Low-orbit satellite Doppler positioning speed measurement method and system and storage medium

Abstract

The invention discloses a low-orbit satellite Doppler positioning speed measurement method and system and a storage medium. The method comprises the following steps: acquiring Doppler frequency shift and satellite ephemeris information of visible low-orbit satellites in a view field range at the same moment; within the time T, the speed and the position of the ground terminal are solved step by step through the least square method, and convergence from an initial value to an approximate value is achieved; wherein the initial position and the initial speed of the ground terminal are set to be zero; and after the time T, synchronously resolving the speed and the position of the ground terminal by using a least square method to obtain the accurate values of the speed and the position of the ground terminal. By means of the method, Doppler velocity measurement positioning can be achieved when the initial value of the ground terminal is zero, and the functions of positioning and velocity measurement of the dynamic ground terminal can be achieved at the same time. By means of the method, when Doppler positioning is carried out from the initial value of zero, the positioning speed measurement function can be achieved within one minute, and the cold start performance of Doppler positioning is guaranteed.

Description

Technical Field

[0001] The present invention relates to the Doppler positioning technology of low-earth orbit satellites, in particular to a Doppler positioning and velocity measurement method, system and storage medium for low-earth orbit satellites. Background Art

[0002] Doppler positioning of low-earth orbit satellites utilizes the characteristics of the relative motion between low-earth orbit satellites and ground terminals. The ground terminals detect the Doppler frequency shift of the signals of low-earth orbit satellites, and at the same time collect information such as the position and velocity of the low-earth orbit satellites, and use the least squares method to calculate the position and velocity of the ground terminals.

[0003] There is relative motion between the satellite and the receiver, resulting in the frequency of the signal transmitted by the satellite being different from the frequency received by the receiver. The difference is the Doppler frequency shift, and the calculation formula is

[0004]

[0005] where df represents the Doppler frequency shift, f 0 represents the signal standard frequency, c represents the speed of light in vacuum, v s =(v x s , v y s , v z s ) T represents the satellite velocity, v=(v x , v y , v z ) T represents the receiver velocity, r s =(x s , y s , z s ) T represents the satellite position, r=(x, y, z) T represents the receiver position, f u represents the fixed frequency difference generated by the receiver clock drift, ε f represents the random measurement error.

[0006] In formula (1), c is a constant, df, f 0 are obtained by receiver observation, v s , r s are obtained by solving the ephemeris file. Only the receiver position r, the receiver velocity v and the fixed frequency offset f u are left in the formula, a total of 7 unknowns. For a static target, the receiver velocity v is 0, and only r=(x, y, z) T and f u are left, with four unknowns, and the least squares method is used for calculation. It is known that The calculation formula is

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

[0008] In formula (2), F = [δdf 0 … δdfi i … δdf n ) T . Where

[0009]

[0010]

[0011] δdf i = df i - df i (X 0 )

[0012] represents the measured Doppler frequency shift, df i (X 0 ) represents the value of df calculated when X takes X 0 . i Value.

[0013] After obtaining dX, calculate

[0014] X 1 = X 0 + dX (3)

[0015] Judge whether the modulus of dX is less than the convergence threshold. If X 1 is satisfied, it is the solution result; if not, let X 0 = X 1 , repeat formulas (2) and (3) until the convergence condition is satisfied.

[0016] For a dynamic target, dX represents G represents Where

[0017]

[0018] Calculate dX: dX = (G T G) -1 G T F, update X: X 1 = X 0 + dX. Repeat the iteration until the modulus of dX is less than the convergence threshold.

[0019] At present, Doppler positioning of low-Earth orbit satellites can achieve meter-level positioning and centimeter-level speed determination. However, when the initial position of the ground terminal is unknown, especially for dynamic ground terminals, it is difficult for the Doppler positioning algorithm to achieve the positioning function, and the calculated results have large errors.

[0020] Shi Chuang ("Revisiting Doppler positioning performance with LEO satellites"), for static terminals, when the initial value error is less than 300 km, a positioning accuracy of 3 - 6 m is achieved.

