Low Earth Orbit (LEO) satellite Doppler positioning and velocity measurement methods, systems, and storage media

Abstract

This invention discloses a method, system, and storage medium for Doppler positioning and velocity measurement of low-Earth orbit (LEO) satellites. It acquires the Doppler frequency shift and ephemeris information of visible LEO satellites within the field of view at the same time. Within time T, the velocity and position of a ground terminal are calculated step-by-step using the least squares method, achieving convergence from initial values ​​to approximate values. The initial position and velocity of the ground terminal are both set to zero. After time T, the velocity and position of the ground terminal are simultaneously calculated using the least squares method to obtain accurate values. This method allows for Doppler velocity and velocity measurement positioning even with an initial ground terminal value of zero, simultaneously enabling positioning and velocity measurement of dynamic ground terminals. Furthermore, this method allows for Doppler positioning and velocity measurement to be achieved within one minute when starting from zero initial values, ensuring cold-start performance for Doppler positioning.

Description

Technical Field

[0001] This invention relates to low-Earth orbit satellite Doppler positioning technology, and in particular to a low-Earth orbit satellite Doppler positioning and velocity measurement method, system and storage medium. Background Technology

[0002] Low Earth Orbit (LEO) satellite Doppler positioning utilizes the motion characteristics of LEO satellites relative to ground terminals. The ground terminal detects the Doppler frequency shift of the LEO satellite signal and simultaneously collects information such as the position and velocity of the LEO satellite. The least squares method is then used to calculate the position and velocity of the ground terminal.

[0003] The relative motion between the satellite and the receiver causes a difference between the frequency of the signal transmitted by the satellite and the frequency received by the receiver; this difference is called the Doppler frequency shift, calculated using the formula:

[0004]

[0005] Where df represents the Doppler frequency shift, f0 represents the standard frequency of the signal, c represents the speed of light in a vacuum, and v s =(v x s ,v y s ,v z s ) T Represents the satellite velocity, v = (v x ,v y ,v z ) T The receiver speed is represented by r. s =(x s ,y s ,z s ) T Representing the satellite's position, r = (x, y, z) T Indicates the receiver position, f u ε represents the fixed frequency difference caused by receiver clock drift. f This indicates random measurement error.

[0006] In formula (1), c is a constant, df and f0 are obtained from receiver observations, and v s r s This is obtained by resolving the ephemeris file. The formula now only contains the receiver position r, receiver velocity v, and fixed frequency offset f. u There are 7 unknowns. For a static target, the receiver velocity v is 0, leaving only r = (x, y, z). T and f u Four unknowns are solved using the least squares method. (The given information is missing.) The calculation formula is

[0007] dX=(G T G) -1 G T F (2)

[0008] In formula (2), F = [δdf0… δdfi] i … δdf n ] T .in

[0009]

[0010]

[0011] δdf i =df i -df i (X0)

[0012] df represents the measured Doppler frequency shift. i (X0) represents the df calculated when X takes the value X0. i The value of .

[0013] After obtaining dX, calculate

[0014] X1=X0+dX (3)

[0015] Determine if the magnitude of dX is less than the convergence threshold. If it is, X1 is the solution result; if not, let X0 = X1 and repeat formulas (2) and (3) until the convergence condition is met.

[0016] For a dynamic objective, dX represents G indicates in

[0017] Calculate dX: dX = (G T G) -1 G T F, update X: X1 = X0 + dX. Repeat the iteration until the magnitude of dX is less than the convergence threshold.

[0018] Currently, Doppler positioning by low-Earth orbit satellites can achieve meter-level positioning and centimeter-level velocity determination. However, when the initial position of the ground terminal is unknown, especially for dynamic ground terminals, Doppler positioning algorithms struggle to achieve positioning functionality, and the calculated results have significant errors.

[0019] Shi Chuang (《Revisiting Doppler positioning performance with LEOsatellites》) achieved a positioning accuracy of 3-6m for static terminals with an initial error of less than 300km.

[0020] Guo Fei (“Instantaneous velocity determination and positioning using Doppler shift from a LEO constellation”) proposed that, for static terminals, the positioning accuracy is better than 1 dm when the initial value error is less than 1 km. By adding noise to the static terminal to simulate a dynamic terminal, the positioning accuracy is better than 1 m.

