CN110727003A - Pseudo-range simulation method of Beidou satellite navigation system - Google Patents

Pseudo-range simulation method of Beidou satellite navigation system Download PDF

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CN110727003A
CN110727003A CN201911172330.8A CN201911172330A CN110727003A CN 110727003 A CN110727003 A CN 110727003A CN 201911172330 A CN201911172330 A CN 201911172330A CN 110727003 A CN110727003 A CN 110727003A
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satellite
time
receiver
clock
signal
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李怀建
刘阳
杜小菁
徐荣景
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Beijing University of Technology
Beijing Institute of Technology BIT
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Beijing University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/23—Testing, monitoring, correcting or calibrating of receiver elements

Abstract

The invention relates to a pseudo-range simulation method of a Beidou satellite navigation system, and belongs to the technical field of satellite navigation positioning. The method calculates signal emission time by giving an initial pseudo-range; obtaining corrected signal transmitting time by correcting the difference value of the satellite clock total clock; judging whether the satellite is visible or not for the receiver, if so, calculating the geometric distance between the satellite and the receiver and the propagation delay caused by atmospheric refraction, updating the pseudo range until the pseudo range meeting the precision requirement is obtained, then generating a corresponding satellite signal by a navigation satellite signal simulator to be emitted, receiving the satellite signal by the receiver, processing and resolving the satellite signal, namely positioning to the position and the simulation time preset by simulation input in advance, and obtaining a Beidou satellite positioning scene which is the same as an external field in a laboratory for testing the performance of the receiver and achieving the purpose of testing the performance of the receiver by simulation.

Description

Pseudo-range simulation method of Beidou satellite navigation system
Technical Field
The invention relates to a pseudo-range simulation method of a Beidou satellite navigation system, and belongs to the technical field of satellite navigation positioning.
Background
The global satellite navigation system is an important spatial information infrastructure, and the united states GPS and russian GLONASS systems are relatively mature satellite navigation systems. And after the Beidou navigation test system is built in 2000, China also becomes the third country with the autonomous satellite navigation system in the world after America and Russia. In 12 months 2012, the beidou system firstly has the capabilities of positioning, navigation and time service and short message communication service covering the asia-pacific region. The simulation method is an important means for researching the performance of the navigation system, for some navigation system experiments, the navigation receiver is often arranged on a high-dynamic carrier such as a missile, an airplane and the like, the cost is high in practice and even difficult to achieve when the navigation receiver is tested, at the moment, the navigation receiver can be replaced by a navigation satellite signal simulator in a simulation mode, Beidou satellite signals under various real environments can be generated, the positioning requirements of the experiments are met, the simulation method has important application values in the fields of research and development tests of the navigation receiver and navigation interference equipment, simulation research of the navigation system and the like, and with the increasingly wide application field of the Beidou system, the development of various high-performance navigation satellite signal simulators aiming at the Beidou system becomes an inevitable trend.
The pseudo range is a most basic distance measurement value in the navigation system, and the pseudo range directly determines the positioning precision, so that the pseudo range simulated by the navigation satellite simulator needs to be consistent with the real situation, and the effectiveness of a simulation experiment of the navigation system can be ensured. The existing method adopts a mechanical equation integration method to carry out constellation simulation, utilizes an analytic method to calculate each order derivative of the satellite position, a user inputs position, speed, acceleration and jerk sampling values to obtain the satellite-ground apparent distance change rate, and calculates the high order derivative of a pseudo range error item through a difference method, so that the precision is low; the existing method also adopts an expression for deriving a user high-order derivative by adopting analytical modeling, the satellite position high-order derivative is calculated by adopting a polynomial, and the pseudorange is fitted by the high-order polynomial, so that the precision is low.
The pseudo range obtained by the existing method is low in precision and large in calculation amount, calculation time is increased, real-time performance of a navigation satellite signal simulator is affected, and the method is not suitable for being used when only the position of a navigation receiver is provided if a Kepler orbit element is adopted in a satellite constellation in simulation.