[0021] Guo Fei ("Instantaneous velocity determination and positioning using Doppler shift from a LEO constellation"), for static terminals, when the initial value error is less than 1 km, the positioning accuracy is better than 1 dm. By adding noise to the static terminal to simulate a dynamic terminal, a positioning accuracy better than 1 m is achieved.

[0022] Mark L. Psiaki ("Navigation using carrier Doppler shift from a LEO constellation TRANSIT on steroids"), for static terminals, when the initial value error is less than 10 km, by adding noise to the static terminal to simulate a dynamic scenario, the positioning accuracy is better than 1 m, and the speed determination accuracy is better than 0.01 m / s.

[0023] The above-mentioned literatures all use the method of static + noise to simulate dynamic scenarios and lack tests on dynamic scenarios. At the same time, the error of the initial position relative to the true value is less than 300 km. Summary of the Invention

[0024] The technical problem to be solved by the present invention is to provide a low-Earth orbit satellite Doppler positioning and velocity measurement method, system and storage medium in view of the deficiencies of the prior art. When the initial value of the ground terminal is set to zero, positioning and velocity measurement calculations are performed on static or dynamic ground terminals, and the final positioning accuracy is at the meter level and the speed determination accuracy is at the centimeter level.

[0025] To solve the above technical problem, the technical solution adopted by the present invention is: A low-Earth orbit satellite Doppler positioning and velocity measurement method, including the following steps:

[0026] Obtain the Doppler frequency shift and satellite ephemeris information of visible low-Earth orbit satellites within the field of view at the same moment;

[0027] Within time T, the velocity and position of the ground terminal are solved 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;

[0028] After time T, the velocity and position of the ground terminal are solved synchronously using the least squares method to obtain the accurate values of the velocity and position of the ground terminal.

[0029] The specific implementation process of solving the velocity and position of the ground terminal step by step using the least squares method to achieve convergence from the initial value to the approximate value includes:

[0030] The velocity calculation formula of the ground terminal is: F 1 =[δdf 1 … δdf i … δdf n T , df i is the true value of the Doppler frequency shift obtained through the observation of the ground terminal, is the Doppler frequency shift estimated value calculated through the observation equation 0 、velocity v=v 0 、clock drift rate when the position of the ground terminal at the previous moment is r=r ; df u represents the update term of the clock drift rate of the ground terminal; f 0 is the nominal carrier frequency of the satellite signal, c is the speed of light in vacuum, r 0 =[x 0 y 0 z 0 T =0,x 0 、y 0 、z 0 represent the three-dimensional coordinates of the ground terminal in the Earth-Centered Earth-Fixed coordinate system at the previous moment, is the three-dimensional position vector of the i-th satellite,

[0031] Update the velocity and clock drift rate of the ground terminal: Obtain the velocity v 1 of the ground terminal at the current moment and the clock drift rate

[0032] The calculation formula for the position of the ground terminal is F 2 =[δdf 1′ … δdf i′ … δdf​​n′ T , is the estimated Doppler frequency shift calculated through the observation equation 0 when the position of the ground terminal at the previous moment is r = r 0 , the speed is v = v , and the clock drift rate ; dr = [dx dy dz] T represents the update term of the ground terminal speed, which respectively represent the three-dimensional speeds of the ground terminal at the updated current moment in the Earth-centered Earth-fixed coordinate system, v 1 represents the three-dimensional speed vector of the ground terminal at the updated current moment in the Earth-centered Earth-fixed coordinate system; df u represents the update term of the ground terminal clock drift rate, is the three-dimensional speed vector of the i-th satellite, is the three-dimensional position vector of the i-th satellite,

[0033] Update the position and clock drift rate of the ground terminal to obtain the position r of the ground terminal at the current moment 1 and the new clock drift rate where

[0034] is the clock drift rate of the ground terminal at the previous moment. 1 When ‖dr‖ is less than the threshold value, output the final position and clock drift rate of the ground terminal; if ‖dr‖ is greater than the threshold value, then assign the values of r 1 and v 0 and v 0 respectively to r and and repeat to update the position and clock drift rate of the ground terminal until ‖dr‖ is less than the threshold value or the number of iterations is greater than the set number of times.