[0021] Mark L. Psiaki (Navigation using carrier Doppler shift from a LEOconstellation TRANSIT on steroids) found that, for static terminals with an initial error of less than 10km, by adding noise to the static terminal to simulate a dynamic scene, the positioning accuracy is better than 1m and the speed accuracy is better than 0.01m / s.

[0022] The aforementioned literature all uses a static + noise method to simulate dynamic scenes, lacking experiments on dynamic scenes. Meanwhile, the error of the initial position relative to the true value is less than 300 km. Summary of the Invention

[0023] The technical problem to be solved by the present invention is to provide a low-orbit satellite Doppler positioning and velocity measurement method, system and storage medium to address the shortcomings of the existing technology. When the initial value of the ground terminal is set to zero, the positioning and velocity measurement of the ground static or dynamic terminal is calculated, and the final positioning accuracy is at the meter level and the velocity measurement accuracy is at the centimeter level.

[0024] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a low-orbit satellite Doppler positioning and velocity measurement method, comprising the following steps:

[0025] Acquire Doppler shift and satellite ephemeris information of visible low-Earth orbit satellites within the field of view at the same time;

[0026] Within time T, the velocity and position of the ground terminal are calculated step by step using the least squares method to achieve convergence from the initial value to the approximate value; wherein, the initial position and initial velocity of the ground terminal are both set to zero;

[0027] After time T, the velocity and position of the ground terminal are simultaneously calculated using the least squares method to obtain the accurate values ​​of the velocity and position of the ground terminal.

[0028] The specific implementation process of using the least squares method to solve for the velocity and position of the ground terminal step by step, and achieving convergence from the initial value to the approximate value, includes:

[0029] The formula for calculating the speed of the ground terminal is: F1=[δdf 1 … δdf i … δdf n ] T , df i The Doppler frequency shift value is obtained through observations from a ground terminal. It is based on the ground terminal's position r=r0, velocity v=v0, and clock drift rate at the previous moment. At that time, through the observation equation The calculated Doppler frequency shift estimate, df u An update term representing the clock drift rate of the ground terminal; f0 is the nominal carrier frequency of the satellite signal, c is the speed of light in a vacuum, and r0 = [x0y0z0]. T =0, where x0, y0, and z0 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system at the previous moment. Let i be the three-dimensional position vector of the i-th satellite.

[0030] Update the speed and clock drift rate of the ground terminal: Obtain the current ground terminal's velocity v1 and clock drift rate.

[0031] The formula for calculating the location of the ground terminal is as follows: F2=[δdf 1′ … δdf i′ … δdf n′ ] T , It is based on the ground terminal's position r=r0, velocity v=v0, and clock drift rate at the previous moment. Time through observation equation The calculated Doppler frequency shift estimate; dr = [dx dy dz] T The update item representing the speed of the ground terminal. v1 represents the updated three-dimensional velocity of the ground terminal in the geocentric-geofixed coordinate system at the current moment, and v2 represents the updated three-dimensional velocity vector of the ground terminal in the geocentric-geofixed coordinate system at the current moment. df u The update term represents the clock drift rate of the ground terminal. Let be the three-dimensional velocity vector of the i-th satellite. Let i be the three-dimensional position vector of the i-th satellite.

[0032] Update ground terminal position and clock drift rate Obtain the current ground terminal position r1 and the new clock drift rate. This represents the ground terminal clock drift rate at the previous moment.

[0033] When ||dr|| is less than the threshold value, the final ground terminal position and clock drift rate are output; if ||dr|| is greater than the threshold value, the values ​​of r1 and v1 are assigned to r0 and v0 respectively, and the formula is reused. and Update the ground terminal position and clock drift rate until |dr| is less than the threshold value, or the number of iterations is greater than the set number.

[0034] After time T, the specific implementation process of simultaneously calculating the velocity and position of the ground terminal using the least squares method to obtain the precise values ​​of the ground terminal's velocity and position includes:

[0035] The speed and clock drift rate of the ground terminal are updated using the following formula:

[0036] Update the ground terminal's position and clock drift rate using the following formula:

[0037] in, x2, y2, and z2 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system at the previous moment, and F1 = [δdf 1 … δdf i … δdf n ] T , df i Observed via ground terminal It is based on the ground terminal's position being r = r², its velocity being v = v², and its clock drift rate being... Time through observation equation The calculated true values ​​of Doppler frequency shift, r2, v2, Let f0 be the position, velocity, and clock drift rate of the ground terminal, calculated step-by-step using the least squares method within time T, where f0 is the nominal carrier frequency of the satellite signal, c is the speed of light in vacuum, and r0 = [x0, y0, z0]. T =0, where x0, y0, and z0 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system at the previous moment. Let be the three-dimensional position vector of the i-th satellite. Let v1, v2, and r3 represent the updated three-dimensional velocity of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment, respectively. Let v3 represent the updated three-dimensional velocity vector of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment, respectively. Let r3 represent the updated three-dimensional position vector of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment. This represents the updated clock drift rate at the current moment, dr = [dx dy dz] T The update term representing the ground terminal speed, df u This is an update item representing the clock drift rate of the ground terminal.