Disclosure of Invention
The invention aims to solve the problems of low pseudo-range precision, poor real-time performance and small application range of the conventional pseudo-range simulation, and provides a pseudo-range simulation method of a Beidou satellite navigation system. In the real case, the navigation receiver uses pseudoranges for position resolving, whereas at the present moment the signals received by the receiver from the visible satellites were transmitted by the satellites at a previous moment, the receiver receiving these signals in the same epoch, but for different satellites in different epochs. When a simulation experiment is carried out by using a navigation satellite signal simulator, the position of a receiver and the signal receiving time are input and set in the navigation satellite signal simulator in advance, delay exists between signal receiving and transmitting, and the delay between signal receiving and transmitting is closely related to the geometric distance between the satellite and the receiver, the propagation delay caused by atmospheric refraction and the like, so that the position of the satellite at the signal transmitting moment and the signal transmitting time need to be calculated, the navigation satellite signal simulator needs to calculate a pseudo range, and a satellite signal is generated and transmitted.
A pseudo-range simulation method of a Beidou satellite navigation system comprises the following steps:
step 1, giving an initial pseudo range, and calculating signal transmission time through the pseudo range;
the expression of the pseudorange ρ is:
ρ＝c(tr-ts) (1)
in the formula, trFor signal reception time, tsIs the signal emission time, c is the speed of light;
the signal propagation time τ is expressed as:
Figure BDA0002289058070000021
then:
ts＝tr-τ (3)
step 2, calculating the error of the satellite clock;
due to the time deviation, the existence of frequency drift and the reason that satellite errors can be accumulated along with time, the satellite time slightly deviates from the system time, and the error generated by the satellite time deviation is defined as a satellite clock error; the satellite clock error Δ t is expressed as a second order polynomial as follows:
Δt＝a0+a1(ts-toc)+a2(ts-toc)2(4)
in the formula, tocFor ephemeris reference time, a0Is a zero offset correction parameter of the star clock, a1Correction of parameters for the clock speed of the star clock, a2Correcting parameters for the clock speed rate of the star clock;
step 3, calculating a relativistic effect correction quantity;
the Beidou satellite runs at a high speed on the orbit, and generates a large relative speed for a ground receiver, and according to a theory of relativity, a satellite clock generates deviation with a ground clock;
in order to correct the influence of this deviation, the error caused by the relativistic effect, the correction quantity Δ t of which must be compensated in the error correction stagerThe calculation formula of (2) is as follows:
Figure BDA0002289058070000031
in the formula, esIs the satellite orbital eccentricity, asFor the long radius of the satellite orbit, EkFor the satellite near point angle, F is a constant defined as:
Figure BDA0002289058070000032
wherein μ is an attractive force constant;
step 4, obtaining corrected signal transmitting time by correcting the satellite clock total clock difference value;
total clock difference delta t of satellite clocksComprises the following steps:
δts＝Δt+Δtr-TGD(7)
in the formula, TGDThe time delay correction value is a group wave time delay correction value;
the corrected signal transmission time t is:
t＝ts-δts(8)
step 5, calculating the position and the speed of the satellite at the transmitting moment;
after the corrected signal transmitting time t is obtained, substituting the corrected signal transmitting time t into a satellite orbit theory to obtain the position and the speed of a satellite at the signal transmitting moment in an orbit plane rectangular coordinate system;
position (x) of satellite in earth-centered earth-fixed rectangular coordinate systemk,yk,zk) The calculation is as follows:
Figure BDA0002289058070000033
wherein (x'k,y'k) For the position of the satellite in a rectangular coordinate system of the orbital plane, ikIs the track inclination angle; omegakThe right ascension of the satellite orbit;
speed of satellite in earth-centered earth-fixed rectangular coordinate system
Figure BDA0002289058070000034
The calculation is as follows:
Figure BDA0002289058070000041
