A doppler real-time positioning and velocity measurement method and system for a large-scale low earth orbit constellation

Abstract

The application relates to a Doppler real-time positioning and velocity measurement method and system of a large-scale low-orbit constellation, which comprises the following steps: S1: acquiring Doppler observation data and ephemeris information of low-orbit satellites, and denoising the Doppler observation data; S2: calculating a subsatellite point position and an initial position of a communication terminal according to the position of the satellites in the ephemeris information of the low-orbit satellites; S3: constructing a state vector composed of the position and velocity of the communication terminal at a certain moment, and a state estimation equation of the communication terminal at the next moment; S4: selecting a reference satellite, and constructing an inter-satellite single-difference Doppler observation equation of each available satellite and the reference satellite; and S5: based on the initial position of the communication terminal and the Doppler information, the position and velocity of the communication terminal are solved in real time by using a Kalman filtering method, a least square method or a gradient descent method. The application does not need an operator to provide additional infrastructure and technical support, can be applied to commercial low-orbit communication, and has the advantages of low cost and anti-interference.

Description

Technical Field

[0001] This invention relates to the fields of satellite navigation and low-Earth orbit satellite communication, and in particular to a Doppler real-time positioning and velocity measurement method and system for a large-scale low-Earth orbit satellite constellation. Background Technology

[0002] Large-scale low-Earth orbit (LEO) constellations offer advantages such as high bandwidth, low latency, easy access, and strong security in communications. Therefore, major countries worldwide are planning, developing, and constructing large-scale LEO communication constellations. For example, the US Starlink LEO constellation planned to deploy 42,000 LEO satellites in its first and second phases; currently, over 2,000 satellites are in orbit.

[0003] In the field of satellite navigation, large-scale low-Earth orbit (LEO) constellations can achieve navigation functions through signal enhancement. That is, LEO satellites carry navigation payloads, which, in conjunction with ground control systems, modulate navigation information and broadcast navigation signals, thus enabling ground users to navigate. Domestically, the experimental satellites of the Hongyan and Hongyun LEO constellations carry navigation payloads, transmitting navigation signals and using ranging codes for navigation calculations. However, in complex environments, navigation signals are susceptible to interference and spoofing. Furthermore, this LEO constellation navigation scheme requires LEO satellites to carry additional navigation payloads, and communication terminals also need to be redesigned, resulting in high costs for operators and users, and increasing the operational complexity of ground control systems, making it unsuitable for direct application to commercial LEO communication terminals. Currently, the US Starlink system has achieved preliminary communication capabilities; although it does not carry dedicated navigation payloads, the carrier wave portion of its communication signals can still be used for navigation and positioning. However, the carrier wave in the communication signal is difficult to track accurately due to the need to modulate communication information, making carrier recovery challenging and requiring high computational power from the communication terminal. Moreover, without pseudo-random ranging codes, positioning calculations solely based on carrier information cannot fix the ambiguity in the carrier information. Furthermore, most low-Earth orbit (LEO) communication satellites use C-band or K-band signals, which have relatively high frequencies and suffer from severe multipath effects. These issues limit the performance of navigation and positioning using the carrier signals of LEO communication satellites. Therefore, it is necessary to propose a navigation and positioning method suitable for large-scale LEO communication constellations and communication terminals. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a Doppler real-time positioning and velocity measurement method and system for a low-Earth orbit (LEO) constellation containing a large number of LEO satellites. By extracting Doppler observation data from the communication signals of the communication terminal and combining it with the ephemeris information of the LEO satellites, the position and velocity of the communication terminal are calculated in real time without the need for operators to provide additional infrastructure and technical support. This method can be applied to commercial LEO communication terminals, reducing costs and operational complexity.

[0005] The technical solution adopted is as follows:

[0006] This invention provides a large-scale low-Earth orbit constellation Doppler real-time positioning and velocity measurement method, specifically comprising:

[0007] S1: Acquire Doppler observation data and ephemeris information of low-Earth orbit (LEO) satellites: Obtain communication signals from all available LEO satellites within the LEO constellation through the communication terminal of the LEO constellation, extract Doppler observation data and ephemeris information from each LEO satellite, and perform noise reduction on the Doppler observation data; the ephemeris information includes the position, velocity, clock drift, and orbit information of the LEO satellites;

[0008] S2: Obtain the initial position of the communication terminal: Calculate the sub-satellite position of the low-orbit satellite based on the position of the low-orbit satellite in the ephemeris information, and then calculate the initial position of the communication terminal based on the sub-satellite position.