[0038] When ||dr|| is less than the threshold value, the final ground terminal position and clock drift rate are output; if ||dr|| is greater than the threshold value, the values ​​of r3 and v3 are assigned to r2 and v2 respectively, and the formula is reused. and Update the ground terminal position and clock drift rate until |dr| is less than the threshold value.

[0039] In this invention, T represents 1 minute.

[0040] As an inventive concept, the present invention also provides a low-orbit satellite Doppler positioning and velocity measurement system, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program to implement the steps of the above method.

[0041] As an inventive concept, the present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon; when the computer program / instructions are executed by a processor, they implement the steps of the above-described method.

[0042] Compared with existing technologies, the beneficial effects of this invention are as follows: Compared with the traditional least squares algorithm that simultaneously calculates the velocity and position of the ground terminal, this invention chooses to calculate the position and velocity of the terminal separately, thus solving the nonlinearity problem of least squares solution. Using the method of this invention, Doppler velocity and positioning can be achieved when the initial value of the ground terminal is zero, and the positioning and velocity measurement functions of dynamic ground terminals can be realized simultaneously. Using the method of this invention, when performing Doppler positioning from a zero initial value, the positioning and velocity measurement functions can be realized within 1 minute, ensuring the cold start performance of Doppler positioning. Attached Figure Description

[0043] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0044] Figure 2 The following are schematic diagrams of the ground terminal trajectory in an embodiment of the present invention: (a) trajectory of an airplane in simulation, (b) trajectory of a car in simulation, (c) trajectory of a helicopter in simulation, and (d) trajectory of a train in simulation.

[0045] Figure 3 The diagram shows the convergence speed of the method in the embodiment of the present invention; (a) a diagram of the positioning error starting from time 0, and (b) a diagram of the velocity measurement error starting from time 0.

[0046] Figure 4 The following are statistical diagrams of positioning errors after convergence of the method in the embodiments of the present invention: (a) Schematic diagram of positioning error after algorithm convergence, (b) Schematic diagram of speed measurement error after algorithm convergence. Detailed Implementation

[0047] 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.

[0048] Example 1

[0049] This invention provides a low-Earth orbit satellite Doppler positioning and velocity measurement method, the specific implementation process of which includes:

[0050] Step 1: The ground terminal acquires the Doppler shift and satellite ephemeris information of visible low-orbit satellites within the field of view at the same time;

[0051] Step 2: Set the initial position and initial velocity of the ground terminal to zero;

[0052] Step 3: Within one minute, calculate the location of the ground terminal using the least squares method, reducing the number of algorithm iterations to below 10;

[0053] Step 4: After the number of algorithm iterations is reduced to below 10, the speed and position of the ground terminal are calculated synchronously using the least squares method to obtain the speed and position of the terminal.

[0054] Step 1 specifically includes the following steps:

[0055] The ground terminal acquires the Doppler frequency shift and satellite ephemeris information of n visible satellites within the field of view at time k, where n≥7;

[0056] The satellite ephemeris information obtained by the ground terminal should be able to be used to calculate the position coordinates and three-dimensional velocity of visible satellites in the geocentric-ground-fixed coordinate system;

[0057] It is evident that the satellite is a low-orbit satellite with the same nominal frequency and is known.

[0058] Step 2 specifically includes the following steps:

[0059] The initial position of the ground terminal is r0 = [x0 y0 z0] T =0; Initial velocity of the ground terminal

[0060] Step 3 specifically includes the following steps:

[0061] At the start of the solution process, the Doppler frequency shift observation equation for a specific moment is constructed:

[0062]

[0063] At this specific moment, df i For the Doppler frequency shift observation of the i-th satellite; f0 is the nominal carrier frequency of the satellite signal; c is the speed of light in vacuum; Let be the three-dimensional velocity vector of the i-th satellite. v is the three-dimensional velocity vector of the ground terminal, v = [v x v y v z ] T ; Let i be the three-dimensional position vector of the i-th satellite. r is the three-dimensional position vector of the ground terminal, r = [xyz] T ;f u The clock drift rate of the ground terminal; Let represent the observation noise of the i-th satellite.