in the formula (I), the compound is shown in the specification,
Figure BDA0002289058070000042
the velocity of the satellite in the orbital plane rectangular coordinate system,
Figure BDA0002289058070000043
for track inclination ikA derivative with respect to time;to the right ascension omega of the satellite orbitkA derivative with respect to time; (x'k,y'k)、
Figure BDA0002289058070000045
ik、Ωk、Andthe ephemeris data are calculated and obtained by a navigation satellite signal simulator;
step 6, judging whether the satellite is visible or not for the receiver, if not, ending, and if so, performing step 7;
obtaining satellite position (x)k,yk,zk) Then, the known receiver position is (x)r,yr,zr) Then the receiver-to-satellite observation vector is:
Figure BDA0002289058070000048
where Δ E, Δ N, and Δ U are the east, north, and sky components of the observation vector, respectively, and S is a coordinate transformation matrix defined by the longitude λ and latitude φ of the receiver position:
Figure BDA0002289058070000049
after the observation vector from the receiver to the satellite is obtained, the satellite elevation angle θ is:
Figure BDA00022890580700000410
if the satellite elevation angle is larger than 0 degrees, the satellite can be seen; if the elevation angle of the satellite is less than or equal to 0 degrees, the satellite is invisible and cannot be used for positioning, and the iteration is ended;
step 7, calculating a geometric distance r between the satellite and the receiver and propagation delay caused by atmospheric refraction, updating the signal propagation time tau to obtain a new pseudo range, ending if the pseudo range precision meets the requirement, and replacing the new pseudo range in the step 1 if the pseudo range precision does not meet the requirement, and performing iterative calculation until the requirement is met;
the geometrical distance of the receiver to the satellite is:
Figure BDA0002289058070000051
considering the propagation delay caused by atmospheric refraction, calculating ionospheric delay I and tropospheric delay T of satellite signal propagation by using an atmospheric mathematical model, and then:
Figure BDA0002289058070000052
after the pseudo range meeting the precision requirement is obtained, the navigation satellite signal simulator generates a corresponding satellite signal to be transmitted, the receiver receives the satellite signal, positioning calculation is carried out after processing, namely the position and the simulation time which are preset by simulation input can be positioned, and a Beidou satellite positioning scene which is the same as an external field can be obtained in a laboratory for testing the performance of the receiver.
The method can calculate the high-precision pseudo range through iteration when only the position of the receiver is provided, provide data for the positioning of the receiver and achieve the aim of simulating and testing the performance of the receiver.
Advantageous effects
1. The pseudo range calculated by the method is high in precision, and the obtained simulation scene is consistent with a real scene.
2. The invention has relatively small calculation amount, shortens the calculation time and ensures the simulation real-time performance of the navigation signal simulator.
3. The invention only needs to input the static position of the receiver or the dynamic track of the receiver in the navigation signal simulator, has less information required to be provided by simulation, can meet different simulation requirements and has wide application range.
Drawings
Fig. 1 is a schematic flow chart of a pseudo-range simulation method.
Detailed Description
The invention is further described with reference to the following figures and examples.
In order to verify the feasibility of the method, the receiver arranged in the navigation satellite signal simulator needs to be positioned to the positions of the east longitude 116 degrees, the north latitude 40 degrees and the height 1000m, namely the positions of the earth-center-earth-fixed rectangular coordinate system are (-2145157.653m,4398224.977m and 4078628.360m), and the simulation time is set to be 1 month in 2020, 1 day in 0 hour. According to the actual situation of the Beidou satellite, important information such as satellite clock error correction parameters, ephemeris parameters, ionosphere delay, troposphere delay and the like is set, and the navigation satellite signal simulator can generate a navigation message containing the information into a satellite signal to be transmitted for positioning.