[0035] After time T, the specific implementation process of synchronously calculating the speed and position of the ground terminal using the least squares method to obtain the accurate values of the speed and position of the ground terminal includes:

[0036] Update the speed and clock drift rate of the ground terminal using the following formula:

[0037] Update the position and clock drift rate of the ground terminal using the following formula:

[0038] where ​ x 2 、y 2 、z 2 respectively represent the three - dimensional coordinates of the ground terminal in the Earth - centered Earth - fixed coordinate system at the previous moment. F 1 =[δdf 1 … δdf i … δdf n T , df i is obtained through the observation of the ground terminal. is the true value of the Doppler frequency shift calculated through the observation equation when the position of the ground terminal is r = r 2 、the speed is v = v 2 、and the clock drift rate is at time T. r 、v 2 、 2 、 are respectively the position, speed, and clock drift rate of the ground terminal obtained by step - by - step solution using the least - squares method within time T. f 0 is the nominal carrier frequency of the satellite signal, c is the speed of light in vacuum, r 0 =[x 0 y 0 z 0 T =0, x 0 、y 0 、z 0 represent the three - dimensional coordinates of the ground terminal in the Earth - centered Earth - fixed coordinate system at the previous moment. is the three - dimensional position vector of the i - th satellite. respectively represent the three - dimensional velocities of the ground terminal in the Earth - centered Earth - fixed coordinate system at the updated current moment. v 3 represents the three - dimensional velocity vector of the ground terminal in the Earth - centered Earth - fixed coordinate system at the updated current moment. r 3 represents the three - dimensional position vector of the ground terminal in the Earth - centered Earth - fixed coordinate system at the updated current moment. represents the clock drift rate at the updated current moment. dr = [dx dy dz] T represents the update term of the ground terminal speed. df u represents the update term of the ground terminal clock drift rate.

[0039] When ‖dr‖ is less than the threshold value, the final position and clock drift rate of the ground terminal are output; if ‖dr‖ is greater than the threshold value, the values of r 3 and v 3 are respectively assigned to r 2 and v 2 , and the formula is reused.​​ and Update the ground terminal position and clock drift rate until ‖dr‖ is less than the threshold value.

[0040] In the present invention, T is 1 minute.

[0041] As an inventive concept, the present invention also provides a low-earth orbit satellite Doppler positioning and velocity measurement system, including a memory, a processor, and a computer program stored on the memory; the processor executes the computer program to implement the steps of the above method.

[0042] As an inventive concept, the present invention also provides a computer-readable storage medium, on which a computer program / instructions are stored; when the computer program / instructions are executed by the processor, the steps of the above method are implemented.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows: compared with the traditional least squares algorithm for simultaneously solving the speed and position of the ground terminal, the present invention selects to calculate the position and speed of the terminal separately, solving the non-linear problem of least squares solution. Through the method of the present invention, Doppler velocity measurement and positioning can be realized when the initial value of the ground terminal is zero, and the positioning and velocity measurement functions of the dynamic ground terminal can be realized simultaneously. Through the method of the present invention, when performing Doppler positioning from zero initial value, the positioning and velocity measurement functions can be realized within 1 minute, ensuring the cold start performance of Doppler positioning. Description of the Drawings

[0044] Figure 1 is the flowchart of the method of the embodiment of the present invention;

[0045] Figure 2 is the schematic diagram of the ground terminal trajectory of the embodiment of the present invention; (a) the trajectory diagram of the airplane in the simulation, (b) the trajectory diagram of the car in the simulation, (c) the trajectory diagram of the helicopter in the simulation, (d) the trajectory diagram of the train in the simulation;