[0064] The solution process for step 3 is as follows:

[0065] Within one minute, the calculation process of step 3 is performed once every second. First, based on the terminal position of the previous second (which is initially zero), the terminal velocity of the current second is calculated. Then, based on the obtained terminal velocity of the current second, the terminal position of the current second is iteratively calculated using the least squares method. The iteration ends when the difference between the results of two iterations is less than a threshold value.

[0066] The formula for calculating the ground terminal velocity is as follows:

[0067] Where F1=[δdf 1 … δdfi … δdf n ] T , df i The Doppler frequency shift value is obtained through observations from a ground terminal. It is based on the ground terminal's position r=r0, velocity v=v0, and clock drift rate in the previous second. At that time, through the observation equation The calculated Doppler frequency shift estimate;

[0068] x0, y0, and z0 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second (these values ​​are initially set to 0), and r0 represents the three-dimensional position vector of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second.

[0069] dv = [dv x dv y dv z ] T The update item representing the ground terminal speed is unknown;

[0070] df u The update term representing the clock drift rate of the ground terminal is unknown.

[0071] Calculated

[0072] Update the speed and clock drift rate of the ground terminal: Get the speed of the ground terminal in this second and clock drift rate.

[0073] In step 3, the speed only needs to be calculated once.

[0074] After the velocity calculation is completed, the position of the ground terminal is calculated using the least squares method. The formula for calculating the position of the ground terminal is as follows:

[0075] Where F2=[δdf 1′ … δdf 1′ … δdf n′ ] T , df i The Doppler frequency shift value is obtained through observations from a ground terminal. It is based on the ground terminal's position r=r0, velocity v=v0, and clock drift rate in the previous second. Time through observation equation Calculated;

[0076]

[0077] x0, y0, and z0 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second (these values ​​are initially set to 0), and r0 represents the three-dimensional position vector of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second. v1 and v2 represent the three-dimensional velocity of the ground terminal in the geocentric-geocentric coordinate system in the updated second, respectively. v3 represents the three-dimensional velocity vector of the ground terminal in the geocentric-geocentric coordinate system in the updated second.

[0078] dr = [dx dy dz] T The update item representing the ground terminal speed is unknown;

[0079] df u The update term representing the clock drift rate of the ground terminal is unknown.

[0080] Calculated

[0081]

[0082] Update position and clock drift rate

[0083]

[0084] Determine the magnitude of dr; if |dr| is less than a threshold value (usually set to 10)... -6 If r1 and v1 are obtained, they are the position and velocity of the ground terminal in this second. If ‖dr‖ is greater than the threshold value, the values ​​of r1 and v1 are assigned to r0 and v0, and the new r1 and v1 are calculated by repeatedly using formulas (2) and (3) until the convergence condition (‖dr‖ is less than the threshold value) is met, or the number of least squares iterations is greater than 1000.

[0085] Within one minute, new satellite signals are received every second, thus obtaining a new Doppler frequency shift df. i and satellite position and satellite speed Therefore, step 3 needs to be performed every second. When the number of least squares iterations is less than 10 in a given second, the goal of step 3 is considered to have been achieved, and step 3 can be terminated to proceed to step 4. This process should not take more than 1 minute.

[0086] After the number of iterations of the least squares method falls below 10, proceed to step 4. The output of step 3 is the ground terminal position r1, velocity v1, and clock drift rate. Step 4 specifically includes the following steps:

[0087] After entering step 4, the algorithm has achieved a certain positioning accuracy, and can then achieve real-time positioning with an accuracy of 1 meter. The general operation is as follows: the calculation process of step 4 is performed once every second. Based on the position r2 of the ground terminal in the previous second (at the beginning of step 4, the value of this variable is selected from the calculation result r2 = r1 in step 3), the velocity v3 of the ground terminal at this moment is calculated. Based on the velocity v3 of the ground terminal at this moment, the position r3 of the ground terminal at this moment is calculated. The velocity and position of the ground terminal are calculated iteratively. The iteration ends when the difference between the results of two consecutive iterations is lower than a threshold value.

