A GNSS simulator mathematical simulation system

Abstract

The present invention proposes a GNSS simulator mathematical simulation system, which includes a constellation satellite orbit and clock parameter simulation subsystem, a navigation message generation subsystem, a user trajectory simulation subsystem, an integrity simulation subsystem, a space environment effect simulation subsystem and a simulation data generation subsystem for data interaction; the constellation satellite orbit and clock parameter simulation subsystem is composed of a space-time system model, an auxiliary database, satellite theoretical orbit data, and satellite clock theoretical parameters; the space-time system model has a built-in time system model and a coordinate system model, and the auxiliary database has built-in astronomical constants and environmental parameter values in the constellation satellite orbit and clock parameter simulation; the satellite theoretical orbit data calculates gravitational acceleration based on the input initial time, initial position velocity, integration time, and model selection control parameter data, and then uses the satellite motion equation to perform numerical integration operations on it to obtain the constellation satellite motion orbit.

Description

Technical Field

[0001] The invention belongs to the technical field of mathematical simulation, and in particular relates to a mathematical simulation system of a GNSS simulator. Background Art

[0002] Currently, GNSS satellite signal simulators are essential equipment for performance testing and algorithm verification of satellite navigation receivers. With the advancement of the times, countries are actively building and developing their own satellite navigation systems. Satellite navigation technology has evolved from the era of GPS alone to a multi-system GNSS navigation era, integrating GPS, GLONASS, BDS, GALILEO, and other compatible systems. In the future, multi-mode GNSS receivers will become a mainstream market. The need for satellite signal simulation has arisen to further study navigation system architecture and verify GNSS receiver performance indicators such as sensitivity, positioning accuracy, and compatibility.

[0003] A GNSS simulator is a simulation system that combines software and hardware, and can restore the real information of the satellite navigation system to the greatest extent possible for experimental testing and verification. As one of the most important parts of a GNSS simulator, the mathematical simulation system can provide constellation and orbit data simulation, space environment simulation, user orbit data simulation, navigation message simulation, observation data simulation, integrity simulation, etc. However, as my country's GNSS simulator technology is not yet fully mature, the above is still in the conceptual stage. The feasibility of the mathematical simulation system of the GNSS simulator and how to implement it are still relatively difficult problems. Summary of the Invention

[0004] The present invention proposes a mathematical simulation system for a GNSS simulator, which provides a complete and feasible solution for simulating constellation and orbit data, space environment, user orbit data, navigation messages, observation data simulation, integrity, etc. in the GNSS simulator, and provides effective theoretical support for the independent research and development of the GNSS simulator.

[0005] The technical solution of the present invention is achieved as follows: a GNSS simulator mathematical simulation system includes a constellation satellite orbit and clock parameter simulation subsystem, a navigation message generation subsystem, a user trajectory simulation subsystem, an integrity simulation subsystem, a space environment effect simulation subsystem and a simulation data generation subsystem, and data interaction is performed between the subsystems;

[0006] The constellation satellite orbit and clock parameter simulation subsystem consists of a space-time system model, an auxiliary database, satellite theoretical orbit data, and satellite clock theoretical parameters. The space-time system model has a built-in time system model and a coordinate system model, and the auxiliary database has built-in astronomical constants and environmental parameter values for the constellation satellite orbit and clock parameter simulation. The satellite theoretical orbit data calculates gravitational acceleration based on the input initial time, initial position velocity, integration time, and model selection control parameter data, and then uses the satellite's motion equation to perform numerical integration operations to obtain the constellation satellite's motion orbit. The satellite clock theoretical parameters are statistically calculated based on the deviation between the satellite clock face time and the standard time.

[0007] The navigation message generation subsystem generates downlink navigation messages based on the constellation satellite status, satellite orbit data, satellite clock data, space environment simulation data, wide area differential information, and integrity information;

[0008] The user trajectory simulation subsystem simulates the user's movement and generates the user's coordinate trajectory data, and provides support to the mathematical simulation subsystem for simulating the user receiver observation data;

[0009] When the satellite navigation system cannot provide navigation and positioning information services that meet user needs, the integrity simulation subsystem is triggered to simulate the integrity information generated and set the navigation satellite error and status through the simulation test system;

[0010] The space environment effect simulation subsystem includes ionospheric delay, tropospheric delay, multipath effect, relativistic effect and earth rotation effect, and monitoring station receiver error term, and examines the degree to which each error approaches the natural environment conditions and analyzes the error in signal propagation;

[0011] The simulation data generation subsystem generates pseudorange simulation, pseudorange rate simulation, carrier phase simulation, satellite-ground and inter-station time synchronization data.

