CN109901206B - Single-star positioning and time service method based on low-orbit satellite radio range signal - Google Patents
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Abstract
The invention belongs to the technical field of satellite communication and satellite navigation, and discloses a single-star positioning and time service method based on a low-orbit satellite radio range signal. The invention can reduce the cost and the power consumption of the receiver, is applied to the field of low-cost position service sensors such as the Internet of things, search and rescue and the like, and can accurately solve the three-dimensional coordinates of a user and the clock deviation of the receiver only by simultaneously receiving ranging signals from a low-orbit satellite at a plurality of moments.
Description
Technical Field
The invention belongs to the technical field of satellite communication and satellite navigation, and particularly relates to a single-star positioning and timing method based on low-orbit satellite radio range signals.
Background
Currently, the closest prior art:
the low-orbit satellite navigation enhancement technology can obviously improve the convergence time of the precise positioning of a global satellite positioning system (GNSS), so that the low-orbit satellite of Lopa nationality I developed by the university of Wuhan has the capability of broadcasting double-frequency ranging signals, and the possibility of low-orbit satellite navigation is successfully demonstrated. Low-orbit satellite communication constellations such as a wild goose constellation of a spaceflight science and technology group and a rainbow cloud constellation of a spaceflight industry group all list low-orbit satellite navigation enhancement as one of main businesses of the constellations. Low-orbit communication satellite constellations can be divided into two categories according to the type of service: broadband communication service and narrowband internet of things service. The service of the internet of things also has a positioning requirement. On the other hand, the integration of communication and navigation service is a development trend of future navigation, and the integration of the communication and navigation service on the signal level can save spectrum resources, realize one-star multi-use, thereby reducing satellite operation cost.
The key problem of channel integration is to make the communication signal have a ranging function so as to perform positioning, but the key problem of using a low-orbit communication constellation to perform navigation is to solve, namely the communication constellation generally can only ensure that at least 1 communication satellite signal is received at the same place, and GNSS positioning needs at least 4 visible satellites to perform positioning.
Thus, existing GNSS positioning algorithms are not suitable for low-orbit communication satellite positioning. There are also some constellations historically using low-orbit satellites, such as the precursor Transit system of GPS satellites, but these constellations are all positioned based on doppler observations, rather than using range measurements. The accuracy of the doppler measurement is relatively low, so that the positioning performance of the low-orbit satellite-based doppler positioning system is poor and gradually replaced. If the signals of the low-orbit communication satellite have the positioning function, the system can meet the application of the Internet of things, personnel search and rescue, logistics tracking and the like, reduces the positioning cost and has good development and application prospects.
However, no related study has been seen on how to achieve accurate user three-dimensional coordinate calculation using ranging signals of a single communication satellite.
In summary, the problems of the prior art are:
the basic principle of satellite positioning at present is to synchronously observe ranging signals of 4 or more than 4 visible satellites to determine three-dimensional coordinates and clock deviation of a user. This method is not suitable for positioning low-orbit satellites and other geospatial aerostats. Because the low orbit satellite orbit is lower, the signal coverage is small, hundreds to thousands of satellites need to be transmitted to realize the global signal coverage, and the cost is high. The low-orbit communication constellation can only ensure the single coverage of ground communication signals and cannot meet the positioning condition of the traditional satellite positioning algorithm. It is difficult to perform navigation positioning using signals of low-orbit communication satellites.
The existing positioning technology is to position by using a Gaussian Newton method iteration method, and the Gaussian Newton method has local convergence and needs to provide approximate coordinates. For middle and high orbit satellites, the distance between the satellites and the ground is 2 ten thousand kilometers, so that under the condition that the position of a ground receiver is unknown, the convergence requirement can be met by taking the earth center through approximate coordinates. And the low orbit satellite is only hundreds of kilometers away from the ground, and the earth center is selected as an approximate coordinate, so that the positioning is not converged.
The existing positioning technology requires that the space geometrical distribution of the visible satellites is dispersed as much as possible. For a single satellite, the trajectory of the point under the satellite is approximately a straight line during the passing period, and the geometric configuration is poor, so that the equation is sick or singular, and the existing positioning algorithm cannot directly perform positioning calculation.