[0009] S3: Construct the state vector of the position and velocity of the communication terminal at a certain moment, and the state estimation equation for estimating the position and velocity of the communication terminal at the next moment;

[0010] S4: Select a reference satellite from all available low-orbit satellites, construct the inter-satellite single-difference Doppler observation equation between each other available satellite and the reference satellite, linearize each inter-satellite single-difference Doppler observation equation and superimpose them to finally obtain the linear observation equation set at the current observation time.

[0011] S5: Based on the constructed state vector, state estimation equation, and linear observation equation set of the communication terminal, the position and velocity of the communication terminal are calculated in real time using the Kalman filtering method, the least squares method, or the gradient descent method.

[0012] Optionally, in step S1, the method for denoising the Doppler observation data includes sliding window filtering or polynomial fitting.

[0013] Optionally, in step S1, the Doppler observation data is subjected to polynomial fitting for smoothing and noise reduction, specifically as follows:

[0014] After acquiring n observations (n ​​epochs) of the j-th low-Earth orbit satellite via the communication terminal, a polynomial can be used to fit these n observations at n time points, thereby reducing the noise in the Doppler observation data. Assume these n Doppler observation values ​​are... At any time t k The quadratic polynomial of Doppler observation data can be expressed as:

[0015]

[0016] Here, parameters x0, x1, and x2 are the parameters to be fitted; these n Doppler observation data can form n equations, and the fitting parameters can be solved using the least squares method to finally obtain the denoised Doppler observation data.

[0017] Optionally, in step S2, the specific method for obtaining the initial position of the communication terminal is as follows: assuming there are m observable satellites at a certain epoch; the Earth-fixed coordinates of the low-orbit satellites are respectively: (x... 1 ,y 1 ,z 1 ), (x 2 ,y 2 ,z 2 ), …(x m ,y m ,z m The Earth-fixed coordinates of a low-Earth orbit (LEO) satellite can be converted into the longitude, latitude, and geodetic height of its nadir point. Based on n observations of the j-th LEO satellite, the longitude and latitude of its nadir point are calculated as B. j and L j Then, taking the average of m satellites yields B. 0 and L 0 That is, the approximate longitude L0 and latitude B0 of the communication terminal are:

[0018]

[0019]

[0020] In this method, the geodetic height of the communication terminal is assumed to be 0. The approximate location error of the communication terminal determined by this method is approximately 200 km. The aforementioned approximate location coordinates of the communication terminal are used as the initial position for Doppler positioning of the communication terminal.

[0021] Optionally, in step S3, the state estimation equation of the communication terminal is constructed using position, velocity, and acceleration, or when the acceleration is constant, it is constructed using only position and velocity.

[0022] Optionally, in step S3, the specific method for constructing the state vector and state estimation equation of the communication terminal is as follows:

[0023] Communication terminal at t k-1 The state vector at time step can be expressed as in To obtain the initial position coordinates of the communication terminal in the x, y, and z directions according to step S2; For the corresponding velocities in the x, y, and z directions, the communication terminal at t k The state estimation equation at time t can be obtained through the state transition matrix. The estimated result is:

[0024]

[0025] in,

[0026]

[0027]

[0028] For the acceleration matrix, For the current t k The accelerations in the x, y, and z directions at time t;

[0029] Δt=t k -t k-1 .

[0030] Optionally, in step S4, the method of selecting a reference satellite includes selecting the satellite with the highest elevation angle or specifying a certain satellite as the reference satellite based on the satellite hardware conditions.

[0031] Optionally, in step S4, assuming the s-th satellite is selected as the reference satellite, the Doppler observation equation for the s-th satellite is:

[0032]

[0033] in, The noise-reduced Doppler observation data of the low-Earth orbit satellite s received by the communication terminal. The wavelength of the communication signal; and These represent the speeds of the low-Earth orbit satellite 's' and the communication terminal, respectively. and represents the coordinate positions of the low-orbit satellite s and the communication terminal, respectively; c is the speed of light; and These represent the clock drift of the communication terminal and the low-Earth orbit satellite s, respectively. and These are the tropospheric and ionospheric delay rates, respectively. Represents the rate of change of relativistic effects. This represents other frequency-independent error rates of change (such as changes in the antenna phase center). This includes communication terminal noise and other unmodeled errors.