As shown in the schematic flow chart of the pseudo-range simulation method in fig. 1, in a simulation experiment, a position and simulation time to be positioned by a receiver are set according to simulation requirements, and then a pseudo-range is calculated according to the pseudo-range simulation method of the beidou satellite navigation system, wherein the pseudo-range simulation iterative algorithm of the beidou satellite navigation system comprises the following steps:
1. calculating signal transmission time
Pseudo range rho is signal receiving time trAnd a signal transmission time tsThe difference between is multiplied by the speed of light c:
ρ＝c(tr-ts) (16)
defining the signal propagation time τ as:
Figure BDA0002289058070000061
initially, the propagation time tau of signal is set to 78ms, and the receiving time t of known signal is setrThen signal transmission time tsComprises the following steps:
ts＝tr-τ (18)
2. calculating clock error of satellite clock
The satellite time will always deviate slightly from the system time due to time drift, the presence of frequency drift, and the accumulation of satellite errors over time, the resulting errors being defined as satellite clock errors. The satellite clock error can be expressed as a second order polynomial as follows:
Δt＝a0+a1(ts-toc)+a2(ts-toc)2(19)
in the formula, tocFor ephemeris reference time, a0Is a zero offset correction parameter of the star clock, a1Correction of parameters for the clock speed of the star clock, a2The parameters are provided for the clock speed rate correction parameters of the star clock and the navigation messages.
3. Calculating relativistic effect correction
The Beidou satellite runs at a high speed on the orbit, and generates a large relative speed for a ground receiver. According to the theory of relativity, the satellite clock generates a certain deviation from the ground clock. The orbit heights and average speeds of the Beidou GEO/IGSO and the MEO are different, so that the clocks of the Beidou GEO/IGSO and the MEO are influenced differently by relativistic effects, the satellite-borne atomic clock of the GEO/IGSO is 46.6 mu s per day, and the satellite-borne atomic clock of the MEO is 40.6 mu s per day
To correct this effect, the error caused by the relativistic effect, the correction Δ t, must be compensated in an error correction unitrThe calculation formula of (2) is as follows:
in the formula, esIs the satellite orbital eccentricity, asIs the long radius of the track, EkFor the satellite near point angle, F is a constant defined as:
Figure BDA0002289058070000071
where μ is an attraction constant.
4. Correcting satellite clock total clock difference
Taking into account group-wave delay correction values TGDGiven by the first data block of the satellite navigation message, the satellite clock total clock difference value deltatsComprises the following steps:
δts＝Δt+Δtr-TGD(22)
the corrected signal transmission time t is:
t＝ts-δts(23)
5. calculating satellite positions and velocities;
and after the corrected signal transmitting time t is obtained, substituting the corrected signal transmitting time t into a satellite orbit theory, obtaining the satellite position and the satellite speed at the signal transmitting moment by using ephemeris parameters in a navigation message, and considering that the earth always rotates in the processes of transmitting, spreading and receiving satellite signals and the satellite position needs to be corrected. The following table shows ephemeris parameters and their meaning.
Ephemeris parameters and their meaning
Figure BDA0002289058070000072
Figure BDA0002289058070000081
The satellite position and velocity calculation steps can be summarized as follows:
(1) calculating the planned time tk
tk＝t-toe(24)
For a valid ephemeris, the value of t should be at toeWithin two hours before and after, thus tkShould be less than 7200s in absolute value. And because the Beidou time is cleared every week, t is sometimes zerokA 604800s deviation occurs. If equation (24) calculates tkAbove 302400s, 604800s should be subtracted; if t iskLess than 302400s, 604800s should be added. In case of normal operation of the receiver, tkShould be negative.