[0088] The formula for calculating the ground terminal velocity is as follows:

[0089] Where F1=[δdf 1 … δdf i … δdf n ] T , df i Observed via ground terminal It is based on the ground terminal's position being r = r², its velocity being v = v², and its clock drift rate being... Time through observation equation Calculated;

[0090] x2, y2, and z2 represent the three-dimensional coordinates of the ground terminal in the geocentric-geo-fixed coordinate system in the previous second (these values ​​are x1, y1, and z1 at the beginning of step 4), and r2 represents the three-dimensional position vector of the ground terminal in the geocentric-geo-fixed coordinate system in the previous second.

[0091] dv = [dv x dv y dv z ] T The update item representing the ground terminal speed is unknown;

[0092] df u The update term representing the clock drift rate of the ground terminal is unknown.

[0093] Calculated

[0094]

[0095] Update the speed and clock drift rate of the ground terminal:

[0096]

[0097] Obtain the speed and clock drift rate of the ground terminal at this moment.

[0098] The formula for calculating the location of the ground terminal is as follows:

[0099] Where F2=[δdf 1′ … δdf 1′ … δdf n′ ] T , df i Observed via ground terminal It is based on the ground terminal's position as r2, speed as v3, and clock drift rate as... Time through observation equation Calculated;

[0100]

[0101] x2, y2, and z2 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second (these values ​​are x1, y1, and z1 at the beginning of step 4), and r2 represents the three-dimensional position vector of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second. v1 and v2 respectively represent the three-dimensional velocity of the ground terminal in the geocentric-geocentric coordinate system in the updated second, and v3 represents the three-dimensional velocity vector of the ground terminal in the geocentric-geocentric coordinate system in the updated second.

[0102] dr = [dx dy dz] T The update item representing the ground terminal speed is unknown;

[0103] df u The update term representing the clock drift rate of the ground terminal is unknown.

[0104] [Calculated]

[0105]

[0106] Update position and clock drift rate

[0107]

[0108] Determine the magnitude of dr; if |dr| is less than a threshold value (usually set to 10)... -6 If r3 and v3 are obtained, they are the position and velocity of the ground terminal in this second. If ‖dr‖ is greater than the threshold value, the values ​​of r3 and v3 are assigned to r2 and v2. Formulas (4)(5) and (6)(7) are used repeatedly to calculate new r3 and v3 until the convergence condition (‖dr‖ is less than the threshold value) is met.

[0109] After entering step 4, the calculation process of step 4 is used every second. After the iteration is completed, the final output results r3 and v3 are the position and velocity of the ground terminal at that moment.

[0110] This invention utilizes a GNSS navigation signal simulation system to design a low-Earth orbit satellite constellation and ground terminals in different motion states to verify the performance of the method proposed in this invention.

[0111] The ground terminal trajectory parameters are shown in Table 1:

[0112] Table 1 Ground Terminal Trajectory Parameters

[0113]

[0114] The positioning error is no more than 2m, and the speed measurement error is no more than 1cm / s.

[0115] The positioning and speed measurement accuracy is shown in Table 2:

[0116] Table 2 Positioning and speed measurement accuracy

[0117]

[0118] In this embodiment of the invention, accuracy means that, with the true value as the center and accuracy as the radius, 95% of the positioning results at any given time fall within the circle. The positioning accuracy is at the meter level, and the velocity measurement accuracy is less than 1 cm / s.

[0119] Example 2

[0120] Embodiment 2 of the present invention provides a system corresponding to Embodiment 1 above, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method of Embodiment 1 above.

[0121] In some implementations, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0122] In other implementations, the processor can be any type of general-purpose processor, such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation here.

[0123] Example 3

[0124] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to Embodiment 1 above, on which a computer program / instructions are stored. When the computer program / instructions are executed by a processor, they implement the steps of the method of Embodiment 1 above.