[0046] Figure 3 is the schematic diagram of the convergence speed of the method of the embodiment of the present invention; (a) the schematic diagram of the positioning error starting from time 0, (b) the schematic diagram of the velocity measurement error starting from time 0;

[0047] Figure 4 is the statistical chart of the positioning error after the method of the embodiment of the present invention converges; (a) the schematic diagram of the positioning error after the algorithm converges, (b) the schematic diagram of the velocity measurement error after the algorithm converges. Detailed Embodiment

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0049] Embodiment 1

[0050] An embodiment of the present invention provides a method for Doppler positioning and velocity measurement of low-earth orbit satellites. The specific implementation process includes:

[0051] Step 1: The ground terminal acquires the Doppler frequency shift and satellite ephemeris information of the visible low-earth orbit satellites within the field of view at the same moment.

[0052] Step 2: Set the initial position and initial velocity of the ground terminal to zero.

[0053] Step 3: Within one minute, use the least squares method to solve the position of the ground terminal, reducing the number of algorithm iterations to less than 10.

[0054] Step 4: After the number of algorithm iterations is reduced to less than 10, use the least squares method to synchronously solve the velocity and position of the ground terminal to obtain the velocity and position of the terminal.

[0055] Among them, Step 1 specifically includes the following steps:

[0056] 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.

[0057] The satellite ephemeris information acquired by the ground terminal should be available for solving the position coordinates and three-dimensional velocity of the visible satellites in the Earth-centered Earth-fixed coordinate system.

[0058] The visible satellites refer to low-earth orbit satellites with the same nominal frequency and known.

[0059] Among them, Step 2 specifically includes the following steps:

[0060] The initial position r of the ground terminal 0 =[x 0 y 0 z 0 T =0; the initial velocity of the ground terminal

[0061] Among them, Step 3 specifically includes the following steps:

[0062] At the start of the solution, construct the Doppler frequency shift observation equation at a specific moment:​

[0063]

[0064] where, at this specific moment, df i is the Doppler frequency shift measurement of the i-th satellite; f 0 is the nominal carrier frequency of the satellite signal; c is the speed of light in vacuum; is 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 ; is the three-dimensional position vector of the i-th satellite, r is the three-dimensional position vector of the ground terminal, r = [x y z] T ; f u is the clock drift rate of the ground terminal; is the observation noise of the i-th satellite.

[0065] The solution process of step 3 is as follows:

[0066] Within one minute, the calculation process of step 3 is performed once per second. First, based on the terminal position of the previous second (which is zero at the initial moment), the terminal velocity of this second is calculated; then, based on the obtained terminal velocity of this second, the terminal position of this second is iteratively calculated using the least squares method, and the judgment condition for the end of the iteration is that the difference between the results of the previous and current iterations is lower than the threshold value.

[0067] Among them, the calculation formula for the ground terminal velocity is:

[0068] where F 1 = [δdf 1 … δdf i … δdf n T , df i is the true value of the Doppler frequency shift obtained through ground terminal observation, is the estimated value of the Doppler frequency shift calculated through the observation equation 0 when based on the position r = r 0 and velocity v = v of the ground terminal of the previous second and the clock drift rate ;

[0069] x 0 、y 0 、z 0 ​​respectively represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second (this value is taken as 0 at the initial moment), r 0 represents the three-dimensional position vector of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second.

[0070] dv = [dv x dv y dv z T represents the update term of the ground terminal velocity, which is unknown;

[0071] df u represents the update term of the ground terminal clock drift rate, which is unknown.

[0072] Calculated

[0073] Update the velocity and clock drift rate of the ground terminal: Obtain the velocity of the ground terminal in this second and the clock drift rate.

[0074] In step 3, the velocity only needs to be calculated preferentially once.