(2) Calculating the average angular velocity n of the satellite
The average angular velocity n of the satellite in the ideal case is:
Figure BDA0002289058070000082
substituting the average angular velocity correction value delta n to obtain:
n＝n0+Δn (26)
(3) calculating mean and near point angle M of signal emission timek
Ephemeris parameter M0Substituting into a model thatMean and near point angle M of emission time can be obtainedk：
Mk＝M0+n·tk(27)
(4) Calculating the angle of approach point E of signal transmission timek
The mean and near point angle M is calculated by the formula (27)kIn combination with ephemeris parameters esThe approximate point angle E can be solved by an iterative methodk. The three relations are given as follows:
M＝E-essinE (28)
and solving by adopting an iteration method, and generally performing 2-3 times of iteration to obtain an iteration solution with high convergence precision.
(5) Calculating true near point angle v of signal transmitting timek
νkAnd Ek、esThe relationship of (a) to (b) is as follows:
Figure BDA0002289058070000091
νkhas a value of (-pi, pi)](arc) inside.
(6) Calculating the angular distance phi of the rising point at the time of signal transmissionk
ΦkThe calculation formula of (2) is as follows:
Φk＝νk+ω (30)
(7) perturbation correction term delta u for calculating signal emission timek、δrkAnd δ ik
Perturbation correction term δ uk、δrkAnd δ ikFrom C in ephemeris parametersuc、Cus、Crc、Crs、Cic、CisAngle distance of elevation crossing phi derived from equation (30)kAnd (3) obtaining:
(8) calculating the elevation intersection angular distance u after perturbation correctionkSatellite radial length rkAnd track inclination angle ik
Substituting the perturbation correction amount obtained by the formula (31) into the following formulas to obtain the elevation intersection angular distance ukSatellite radial length rkAnd track inclination angle ik：
Figure BDA0002289058070000093
(9) Calculating position (x ') of satellite in orbital plane rectangular coordinate system'k,y'k)
Will polar coordinate (r)k,uk) Converting the position of the rectangular coordinate system in the rail plane to obtain (x'k,y'k)：
Figure BDA0002289058070000094
(10) Calculating the rising point right ascension omega of the signal emission momentk
Ascent point right ascension omegakThe following linear model was used:
Figure BDA0002289058070000095
in the formula (I), the compound is shown in the specification,
Figure BDA0002289058070000101
is the angular rate of rotation of the earth, and is a constant.
(11) Calculating the position (x) of the satellite in the Earth's center-Earth-fixed rectangular coordinate systemk,yk,zk)
Orbital plane rectangular coordinate system rotated about its X-axis by-ikThen rotates-omega around the rotated Z axiskAnd then the system can be converted into a ground-centered ground-fixed rectangular coordinate system. The coordinate rotation transformation formula is utilized to obtain:
(12) calculating the angle of approach point E of signal transmission timekDerivative with respect to time
Figure BDA0002289058070000103
Figure BDA0002289058070000104
In the formula (I), the compound is shown in the specification,
Figure BDA0002289058070000105
is a flat proximal angle MkDerivative with respect to time.
(13) Calculating the angular distance phi of the rising point at the time of signal transmissionkDerivative with respect to time
Figure BDA0002289058070000106
In the formula (I), the compound is shown in the specification,
Figure BDA0002289058070000108
is a true proximal angle vkDerivative with respect to time.
(14) Calculating the time derivative of the perturbation correction term at the time of signal emission
Figure BDA0002289058070000109
And
Figure BDA00022890580700001010
Figure BDA00022890580700001011
(15) for calculating the moment of emission of the signal
Figure BDA00022890580700001012
And
Figure BDA00022890580700001013
in the formula (I), the compound is shown in the specification,
Figure BDA00022890580700001015
is the lift intersection angular distance ukThe derivative with respect to time is that of,
Figure BDA00022890580700001016
as the satellite radial length rkThe derivative with respect to time is that of,
Figure BDA00022890580700001017
for track inclination ikThe derivative with respect to time is that of,
Figure BDA00022890580700001018
to the right ascension omega of the satellite orbitkDerivative with respect to time.
