Low-orbit constellation performance evaluation method for enhancing BDSBAS

Abstract

The invention provides a low-orbit constellation performance evaluation method for enhancing BDSBAS, and relates to the technical field of satellite-based enhancement. The method comprises the following steps: firstly, constructing a low-orbit constellation coverage model, and carrying out coverage performance calculation on a low-orbit constellation in the aspect of enhancing BDSBAS performance; introducing a Beidou satellite base on the basis of a low-orbit constellation, and carrying out analysis and calculation of inter-satellite visibility performance by using a visibility model; calculating the monitoring geometric accuracy factor SSDOP of the Beidou navigation satellite based on the ephemeris and clock error correction accuracy of the Beidou navigation satellite when the low earth orbit satellite is used as a monitoring station; and finally, the monitoring geometric accuracy factor of the Beidou navigation satellite and the coverage and visibility of the low-orbit satellite constellation are used as evaluation criteria to evaluate whether the low-orbit satellite constellation can be used for enhancing the service performance of the BDSBAS system. According to the method, the contribution of the low-orbit satellite constellation to the performance improvement of the BDSBAS is quantified, and a theoretical basis is provided for the design optimization of the BDSBAS.

Description

Technical Field

[0001] The present invention relates to the field of satellite-based augmentation technology, and in particular, to a method for evaluating the performance of a low-Earth orbit constellation for enhancing BDSBAS. Background Art

[0002] The BeiDou Satellite Based Augmentation System (BDSBAS) continuously tracks and observes navigation satellites through a certain number of ground monitoring stations, and then transmits the observation data to the master control station. The master control station uses the observation data to calculate the satellite orbit correction, clock error correction, and integrity information, and then broadcasts them to the user terminal through a Geostationary Earth Orbit (GEO) satellite. After receiving the correction, the user receiver can correct the satellite ephemeris orbit clock error to improve the positioning accuracy. At the same time, the protection level is calculated using the received integrity parameters to measure whether the current navigation service meets the user's needs. This technology is mainly used in the field of civil aviation. With the maturity of this technology, it has been gradually widely applied in high-integrity demand fields such as autonomous driving, unmanned aerial vehicles, marine shipping, low-altitude economy, and disaster emergency. However, the construction of overseas monitoring stations for BDSBAS is restricted, and the system service can only cover China and its surrounding areas, unable to achieve global integrity monitoring of the Beidou system. Therefore, in view of the problem of insufficient overseas ground monitoring stations for BDSBAS, it is considered to use low-Earth orbit (LEO) satellites as the space-based monitoring stations for BDSBAS to achieve global continuous monitoring of Beidou satellites. However, LEO satellites face problems such as a relatively small ground coverage range of a single satellite, resulting in poor temporal and spatial continuity of monitoring, and differences in observation conditions, observation accuracy, and data transmission stability between different satellites. Existing research on low-Earth orbit constellations mainly stays in the fields of joint positioning of low-Earth orbit satellite constellations and precise orbit determination of low-Earth orbit satellite constellations, and the performance requirements for low-Earth orbit constellations in these fields are different from the performance requirements for low-Earth orbit satellite constellations as space-based monitoring stations to enhance BDSBAS. Therefore, how to measure the improvement effect of low-Earth orbit satellite constellations on BDSBAS has become a research hotspot in this field. The present invention performs relevant performance calculations on the low-Earth orbit satellite constellation for enhancing BDSBAS by establishing a performance model, so as to evaluate whether the constellation meets the relevant performance requirements as a space-based monitoring station for BDSBAS. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for evaluating the performance of a low-Earth orbit constellation for enhancing BDSBAS in view of the above-mentioned deficiencies of the prior art, so as to measure the improvement effect of the low-Earth orbit satellite constellation on BDSBAS, quantify the contribution of the low-Earth orbit satellite constellation to the performance improvement of BDSBAS, and provide a theoretical basis for the design and optimization of BDSBAS.

[0004] To solve the above technical problems, the technical solution adopted by the present invention is as follows: A method for evaluating the performance of a low-earth orbit constellation for enhancing BDS BAS constructs a low-earth orbit constellation coverage model and calculates the coverage performance of the low-earth orbit constellation in enhancing the performance of BDS BAS; on the basis of the low-earth orbit constellation, the Beidou constellation is introduced, and the inter-satellite visibility performance is analyzed and calculated using the visibility model; based on the Geometric Dilution of Precision (GDOP), the improved Satellite Surveillance Dilution of Precision (SSDOP) is obtained; based on the Beidou navigation satellite ephemeris and clock error correction accuracy, when the low-earth orbit satellite is used as a space-based monitoring station, the Satellite Surveillance Dilution of Precision (SSDOP) of the Beidou navigation satellite is calculated; the Satellite Surveillance Dilution of Precision of the Beidou navigation satellite, together with the coverage and visibility of the low-earth orbit satellite constellation, is used as an evaluation criterion to evaluate whether the low-earth orbit constellation can be used to enhance the service performance of the BDS BAS system. The specific steps are as follows:

[0005] Step 1: Establish a low-earth orbit constellation coverage model, determine the average coverage multiplicity of the ground area, and evaluate the coverage of the low-earth orbit satellite constellation;

