (5):

[0041]

[0042]

[0043]

[0044] The time interval Δt can be arbitrarily selected in the interval (0, P / 2], but reasonable selection according to the complexity of the satellite orbit extrapolation dynamics model can reduce the total calculation time. Preferably, for a high-precision dynamics model, in order to reduce the orbit extrapolation time during subsequent local optimization, it is recommended that Δt be 1 minute. For a simplified dynamics model, the orbit extrapolation time is very short. In order to reduce the number of time points, it is recommended that Δt be P / 2;

[0045] The ground distance calculation method between the satellite sub-satellite point and the target point is shown in formula (6):

[0046]

[0047] Where L is the ground distance between the satellite sub-satellite point and the target, R e is the radius of the Earth, r satellite is the radius vector from the center of the Earth to the satellite, r target is the radius vector from the center of the earth to the target point;

[0048] Step 2, for k = 2, 3, L, n-1, if L k-1 >L k <L k+1 , record the interval where L may have a minimum value [E k-1 ,E k+1 ], if t k-1 <t0, use E k Replace E k-1 , if t k+1 >t f , use E k Replace E k+1 ; For k = 3, 4, L, n-1, if L k-1 =L k And L k-1 ≤L k-2 And L k ≤L k+1 , record the interval where L may have a minimum value [E k-1 ,E k ]; all the above intervals are recorded as i=1,2,L,m;

[0049] Step 3, for i=1,2,L,m, is the initial number of orbital elements. The ground distance between the sub-satellite point and the target point is only related to time. A one-dimensional search algorithm is used to solve and record the interval Minimum ground distance between the inner subsatellite point and the target point and the corresponding time The one-dimensional search algorithm is the golden section method, which has been widely described in public literature; the dynamic model used for satellite orbit extrapolation is consistent with step 1;

[0050] Step 4, for i=1,2,L,m, if Less than or equal to the equivalent half width W of satellite earth observation eq , then the time is the passing time of the satellite observable target, and all observable passing times are recorded as j=1,2,L,s;

[0051] The calculation method of the equivalent half-width of satellite earth observation is shown in formula (7):

[0052]

[0053] Where W sensor is the sensor width of the satellite when there is no lateral swing, θ swath is the geocentric angle corresponding to the half width of the satellite sensor, r is the distance from the center of the earth, R eis the radius of the earth, c is the distance from the satellite to the ground boundary of the sensor width, β swath is the semi-conical angle corresponding to the field of view of the satellite sensor, is the maximum roll angle of the satellite, β is the equivalent field of view semi-cone angle after considering the roll of the satellite, W eq is the equivalent half-width of satellite earth observation;

[0054] Step 5: sort by time j=1,2,L,s are sorted to obtain the satellite observation over-the-top time of the ground target sorted by time k=1,2,L,s.

Claims

1. A method for fast and high-precision calculation of satellite earth observation overpass time, characterized in that: Please follow the steps below to implement: Step 1: Note that the calculation time interval is [t0,t f ], calculate and record t0-60s, from t0 to t f The time points with intervals of Δt and t f The satellite orbit epoch root number E at +60s i And the ground distance L between the subsatellite point and the target point i , i=1,2,L,n; Step 2, select k = 2, 3, L, n-1, if L k-1 >L k <L k+1 , record the interval where L has a minimum value [E k-1 ,E k+1 ], if t k-1 <t0, use E k Replace E k-1 , if t k+1 >t f , use E k Replace E k+1 ; Select k = 3, 4, L, n-1, if L k-1 =L k And L k-1 ≤L k-2 And L k ≤L k+1 , record the interval where L has a minimum value [E k-1 ,E k ]; all the above intervals are recorded as Step 3, select i = 1, 2, L, m, and is the initial number of orbital elements. The ground distance between the sub-satellite point and the target point is only related to time. A one-dimensional search algorithm is used to solve and record the interval Minimum ground distance between the inner subsatellite point and the target point and the corresponding time Step 4, select i = 1, 2, L, m, if Less than or equal to the equivalent half width W of satellite earth observation eq , then the time is the passing time of the satellite observable target, and all observable passing times are recorded as Step 5: sort by time Sort by time to obtain the satellite observation over-the-top moments of ground targets sorted by time 2. The method for fast and high-precision calculation of satellite earth observation overpass time according to claim 1, characterized in that: The range of Δt is 0<Δt≤P / 2, where P is the satellite orbit period. Preferably, for a high-precision dynamic model, in order to reduce the time spent on orbit extrapolation during subsequent local optimization, Δt is taken as 1 minute. For a simplified dynamic model, orbit extrapolation takes very little time, and in order to reduce the number of time points, Δt is taken as P / 2.

3. A method for fast and high-precision calculation of satellite earth observation overpass time according to claim 1 or 2, characterized in that: In step 1, t0-60s and the time from t0 to t f The time points with intervals of Δt and t f The specific process of the satellite orbit elements at +60s and the ground distance between the sub-satellite point and the target point is as follows: A high-precision dynamic model is used to calculate the number of satellite orbit elements at each time point, as shown in formula (1): In the formula, r is the satellite radius vector, μ is the earth's gravitational constant, and a perturbed is the total perturbation acceleration including the non-spherical perturbation of the Earth, the atmospheric drag perturbation, the third body gravitational perturbation and the light pressure perturbation; The ground distance calculation method between the satellite sub-satellite point and the target point is shown in formula (6): Where L is the ground distance between the satellite sub-satellite point and the target, R e is the radius of the Earth, r satellite is the radius vector from the center of the Earth to the satellite, r target is the radius vector from the center of the earth to the target point.

4. A method for fast and high-precision calculation of satellite earth observation overpass time according to claim 1 or 2, characterized in that: When calculating the satellite orbit elements at each time point in step 1, if the accuracy requirement is moderate, in order to obtain a faster calculation speed, the average orbit motion model that only considers the J2 perturbation is adopted, as shown in formula (2): Where a is the semi-major axis of the orbit, e is the eccentricity, incl is the orbit inclination, Ω is the right ascension of the ascending node, ω is the argument of perigee, M is the mean anomaly, t is the time, t0 is the initial time, According to formula (3), According to formula (4), Calculate according to formula (5):

5. The method for fast and high-precision calculation of satellite earth observation overpass time according to claim 1 is characterized in that: The one-dimensional search algorithm in step 3 is the golden section method, and the dynamic model used for satellite orbit extrapolation is the same as that in step 1.

6. The method for fast and high-precision calculation of satellite earth observation overpass time according to claim 1, characterized in that: The calculation process of calculating the equivalent half width of satellite earth observation in step 4 is as follows: Where W sensor is the sensor width of the satellite when there is no lateral swing, θ swath is the geocentric angle corresponding to the half width of the satellite sensor, r is the distance from the center of the earth, R e is the radius of the earth, c is the distance from the satellite to the ground boundary of the sensor width, β swath is the semi-conical angle corresponding to the field of view of the satellite sensor, is the maximum roll angle of the satellite, β is the equivalent field of view semi-cone angle after considering the roll of the satellite, W eq is the equivalent half-width of satellite earth observation.

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