[0012] As a preferred embodiment, the space-time system model is composed of a time system model and a coordinate system model, wherein the time system model includes barycenter dynamics time TDB: a time variable used for planetary / lunar ephemeris and precession and nutation calculations; terrestrial time TT: a time variable used to describe the motion equation relative to the Earth's center of mass; universal time UT1: used for coordinate conversion process parameter calculations; atomic time TAI: used for coordinate conversion process parameter calculations; Greenwich sidereal time GST: including GMST and GAST; used for coordinate conversion process parameter calculations; coordinated universal time UTC: a time record standard for simulation start and end times, ground launches, and tracking; navigation satellite time NST: BD-2's time system BDT, the conversion parameters to UTC are provided by the BD-2 navigation signal;

[0013] Coordinate system models include the Geocentric Inertial Coordinate System (J2000), used for calculating satellite orbits; the Geocentric Earth-Fixed Coordinate System (CGS2000), used to represent the trajectories of ground stations and users other than satellites; the Station-Centered Coordinate System (RCS), a northeast-celestial coordinate system used to calculate observation elevation angles and station altitudes; and the RTN Coordinate System, defined by the satellite's center of mass as its origin and its radial, tangential, and normal axes. In addition, there are geodetic and stellar coordinate systems. Different coordinate systems can be converted to each other using transformation matrices. Some conversions require precession and nutation models, data on Earth's polar motion, and Earth's rotation rate.

[0014] As a preferred embodiment, the astronomical constants in the auxiliary database include the Earth's radius, the Earth's gravitational constant and the speed of light data, and the environmental parameters include the Earth's gravitational potential coefficient, the Earth's rotation parameters, JPL ephemeris, solar radiation flux, geomagnetic index, satellite geometry and physical parameters.

[0015] As a preferred embodiment, the navigation message generation subsystem generates data in the downlink navigation message including satellite ephemeris parameters, satellite clock correction parameters, satellite working status, data reference epoch, group delay parameters, satellite almanac, ionospheric delay correction parameters, time system correction parameters, wide-area differential information and system integrity information.

[0016] As a preferred embodiment, the data in the navigation message is obtained by receiving the corresponding results generated by the information processing system. On the other hand, the simulation test system also calculates according to the corresponding algorithm, obtains the navigation parameters and algorithm by referring to the results, and obtains the satellite broadcast ephemeris by setting the initial value of the broadcast ephemeris, the observation value of the preset time, the corresponding state equation and the observation equation, and performing least squares fitting on the satellite orbit.

[0017] As a preferred embodiment, the user trajectory simulation subsystem also performs data transmission and file reading through the communication port, so that the mathematical simulation subsystem directly reads external user trajectory data through the communication port.

[0018] As a preferred implementation method, the data read by the mathematical simulation subsystem specifically generates three types of data classification. The first type is a simple user trajectory for static receiver testing, which requires the input of the receiver's position information; the second type is the receiver speed test trajectory. The speed test is mainly used to test the receiver's speed measurement performance, including linear motion trajectories and circular motion trajectories; the third type is the receiver acceleration test trajectory. The acceleration test is mainly used to test the dynamic performance of the receiver loop, including circular motion trajectories and spiral motion trajectories.

[0019] As a preferred embodiment, the navigation satellite errors and states of the simulation test system in the integrity simulation subsystem are generated in two ways. The first way is to use the ground operation and control system to generate them based on the received pseudo-range observation values through the information processing system. The second way is to use the simulation test system to directly generate them based on the errors / states.

[0020] As a preferred embodiment, the satellite-ground and inter-station time synchronization data includes satellite-ground bidirectional measurement pseudorange, pseudorange rate and carrier phase; inter-station time synchronization data and SLR data, wherein the process of generating satellite-ground bidirectional measurement data is consistent with the basic observation data of the monitoring station, and the measurement data from the ground time synchronization station to the satellite is added.

[0021] After adopting the above technical solution, the beneficial effects of the present invention are:

[0022] 1. The GNSS simulator mathematical simulation system provided by the present invention can restore the real information of the GNSS satellite navigation system to the greatest extent, and can provide constellation and orbit data simulation, space environment simulation, user orbit data simulation, navigation message simulation, observation data simulation, integrity simulation, etc., which can be used for ground experimental testing and verification of relevant satellite terminals and onboard equipment.