[0006] Step 1.1: Establish a coverage model for a single low-earth orbit satellite and determine the spherical cap surface area covered by the low-earth orbit satellite; set the satellite altitude cut-off angle as the judgment condition for whether the satellite is visible to the ground;

[0007] The low-earth orbit constellation coverage model is a tool for measuring the ground coverage area of a single satellite, the coverage multiplicity and coverage rate of multiple satellites to the ground; the ground coverage area of the low-earth orbit satellite is directly related to the orbital altitude of the satellite and the satellite altitude cut-off angle; the coverage model of a single low-earth orbit satellite is as follows:

[0008]

[0009] Among them, R is the radius of the earth, R = 6378 km, H is the orbital altitude of the satellite, α is the satellite altitude cut-off angle, and ψ is the semi-central angle within the visible radian range of the satellite to the ground;

[0010] According to the semi-central angle ψ within the visible radian range of the satellite to the ground, the spherical cap surface area S covered by the low-earth orbit satellite is derived cov , as shown in the following formula:

[0011] S cov = 2πR 2 (1 - cosψ)

[0012] The spherical cap surface area covered by a low-earth orbit satellite is the coverage area of a single satellite. The larger the coverage area of a single satellite, the higher the coverage multiplicity.

[0013] Step 1.2: Determine the altitude cutoff angle of the satellite according to the coverage model of a single low-earth orbit satellite, and calculate the average coverage multiplicity of the satellite in the ground area.

[0014] Divide the ground area into grid points, and set the latitude and longitude of the ground grid points as (L e , l e ), and the latitude and longitude of the satellite as (L s , l s ). Then, the following relationship exists among the satellite, the ground grid point, and the earth's center:

[0015] cos(γ) = cos(L e )cos(L s )cos(l s - l e ) + sin(L e )sin(L s )

[0016] where γ is the angle between the line connecting the satellite and the earth's center and the line connecting the ground grid point and the earth's center.

[0017] The distance d between the satellite and the ground station is shown in the following formula:

[0018]

[0019] where r s is the distance from the satellite to the earth's center, and r e is the distance from the ground grid point to the earth's center.

[0020] Calculate the satellite elevation angle El of the ground grid point through the trigonometric relationship between d and γ, as shown in the following formula:

[0021]

[0022] Set the altitude of the simulation satellite appropriately according to the actual situation and simulation performance requirements, and then determine the altitude cutoff angle α of the satellite according to the coverage model of a single low-earth orbit satellite in Step 1.1.

[0023] The number of satellites N j received by the ground grid point at time j is shown in the following formula:

[0024]

[0025] m = 1 + Δt·q

[0026]

[0027] where T is the operating period of the satellite constellation, Δt is the sampling step, and q is the number of samplings; m is the sampling time for each time, n is the total number of satellites in the low-earth orbit satellite constellation, and Visibility i is the visibility of the i-th satellite. If the elevation angle El of the ground grid point calculated is greater than α and less than π - α (within the visible range), then Visibility i = 1, otherwise it is 0;

[0028] Then the average coverage multiplicity N of the ground area is:

[0029]

[0030] Step 2: Introduce the Beidou constellation on the basis of the low-earth orbit constellation, establish a visibility model of the low-earth orbit satellites as space-based monitoring stations for Beidou navigation satellites, calculate the visibility judgment numbers between the low-earth orbit satellites and Beidou navigation satellites, count the number of visible satellites, and evaluate the observation performance of the low-earth orbit constellation for Beidou navigation satellites;

[0031] Step 2.1: Calculate the elevation angle between the low-earth orbit satellite and the Beidou navigation satellite;

[0032] Obtain the three-dimensional coordinates of the low-earth orbit satellite i and the Beidou navigation satellite k in the Earth-centered Earth-fixed coordinate system ECEF as follows:

[0033]

[0034] where, [x (i) , y (i) , z (i) T and [x k , y k , z k T represent the coordinates of the low-earth orbit satellite i and the Beidou navigation satellite k in three-dimensional space respectively;

[0035] The observation vector from the low-earth orbit satellite to the Beidou navigation satellite is:

[0036]

[0037] where Δx, Δy, and Δz are the observation vectors in the ECEF coordinate system;

[0038] The unit observation vector 1 of the spatial position of the Beidou navigation satellite relative to the low-earth orbit satellite i (i) is:

[0039]

[0040] ​​The observed vector from a low Earth orbit satellite to a BeiDou navigation satellite in the ECEF coordinate system is used to obtain the observed vector in the local geodetic coordinate system. The transformation formula is as follows:

[0041]

[0042] Where Δe, Δn, and Δu are the observed vectors of the low Earth orbit satellite in the local geodetic coordinate system. Δe is the eastward component, Δn is the northward component, and Δu is the upward component; S is the coordinate transformation matrix, as shown below:

[0043]

[0044] Where, λ are the latitude and longitude of the low Earth orbit satellite in the geodetic coordinate system respectively;

[0045] The elevation angle between the low Earth orbit satellite and the BeiDou navigation satellite is calculated through the observed vector in the local geodetic coordinate system, as shown in the following formula:

[0046]

[0047] Where θ is the elevation angle between the low Earth orbit satellite and the BeiDou navigation satellite;

[0048] Step 2.2: Generate the visibility observation matrix and count the number of visible satellites;