The existing low-orbit satellite positioning methods are all based on Doppler observed values, the Doppler observed values are limited by measurement precision, the noise is usually larger, and the requirement of high-precision single-star positioning cannot be met.
The existing satellite navigation ground receiver needs to track tens or even hundreds of satellite channels at the same time, and the positioning equipment has a complex structure and high power consumption and is not suitable for low-cost miniaturized terminal equipment of the Internet of things.
The difficulty of solving the technical problems is as follows:
to solve the above problems, a special algorithm needs to be designed to solve the problem of low-orbit satellite single-star positioning to break through the difficulties. The direct solution of single star positioning has the problems of non-convergence of iteration and pathological condition of equation, so that the positioning result is unstable, unreliable and even impossible to position. In the system implementation level, a special ranging signal transmitter needs to be developed and mounted on a low-orbit satellite, and a special receiver needs to be designed on the ground to track the ranging signal.
Meaning of solving the technical problems:
the realization of user positioning by using a single low-orbit satellite ranging signal is a key problem for realizing integrated design of low-orbit satellite communication and navigation. Communication satellites require only a single coverage of a signal, whereas navigation systems require at least 4 coverage of a signal. The positioning method can realize the determination and time service of the three-dimensional coordinates of the user through distance measurement by using the communication signals with single coverage. At present, low-orbit satellite communication constellations at home and abroad are rapidly developed, and a wild goose constellation of a spaceflight technological group and a rainbow cloud constellation of a spaceflight technological group are both composed of hundreds of low-orbit communication satellites. If the communication payload is capable of providing ranging information, the positioning and timing of the ground user may be accomplished using the low-orbit satellite communication signals. The method can be integrated with satellite phones and the like, realizes communication and positioning, and has great development and application potential.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a single-star positioning and time service method based on a low-orbit satellite radio range signal. The invention uses a single low-orbit satellite ranging signal to realize the determination of the three-dimensional coordinates of the user, and can be used for determining the position of the user based on communication satellite signals.
The invention is realized in such a way that a single star positioning and time service method based on a low-orbit satellite radio distance signal is realized, the single star positioning and time service method based on the low-orbit satellite radio distance signal utilizes a non-iterative approximate coordinate solving method to calculate the approximate three-dimensional coordinate and the receiver clock difference of a ground receiver, and then utilizes the result of calculating the approximate three-dimensional coordinate and the receiver clock difference of the ground receiver as an approximate value to carry out iterative calculation to solve the three-dimensional coordinate and the receiver clock difference of a user;
further, the single-star positioning and time service method based on the low-orbit satellite radio range signal further comprises the following steps: the calculation is performed using various forms of ranging signals, including ranging codes, pilot codes, carrier phases, lasers, periodically recurring data frame headers and signals of opportunity, for implementing a range measurement mode between the signal transmitter and the receiver.
Further, the single-star positioning and time service method based on the low-orbit satellite radio range signal specifically comprises the following steps:
the method comprises the steps that firstly, a receiver observes pseudo-range or carrier phase observation values of n epochs, and low-orbit satellite coordinates corresponding to the n epochs and deviation between a clock of a low-orbit satellite signal transmitter and a reference time system are obtained through analysis of telegrams or other modes; pseudo-range and carrier phase observations, as well as coordinates of the satellites, clock differences are used as inputs to the algorithm;
step two, the form of the square of the observed values of the pseudo-range and the carrier phase is expressed as:
(r i -dt) 2 ＝||s i -x|| 2 ；
wherein r is i Representing pseudorange and carrier phase observations; receiver clock differences are represented for pseudorange observations dt and equivalent receiver clock differences are represented for carrier phase observations dt; assuming no cycle slip occurs during positioning, the carrier phase ambiguity parameter is constant during positioning; in the approximate coordinate solution process, the receiver clock difference is approximately treated as a constant, and the equivalent receiver clock difference parameters include clock difference and carrier phase parameters that do not change during positioning; satellite sitting mark s i ＝[x i ，y i ，z i ]The user receiver coordinates are noted as x= [ x ] r ，y r ，z r ]