[0023] 2. The mathematical simulation system of the GNSS simulator proposed in this invention is a completely independent research. All relevant functions have undergone sufficient feasibility analysis and detailed theoretical verification. The entire mathematical simulation system can be deployed on hardware equipment in the form of software. After the integration of software and hardware, engineering applications can be realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0025] Figure 1 This is a diagram showing the overall architecture of a mathematical simulation system for a GNSS simulator according to an embodiment of the present invention;

[0026] Figure 2 This is a structural diagram of a space-time system model in an embodiment of the present invention;

[0027] Figure 3 This is a structural diagram of an auxiliary parameter library in an embodiment of the present invention;

[0028] Figure 4 This is a basic flow chart for generating theoretical orbit data of navigation satellites in an embodiment of the present invention;

[0029] Figure 5 This is a basic flow chart for generating satellite clock error parameters using IGS clock error data in an embodiment of the present invention;

[0030] Figure 6 This is a flow chart of integrity error calculation in an embodiment of the present invention;

[0031] Figure 7 This is a flow chart of space environment effect error simulation in an embodiment of the present invention. DETAILED DESCRIPTION

[0032] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0033] Example:

[0034] like Figures 1 to 7 As shown, the present invention provides a GNSS simulator mathematical simulation system, which mainly includes a constellation satellite orbit and clock parameter simulation subsystem, a navigation message generation subsystem, a user trajectory simulation subsystem, an integrity simulation subsystem, a space environment effect simulation subsystem, and a simulation data generation subsystem.

[0035] In the embodiment of the present application, the constellation satellite orbit and clock parameter simulation subsystem is mainly composed of a space-time system model, an auxiliary database, satellite theoretical orbit data, and satellite clock theoretical parameters;

[0036] The space-time system model primarily consists of a time system model and a coordinate system model. The time system primarily includes barycentric dynamic time (TDB), Earth time (TT), universal time (UT1), atomic time (TAI), Greenwich mean sidereal time (GST), coordinated universal time (UTC), and navigation satellite time (NST). The coordinate systems primarily include the geocentric inertial coordinate system (J2000), the Earth-centered Earth-fixed coordinate system (CGS2000), the station-centered coordinate system (RCS), the RTN coordinate system (RTN), the geodetic coordinate system, and the stellar coordinate system. Different coordinate systems can be converted to each other using transformation matrices. Some conversion processes require the use of precession and nutation models, Earth's polar motion data, and Earth's rotation rate.

[0037] The auxiliary database is established on the basis of many relatively fixed astronomical constants and environmental parameter values involved in the simulation of constellation satellite orbit and clock parameters, so as to facilitate system management and the call of other models. The astronomical constants include the radius of the earth, the gravitational constant of the earth and the speed of light; the environmental parameters include the gravitational potential coefficient of the earth, the earth's rotation parameters (updated every 5 days), JPL ephemeris, solar radiation flux, geomagnetic index, satellite geometry and physical parameters, etc.

[0038] The satellite theoretical orbit data is calculated based on the input initial time, initial position velocity, integration time, model selection control parameters and other data, and then the satellite's motion equation is used to perform numerical integration operations to obtain the constellation satellite motion orbit.

[0039] Theoretical satellite clock parameters are calculated by comprehensively considering the deviation of the satellite clock's face time from standard time. Specifically, the deviation can be divided into two main components: systematic error and noise error. The noise error that affects the clock frequency standard is very complex. In addition to common high-frequency thermal noise and shot noise, it also contains a rich variety of low-frequency noise components, such as flicker noise and random walk noise. This makes it difficult to accurately model and describe it. Simple fitting using measured data would lose the noise characteristics of the satellite clock. Therefore, this system introduces a scaling factor that retains the residuals of the fitted sampling points and then amplifies or reduces them overall. This not only preserves the clock noise characteristics but also allows the scaling factor to set the desired clock accuracy.

[0040] The IGS provides standard clock error data files for GPS satellites. Analysis of IGS GPS satellite clock error data reveals that the clock errors of most GPS satellites, composed of a0 and a1, vary very closely in a linear fashion. Therefore, the frequency deviation and drift rate of the GPS satellite clocks can be fitted based on actual clock error data over a period of time. The residual after deducting the systematic error at the sampling point is retained as the random error of the satellite clock. The deviation between the clock face time and standard time can be divided into four parts:

[0041] Δt=a0+a1t+a2t 2 +ε(t)

[0042] Where t is the simulation system time, representing the true value; a0 represents the absolute magnitude of the clock error; a1 represents the clock accuracy; a2 reflects the frequency drift rate; and ε(t) represents the time-related noise. Due to the short sampling interval, the clock error between sampling points can be calculated using interpolation.

[0043] In order to meet the user's requirements, that is, to simulate a time series with a given accuracy and stability, a scaling factor can be introduced. The clock error of the simulated time series can be expressed as:

[0044] Δt=c0a0+c1a1t+c2a2t 2 +c ε ε(t)

[0045] Among them, c0, c1, c2, c ε These are the corresponding scaling factors for the four parts respectively.