[0049] Set the simulation duration t and the simulation step Δt', then the number of samples is l:

[0050]

[0051] If the number of satellites in the low Earth orbit constellation is n and the number of BeiDou navigation satellites in the BeiDou constellation is m, by calculating the elevation angle θ between all low Earth orbit satellites and BeiDou navigation satellites at a certain sampling moment, a visibility matrix of A m×n is formed, as shown below:

[0052]

[0053] In the formula, Visibility′ (i,j) is the visibility judgment number between the low Earth orbit satellite i and the BeiDou navigation satellite j within a certain second, that is, the observed elevation angle θ of the low Earth orbit satellite to the BeiDou satellite calculated within the sampling time is compared with the satellite altitude cut-off angle α. If α < θ < π - α, then Visibility′ (i,j) is determined to be 1 visible, otherwise 0 invisible. The sum of all visibility judgment numbers within this sampling time is the observation performance of the low Earth orbit constellation on the BeiDou navigation satellite;

[0054] Perform l samplings on the low-earth orbit satellite constellation and the Beidou constellation to obtain l visibility matrices, which reflect the observation performance of the low-earth orbit constellation on Beidou navigation satellites at each sampling moment;

[0055] Step 3: Solve the correction accuracy of the ephemeris error and clock error of Beidou navigation satellites when low-earth orbit satellites are used as monitoring stations by the least squares method, and further calculate the surveillance geometric dilution of precision of Beidou navigation satellites;

[0056] Solve the correction accuracy P0 of the ephemeris error of Beidou navigation satellites by the least squares method, as shown in the following formula:

[0057]

[0058] where, l i j is the unit direction vector between the low-earth orbit satellite i as the monitoring station and the Beidou navigation satellite j, is the unit direction vector between the ground monitoring station with a unified time standard and the Beidou navigation satellite j, M is the number of monitoring stations observing the Beidou navigation satellite j; B0 is the noise covariance matrix in the pseudorange residuals, as shown in the following formula:

[0059] B0 = 2B

[0060] B = σ 2 I M×M

[0061] where, σ 2 is the measurement noise error, I M×M is the identity matrix, and B is an intermediate variable;

[0062] Calculate the correction accuracy P c of the clock error of Beidou navigation satellites by the least squares method, as shown in the following formula:

[0063]

[0064] where,

[0065] Then, when the low-earth orbit satellite is used as the monitoring station, the solution formula for the satellite surveillance geometric dilution of precision (SSDOP) of Beidou navigation satellites is as follows:

[0066]

[0067] where, σ x , σ y , σ z are the correction precisions of the satellite ephemeris error of Beidou navigation satellites in the X, Y, and Z directions, σ represents the standard deviation of the clock error of Beidou navigation satellites; tr represents the trace operation, PUDRE is the covariance matrix of the estimated values of the ephemeris error and clock error of the Beidou navigation satellite, which is composed of the ephemeris error correction accuracy P0 of the Beidou navigation satellite and the satellite clock error correction accuracy P c and is shown by the following formula:

[0068]

[0069]

[0070] where G is the geometric observation matrix, as shown by the following formula:

[0071]

[0072] where is the position vector between the Beidou navigation satellite j and the monitoring station i, i = 1, 2,..., m + n, m is the number of low-earth orbit satellites, and n is the number of ground stations; (x j , y j , z j ) is the position coordinate of the Beidou navigation satellite in the inertial coordinate system; the vector composed of the first three elements in each row of the geometric observation matrix G is the reverse of the unit observation vector

[0073] Step 4: Evaluate whether the low-earth orbit satellite constellation can be used to enhance the service performance of BDSBSA; comprehensively evaluate whether the low-earth orbit constellation can be used to enhance the service performance of BDSBSA according to the three indicators of the low-earth orbit constellation coverage, the visibility of the low-earth orbit satellite constellation to the Beidou navigation satellite, and the satellite surveillance geometric dilution of precision SSDOP value of the Beidou navigation satellite calculated by simulation in Steps 1-3.

[0074] The beneficial effects of adopting the above technical solution are as follows: A method for evaluating the performance of a low-earth orbit constellation for enhancing BDSBAS provided by the present invention calculates the coverage performance of the low-earth orbit constellation in enhancing the performance of BDSBAS by constructing a low-earth orbit constellation coverage model; introduces the Beidou constellation on the basis of the low-earth orbit constellation, and uses the visibility model to carry out the analysis and calculation of the inter-satellite visibility performance; obtains the improved satellite surveillance geometric dilution of precision SSDOP based on the satellite geometric dilution of precision, and calculates the influence degree of the layout of different monitoring stations on the ephemeris and clock errors of the Beidou navigation satellite by calculating the SSDOP of the Beidou navigation satellite. This indicator can not only adapt to the characteristics of fast orbital speed and variable constellation structure of low-earth orbit satellites, but also clearly reflect the performance contribution of the low-earth orbit satellite constellation to BDSBAS. This method quantifies the contribution of the low-earth orbit satellite constellation to the performance improvement of BDSBAS and provides a theoretical basis for the design optimization of BDSBAS. Description of the Drawings

[0075] Figure 1Flowchart of a method for evaluating the performance of a low-earth orbit constellation for enhancing BDSBAS provided by an embodiment of the present invention;