Formula (r) i -dt) 2 ＝||s i -x|| 2 Expressed in the following form:
defining an extended four-dimensional vector S i ＝[s i ，P i ]，X＝[x，dt]The method comprises the steps of carrying out a first treatment on the surface of the The lorentz product defining two four-dimensional vectors is:
<X·T>＝x 1 y 1 +x 2 y 2 +x 3 y 3 -x 4 y 4
then
Expressed in the form of vectors:
the above abbreviations are:
2AX＝e n <X·X>+b
in e n Is an n x 1 vector and all its elements are 1;
equation 2ax=e n <X·X>Both sides of the equation of +b contain unknown parameter vectors X and cannot be directly solved; equation 2ax=e n <X·X>The first term to the right of +b is eliminated by the difference between observations, as for all observation equations; defining a differential operation matrix D= [ -e n-1 ，I n-1 ]Then equation 2ax=e n <X·X>+b is expressed as:
2DAX＝Db：
step three, equation 2 dax=db is solved by using a least square parameter estimation method, and the parameters to be solved are:
step four, adopting a regularization method to calculate a position vector X= [ X ] r ，y r ，z r ，d t ]Performing further refinement;
fifthly, obtaining a stable numerical solution through biased estimation by adopting a regularization method;
step six, opposite type
The derived parameter estimates are:
wherein I is a 4×4 identity matrix, l=r-r 0 ；
Step seven, after solving by using a regularization method to obtain stable parameter increment, updating parameters by using the following formula:
X i ＝X i-1 +dX
wherein subscripts i-1 and i represent the number of iterations;
step eight, after the new completion, judging whether the solved parameter increment dX is smaller than the limit value of iteration termination, if so, terminating the iteration and turning to step nine, otherwise, returning to step four to continue the iteration calculation; in iterative calculation, the parameter updated by the ith time is used as an initial value, and the approximation r is restarted 0 And solving the parameter increment dX again;
and step nine, outputting the obtained parameter X vector as a final coordinate and receiver clock error after iteration convergence, and taking the final coordinate and receiver clock error as a final result of positioning and timing.
Further, in the fourth step, the regularization method includes:
processing receiver clock using a clock linear model, the parameter vector of which is expressed as
In->
For the receiver clock rate of change, the corresponding equation design matrix is:
t is in 0 ，t 1 ，…t n Is the observation time.
Further, in the fifth step, the estimation criterion of the regularization method is:
alpha in the formula is regularization parameter; the regularization parameter solving method is calculated through a generalized cross checking method, the minimum value of a generalized cross checking function is determined through the calculating method, and the generalized cross checking function is expressed as:
where H (α) is a function of the regularization parameter α, expressed as:
H(α)＝A(A T A+αI) -1 A T
the minimum value of the generalized cross checking function is obtained by a dichotomy search.
Another object of the present invention is to provide a low-orbit satellite radio ranging signal-based single-star positioning and timing system for implementing the low-orbit satellite radio ranging signal-based single-star positioning and timing method, the low-orbit satellite radio ranging signal-based single-star positioning and timing system comprising:
low-orbit satellite device broadcasting signal to ground; broadcasting a modulated ranging code, a pilot frequency code and repeatedly-appearing data frame head characteristic information for ranging or time service;
the ground receiver may track and demodulate ranging signals from low-orbit satellites and perform single-star positioning calculations.
Further, the transmitter carrying platform of the radio ranging signal comprises a low-orbit satellite, and can also be an unmanned plane or other aerostat platforms;
the low orbit satellite signal transmitter should contain high quality crystal oscillator types including, but not limited to, high stability crystal oscillator, chip scale atomic clocks or atomic clocks.
Further, the ground receiver is equipped with a normal crystal oscillator XO, a temperature compensated crystal oscillator TCXO or other crystal oscillator with high stability.
Another object of the present invention is to provide a global positioning terminal for implementing the single-star positioning and timing method based on low-orbit satellite radio range signals.
Another object of the present invention is to provide a global positioning network platform for implementing the single-star positioning and timing method based on low-orbit satellite radio range signals.
In summary, the invention has the advantages and positive effects that:
the invention can realize positioning by continuously tracking the signal of one satellite, and the radio frequency front end of the receiver only needs to support a single channel, so that the invention has simple structure and low power consumption and is suitable for miniaturized terminal equipment of the Internet of things with low cost.