[0046] Let the simulated time series be xj ,j=1,2,3…k, and define:

[0047]

[0048] Where τ is the sampling period. Then the Allan variance of the simulated time series is:

[0049]

[0050] Substitute Δt into y i ,have to:

[0051]

[0052] Among them, Δε(t i )=(ε i+1 -ε i ) / τ will be y i Substitute σ A ,have to:

[0053]

[0054] Among them, δε(t i )=Δε i+1 -Δε i For atomic clocks on satellites, the stability is generally greater than 10 -14 , the drift rate a2 is less than 10 -18 s / s 2 , so the size of the above formula mainly depends on the second term in the brackets, so it can be approximately simplified to:

[0055]

[0056] Among them, σ Areal It indicates the approximate stability of the original data. As can be seen from the above formula, by setting c ε The size of can control the stability of the simulated time series.

[0057] In this way, by setting an appropriate scaling factor, a simulated time series with the desired accuracy and stability can be obtained. When implementing the program, it is necessary to pre-store the actual clock error parameters and their corresponding accuracy and stability during the simulation period, and calculate the corresponding scaling factor based on the indicator requirements entered by the user.

[0058] In the embodiment of the present application, the navigation message generation subsystem simulates and generates downlink navigation messages based on the constellation satellite status, satellite orbit data, satellite clock data, space environment simulation data, wide-area differential information, and integrity information for testing user receivers. Specifically, it includes satellite ephemeris parameters, satellite clock correction parameters, satellite working status, data reference epoch, group delay parameters, satellite almanac, ionospheric delay correction parameters, time system correction parameters, wide-area differential information (for GEO satellites), and system integrity information. Satellite clock correction parameters include clock error, clock speed, and clock drift. On the one hand, the acquisition of satellite navigation message data can be achieved by receiving the corresponding results generated by the information processing system. On the other hand, the simulation test system can also be calculated according to the corresponding algorithm. By referring to relevant research results, a navigation parameter and algorithm are given. By setting the initial value of the broadcast ephemeris, the satellite orbit is fitted with the least squares method according to the observation value, the corresponding state equation, and the observation equation over a period of time to obtain the satellite broadcast ephemeris.

[0059] In the embodiments of the present application, the user trajectory simulation subsystem simulates the user's movements and generates the user's coordinate trajectory data. This provides support for the mathematical simulation subsystem's simulation of the user's receiver observation data. User trajectory simulation can be performed in two ways: one is to establish a complete dynamic and kinematic model, determine the user's force conditions, and then perform dynamic and kinematic simulation of the user; the other is to establish only the user's kinematic model, and perform kinematic simulation after the simulation tester inputs motion control parameters.

[0060] In addition to being able to directly generate user trajectories, the user trajectory simulation subsystem also provides communication ports and file reading capabilities, allowing the mathematical simulation subsystem to directly read external user trajectory data through the communication port. The specific data generated is classified as follows:

[0061] Simple user trajectory for static receiver testing, requiring only the receiver's location information to be input;

[0062] Receiver speed test trajectory. The speed test is mainly used to verify the speed measurement performance of the receiver, including linear motion trajectory and circular motion trajectory;

[0063] Receiver acceleration test trajectory, acceleration test is mainly used to verify the dynamic performance of the receiver loop, including circular motion trajectory and spiral motion trajectory.

[0064] In the embodiments of the present application, the integrity simulation subsystem's function is to promptly notify users when a satellite navigation system fails to provide navigation and positioning information services that meet their needs. The integrity information generated by this system's simulation refers to information that indicates a navigation satellite cannot be used for navigation due to errors and changes in its status caused by a malfunction. This integrity information can be generated by the simulation test system by setting the navigation satellite's errors and status, and then by the ground control system based on received pseudorange observations via the information processing system. Alternatively, the simulation test system can generate this information directly based on the errors / status.

[0065] The integrity model of the simulation test system is as follows:

[0066] 1. Determine whether the current time has reached the integrity simulation time, and add a certain initial error to the pseudorange simulation value of one or more satellites according to the pseudorange URE status table.

[0067] 2. Calculate the additional pseudorange error over time

[0068] The actual pseudorange additional error is calculated according to the rules described by the following three models, namely linear model, sinusoidal model and joint linear model and sinusoidal model;

[0069] In fact, in addition to loading satellite fault information into pseudorange observations, constellation satellite navigation messages can also preset various fault modes, including satellite clock error, satellite ephemeris error, and wide-area differential correction error.