[0075] After the velocity calculation is completed, use the least squares method to calculate the position of the ground terminal. The calculation formula for the ground terminal position is

[0076] where F 2 = [δdf 1′ … δdf 1′ … δdf n′ T , df i is the true value of the Doppler frequency shift obtained through the observation of the ground terminal, is calculated according to the position r = r of the ground terminal in the previous second 0 , velocity v = v 0 , clock drift rate through the observation equation when calculating;

[0077]

[0078] x 0 、y 0 、z 0 respectively represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second (this value is taken as 0 at the initial moment), r 0 represents the three-dimensional position vector of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second, ​​respectively represent the three-dimensional velocity of the ground terminal in the Earth-centered Earth-fixed coordinate system at this updated second, v 1 represents the three-dimensional velocity vector of the ground terminal in the Earth-centered Earth-fixed coordinate system at this updated second.

[0079] dr = [dx dy dz] T represents the update term of the ground terminal velocity, which is unknown;

[0080] df u represents the update term of the ground terminal clock drift rate, which is unknown.

[0081] Calculated

[0082]

[0083] Update the position and clock drift rate

[0084]

[0085] Judge the magnitude of the modulus of dr. If ‖dr‖ is less than the threshold value (generally set to 10 -6 , then the obtained r 1 and v 1 are the position and velocity of the ground terminal at this second; if ‖dr‖ is greater than the threshold value, then assign the values of r 1 and v 1 to r 0 and v 0 , and repeatedly use formulas (2) and (3) to calculate the new r 1 and v 1 until the convergence condition (‖dr‖ is less than the threshold value) is satisfied, or the number of iterations of the least squares method is greater than 1000.

[0086] Within one minute, new satellite signals are received every second, thereby obtaining the new Doppler frequency shift df i and the satellite position and the satellite velocity Therefore, the operations in step 3 need to be performed every second. When the number of iterations of the least squares method in the calculation of a certain second is less than 10, it is considered that the goal of step 3 has been achieved, and step 3 can be ended and step 4 can be entered. The duration required for this process will not exceed 1 minute.

[0087] After the number of iterations of the least squares method is less than 10, enter step 4. The output result of step 3 is the ground terminal position r 1 , velocity v 1 , clock drift rate Among them, step 4 specifically includes the following steps:

[0088] After entering Step 4, the algorithm has achieved a certain positioning accuracy, and then real-time positioning with an accuracy of 1 m can be achieved. The general operation is to perform the calculation process of Step 4 in real time every second, and based on the position r of the ground terminal in the previous second 2 (when initially performing Step 4, the value of this variable is selected as the calculation result r of Step 3 2 = r 1 ), calculate the speed v of the ground terminal at this moment 3 , and based on the obtained speed v of the ground terminal at this moment 3 , calculate the position r of the ground terminal at this moment 3 ; repeatedly iterate to calculate the speed and position of the ground terminal, and end the iteration when the difference between the results of the two consecutive iterations is lower than the threshold value.

[0089] Among them, the calculation formula for the speed of the ground terminal is

[0090] where F 1 = [δdf 1 … δdf i … δdf n T , df i is obtained through the observation of the ground terminal, is calculated according to the position of the ground terminal being r = r 2 , speed being v = v 2 , clock drift rate being through the observation equation ;

[0091] x 2 , y 2 , z 2 respectively represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second (when initially starting Step 4, this value is taken as x 1 , y 1 , z 1 ), and r 2 represents the three-dimensional position vector of the ground terminal in the Earth-centered Earth-fixed coordinate system in the previous second.

[0092] dv = [dv x dv y dv z T represents the update term of the ground terminal speed and is unknown;

[0093] df u represents the update term of the ground terminal clock drift rate and is unknown.

[0094] ​​Calculated

[0095]

[0096] Update the speed and clock drift rate of the ground terminal:

[0097]

[0098] Obtain the speed and clock drift rate of the ground terminal at this moment.