The method is suitable for realizing the receiver positioning based on the ranging signals of the mobile signal source in principle, is not limited by the modulation mode of the ranging signals, is not limited by the motion state and track of the mobile signal source, and is only applied to the low orbit satellite.
Compared with the Doppler positioning technology, the method for realizing positioning based on the ranging signals has higher positioning precision. The ranging signal can use the carrier phase with centimeter-level or even millimeter-level precision output by the phase-locked loop, so that the meter-level precision positioning can be realized, the Doppler observation value output by the frequency-locked loop has larger observation noise, and the positioning precision of hundred meters or even kilometers can be realized generally.
The method for realizing positioning based on the ranging signals can solve the problem of positioning non-convergence caused by the initial value problem and the problem of positioning instability caused by the equation disease state, and provides accurate, continuous and reliable positioning results.
Compared with a single-star positioning method based on a GNSS system, the method for realizing positioning based on the ranging signals has the advantages that the first positioning time is increased from a plurality of hours to a minute level, the stability requirement on a clock is reduced to a common temperature compensation crystal oscillator, the cost is lower, and the positioning effect is better.
The method for realizing positioning based on the ranging signals can be simultaneously used for single-satellite time service, and the time service precision is in the order of ten nanoseconds and is superior to that based on single GNSS satellite time service.
Drawings
Fig. 1 is a schematic diagram of a low-orbit satellite single-star positioning method based on ranging signals according to an embodiment of the present invention. The receiver in this figure can track the same low-orbit satellite t 1 ，t 2 ，t 3 ，t 4 And waiting for ranging signals at more than four times, and then calculating an accurate receiver position using the methods described herein.
Fig. 2 is a comparison of geometric relationships between a middle-high orbit satellite and a low orbit satellite in positioning according to an embodiment of the present invention. Under the condition of unknown approximate coordinates, if the earth center is used for approximation, the ratio of the approximate coordinate error of the medium orbit satellite to the observed value is about 6378:20200≡1:4, and for low-orbit satellites, the ratio of the approximate coordinate error to the observed value is about 6378:650≡10:1, that is, the approximate coordinate error is far greater than the magnitude of the observed value itself, the iteration of the gauss newton method cannot converge.
Fig. 3 is a flowchart of a single-star positioning method based on a low-orbit satellite ranging signal according to an embodiment of the present invention.
Fig. 4 is a simulation calculation result of the positioning method according to the embodiment of the present invention.
The simulation calculation adopts Lopa nationality first low-orbit satellite orbit and Wuhan as ground stations, and the figure shows the influence of different ranging error levels on positioning accuracy.
Fig. 5 is a simulation calculation result of the positioning method provided by the implementation of the present invention. The simulation calculation uses the Lopa nationality first satellite transit arc section orbit, adopts carrier phase observation values to carry out user positioning and time service, and has positioning and time service precision in China and peripheral areas.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
In the prior art, the determination of the three-dimensional coordinates of the user is not realized by using a single low-orbit satellite ranging signal, so that the determination of the user position is inaccurate.
In order to solve the above problems, the present invention will be described in detail with reference to specific embodiments.
In the invention, in the positioning function realized by adopting the low-orbit communication satellite signals, how to calculate the satellite position of the user by adopting the signals of the single LEO satellite. The basic principle of satellite navigation satellite positioning at present is to solve the three-dimensional coordinates of a user and the clock error of a receiver of the user by using at least four visible satellites. Under the general condition of a low-orbit communication satellite, only single coverage of surface signals can be ensured, and the basic requirement of navigation positioning cannot be met. In order to solve the problem, the invention proposes a method for determining the three-dimensional coordinates of a user by using a single LEO satellite signal, and the principle of the method is shown in figure 1. The core of single-star positioning is to use a single satellite as a plurality of satellites by utilizing the joint solution of ranging signals of a plurality of epochs, and the premise is that the clock error of a receiver can be modeled during observation.