[0070] In the embodiment of the present application, the space environment effect simulation subsystem simulates error terms such as ionospheric delay, tropospheric delay, multipath effect, relativistic effect, earth rotation effect, and monitoring station receiver, and examines the degree to which each error approaches natural environment conditions and studies the errors caused by signal propagation;

[0071] 1. Ionospheric delay model:

[0072] The system provides commonly used practical formulas. The carrier phase propagation delay caused by the ionosphere can be expressed as:

[0073]

[0074] The pseudo code propagation delay can be expressed as:

[0075]

[0076] where TEC = ∫ s Nds is the total electron content (TEC) on the electromagnetic wave propagation path. Under the condition that TEC is accurately known, the effect of calculating the ionospheric delay using the above formula is above 99%.

[0077] 2. Tropospheric delay model:

[0078] A variety of refractive index delay models have been developed. The improved Hopfield model and the Saastamoinen model provide results that are within a few millimeters of those calculated using the US Standard Atmosphere. At zenith angles, the water vapor fraction errors of various models are within 20 mm. Both models meet the system's requirements, and therefore, the improved Hopfield and Saastamoinen models will be used in the system's tropospheric simulations. The models are described below:

[0079] (1) Improved Hopfield model

[0080] The improved Hopfield model directly gives the dry and wet component refraction corrections on the propagation path. The sum of the two is the total tropospheric delay correction ΔD trop :

[0081] ΔD trop =ΔD dry +ΔD wet

[0082] Here, the tropospheric refraction distance corrections for the dry and wet components are:

[0083]

[0084] where the ground refractive index for the dry and wet components is given by:

[0085] N dry =(0.776×10 -4 )·P / T

[0086] N wet =0.373·e / T 2

[0087]

[0088] Where: T is the user's ground absolute temperature (Kelvin), P is the ground atmospheric pressure (millibars), e is the water vapor pressure (millibars), and H is the relative humidity percentage. dry 、r wet They represent the distance from the user to the intersection of the propagation path and the boundary surface where the dry and wet refractive indices tend to zero:

[0089]

[0090] Where: r0 is the user's geocentric radius (meters), E is the satellite's altitude angle, h i is the height of the boundary surface where the refractive index of the dry and wet components approaches zero:

[0091] h dry =40136+148.72(T-273.16)

[0092] h wet =11000

[0093] The other coefficients in the improved Hopfield model are:

[0094]

[0095] (2) Saastamoinen model

[0096] The dry and wet delay components of the Saastamoinen model in the zenith direction are:

[0097]

[0098] Where: P0 is the total surface pressure in millibars, e0 is the surface water bias pressure in millibars, T0 is the absolute temperature in Kelvin (T0 = 273.16 + t0), and f(φ,H) is the function that calculates the change in gravity:

[0099] f(φ,H)=1-0.0026cos(2φ)-0.0003H

[0100] Where: φ is the user's latitude, The unit is kilometers, where h0 is the user's altitude.

[0101] Since the relative humidity of the air W0 is often directly recorded in observation, e0 must be obtained by calculation.

[0102] e0=e w W0

[0103] Among them: e w It is called the saturated water vapor pressure of a pure horizontal liquid surface and is measured in millibars.

[0104] 3. Multipath effect model:

[0105] The impact of multipath on RNSS is complex and closely related to the environment, making it difficult to accurately simulate using parameter models. The system will provide simulation functions for relevant multipath effects: typical multipath effects caused by ground and ground object reflections.

[0106] Multipath signals can be represented by several relative quantities compared to the direct signal, usually relative delay δ, relative amplitude α, phase angle θ and phase angle change rate. Among them, δ depends entirely on the environment in which the receiver is located, while α and θ are determined by the environment and the user's antenna characteristics. The difference between the two depends on the user's movement trajectory and the environmental factors encountered during the movement. Based on the generation mechanism of multipath signals, a static multipath effect analytical model is used in the system multipath error simulation, as described below.

[0107] In static conditions, can be approximated to 0. At the same time, knowing the positions of the reflection source and the receiver, the relative propagation delay δ can be calculated, and the phase angle θ = 2π(δ / T) can be further obtained. In order to calculate the carrier delay of the synthesized multipath, the signal expression emitted from the satellite's PNR ranging system is simplified to:

[0108]

[0109] Where: A is the amplitude, w0 is the receiver frequency (carrier frequency plus Doppler shift), and P(t) is the PRN code. The expression of the multipath signal is:

[0110]

[0111] The composite signal of the direct signal and the multipath signal is:

[0112]

[0113] Where: A′=AP(t), The composite signal of the two signals can be expressed as:

[0114]

[0115] k=(1+2αcosθ+α 2 ) 1 / 2

[0116] ψ=tan -1 {αsinθ / (αcosθ+1)}

[0117] Where: ψ is the relative phase of the composite signal of the multipath signal and the direct signal.