[0099] The calculation formula for the ground terminal position is

[0100] where F 2 = [δdf 1′ … δdf 1′ … δdf n′ T , df i is obtained through the observation of the ground terminal, is based on the position of the ground terminal being r 2 , speed being v 3 , and clock drift rate being when calculated through the observation equation ;

[0101]

[0102] x 2 、y 2 、z 2 respectively represent the three-dimensional coordinates of the ground terminal in the Earth-Centered Earth-Fixed coordinate system in the previous second (the value is taken as x 1 、y 1 、z 1 ) at the beginning of step 4, r 2 represents the three-dimensional position vector of the ground terminal in the Earth-Centered Earth-Fixed coordinate system in the previous second, respectively represent the three-dimensional speeds of the updated ground terminal in the Earth-Centered Earth-Fixed coordinate system in this second, v 3 represents the three-dimensional speed vector of the updated ground terminal in the Earth-Centered Earth-Fixed coordinate system in this second.

[0103] dr = [dx dy dz] T represents the update term of the ground terminal speed and is unknown;

[0104] df u represents the update term of the ground terminal clock drift rate and is unknown.

[0105] [Calculated

[0106] ​

[0107] Update the position and clock drift rate

[0108]

[0109] Judge the magnitude of the dr modulus value. If ‖dr‖ is less than the threshold value (usually set to 10 -6 , then the obtained r 3 and v 3 are the position and velocity of the ground terminal at this second; if ‖dr‖ is greater than the threshold value, then assign the values of r 3 and v 3 to r 2 and v 2 , and repeatedly use formulas (4)(5) and (6)(7) to calculate new r 3 and v 3 until the convergence condition (‖dr‖ is less than the threshold value) is met.

[0110] After entering step 4, the calculation process of step 4 is adopted every second. After the iteration ends, the final output results r 3 and v 3 are the position and velocity of the ground terminal at this moment.

[0111] In the embodiment of the present invention, a GNSS navigation signal simulation system is used to design a low-earth orbit satellite constellation and ground terminals in different motion states to verify the performance of the method proposed in the embodiment of the present invention.

[0112] The trajectory parameters of the ground terminal are shown in Table 1:

[0113] Table 1 Trajectory parameters of the ground terminal

[0114]

[0115] The positioning error does not exceed 2m, and the velocity measurement error does not exceed 1cm / s.

[0116] The positioning and velocity measurement accuracies are shown in Table 2:

[0117] Table 2 Positioning and velocity measurement accuracies

[0118]

[0119] In the embodiment of the present invention, the meaning of accuracy is: with the true value as the center and the accuracy as the radius, 95% of the positioning results at all times fall within the circle. The positioning accuracy is at the meter level, and the velocity measurement accuracy is lower than 1cm / s.

[0120] Embodiment 2

[0121] Embodiment 2 of the present invention provides a system corresponding to Embodiment 1 above, including a memory, a processor, and a computer program stored on the memory; the processor executes the computer program on the memory to implement the steps of the method in Embodiment 1 above.

[0122] In some implementations, the memory may be a high-speed random access memory (RAM: Random Access Memory), and may also include non-volatile memory, such as at least one disk memory.

[0123] In other implementations, the processor may be a general-purpose processor of various types such as a central processing unit (CPU) or a digital signal processor (DSP), which is not limited herein.

[0124] Embodiment 3

[0125] 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, the steps of the method in Embodiment 1 above are implemented.

[0126] A computer-readable storage medium may be a tangible device that holds and stores instructions used by an instruction execution device. A computer-readable storage medium may 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 of the above.

[0127] Those skilled in the art should understand that the embodiments of the present application may be provided as a method, a system, or a computer program product. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program code. The solutions in the embodiments of the present application may be implemented in various computer languages. For example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript.

[0128] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of flows and / or blocks in the flowchart and / or block diagram can also be implemented. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a means for implementing the functions specified in one or more flows Figure 1 or more flows and / or blocks Figure 1 or a means for implementing the functions specified in one or more blocks.

[0129] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more flows Figure 1 or more flows and / or blocks Figure 1 or steps for implementing the functions specified in one or more blocks.

[0130] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications once they know the basic creative concepts. Therefore, the appended claims are intended to be construed to include the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0131] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application is also intended to include these changes and modifications.