[0034] The inter-satellite single-difference Doppler observation equation between the j-th satellite and the s-th satellite is:

[0035]

[0036] Linearizing the above inter-satellite single-difference Doppler observation equations yields:

[0037] z j,s =h j,s ·X

[0038] in, The state vector of the communication terminal is X = (xyzuvw) T ;

[0039] Design matrix h j,s for:

[0040]

[0041] in, These represent the direction cosines of the reference satellite s and the communication terminal in x, y, and z, respectively; Let x, y, and z represent the direction cosines of the low-orbit satellite j and the communication terminal, respectively. and These represent the approximate geometric distances between the reference satellite s and the low-orbit satellite j and the communication terminal, respectively.

[0042] In t k At time t, the inter-satellite single-difference Doppler observation equations between all m available satellites and the reference satellite s are linearized and then superimposed to finally obtain the current observation t. k The linear observation equations at time t are:

[0043]

[0044] in,

[0045] The superimposed design matrix is

[0046] Optionally, in step S5, the specific steps for calculating the position and speed of the communication terminal in real time using Kalman filtering are as follows:

[0047] S5-1, with t k-1 The state vector of the communication terminal at time t As initial values, estimate the variance-covariance matrix at that moment. The variance covariance matrix It can be given based on experience;

[0048] S5-2. Obtaining the state transition matrix of the communication terminal using a constant acceleration motion model. According to t k State estimation equation of the communication terminal at time t A preliminary estimate of the communication terminal's state vector is obtained through calculation;

[0049] S5-3, Calculate t k The variance-covariance matrix of the preliminary estimate of the state vector at time step is:

[0050] in, This is the process noise variance matrix of the state estimation equation based on the constant acceleration motion model. The acceleration noise matrix for the state estimation equation can be given by empirical parameters;

[0051] S5-4. Obtaining the observation residuals from the linear observation equations. Calculate the filter gain in, It is a matrix composed of the variances and covariances of multiple inter-satellite single-difference Doppler observations;

[0052] S5-5. Using the filter gain, estimate t according to the state estimation equation. k Updated estimate of the state vector at time step As t k The real-time position and velocity values ​​of the communication terminal are recorded and used as the initial values ​​for the next moment, inputting them into step S5-1; simultaneously, t is obtained. k The variance-covariance matrix of the updated state vector at time step

[0053] S5-6. Repeat steps S5-1 to S5-5 above, iteratively updating and outputting the position and speed values ​​of the communication terminal in real time until the communication terminal is powered off or shut down.

[0054] A large-scale low-Earth orbit (LEO) constellation Doppler real-time positioning and velocity measurement system includes a communication terminal 111, a large-scale LEO constellation 100, and multiple LEO satellites 101, 102, 103, and 104, as well as multiple corresponding communication links. The multiple communication links include multiple polling communication links 105, 107, and 108 and a physical communication link 106, which are used for communication between the communication terminal device 111 of the communication terminal 110 and the LEO satellites. The system uses the large-scale LEO constellation Doppler real-time positioning and velocity measurement method of the present invention to obtain the position and velocity information of the communication terminal.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0056] 1. The present invention provides a Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation, which can directly obtain the real-time position and velocity of the communication terminal using communication signals. It does not require the low-Earth orbit satellite to carry a special navigation payload, and can be applied to commercial low-Earth orbit communication terminals. It has advantages such as low cost, anti-interference, and anti-spoofing.

[0057] 2. This invention calculates the real-time position and velocity of the communication terminal based on Doppler observation information and ephemeris information of the communication signal. Depending on the crystal oscillator performance of the communication terminal equipment, the positioning accuracy can reach the meter level and the velocity measurement accuracy can reach the centimeter level. Attached Figure Description

[0058] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0059] Figure 1 The system composition of the large-scale low-Earth orbit constellation Doppler positioning and velocity measurement method provided by the present invention;

[0060] Figure 2 The flowchart illustrates the large-scale low-Earth orbit constellation Doppler positioning and velocity measurement method provided by this invention.

[0061] Explanation of reference numerals in the attached figures

[0062] 100 Large-scale low-Earth orbit constellation, 101 Low-Earth orbit satellites, 102 Low-Earth orbit satellites, 103 Low-Earth orbit satellites, 104 Low-Earth orbit satellites, 105 Polling communication link, 106 Actual communication link, 107 Polling communication link, 108 Polling communication link, 110 Communication terminal, 111 Communication terminal equipment Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] The technical solution of the present invention will be described in detail below through a specific embodiment.