The observation equation for positioning using low-orbit satellite ranging code and carrier phase can be expressed approximately as:
P i ＝ρ+c(δt S -δt R )+∈ Pi
L i ＝ρ+c(δt S -δt R )+λ i N i +∈ φi (1)
wherein ρ is the geometric distance δt S And δt R Respectively representing satellite clock difference and receiver clock difference, lambda l And N i Indicating wavelength and carrier phase ambiguity for the i-th frequency. The satellite coordinates and satellite clock differences can be obtained through ephemeris, and the receiver clock differences and the user coordinates can be used as parameter estimation. For simplicity of expression, error sources such as satellite orbit errors, tropospheric delays, ionospheric delay errors and related hardware delay deviations can be utilized during data processingThe partial correction or the empirical model. The determination of the position of the user by means of the ephemeris requires solving two key problems, namely the problem of non-convergence of the positioning iteration and the problem of the pathological condition of the equation due to too large nonlinear errors.
Solving the user coordinates from the geometric distance can be expressed as:
the representation of the geometrical distance in the observed value and the parameter x to be solved r ,y r ,z r The nonlinear relation is developed at an approximate value by using a Taylor series, and the conventional method is as shown in the formula:
the remainder delta in the formula represents linearization error, the relation between the remainder delta and the approximate coordinate is solved by using a Gaussian Newton method under the condition that the user coordinate is unknown, the initial coordinate can be set to be zero, and then the initial coordinate can be converged to the meter-level positioning order through 3-4 iterations. The distance from the middle-high orbit satellite signal to the ground is 20000 km or more, and the earth radius is about 6400 km. Therefore, even if the initial value is set to zero, the initial position error is only about 1/3 of the measured distance. For low orbit satellites, the orbit altitude is 500km-1500km, and if the initial value is still set to 0, the initial error and the measured distance error will reach 3-10 times the distance. The Gaussian Newton position location has local convergence, and the condition of excessive initial value error leads to the fact that the parameter can not be converged to be near the true value.
On the other hand, the ideal condition for determining the three-dimensional coordinates of the user is that satellites are uniformly distributed in the air, and certain variation ranges exist in the north, east and high directions, so that the corresponding coordinate components are good in observability. The orbit of the low orbit satellite generally moves along the same direction within a certain time, so that one direction has better precision in the plane direction, the other direction has relatively poorer precision, even the condition of singular or pathological equation appears, and certain challenges exist on how to improve the positioning precision of the direction under the condition to obtain a stable and reliable positioning result.
Fig. 2 is a comparison of geometric relationships between a middle-high orbit satellite and a low orbit satellite in positioning according to an embodiment of the present invention. Under the condition of unknown approximate coordinates, if the earth center is used for approximation, the ratio of the approximate coordinate error of the medium orbit satellite to the observed value is about 6378:20200≡1:4, and for low-orbit satellites, the ratio of the approximate coordinate error to the observed value is about 6378:650≡10:1, that is, the approximate coordinate error is far greater than the magnitude of the observed value itself, the iteration of the gauss newton method cannot converge.
The invention provides a single-star positioning and timing system based on low-orbit satellite radio distance signals for implementing the single-star positioning and timing method based on low-orbit satellite radio distance signals, which comprises the following steps:
low-orbit satellite device broadcasting signal to ground; broadcasting a modulated ranging code, a pilot frequency code and repeatedly-appearing data frame head characteristic information for ranging or time service;
the ground receiver may track and demodulate ranging signals from low-orbit satellites and perform single-star positioning calculations.
The transmitter-mounted platform of the radio ranging signal comprises a low-orbit satellite, and can also be a unmanned plane or other aerostat platform;
the low orbit satellite signal transmitter should contain high quality crystal oscillator types including, but not limited to, high stability crystal oscillator, chip scale atomic clocks or atomic clocks.
The ground receiver is equipped with a normal crystal oscillator XO, a temperature compensation crystal oscillator TCXO or other crystal oscillators with high stability.
In the embodiment of the invention, the invention provides a two-step method for positioning and timing a single low-orbit satellite ranging signal. The first step is to obtain reliable approximate coordinates by using a non-iterative approximation algorithm, and then refine the approximate coordinates by using a regularization method to obtain a high-precision positioning time service result. The specific implementation steps are shown in fig. 3:
s101: the receiver observes the pseudorange or carrier phase observations for n epochs and obtains the low-orbit satellite coordinates corresponding to the n epochs and the offset between the low-orbit satellite signal transmitter clock and the reference time system by parsing the text or otherwise. Pseudo-range and carrier phase observations, as well as the coordinates of the satellites, the clock differences are used as inputs to the algorithm.