[0125] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0126] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0127] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0128] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0129] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0130] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A low-orbit satellite Doppler positioning and velocity measurement method, characterized in that, Includes the following steps: Acquire Doppler shift and satellite ephemeris information of visible low-Earth orbit satellites within the field of view at the same time; Within time T, the velocity and position of the ground terminal are calculated step by step using the least squares method to achieve convergence from the initial value to the approximate value; wherein, the initial position and initial velocity of the ground terminal are both set to zero; after time T, the velocity and position of the ground terminal are calculated synchronously using the least squares method to obtain the accurate values ​​of the velocity and position of the ground terminal; The specific implementation process of using the least squares method to solve for the velocity and position of the ground terminal step by step, and achieving convergence from the initial value to the approximate value, includes: The formula for calculating the speed of the ground terminal is: F1=[δdf 1 … δdf i … δdf n ] T , df i The Doppler frequency shift value is obtained through observations from a ground terminal. It is based on the ground terminal's position r=r0, velocity v=v0, and clock drift rate at the previous moment. At that time, through the observation equation The calculated Doppler frequency shift estimate, df u An update item representing the clock drift rate of the ground terminal; f0 is the nominal carrier frequency of the satellite signal, and c is the speed of light in a vacuum. r0 = [x0y0z0] T =0, where x0, y0, and z0 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system at the previous moment. Let i be the three-dimensional position vector of the i-th satellite. Update the speed and clock drift rate of the ground terminal: Obtain the current ground terminal's velocity v1 and clock drift rate. The formula for calculating the location of the ground terminal is as follows: F2=[δdf 1′ … δdf i′ … δdf n′ ] T , It is based on the ground terminal's position r=r0, velocity v=v0, and clock drift rate at the previous moment. Time through observation equation The calculated Doppler frequency shift estimate; dr = [dx dy dz] T The update item representing the speed of the ground terminal. v1 represents the updated three-dimensional velocity of the ground terminal in the geocentric-geofixed coordinate system at the current moment, and v2 represents the updated three-dimensional velocity vector of the ground terminal in the geocentric-geofixed coordinate system at the current moment. df u The update term represents the clock drift rate of the ground terminal. Let be the three-dimensional velocity vector of the i-th satellite. Let i be the three-dimensional position vector of the i-th satellite. Update ground terminal position and clock drift rate Obtain the current ground terminal position r1 and the new clock drift rate. This represents the ground terminal clock drift rate at the previous moment.

2. The low-orbit satellite Doppler positioning and velocity measurement method according to claim 1, characterized in that, When ||dr|| is less than the threshold value, the final ground terminal position and clock drift rate are output; if ||dr|| is greater than the threshold value, the values ​​of r1 and v1 are assigned to r0 and v0 respectively, and the formula is reused. and Update the ground terminal position and clock drift rate until |dr| is less than the threshold value, or the number of iterations is greater than the set number.

3. The low-orbit satellite Doppler positioning and velocity measurement method according to claim 1, characterized in that, After time T, the specific implementation process of simultaneously calculating the velocity and position of the ground terminal using the least squares method to obtain the precise values ​​of the ground terminal's velocity and position includes: The speed and clock drift rate of the ground terminal are updated using the following formula: Update the ground terminal's position and clock drift rate using the following formula: in, x2, y2, and z2 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system at the previous moment, and F1 = [δdf 1 … δdf i … δdf n ] T , df i Observed via ground terminal. It is based on the ground terminal's position being r = r², its velocity being v = v², and its clock drift rate being f. u =f u3 Time through observation equation The calculated true values ​​of Doppler frequency shift, r2, v2, Let f0 be the position, velocity, and clock drift rate of the ground terminal, calculated step-by-step using the least squares method within time T, where f0 is the nominal carrier frequency of the satellite signal, c is the speed of light in vacuum, and r0 = [x0y0z0]. T =0, where x0, y0, and z0 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system at the previous moment. Let be the three-dimensional position vector of the i-th satellite. Let v1, v2, and r3 represent the updated three-dimensional velocity of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment, respectively. Let v3 represent the updated three-dimensional velocity vector of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment, respectively. Let r3 represent the updated three-dimensional position vector of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment. This represents the updated clock drift rate at the current moment, dr = [dx dy dz] T The update term representing the ground terminal speed, df u This is an update item representing the clock drift rate of the ground terminal.

4. The low-orbit satellite Doppler positioning and velocity measurement method according to claim 3, characterized in that, When ||dr|| is less than the threshold value, the final ground terminal position and clock drift rate are output; if ||dr|| is greater than the threshold value, the values ​​of r3 and v3 are assigned to r2 and v2 respectively, and the formula is reused. and Update the ground terminal position and clock drift rate until |dr| is less than the threshold value.

5. The low-orbit satellite Doppler positioning and velocity measurement method according to any one of claims 1 to 4, characterized in that, T is 1 minute.

6. A low-Earth orbit satellite Doppler positioning and velocity measurement system, comprising a memory, a processor, and a computer program stored in the memory; characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program / instructions stored thereon; characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 5.

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