[0065] This invention provides a large-scale low-Earth orbit constellation Doppler real-time positioning and velocity measurement system, such as... Figure 1As shown, the system includes a communication terminal 111, which is the user terminal, allowing users to perform real-time positioning and velocity measurement; a large-scale low-Earth orbit (LEO) constellation 100, which includes multiple LEO satellites 101-104 and corresponding multiple communication links, including multiple polling communication links 105, 107, and 108 and a physical communication link 106, used for communication between the communication terminal device 111 of the communication terminal 110 and the LEO satellites. The system uses the following Doppler real-time positioning and velocity measurement method for the large-scale LEO constellation.

[0066] A method for real-time Doppler positioning and velocity measurement of a large-scale low-Earth orbit constellation, such as Figure 2 The diagram shown is a flowchart of a large-scale low-Earth orbit constellation Doppler positioning and velocity measurement method provided by the present invention.

[0067] The specific steps are as follows:

[0068] Step 1: The communication terminal acquires communication signals from all available low-Earth orbit (LEO) satellites within the LEO constellation and extracts Doppler observation data and ephemeris information for each LEO satellite. The communication terminal acquires the communication signals through polling scanning. The ephemeris information includes the position, velocity, orbit, and clock drift information of the LEO satellites.

[0069] Then, polynomial fitting and smoothing noise reduction are performed on the Doppler observation data. The specific noise reduction method is as follows:

[0070] After acquiring n Doppler observation data (n observation epochs) from the j-th low-Earth orbit satellite via the communication terminal, a polynomial can be used to fit these n Doppler observation data, thereby reducing the noise in the Doppler observation data. Assume that the values ​​of these n Doppler observations, i.e., the values ​​at n times, are... At any time t k The quadratic polynomial of Doppler observation data can be expressed as:

[0071]

[0072] Here, parameters x0, x1, and x2 are the parameters to be fitted; these n Doppler observation data can form n equations, and the fitting parameters can be solved using the least squares method to finally obtain the denoised Doppler observation data.

[0073] Step 2: Calculate the nadir position of the low-Earth orbit satellite based on its position information, and then calculate the initial position of the communication terminal based on the nadir position. The specific method is as follows:

[0074] The approximate location coordinates of the communication terminal can be obtained using the nadir positions of observable low-Earth orbit (LEO) satellites. Assume there are m observable satellites at a given epoch; the Earth-fixed coordinates of the LEO satellites are as follows: (x...)1 ,y 1 ,z 1 ), (x 2 ,y 2 ,z 2 ), …(x m ,y m ,z m The Earth-fixed coordinates of a low-Earth orbit (LEO) satellite can be converted to the longitude, latitude, and geodetic height of its nadir point in the WGS-84 coordinate system. Based on n observations of the j-th LEO satellite, the longitude and latitude of its nadir point are calculated as B. j and L j Then, taking the average of m satellites yields B. 0 and L 0 That is, the approximate longitude L0 and latitude B0 of the communication terminal are:

[0075]

[0076]

[0077] The ground elevation of the communication terminal is assumed to be 0. The approximate position error of the communication terminal determined by this method is approximately 200 km. The aforementioned approximate position coordinates of the communication terminal are used as the initial position for Doppler positioning of the communication terminal.

[0078] Step 3: Construct the state vector of the position and velocity of the communication terminal at a certain moment, and obtain the state estimation equation of the position and velocity of the communication terminal at the next moment;

[0079] Communication terminal at t k-1 The state vector at time step can be expressed as in To obtain the initial position coordinates of the communication terminal in the x, y, and z directions according to step 2; The values ​​for the corresponding x, y, and z directions are initially 0 or estimated, and are continuously updated and iterated. The communication terminal is at t k The state estimation equation at time t can be obtained through the state transition matrix. The estimated result is:

[0080]

[0081] in

[0082]

[0083] Let be the acceleration matrix, where For the current t kThe accelerations in the x, y, and z directions at time t;

[0084] When using a constant acceleration model constant;

[0085] Δt=t k -t k-1 ;

[0086] Step 4: Select a reference satellite from all available satellites, and establish the inter-satellite single difference observation equations and linear observation equations between all other available satellites and the reference satellite.

[0087] The methods for selecting a reference satellite include choosing the satellite with the highest elevation angle or designating a specific satellite as the reference satellite based on the satellite's hardware conditions.