Claims

1. A low-orbit satellite Doppler positioning and speed measurement method, characterized in that: The following steps are involved: Obtain the Doppler shift and satellite ephemeris information of visible low-orbit satellites within the field of view at the same time; Within a time period T, the least squares method is used to solve the speed and position of the ground terminal step by step to achieve convergence from an initial value to an approximate value; wherein the initial position and initial speed of the ground terminal are both set to zero; after time T, the least squares method is used to synchronously solve the speed and position of the ground terminal to obtain the precise values ​​of the speed and position of the ground terminal.

2. The low-orbit satellite Doppler positioning and velocity measurement method according to claim 1, characterized in that: The specific implementation process of using the least squares method to solve the velocity and position of the ground terminal step by step and achieve convergence from the initial value to the approximate value includes: The speed calculation formula of the ground terminal is: df i is the true value of the Doppler frequency shift observed by the ground terminal, It is based on the position r = r0, speed v = v0, and clock drift rate of the ground terminal at the last moment. When , through the observation equation The calculated Doppler shift estimate, df u An update term representing the ground terminal clock drift rate; f0 is the nominal carrier frequency of the satellite signal, c is the speed of light in vacuum, r0=[x0 y0 z0] T = 0, x0, y0, z0 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system at the last moment, is the three-dimensional position vector of the i-th satellite, Update the ground terminal's speed and clock drift rate: Get the speed v1 and clock drift rate of the ground terminal at the current moment The calculation formula for the ground terminal position is: It is based on the position r = r0, speed v = v0, and clock drift rate of the ground terminal at the last moment. Through the observation equation The calculated Doppler shift estimate; represents the update term of the ground terminal velocity, They respectively represent the updated three-dimensional velocity of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment, and v1 represents the updated three-dimensional velocity vector of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment; df u represents the update term of the ground terminal clock drift rate, is the three-dimensional velocity vector of the i-th satellite, is the three-dimensional position vector of the i-th satellite, Update ground terminal position and clock drift rate Get the current ground terminal position r1 and the new clock drift rate is the ground terminal clock drift rate at the previous moment.

3. The low-orbit satellite Doppler positioning and velocity measurement method according to claim 2, 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 repeated 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.

4. The low-orbit satellite Doppler positioning and velocity measurement method according to claim 1, characterized in that: After time T, the speed and position of the ground terminal are solved synchronously by using the least square method. The specific implementation process of obtaining the precise values ​​of the speed and position of the ground terminal includes: The speed and clock drift rate of the ground terminal are updated using the following equation: The position and clock drift rate of the ground terminal are updated using the following equation: in, x2, y2, and z2 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system at the last moment. df i Observed through ground terminals, It is based on the position of the ground terminal r = r2, the speed v = v2, and the clock drift rate Through the observation equation The calculated true value of Doppler frequency shift, r2, v2, are the position, velocity and clock drift rate of the ground terminal obtained by step-by-step solution using the least squares method within time T, f0 is the nominal carrier frequency of the satellite signal, c is the speed of light in vacuum, r0 = [x0y0z0] T = 0, x0, y0, z0 represent the three-dimensional coordinates of the ground terminal in the Earth-centered Earth-fixed coordinate system at the last moment, is the three-dimensional position vector of the i-th satellite, They represent the updated three-dimensional velocity of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment, v3 represents the updated three-dimensional velocity vector of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment, r3 represents the updated three-dimensional position vector of the ground terminal in the Earth-centered Earth-fixed coordinate system at the current moment, Indicates the updated clock drift rate at the current time, dr = [dx dy dz] T represents the update term of ground terminal velocity, df u An update term representing the ground terminal clock drift rate.

5. The low-orbit satellite Doppler positioning and velocity measurement method according to claim 4, 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 repeated and Update the ground terminal position and clock drift rate until ‖dr‖ is less than the threshold.

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

7. A low-orbit satellite Doppler positioning and speed 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 6.

8. A computer-readable storage medium having a computer program / instruction stored thereon; characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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