[0118] When there are multiple multipath effects, there are:

[0119]

[0120] 4. Relativistic effect model:

[0121] According to the theory of special relativity, an oscillator with a frequency of f0 on the surface of the earth is mounted on a s The flying BD-2 satellite will cause frequency offset for users on the ground.

[0122]

[0123] Where: df1=f s -f0;f s is the actual frequency of the oscillator on the aircraft; g is the acceleration of gravity on the ground; c is the speed of light; a m is the average radius of the Earth; R s is the average orbital radius of the spacecraft (satellite).

[0124] On the other hand, according to the principle of general relativity, oscillators on different gravitational potential planes will have frequency shifts due to different gravitational potentials, that is,

[0125]

[0126] Where: For the gravity position.

[0127] Then the frequency change of the oscillator on the BD-2 satellite is

[0128]

[0129] Taking into account the influence of factors such as the Earth's rotation, the Earth's asymmetry, changes in the aircraft's orbital altitude, and changes in the Earth's gravity field, the above formula only corrects the average of the receiver clock frequency offset (basic correction). The residual correction is related to the actual orbital parameters of the satellite and also needs to be corrected.

[0130] 5. Earth rotation effect model:

[0131] Due to the rotation of the earth, the satellite position in orbit when the navigation satellite signal reaches the signal receiver is different from the satellite position in orbit when the satellite signal is transmitted. Therefore, it is necessary to correct the effect of the earth's rotation:

[0132] α=ω e (t R -t T )

[0133]

[0134] Where: (X, Y, Z) is the satellite position coordinates at the time of receiving the signal; (X′, Y′, Z′) is the satellite position coordinates at the time of transmitting the signal; ω e is the angular velocity of the Earth's rotation; t R is the time when the signal is received; t T The time when the signal is transmitted.

[0135] In addition, the BD-2 satellite navigation system is equipped with SLR observation equipment. Therefore, when using SLR measurement data for precise orbit determination, it is necessary to use the Marrini model to correct for atmospheric refraction. In system simulation, the SLR measurement data must be simulated to account for the atmospheric refraction effect.

[0136] 6. Monitoring station receiver error model:

[0137] During the ground operation and control system business processing data testing process, generating basic observation data requires establishing a monitoring station receiver model and generating error data such as receiver clock error, delay, and thermal noise. Based on the type of receiver used by the monitoring station, the receiver clock noise process coefficient is obtained, and the clock error at any time is calculated using Allan variance. The generation process of its clock error parameters is consistent with that of the satellite; the receiver delay can be calibrated using the model provided by the manufacturer and actual measurements; the receiver thermal noise level can be quantitatively expressed as the carrier-to-noise ratio (C / N0) of a 1Hz noise bandwidth, that is,

[0138]

[0139] Where: RP min is the minimum ground receiving power of the satellite signal; k is the Boltzman constant; T sys is the equivalent noise temperature of the system, which is mainly determined by the antenna temperature and the receiver noise temperature. The pseudo-range measurement error of the user receiver is related to the carrier-to-noise ratio, pseudo-random noise code rate, tracking loop bandwidth, and filter bandwidth. The standard deviation of the pseudo-range measurement can be expressed as

[0140]

[0141] Where: c is the speed of light; R c is the pseudo code rate; C s is the code element width; B nm is the DLL loop bandwidth; B FI The filter bandwidth is predicted for the data. It can be seen that the receiver thermal noise level is directly related to the pseudorange measurement accuracy and is an important technical indicator for evaluating the ranging performance of the receiver.

[0142] In the embodiment of the present application, the simulation data generation subsystem mainly includes pseudorange simulation, pseudorange rate simulation, carrier phase simulation, satellite-ground and inter-station time synchronization data, etc. Satellite-ground and inter-station time synchronization data mainly include satellite-ground bidirectional measurement pseudorange, pseudorange rate and carrier phase; inter-station time synchronization data and SLR data. Among them, the process of generating satellite-ground bidirectional measurement data is consistent with the basic observation data of the monitoring station, only the measurement data from the ground time synchronization station to the satellite is added;

[0143] 1. Pseudorange simulation:

[0144]

[0145] Where:

[0146] (x′ s ,y′ s ,z′ s ) is the satellite position coordinate at the time of receiving the signal; (x s ,y s ,z s ) is the satellite position coordinate after adding the effect of the earth's rotation; ω e is the angular velocity of the Earth's rotation; t R is the time when the signal is received; t T is the time when the signal is transmitted; d ion,i is the ionospheric delay of the i-th frequency point; d trop is the tropospheric delay; d m,i is the multipath effect of the ith frequency point; d rel is the relativistic effect; c is the speed of light; dt u is the user receiver clock error; dt s is the satellite clock error, ε i is the random noise of the receiver.