[0088] Inter-satellite single-difference between Doppler observation equations can further reduce the impact of receiver clock drift and satellite orbit errors. Using inter-satellite single-difference in large-scale low-Earth orbit constellations can effectively improve Doppler positioning accuracy. The first step in performing inter-satellite single-difference is selecting a reference satellite; in this invention, the reference satellite is selected based on the signal-to-noise ratio of the received signal. Assuming the s-th satellite is selected as the reference satellite, the Doppler observation equation for the s-th satellite is:

[0089]

[0090] in, The noise-reduced Doppler observation data of the low-Earth orbit satellite s received by the communication terminal. The wavelength of the communication signal; and These represent the speeds of the low-Earth orbit satellite 's' and the communication terminal, respectively. and represents the coordinate positions of the low-orbit satellite s and the communication terminal, respectively; c is the speed of light; and These represent the clock drift of the communication terminal and the low-Earth orbit satellite s, respectively. and These are the tropospheric and ionospheric delay rates, respectively. Represents the rate of change of relativistic effects. This represents other frequency-independent error rates of change (such as changes in the antenna phase center). This includes communication terminal noise and other unmodeled errors.

[0091] The inter-satellite single-difference Doppler observation equation between the j-th satellite and the s-th satellite is:

[0092]

[0093] Linearizing the above inter-satellite single-difference Doppler observation equations yields:

[0094] z j,s =h j,s ·X

[0095] in, The state vector of the communication terminal is X = (xyzuvw) T Design matrix h j,s for

[0096]

[0097] in Let x, y, and z represent the direction cosines of the reference satellite s and the communication terminal, respectively. Let x, y, and z represent the direction cosines of the low-orbit satellite j and the communication terminal, respectively. and These represent the approximate geometric distances between the reference satellite s and the low-orbit satellite j and the communication terminal, respectively.

[0098] In t k At time t, the inter-satellite single-difference Doppler observation equations between all m available satellites and the reference satellite s are linearized and then superimposed to finally obtain the current observation t. k The linear observation equations at time t are:

[0099]

[0100] in, The design matrix is

[0101] The design matrix is ​​constructed by concatenating the linearization coefficients of all available low-Earth orbit satellites. The variance-covariance matrix of the inter-satellite single-difference Doppler observations can be obtained by transforming the variance of the non-difference Doppler measurements.

[0102] Step 5: Real-time calculation of the position and velocity of the communication terminal using Kalman filtering.

[0103] After constructing the state estimation equations and linear observation equations for the communication terminal, the position and velocity of the communication terminal can be calculated using the Kalman filtering method.

[0104] The specific steps for real-time calculation of the communication terminal's position and velocity using actual observation data and Kalman filtering are as follows:

[0105] 5-1, with t k-1 The state vector of the communication terminal at time t As initial values, estimate the variance-covariance matrix at that moment. The variance covariance matrix It can be given based on experience;

[0106] 5-2. Obtain the state transition matrix of the communication terminal using a constant acceleration motion model. According to t k State estimation equation of the communication terminal at time estimation A preliminary estimate of the communication terminal's state vector is obtained through calculation;

[0107] 5-3. Calculate t k The variance-covariance matrix of the preliminary estimate of the state vector at time step is:

[0108] in, This is the process noise variance matrix of the state estimation equation based on the constant acceleration motion model. The acceleration noise matrix for the state estimation equation can be given by empirical parameters;

[0109] 5-4. Obtain the observation residuals from the linear observation equations. Calculate the filter gain in, It is the variance-covariance matrix of the inter-satellite single-difference Doppler observations, also known as the covariance matrix of measurement noise;

[0110] 5-5. Using the filter gain, estimate t according to the state estimation equation. k Updated estimate of the state vector at time step As t k The real-time position and velocity values ​​of the communication terminal are recorded and used as the initial values ​​for the next moment, inputting them into step 5-1; simultaneously, t is obtained. k The variance-covariance matrix of the updated state vector at time step

[0111] 5-6. Repeat steps 5-1 to 5-5 above, continuously iterating and updating, and outputting the position and speed values ​​of the communication terminal in real time until the communication terminal is powered off or shut down.

[0112] Once the state vectors for all moments in the actual observation data have been processed, the updated best estimates of all state vectors are obtained.

[0113] In addition to the Kalman filtering method mentioned above, the least squares and gradient descent methods can also be used to calculate the position and speed of communication terminals.