[0076] Figure 2 Schematic diagram of a low-earth orbit satellite coverage model provided by an embodiment of the present invention;

[0077] Figure 3 Schematic diagram of satellite visibility provided by an embodiment of the present invention. Detailed implementation manners

[0078] The following combines the accompanying drawings and embodiments to further describe in detail the specific implementation manners of the present invention. The following embodiments are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0079] In this embodiment, a method for evaluating the performance of a low-earth orbit constellation for enhancing BDSBAS constructs a low-earth orbit constellation coverage model to calculate the coverage performance of the low-earth orbit constellation in enhancing the performance of BDSBAS; the Beidou constellation is introduced on the basis of the low-earth orbit constellation. The Beidou constellation adopts a simplified general perturbation model (Simplified General Perturbation Model4, SGP4), and uses the visibility model to carry out the analysis and calculation of the inter-satellite visibility performance; based on the Geometric Dilution Precision (GDOP), the improved Satellite Surveillance Dilution of Precision (SSDOP) is obtained; based on the Beidou navigation satellite ephemeris and the clock error correction precision, when the low-earth orbit satellite is used as a monitoring station, the Satellite Surveillance Dilution of Precision (SSDOP) of the Beidou navigation satellite is calculated; the Satellite Surveillance Dilution of Precision of the Beidou navigation satellite and the coverage and visibility of the low-earth orbit satellite constellation are used together as evaluation criteria to evaluate whether the low-earth orbit constellation can be used to enhance the service performance of the BDSBAS system. As Figure 1 shown, it specifically includes the following steps:

[0080] Step 1: Establish a low-earth orbit constellation coverage model, determine the average coverage multiplicity of the ground area, and evaluate the coverage of the low-earth orbit satellite constellation;

[0081] The satellite elevation cut-off angle is the angle between the straight line from the satellite to the observation point and the plane where the observation point is located. The setting of the elevation cut-off angle determines the search range of the user for satellites. Therefore, the coverage performance of the satellite constellation is determined by the coverage performance of each single satellite, and the coverage performance of a single satellite is determined by the orbital parameters of the satellite. At the same elevation cut-off angle, the satellite coverage area is proportional to the orbital altitude. The higher the satellite orbit, the larger the coverage range. At the same orbital altitude, the satellite coverage area is inversely proportional to the elevation cut-off angle. The smaller the elevation cut-off angle of the satellite, the larger the coverage area. As Figure 2 shown, in the low-earth orbit satellite coverage model, the ground coverage area of the satellite is the spherical surface S centered on C cov , and this area is jointly determined by the orbital altitude and elevation cut-off angle of the satellite.

[0082] Step 1.1: Establish the coverage model of a single low-earth orbit satellite, determine the spherical cap surface area covered by the low-earth orbit satellite; set the satellite elevation cut-off angle as the judgment condition for whether the satellite is visible to the ground;

[0083] The low-earth orbit constellation coverage model is an important tool for measuring the ground coverage area of a single satellite, the coverage multiplicity and coverage rate of multiple satellites to the ground; the ground coverage area of a low-earth orbit satellite is directly related to the orbital altitude of the satellite and the elevation cut-off angle of the satellite; the coverage model of a single low-earth orbit satellite is as follows:

[0084]

[0085] Among them, R is the radius of the earth, R = 6378 km, H is the orbital altitude of the satellite, α is the satellite elevation cut-off angle, and ψ is the semi-central angle within the visible radian range of the satellite to the ground;

[0086] Derive the spherical cap surface area S covered by the low-earth orbit satellite according to the semi-central angle ψ within the visible radian range of the satellite to the ground cov , as shown in the following formula:

[0087] S cov = 2πR 2 (1 - cosψ)

[0088] The spherical cap surface area covered by the low-earth orbit satellite is the coverage area of a single satellite. However, the average coverage multiplicity of the satellite in the ground area is defined as the number of satellites covering the specified area; so if the coverage area of a single satellite is larger, the coverage multiplicity is higher; when evaluating the average coverage multiplicity of the satellite according to the coverage model of a single satellite, set an appropriate satellite elevation cut-off angle as the judgment condition for whether the satellite is visible to the ground.

[0089] Step 1.2: Determine the satellite elevation cut-off angle according to the coverage model of a single low-earth orbit satellite, and calculate the average coverage multiplicity of the satellite in the ground area;

[0090] Divide the ground area into grid points, and set the latitude and longitude of the ground grid points as (L e , l e ), and the latitude and longitude of the satellite as (L s , l s ). Then, the following relationship exists among the satellite, the ground grid point, and the earth's center:

[0091] cos(γ) = cos(L e )cos(L s )cos(l s - l e ) + sin(L e )sin(L s )

[0092] where γ is the angle between the line connecting the satellite and the earth's center and the line connecting the ground grid point and the earth's center;

[0093] The distance d between the satellite and the ground station is as shown in the following formula:

[0094]

[0095] where r s is the distance from the satellite to the earth's center, and r e is the distance from the ground grid point to the earth's center;

[0096] Calculate the satellite elevation angle El of the ground grid point through the trigonometric relationship between d and γ, as shown in the following formula:

[0097]