(16) Calculating the speed of the satellite in the rectangular coordinate system of the orbit plane
Figure BDA00022890580700001019
Figure BDA0002289058070000111
(17) Calculating the speed of the satellite in the earth-centered earth-fixed rectangular coordinate system
Figure BDA0002289058070000112
Figure BDA0002289058070000113
6. Judging whether the satellite is visible
Obtaining satellite position (x)k,yk,zk) Then, the known receiver position is (x)r,yr,zr) Then the receiver-to-satellite observation vector is:
Figure BDA0002289058070000114
where Δ E, Δ N, and Δ U are the east, north, and sky components of the observation vector, respectively, and S is a coordinate transformation matrix defined by the longitude λ and latitude φ of the receiver position:
Figure BDA0002289058070000115
after the satellite observation vector at the receiver position is obtained, the satellite elevation angle θ is:
Figure BDA0002289058070000116
if the satellite elevation angle is larger than 0 degrees, the satellite can be seen; otherwise, the satellite is invisible and cannot be used for positioning, and the iteration is ended.
7. Updating signal propagation time
The geometrical distance of the receiver to the satellite is:
Figure BDA0002289058070000117
considering the propagation delay caused by atmospheric refraction, calculating ionospheric delay I and tropospheric delay T of satellite signal propagation by using an atmospheric mathematical model, and then:
Figure BDA0002289058070000121
and updating the signal propagation time, namely updating the pseudo range, comparing the updated signal propagation time with the signal propagation time before updating, if the accuracy is not met, replacing the signal propagation time in the algorithm for recalculation, and repeating the steps until the convergence of the signal propagation time meets the accuracy requirement.
After iterative computation, the positions and pseudo-range information of a plurality of visible satellites are obtained, wherein for one satellite, the satellite position is (-32295346.8460m,27085485.2290m,1031071.1577 m), the satellite elevation angle is 38.93 degrees, and the satellite is visible. Considering that the total clock error of a satellite is 105795.604m, the ionospheric delay 2.2865m and the tropospheric delay 3.8284m of satellite signal propagation, theoretically, the pseudorange should be 37749636.1670m, and actually, the pseudorange calculated by the method is 37749636.1664m, the error is 0.0006m, and the pseudorange precision is high. After the receiver obtains the pseudo range meeting the precision requirement, positioning calculation is carried out, and the position and the simulation time preset by simulation can be positioned, so that a Beidou satellite positioning scene which is the same as an external field can be obtained in a laboratory and used for testing the performance of the receiver.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention, and the present invention includes but is not limited to the embodiments, and various modifications and variations of the present invention are possible. Changes, modifications, substitutions and alterations of the embodiments are within the scope of the present invention without departing from the principle and spirit of the invention.

Claims (1)

1. A pseudo-range simulation method of a Beidou satellite navigation system is characterized by comprising the following steps: the method comprises the following steps:
step 1, giving an initial pseudo range, and calculating signal transmission time through the pseudo range;
the expression of the pseudorange ρ is:
ρ＝c(tr-ts) (1)
in the formula, trFor signal reception time, tsIs the signal emission time, c is the speed of light;
the signal propagation time τ is expressed as:
Figure FDA0002289058060000011
then:
ts＝tr-τ (3)
step 2, calculating the error of the satellite clock;
due to the time deviation, the existence of frequency drift and the reason that satellite errors can be accumulated along with time, the satellite time slightly deviates from the system time, and the error generated by the satellite time deviation is defined as a satellite clock error; the satellite clock error Δ t is expressed as a second order polynomial as follows:
Δt＝a0+a1(ts-toc)+a2(ts-toc)2(4)
in the formula, tocFor ephemeris reference time, a0Is a zero offset correction parameter of the star clock, a1Correction of parameters for the clock speed of the star clock, a2Correcting parameters for the clock speed rate of the star clock;
step 3, calculating a relativistic effect correction quantity;
the Beidou satellite runs at a high speed on the orbit and can generate a large relative speed for a ground receiver; according to the theory of relativity, the satellite clock can generate deviation with the ground clock;