[0114] In summary, this invention presents a method and system for Doppler positioning and velocity measurement of communication terminals using communication signals, designed for large-scale low-Earth orbit (LEO) communication constellations. Compared to the method of mounting navigation payloads on LEO satellites, this method offers advantages such as lower cost, simpler and more direct operation and control, and stronger anti-interference and anti-spoofing capabilities. First, the Doppler observation information collected by the communication terminal is smoothed and filtered to reduce observation noise. Then, ephemeris information of all available satellites is obtained from the communication link, and the approximate position of the communication terminal is estimated based on the satellite nadir position. This approximate position is used as the initial value for Kalman filtering, and subsequently, the position and velocity of the communication terminal are estimated in real time based on the Doppler observation information. This method facilitates the integration of communication and navigation under large-scale LEO communication constellation conditions and can also serve as a supplementary and backup navigation solution when GNSS signals are unavailable, demonstrating broad application prospects.

[0115] Through the description of the above embodiments, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus the necessary general-purpose hardware platform. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROK / RAK, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0116] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation, characterized in that, Specifically, the following steps are included: S1: Acquire Doppler observation data and ephemeris information of low-Earth orbit (LEO) satellites: Obtain communication signals from all available LEO satellites within the LEO constellation through the communication terminal of the LEO constellation, extract Doppler observation data and ephemeris information from each LEO satellite, and perform noise reduction on the Doppler observation data; the ephemeris information includes the position, velocity, clock bias, and clock drift information of the LEO satellites; S2: Obtain the initial position of the communication terminal: Calculate the sub-satellite position of the low-orbit satellite based on the position of the low-orbit satellite in the ephemeris information, and then calculate the initial position of the communication terminal based on the sub-satellite position. S3: Construct a state vector consisting of the position and velocity of the communication terminal at a certain moment, and an equation for estimating the state of the communication terminal at the next moment; S4: Select a reference satellite from all available low-orbit satellites, construct the inter-satellite single-difference Doppler observation equation between each other available satellite and the reference satellite, linearize each inter-satellite single-difference Doppler observation equation and superimpose them to finally obtain the linear observation equation set at the current observation time. S5: Based on the constructed state vector, state estimation equation, and linear observation equation set of the communication terminal, the position and velocity of the communication terminal are calculated in real time using the Kalman filtering method, the least squares method, or the gradient descent method.

2. The Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation according to claim 1, characterized in that, In step S1, the method for denoising the Doppler observation data includes sliding window filtering or polynomial fitting.

3. The Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation according to claim 2, characterized in that, In step S1, the Doppler observation data is subjected to polynomial fitting for smoothing and noise reduction. The specific method is as follows: After acquiring n observations (n ​​epochs) of the j-th low-Earth orbit satellite via the communication terminal, a polynomial is used to fit these n Doppler observations to reduce noise in the Doppler data. It is assumed that the values ​​of these n observations (n ​​times) are... At any time t k The quadratic polynomial expression of the Doppler observation data is: Here, parameters x0, x1, and x2 are the parameters to be fitted; these n Doppler observation data form n equations, and the least squares method is used to solve for the fitting parameters, finally obtaining the noise-reduced Doppler observation data.

4. The Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation according to claim 1, characterized in that, In step S2, the specific method for obtaining the initial position of the communication terminal is as follows: Assume there are m observable satellites at a certain epoch; the Earth-fixed coordinates of the low-orbit satellites are respectively: (x... 1 y 1 , z 1 ), (x 2 y 2 , z 2 ), …(x m y m , z m The Earth-fixed coordinates of the low-orbit satellite are converted to the longitude, latitude, and geodetic height of the nadir point; the longitude and latitude of the nadir point of the j-th low-orbit satellite are calculated as B based on n observations of the j-th low-orbit satellite. j and L j ; Then, taking the average of m satellites, we get B. 0 and L 0 That is, the approximate longitude L0 and latitude B0 of the communication terminal are: In this context, the ground elevation of the communication terminal is assumed to be 0, and the approximate location coordinates of the communication terminal are used as the initial position for Doppler positioning of the communication terminal.

5. The Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation according to claim 1, characterized in that, In step S3, the state estimation equation of the communication terminal is constructed using position, velocity, and acceleration, or when the acceleration is constant, it is constructed using only position and velocity.