[0098] Set the height of the simulation satellite appropriately according to the actual situation and the simulation performance requirements, and then determine the altitude cutoff angle α of the satellite according to the single low-earth orbit satellite coverage model in step 1.1;

[0099] The number of satellites N received by the ground grid point at time j j is as shown in the following formula:

[0100]

[0101] m = 1 + Δt·q

[0102]

[0103] where T is the operating period of the satellite constellation, Δt is the sampling step, q is the number of sampling times; m is the sampling time each time, n is the total number of satellites in the low-earth orbit satellite constellation, Visibility iis the visibility of the i-th satellite. If the satellite elevation angle El of the calculated ground grid point is greater than α and less than π - α (within the visible range), then Visibility i = 1, otherwise it is 0;

[0104] Then the average coverage multiplicity N of the ground area is:

[0105]

[0106] Step 2: On the basis of the low-earth orbit constellation, introduce the Beidou constellation, establish a low-earth orbit satellite visibility model, calculate the visibility judgment number between the observing satellite and the observed satellite, count the number of visible satellites, and evaluate the observation performance of the low-earth orbit constellation on Beidou navigation satellites;

[0107] The satellite visibility model refers to judging whether two satellites are within each other's visible range within the specified satellite elevation angle. This model is based on geometric constraint conditions. By analyzing satellite orbital parameters, position relationships, and the influence of the earth's curvature, it calculates whether the straight-line connection between two satellites is blocked. Usually, the elevation angle is an important factor affecting visibility, which is defined as the angle between the direction of the line connecting the observation point and the satellite and the horizontal plane. Figure 3 is a schematic diagram of satellite visibility. In the figure, due to the earth's occlusion, the sub-satellite point P of the low-earth orbit satellite cannot be monitored by the medium earth orbit (MEO) satellite, but the low-earth orbit satellite can be mutually visible with the MEO, and the elevation angle of the satellite is θ.

[0108] Step 2.1: Calculate the elevation angle between the low-earth orbit satellite and the Beidou navigation satellite;

[0109] Obtain the three-dimensional coordinates of the low-earth orbit satellite i and the Beidou navigation satellite k in the Earth-Centered, Earth-Fixed (ECEF) coordinate system as follows:

[0110]

[0111] where, [x (i) , y (i) , z (i) T and [x k , y k , z k T respectively represent the coordinates of the low-earth orbit satellite i and the Beidou navigation satellite k in three-dimensional space;

[0112] The observation vector from the low-earth orbit satellite to the Beidou navigation satellite is:

[0113] ​​

[0114] where Δx, Δy, and Δz are the observation vectors in the ECEF coordinate system respectively;

[0115] The unit observation vector 1 of the spatial position of the Beidou navigation satellite relative to the low-earth orbit satellite i (i) is:

[0116]

[0117] According to the observation vectors, the observation vectors in the topocentric coordinate system with the low-earth orbit satellite as the coordinate origin can be equivalently obtained. The topocentric coordinate system usually takes the position of the user as the coordinate origin, and the three coordinate axes are the mutually perpendicular east, north, and zenith directions, also known as the east-north-up (ENU) coordinates;

[0118] The observation vectors in the topocentric coordinate system are obtained from the observation vectors from the low-earth orbit satellite to the Beidou navigation satellite in the ECEF coordinate system. The transformation formula is as follows:

[0119]

[0120] where Δe, Δn, and Δu are the observation vectors of the low-earth orbit satellite in the topocentric coordinate system, Δe is the east component, Δn is the north component, and Δu is the zenith component; S is the coordinate transformation matrix, as shown below:

[0121]

[0122] where λ are the latitude and longitude of the low-earth orbit satellite in the geodetic coordinate system respectively; The coordinate transformation process includes two rotation steps: First, rotate the ECEF coordinate system around the Z axis of the earth-centered earth-fixed coordinate system by λ + 90°, and then rotate around the new X axis by 90° - After that, the obtained coordinate system is the topocentric coordinate system.

[0123] Calculate the elevation angle between the low-earth orbit satellite and the Beidou navigation satellite through the observation vectors in the topocentric coordinates, as follows:

[0124]

[0125] where θ is the elevation angle between the low-earth orbit satellite and the Beidou navigation satellite;

[0126] Step 2.2: Generate the visibility observation matrix and count the number of visible satellites;

[0127] Set the simulation duration t and the simulation step size Δt', then the number of sampling times is l:

[0128]

[0129] If the number of satellites in the LEO constellation is \(n\) and the number of Beidou navigation satellites in the Beidou constellation is \(m\), by calculating the elevation angle \(\theta\) between all LEO satellites and Beidou navigation satellites at a certain sampling moment, a visibility matrix \(A\) is formed as follows: m×n The visibility matrix is as follows:

[0130]

[0131] In the formula, Visibility′ (i,j) is the visibility judgment number between the observed satellite \(i\) and the observed satellite \(j\) within a certain second, that is, the elevation angle \(\theta\) of the LEO satellite observing the Beidou satellite calculated within the sampling time. Compared with the satellite altitude cut-off angle \(\alpha\), if \(\alpha\lt\theta\lt\pi - \alpha\), then it is determined that Visibility′ (i,j) is visible with a value of 1, otherwise it is invisible with a value of 0. The sum of all visibility judgment numbers within this sampling time is the observation performance of the LEO constellation for a certain Beidou navigation satellite; then \(l\) samplings are performed to obtain \(l\) visibility matrices;

[0132] The observation matrix calculated at each moment reflects the observation performance of the LEO constellation for all Beidou navigation satellites at that moment. After traversing \(l\) times for the LEO constellation and the Beidou constellation, \(l\) observation matrices are formed, which reflect the observation performance of the LEO constellation for all Beidou navigation satellites within the entire simulation time period.