[0147] Taking into account the differences in I / Q branches and signal wide correlation and narrow correlation mechanisms, civil code and military code measurement pseudoranges with different ranging accuracies are generated.

[0148] 2. Pseudorange rate simulation:

[0149]

[0150] Where:

[0151]

[0152] is the satellite speed at the time of signal reception; is the satellite speed after adding the effect of the Earth's rotation; is the ionospheric delay change rate of the i-th frequency point; is the tropospheric delay variation rate; is the multipath effect change rate of the i-th frequency point; is the rate of change of relativistic effect; c is the speed of light; is the user receiver clock frequency error; is the satellite clock frequency error, is the rate of change of the receiver random noise.

[0153] In order to meet the requirements of RNSS signal continuity, it is also necessary to generate the second-order and third-order derivatives of pseudoranges. Their models can be derived similarly or calculated using the differential method.

[0154] 3. Carrier phase simulation:

[0155]

[0156] Where: i is the carrier wavelength of the satellite's transmitted signal at the i-th frequency point; is the carrier phase observation of the satellite by the antenna; is the influence of the corresponding multipath effect on the carrier phase; N i is the integer ambiguity of the corresponding initial observation epoch.

[0157] 4. Simulation model of satellite-ground time synchronized pseudo-range measurement data:

[0158] (1) Pseudorange measurement data from the time synchronization station to the satellite

[0159]

[0160] Where: OS is the pseudorange value from the time synchronization station O to the satellite S; is the geometric distance between the transmitting antenna of the time synchronization station O and the receiving antenna of the satellite S; t O is the time when the signal is sent; t S is the signal receiving time; δt S is the satellite clock error; δt O is the time synchronization station clock error; δρ ion is the ionospheric delay; δρ trop is the tropospheric delay; δρ rel is the relativistic effect error; δρ offset is the error of the satellite phase center from the center of mass of the star; δρ rot is the Earth's rotation error; δρ del1 is the hardware transmission delay of the time synchronization station; δρ del2 It is the satellite hardware transmission delay.

[0161] (2) Pseudorange measurement data from satellite to time synchronization station

[0162]

[0163] Where: AS is the pseudorange generated value from satellite S to time synchronization station A; is the geometric distance between the transmitting antenna of satellite S and the receiving antenna of time synchronization station A; t S is the time when the signal is sent; t Ais the signal receiving time; δt S is the satellite clock error; δt A is the time synchronization station clock error; δρ ion is the ionospheric delay; δρ trop is the tropospheric delay; δρ mult is the pseudorange measurement error caused by the multipath effect; δρ rel is the relativistic effect error; δρ offset is the error of the satellite phase center from the center of mass of the star; δρ rot is the Earth's rotation error; δρ del3 is the hardware transmission delay of the time synchronization station; δρ del4 It is the satellite hardware transmission delay.

[0164] The simulation model of inter-station time synchronization pseudo-range measurement data can be expressed as follows based on the above model:

[0165] ρ1=ρ OS +ρ SA

[0166] ρ2=ρ AS +ρ SO

[0167] Where: ρ1 is the time synchronization observation value from time synchronization station O to time synchronization station A; ρ OS is the pseudorange observation value from the time synchronization station O to the satellite S; ρ SA is the pseudorange observation value from satellite S to time synchronization station A. ρ2 is the time synchronization observation value from time synchronization station A to time synchronization station O; ρ AS is the pseudorange observation value from time synchronization station A to satellite S; ρ SO is the pseudorange observation value from satellite S to time synchronization station O

[0168] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A GNSS simulator mathematical simulation system, characterized in that: It includes data interaction between the constellation satellite orbit and clock parameter simulation subsystem, navigation message generation subsystem, user trajectory simulation subsystem, integrity simulation subsystem, space environment effect simulation subsystem and simulation data generation subsystem; The constellation satellite orbit and clock parameter simulation subsystem consists of a space-time system model, an auxiliary database, satellite theoretical orbit data, and satellite clock theoretical parameters. The space-time system model has a built-in time system model and a coordinate system model, and the auxiliary database has built-in astronomical constants and environmental parameter values for the constellation satellite orbit and clock parameter simulation. The satellite theoretical orbit data calculates gravitational acceleration based on the input initial time, initial position velocity, integration time, and model selection control parameter data, and then uses the satellite's motion equation to perform numerical integration operations to obtain the constellation satellite's motion orbit. The satellite clock theoretical parameters are statistically calculated based on the deviation between the satellite clock face time and the standard time. The navigation message generation subsystem generates downlink navigation messages based on the constellation satellite status, satellite orbit data, satellite clock data, space environment simulation data, wide area differential information and integrity information simulation; The user trajectory simulation subsystem simulates the user's movement and generates the user's coordinate trajectory data, and provides support to the mathematical simulation subsystem for simulating the user receiver observation data; When the satellite navigation system cannot provide navigation and positioning information services that meet user needs, the integrity simulation subsystem is triggered to simulate the integrity information generated and set the navigation satellite error and status through the simulation test system; The space environment effect simulation subsystem includes ionospheric delay, tropospheric delay, multipath effect, relativistic effect and earth rotation effect, and monitoring station receiver error term, and examines the degree to which each error approaches the natural environment conditions and analyzes the error in signal propagation; The simulation data generation subsystem generates pseudorange simulation, pseudorange rate simulation, carrier phase simulation, satellite-ground and inter-station time synchronization data; The data in the downlink navigation message generated by the navigation message generation subsystem includes satellite ephemeris parameters, satellite clock correction parameters, satellite working status, data reference epoch, group delay parameters, satellite almanac, ionospheric delay correction parameters, time system correction parameters, wide area differential information and system integrity information.