in order to correct the influence of this deviation, the error caused by the relativistic effect, the correction quantity Δ t of which must be compensated in the error correction stagerThe calculation formula of (2) is as follows:
Figure FDA0002289058060000012
in the formula, esIs the satellite orbital eccentricity, asFor the long radius of the satellite orbit, EkFor the satellite near point angle, F is a constant defined as:
Figure FDA0002289058060000013
wherein μ is an attractive force constant;
step 4, obtaining corrected signal transmitting time by correcting the satellite clock total clock difference value;
total clock difference delta t of satellite clocksComprises the following steps:
δts＝Δt+Δtr-TGD(7)
in the formula, TGDThe time delay correction value is a group wave time delay correction value;
the corrected signal transmission time t is:
t＝ts-δts(8)
step 5, calculating the position and the speed of the satellite at the transmitting moment;
after the corrected signal transmitting time t is obtained, substituting the corrected signal transmitting time t into a satellite orbit theory to obtain the position and the speed of a satellite at the signal transmitting moment in an orbit plane rectangular coordinate system;
position (x) of satellite in earth-centered earth-fixed rectangular coordinate systemk,yk,zk) The calculation is as follows:
Figure FDA0002289058060000021
wherein (x'k,y'k) For the position of the satellite in a rectangular coordinate system of the orbital plane, ikIs the track inclination angle; omegakThe right ascension of the satellite orbit;
speed of satellite in earth-centered earth-fixed rectangular coordinate system
Figure FDA0002289058060000022
The calculation is as follows:
in the formula (I), the compound is shown in the specification,
Figure FDA0002289058060000024
the velocity of the satellite in the orbital plane rectangular coordinate system,
Figure FDA0002289058060000025
for track inclination ikA derivative with respect to time;
Figure FDA0002289058060000026
to the right ascension omega of the satellite orbitkA derivative with respect to time; (x'k,y'k)、
Figure FDA0002289058060000027
ik、Ωk、
Figure FDA0002289058060000028
And
Figure FDA0002289058060000029
the ephemeris data are calculated and obtained by a navigation satellite signal simulator;
step 6, judging whether the satellite is visible or not for the receiver, if not, ending, and if so, performing step 7;
obtaining satellite position (x)k,yk,zk) Then, the known receiver position is (x)r,yr,zr) Then the receiver-to-satellite observation vector is:
Figure FDA0002289058060000031
where Δ E, Δ N, and Δ U are the east, north, and sky components of the observation vector, respectively, and S is a coordinate transformation matrix defined by the longitude λ and latitude φ of the receiver position:
Figure FDA0002289058060000032
after the observation vector from the receiver to the satellite is obtained, the satellite elevation angle θ is:
Figure FDA0002289058060000033
if the satellite elevation angle is larger than 0 degrees, the satellite can be seen; if the elevation angle of the satellite is less than or equal to 0 degrees, the satellite is invisible and cannot be used for positioning, and the iteration is ended;
step 7, calculating a geometric distance r between the satellite and the receiver and propagation delay caused by atmospheric refraction, updating the signal propagation time tau to obtain a new pseudo range, ending if the pseudo range precision meets the requirement, and replacing the new pseudo range in the step 1 if the pseudo range precision does not meet the requirement, and performing iterative calculation until the requirement is met;
the geometrical distance of the receiver to the satellite is:
Figure FDA0002289058060000034
considering the propagation delay caused by atmospheric refraction, calculating ionospheric delay I and tropospheric delay T of satellite signal propagation by using an atmospheric mathematical model, and then:
Figure FDA0002289058060000035
after the pseudo range meeting the precision requirement is obtained, the navigation satellite signal simulator generates a corresponding satellite signal to be transmitted, the receiver receives the satellite signal, positioning calculation is carried out after processing, namely the position and the simulation time which are preset by simulation input can be positioned, and a Beidou satellite positioning scene which is the same as an external field can be obtained in a laboratory for testing the performance of the receiver.
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