6. The Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation according to claim 5, characterized in that, In step S3, the specific method for constructing the state vector and state estimation equation of the communication terminal is as follows: Communication terminal at t k-1 The state vector at time step is expressed as in To obtain the initial position coordinates of the communication terminal in the x, y, and z directions according to step S2; For the corresponding velocities in the x, y, and z directions, the communication terminal at t k The state estimation equation at time t can be obtained through the state transition matrix. The estimated result is: in, When using a constant acceleration model Δt=t k -t k-1 。 7. The Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation according to claim 1, characterized in that, The methods for selecting a reference satellite include choosing the satellite with the highest elevation angle or designating a specific satellite as the reference satellite based on the satellite's hardware conditions.

8. The Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation according to claim 7, characterized in that, In step S4, assuming the s-th satellite is selected as the reference satellite, the Doppler observation equation for the s-th satellite is: in, λ represents the noise-reduced Doppler observation data of the low-Earth orbit satellite s received by the communication terminal. fT The wavelength of the communication signal; and These represent the speeds of the low-Earth orbit satellite 's' and the communication terminal, respectively. and represents the coordinate positions of the low-orbit satellite s and the communication terminal, respectively; c is the speed of light; and These represent the clock drift of the communication terminal and the low-Earth orbit satellite s, respectively. and These are the tropospheric and ionospheric delay rates, respectively. Represents the rate of change of relativistic effects. This represents the rate of change of other errors that are independent of frequency. For communication terminal noise and other unmodeled errors; The inter-satellite single-difference Doppler observation equation between the j-th satellite and the s-th satellite is: Linearizing the above inter-satellite single-difference Doppler observation equations yields: z j，s =h j，s ·X in, The state vector of the communication terminal is X = (xyzuvw) T ; Design matrix h j，s for: in, These represent the direction cosines of the reference satellite s and the communication terminal in x, y, and z, respectively; Let x, y, and z represent the direction cosines of the low-orbit satellite j and the communication terminal, respectively. and These represent the approximate geometric distances between the reference satellite s and the low-Earth orbit satellite j and the communication terminal, respectively. In t k At time t, the inter-satellite single-difference Doppler observation equations between all m available satellites and the reference satellite s are linearized and then superimposed to finally obtain the current observation t. k The linear observation equations at time t are: in, The superimposed design matrix is 9. The Doppler real-time positioning and velocity measurement method for a large-scale low-Earth orbit constellation according to claim 1, characterized in that, In step S5, the specific steps for calculating the position and velocity of the communication terminal in real time using actual observation data and Kalman filtering are as follows: S5-1, with t k-1 The state vector of the communication terminal at time t As initial values, estimate the variance-covariance matrix at that moment. The variance covariance matrix Based on experience; S5-2. Obtaining the state transition matrix of the communication terminal using a constant acceleration motion model. According to t k State estimation equation of the communication terminal at time estimation A preliminary estimate of the communication terminal's state vector is obtained through calculation; S5-3, Calculate t k The variance-covariance matrix of the preliminary estimate of the state vector at time step is: in, This is the process noise variance matrix of the state estimation equation based on the constant acceleration motion model. The acceleration noise matrix of the state estimation equation is given by empirical parameters; S5-4. Obtaining the observation residuals from the linear observation equations. Calculate the filter gain in, This is the variance-covariance matrix of the inter-satellite single-difference Doppler observations; S5-5. Using the filter gain, estimate t according to the state estimation equation. k Updated estimate of the state vector at time step As t k The real-time position and velocity values ​​of the communication terminal are recorded and used as the initial values ​​for the next moment, inputting them into step S5-1; simultaneously, t is obtained. k The variance-covariance matrix of the updated state vector at time step S5-6. Repeat steps S5-1 to S5-5 above, iteratively updating and outputting the position and speed values ​​of the communication terminal in real time until the communication terminal is powered off or shut down.

10. A large-scale low-Earth orbit constellation Doppler real-time positioning and velocity measurement system, comprising a communication terminal (110), a large-scale low-Earth orbit constellation (100), the large-scale low-Earth orbit constellation comprising multiple low-Earth orbit satellites, and corresponding multiple communication links, the multiple communication links comprising multiple polling communication links (105), (107), (108) and actual communication links (106), used for communication between the communication terminal equipment (111) of the communication terminal (110) and the low-Earth orbit satellites, the system employing the large-scale low-Earth orbit constellation Doppler real-time positioning and velocity measurement method as described in any one of claims 1-9, to acquire the position and velocity information of the communication terminal in real time.

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