[0133] Step 3: When the LEO satellite is used as a monitoring station, solve the correction accuracy of the ephemeris error and clock error of the Beidou navigation satellite by the least squares method, and further calculate the surveillance geometric dilution of precision of the Beidou navigation satellite;

[0134] The value of the geometric dilution of precision (GDOP) reflects the influence of the graphic structure of the navigation satellite on the positioning accuracy of ground users. Similarly, the present invention proposes the satellite surveillance geometric dilution of precision (SSDOP), which reflects the influence of different station-satellite observation layouts on the ephemeris and satellite clock correction accuracy of satellites. By calculating the comparison of SSDOP values for different monitoring station layouts, the influence of the addition of the LEO satellite constellation on improving the service accuracy of BDSBAS can be evaluated.

[0135] The correction accuracy \(P_0\) of the ephemeris error of the Beidou navigation satellite is solved by the least squares method as shown in the following formula:

[0136]

[0137] Wherein, is the unit direction vector from the LEO satellite \(i\) as the monitoring station to the Beidou navigation satellite \(j\), The unit direction vector between the ground monitoring station for unifying the time standard and the Beidou navigation satellite j, M is the number of monitoring stations observing the Beidou navigation satellite j; B0 is the noise covariance matrix in the pseudorange residual, as shown in the following formula:

[0138] B0 = 2B

[0139] B = σ 2 I M×M

[0140] Among them, σ 2 is the measurement noise error, I M×M is the identity matrix, and B is an intermediate variable;

[0141] The clock error correction accuracy P of the Beidou navigation satellite is calculated using the least squares method c , as shown in the following formula:

[0142]

[0143] Among them,

[0144] Then, when the low-earth orbit satellite is used as a monitoring station, the solution formula for the satellite surveillance geometric dilution of precision (SSDOP) of the Beidou navigation satellite is as follows:

[0145]

[0146] Among them, σ x , σ y , σ z are the satellite ephemeris error correction accuracies of the Beidou navigation satellite in the X, Y, and Z directions, σ represents the standard deviation of the Beidou navigation satellite clock error; tr represents the trace operation, and P UDRE is the covariance matrix of the Beidou navigation satellite ephemeris error and the clock error estimate value, which is composed of the ephemeris error correction accuracy P0 of the Beidou navigation satellite and the satellite clock error correction accuracy P c , as shown in the following formula:

[0147]

[0148] Among them, G is the geometric observation matrix, as shown in the following formula:

[0149]

[0150] Among them, is the position vector between the Beidou navigation satellite j and the monitoring station i, i = 1, 2,..., m + n, m is the number of low-earth orbit satellites, and n is the number of ground stations; (x j , y j , z j) are the position coordinates of the Beidou navigation satellite in the inertial coordinate system; the vector composed of the first three elements in each row of the geometric observation matrix G is the reverse of the unit observation vector

[0151] Step 4: Evaluate whether the LEO satellite constellation can be used to enhance the service performance of BDSBSA;

[0152] Through Steps 1 - 3, three indicators, namely the coverage of the LEO constellation, the visibility of the LEO satellite constellation to the Beidou navigation satellite, and the SSDOP value of the surveillance geometric dilution of precision of the Beidou navigation satellite, are calculated through simulation to evaluate whether the LEO constellation can be used to enhance the service performance of BDSBSA.

[0153] This embodiment gives the following evaluation criteria in combination with three indicators: the coverage of the LEO constellation, the visibility of the LEO satellite constellation to the Beidou navigation satellite, and the SSDOP value of the surveillance geometric dilution of precision of the Beidou navigation satellite:

[0154] (1) Ground coverage performance: Global coverage multiplicity ≥ 1;

[0155] (2) Visibility of the LEO satellite constellation to the Beidou navigation satellite: The number of Beidou navigation satellites monitored ≥ 4 during the entire time period;

[0156] (3) SSDOP value: The SSDOP value of the Beidou navigation satellite is continuously and stably low during the entire time period;

[0157] If the three performance indicators of a certain LEO satellite constellation meet the three criteria of (1), (2), and (3), it proves that the LEO constellation can be used to enhance the service performance of BDSBAS; if it does not meet (1), it proves that the LEO satellite constellation cannot achieve global station deployment as a space - based monitoring station, making BDSBAS unable to provide global services; if it does not meet (2), it proves that the LEO satellite constellation cannot effectively monitor the Beidou navigation satellite during the entire time period as a space - based monitoring station, thus unable to provide reliable observation data for the calculation of the corrections and integrity information of BDSBAS; if it does not meet (3), it proves that the LEO satellite constellation has a poor observation configuration for monitoring the Beidou navigation satellite as a space - based monitoring station and cannot effectively support the reliability of the service performance of BDSBAS.

[0158] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope defined by the claims of the present invention.