2. A GNSS simulator mathematical simulation system according to claim 1, characterized in that: The space-time system model consists of a time system model and a coordinate system model, wherein The time system model includes barycentric dynamic time (TDB): a time variable used for planetary / lunar ephemeris and precession and nutation calculations; terrestrial time (TT): a time variable used to describe the equations of motion relative to the Earth's center of mass; universal time (UT1): used for coordinate conversion process parameter calculations; atomic time (TAI): used for coordinate conversion process parameter calculations; Greenwich sidereal time (GST): including GMST and GAST; used for coordinate conversion process parameter calculations; coordinated universal time (UTC): a time record standard used for simulation start and end times, ground launches, and tracking; and navigation satellite time (NST): BD-2's time system (BDT), with conversion parameters to UTC provided by the BD-2 navigation signal. The coordinate system model includes the Earth-centered inertial coordinate system J2000: for calculating satellite orbits; the Earth-centered Earth-fixed coordinate system CGS2000: for representing the trajectories of ground stations and users other than satellites; the station-centered coordinate system: taken as the northeast celestial coordinate system, used to calculate the observation elevation angle and observation station altitude; the RTN coordinate system: with the satellite's center of mass as the origin and its radial, tangential, and normal axes as the coordinate axis directions.

3. A GNSS simulator mathematical simulation system according to claim 1, characterized in that: The astronomical constants in the auxiliary database include the Earth's radius, the Earth's gravitational constant and the speed of light data, and the environmental parameters include the Earth's gravitational potential coefficient, the Earth's rotation parameters, JPL ephemeris, solar radiation flux, geomagnetic index, satellite geometry and physical parameters.

4. A GNSS simulator mathematical simulation system according to claim 1, characterized in that: The data in the navigation message is obtained by receiving the corresponding results generated by the information processing system. On the other hand, the simulation test system also calculates according to the corresponding algorithm, obtains the navigation parameters and algorithm by referring to the results, and obtains the satellite broadcast ephemeris by setting the initial value of the broadcast ephemeris, the observation value of the preset time, the corresponding state equation and the observation equation, and performing least squares fitting on the satellite orbit.

5. A GNSS simulator mathematical simulation system according to claim 1, characterized in that: The user trajectory simulation subsystem also performs data transmission and file reading through the communication port, so that the mathematical simulation subsystem directly reads external user trajectory data through the communication port.

6. A GNSS simulator mathematical simulation system according to claim 5, characterized in that: The data read by the mathematical simulation subsystem generates three specific data categories. The first category is the simple user trajectory used for static receiver testing, which requires the input of the receiver's position information; the second category is the receiver speed test trajectory. The speed test is mainly used to test the receiver's speed measurement performance, including linear motion trajectory and circular motion trajectory; the third category is the receiver acceleration test trajectory. The acceleration test is mainly used to test the dynamic performance of the receiver loop, including circular motion trajectory and spiral motion trajectory.

7. A GNSS simulator mathematical simulation system according to claim 1, characterized in that: The navigation satellite errors and states of the simulation test system in the integrity simulation subsystem are generated in two ways: the first way is to use the ground control system to generate them based on the received pseudo-range observation values through the information processing system; the second way is to use the simulation test system to directly generate them based on the errors / states.

8. A GNSS simulator mathematical simulation system according to claim 1, characterized in that: The satellite-ground and inter-station time synchronization data include satellite-ground bidirectional measurement pseudorange, pseudorange rate and carrier phase; inter-station time synchronization data and SLR data, wherein the process of generating satellite-ground bidirectional measurement data is consistent with the basic observation data of the monitoring station, and the measurement data from the ground time synchronization station to the satellite is added.

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