Claims

1. A method for evaluating the performance of a low-Earth orbit constellation for enhancing BDSBAS, characterized in that: Construct a low-Earth orbit constellation coverage model to calculate the coverage performance of the low-Earth orbit constellation in enhancing the performance of BDSBAS; Introduce the Beidou constellation on the basis of the low-Earth orbit constellation, and use the visibility model to carry out the analysis and calculation of the inter-satellite visibility performance; Based on the satellite geometric dilution of precision GDOP, obtain the improved satellite surveillance geometric dilution of precision SSDOP; Based on the Beidou navigation satellite ephemeris and clock error correction accuracy, calculate the surveillance geometric dilution of precision SSDOP of the Beidou navigation satellite when the low-Earth orbit satellite is used as a monitoring station; Take the surveillance geometric dilution of precision of the Beidou navigation satellite together with the coverage and visibility of the low-Earth orbit satellite constellation as the evaluation criteria to evaluate whether the low-Earth orbit constellation can be used to enhance the service performance of the BDSBAS system.

2. A method for evaluating the performance of a low-earth orbit constellation for enhancing BDSBAS according to claim 1, characterized in that: It includes the following steps: Step 1: Establish a low-Earth orbit constellation coverage model, determine the average coverage multiplicity of the ground area, and evaluate the coverage of the low-Earth orbit satellite constellation; Step 1.1: Establish a coverage model for a single low-Earth orbit satellite, and determine the spherical cap surface area covered by the low-Earth orbit satellite; Set the satellite altitude cutoff angle as the judgment condition for whether the satellite is visible to the ground; Step 1.2: Determine the satellite altitude cutoff angle according to the single low-Earth orbit satellite coverage model, and calculate the average coverage multiplicity of the satellite in the ground area; Step 2: Introduce the Beidou constellation on the basis of the low-Earth orbit constellation, establish a visibility model of the low-Earth orbit satellite as a space-based monitoring station for the Beidou navigation satellite, calculate the visibility judgment number between the low-Earth orbit satellite and the Beidou navigation satellite, count the number of visible satellites, and evaluate the observation performance of the low-Earth orbit constellation for the Beidou navigation satellite; Step 2.1: Calculate the elevation angle between the low-Earth orbit satellite and the Beidou navigation satellite; Step 2.2: Generate a visibility observation matrix and count the number of visible satellites; Step 3: Solve the ephemeris error and clock error correction accuracy of the Beidou navigation satellite when the low-Earth orbit satellite is used as a monitoring station by the least squares method, and further calculate the surveillance geometric dilution of precision of the Beidou navigation satellite; Step 4: Evaluate whether the low-Earth orbit satellite constellation can be used to enhance the service performance of BDSBSA.

3. A method for evaluating the performance of a low-earth orbit constellation for enhancing BDSBAS according to claim 1, characterized in that: The coverage model of a single low-Earth orbit satellite is as follows: Where, R is the radius of the earth, R = 6378 km, H is the orbital altitude of the satellite, α is the satellite altitude cutoff angle, and ψ is the semi-central angle within the visible radian range of the satellite to the ground; The spherical cap surface area S covered by a low-earth orbit satellite is derived based on the semi-central angle ψ within the visible radian range of the satellite to the ground cov , as shown in the following formula: S cov = 2πR 2 (1 - cosψ) The spherical cap surface area covered by the low-Earth orbit satellite is the coverage area of a single satellite. If the coverage area of a single satellite is larger, the coverage multiplicity is higher.

4. A method for evaluating the performance of a low-earth orbit constellation for enhancing BDSBAS according to claim 3, characterized in that: The said Step 1.2 includes: Divide the ground area into grid points, and set the latitude and longitude of the ground grid points as (L e , l e ), and the latitude and longitude of the satellite as (L s , l s ). Then, the following relationship exists among the satellite, the ground grid point, and the earth's center: cos(γ) = cos(L e )cos(L s )cos(l s - l e ) + sin(L e )sin(L s ) Where, γ is the included angle between the line connecting the satellite and the earth's center and the line connecting the ground grid point and the earth's center; The distance d between the satellite and the ground station is shown by the following formula: where r s is the distance from the satellite to the center of the earth, and r e is the distance from the ground grid point to the center of the earth; Calculate the satellite elevation angle El of the ground grid point through the trigonometric relationship between d and γ, as shown by the following formula: Determine the satellite altitude cutoff angle α according to the simulation satellite altitude set according to the actual situation and simulation performance requirements, thus according to the single low-Earth orbit satellite coverage model in Step 1.1; The number of satellites N received by the ground grid point at time j j As shown in the following formula: m = 1 + Δt·q where T is the operating period of the satellite constellation, Δt is the sampling step, and q is the number of sampling times; m is the sampling time each time, n is the total number of satellites in the low-earth orbit satellite constellation, and Visibility i is the visibility of the i-th satellite. If the satellite elevation angle El of the calculated ground grid point is greater than α and less than π - α, then Visibility i = 1, otherwise it is 0; Then the average coverage multiplicity N of the ground area is:

5. A method for evaluating the performance of a low-earth orbit constellation for enhancing BDSBAS according to claim 4, characterized in that: The said Step 2.1 includes: Obtain the three-dimensional coordinates of the low-Earth orbit satellite i and the BeiDou navigation satellite k in the Earth-Centered Earth-Fixed (ECEF) coordinate system as follows: Among them, [x (i) , y (i) , z (i) T and [x k , y k , z k T respectively represent the coordinates of the low-earth orbit satellite i and the Beidou navigation satellite k in three-dimensional space;​​ The observation vector from the low-Earth orbit satellite to the BeiDou navigation satellite is: where Δx, Δy, and Δz are the observation vectors in the ECEF coordinate system respectively; Unit observation vector 1 of the spatial position of the Beidou navigation satellite relative to the low-earth orbit satellite i (i) is as follows: Obtain the observation vector in the local geodetic coordinate system from the observation vector from the low-Earth orbit satellite to the BeiDou navigation satellite in the ECEF coordinate system. The transformation formula is as follows: where Δe, Δn, and Δu are the observation vectors of the low-Earth orbit satellite in the local geodetic coordinate system. Δe is the eastward component, Δn is the northward component, and Δu is the upward component; S is the coordinate transformation matrix, as shown below: wherein, λ is the latitude and longitude of the low-earth orbit satellite in the geodetic coordinate system, respectively; Calculate the elevation angle between the low-Earth orbit satellite and the BeiDou navigation satellite through the observation vector in the local geodetic coordinate system, as shown in the following formula: where θ is the elevation angle between the low-Earth orbit satellite and the BeiDou navigation satellite.

6. The low-orbit constellation performance evaluation method for enhancing BDSBAS according to claim 5, wherein: The said step 2.2 includes: Set the simulation duration t and the simulation step size Δt', then the number of samples is l: If the number of satellites in the low-earth orbit constellation is \(n\), and the number of Beidou navigation satellites in the Beidou constellation is \(m\), by calculating the elevation angle \(\theta\) between all low-earth orbit satellites and Beidou navigation satellites at a certain sampling moment, a visibility matrix of \(A\) m×n is formed as follows: where Visibility′ (i,j) is the visibility judgment number between the low-earth orbit satellite i and the Beidou navigation satellite j within a certain second, that is, the observation elevation angle θ of the low-earth orbit satellite to the Beidou satellite calculated within the sampling time is compared with the satellite altitude cut-off angle α. If α < θ < π - α, then it is determined that Visibility′ (i,j) is visible with a value of 1, otherwise it is invisible with a value of 0. Then, the sum of all visibility judgment numbers within the sampling time is the observation performance of the low-earth orbit constellation to the Beidou navigation satellite; Perform l samplings on the low-Earth orbit satellite constellation and the BeiDou constellation to obtain l visibility matrices, reflecting the observation performance of the low-Earth orbit constellation on the BeiDou navigation satellite at each sampling moment.

7. A method for evaluating the performance of a low-earth orbit constellation for enhancing BDSBAS according to claim 6, characterized in that: The said step 3 includes: Solve the ephemeris error correction accuracy P0 of the BeiDou navigation satellite by the least squares method, as shown in the following formula: Among them, is the unit direction vector from the low-earth orbit satellite i, which serves as a monitoring station, to the Beidou navigation satellite j. is the unit direction vector between the ground monitoring station with a unified time standard and the Beidou navigation satellite j, and M is the number of monitoring stations that observe the Beidou navigation satellite j; B0 is the noise covariance matrix in the pseudorange residuals, as shown in the following formula: B0 = 2B B = σ 2 I M×M Among them, σ 2 is the measurement noise error, I M×M is the identity matrix, and B is an intermediate variable; Calculate the clock error correction accuracy P of Beidou navigation satellites using the least squares method c , as shown in the following formula: Among them, Then, when the low-Earth orbit satellite is used as a monitoring station, the solution formula for the Satellite Surveillance Dilution of Precision (SSDOP) of the BeiDou navigation satellite is as follows: Among them, σ x , σ y , σ z are the correction precisions of the satellite ephemeris errors of the Beidou navigation satellite in the three directions of X, Y, and Z. σ represents the standard deviation of the Beidou navigation satellite clock error; tr represents the trace operation, and P UDRE is the covariance matrix of the estimated values of the Beidou navigation satellite ephemeris error and clock error, which is composed of the ephemeris error correction precision P0 of the Beidou navigation satellite and the satellite clock error correction precision P c and is shown in the following formula: where G is the geometric observation matrix, as shown in the following formula: Among them, is the position vector of the Beidou navigation satellite j and the monitoring station i, where i = 1, 2, …, m + n, m is the number of low-earth orbit satellites, and n is the number of ground stations; (x j , y j , z j ) are the position coordinates of the Beidou navigation satellite in the inertial coordinate system; the vector formed by the first three elements of each row in the geometric observation matrix G is the reverse of the unit observation vector 8. A method for evaluating the performance of a low-earth orbit constellation for enhancing BDSBAS according to claim 7, characterized in that: The said step 4 comprehensively evaluates whether the low-Earth orbit constellation can be used to enhance the service performance of BDSBSA according to the three indicators of the low-Earth orbit constellation coverage, the visibility of the low-Earth orbit satellite constellation to the BeiDou navigation satellite, and the SSDOP value of the BeiDou navigation satellite monitored geometric precision factor calculated by simulation in steps 1 - 3.

Images