S102: the form of the square of the observations for pseudoranges and carrier phases can be expressed as:
(r i -dt) 2 ＝||s i -x|| 2
(4)
wherein r is i Representing pseudorange and carrier phase observations. Receiver clock differences are represented for pseudorange observations dt and equivalent receiver clock differences are represented for carrier phase observations dt. The carrier phase ambiguity parameter is constant during positioning, assuming no cycle slip occurs during positioning. In the approximate coordinate resolution process, the receiver clock difference can be approximately treated as a constant, so the equivalent receiver clock difference parameters include clock differences that do not change during positioning
And carrier phase parameters. Satellite sitting mark s i ＝[x i ，y i ，z i ]The user receiver coordinates are noted as x= [ x ] r ，y r ，z r ]
Equation (4) can be expressed as follows:
to simplify the expression, the present invention defines an extended four-dimensional vector S i ＝[s i ，P i ]，X＝[x，dt]The lorentz product defining two four-dimensional vectors is:
<X·Y>＝x 1 y 1 +x 2 y 2 +x 3 y 3 -x 4 y 4
(6)
then, equation (5) can be expressed as the following vector form:
the above can be abbreviated as:
2AX＝e n <X·X>+b (8) where e n Is an n x 1 vector and all its elements are 1.
The equation of equation (8) contains an unknown parameter vector X on both sides, so the equation cannot be solved directly. Fortunately, the first term to the right of equation (8) is the same for all observation equations, so this term can be eliminated by the difference between observations. Defining a differential operation matrix D= [ -e n-1 ，I n-1 ]Then equation (8) can be expressed as:
2DAX＝Db (9)。
s103: equation (9) can be solved by using a least square parameter estimation method, and the parameters to be solved are:
the method is a solving method of approximate coordinates, and cannot obtain an optimal solution of user coordinates. However, the method allows one-step solving of the user coordinates without requiring iteration, so that the problem of iteration divergence can be avoided. In general, the method can obtain the user approximate coordinates with the accuracy of hundreds of meters to kilometers, and the approximate solution can completely meet the accuracy requirement of the initial value which is the iteration of the Gaussian Newton method.
S104: then regularization is used to determine the position vector x= [ X ] for the first step r ，y r ，z r ，d t ]Further refinement is performed. The regularization method comprises the following steps:
linearizing the ranging observation value according to a Taylor formula (3) to obtain a linear system:
v＝A×dX-(r-r 0 ) (11) wherein V represents the residual error of parameter estimation, A is the design matrix of parameters, dX represents the increment of the parameter X, r represents the column vector r consisting of n epochs of pseudo-range or carrier-phase observations 0 . Representing the geometric distance and approximations of the various error sources. Wherein the initial value ρ of the geometric distance 0 The method is obtained by calculating the approximate coordinates and satellite positions calculated by the first non-iterative method, and other error sources can be given by calculation of broadcast ephemeris, empirical models and the like. The design matrix a may be expressed specifically as:
rho in i Representing the geometric distance of the user to the satellite coordinates at the i-th epoch instant.
For the earth surface receiving station, the single transit time of the low orbit satellite is not more than 10 minutes, and the visible arc section of the satellite is long enough to realize the three-dimensional positioning of the user, and preliminary experiments show that at least about 300 seconds of ranging signals are required to be continuously observed to ensure that the three-dimensional coordinates can be correctly solved. The corresponding parameter vector in equation (12) is x= [ X ] r ，y r ，z r ，dt]Only one clock skew parameter is considered. The default assumption is that the receiver clock bias can be considered a constant during the period of time required for positioning. However, since the receiver generally uses a low-cost temperature compensation crystal oscillator, the frequency stability and the frequency accuracy of the crystal oscillator are not high, and thus, a large clock error is introduced when a constant model is used for estimating the clock error in many times. For this case, the present invention uses a clock-difference linear model to handle the receiver clock-difference problem, the parameter vector of the model being expressed as
In->
For the receiver clock rate of change, the corresponding equation design matrix is:
t is in 0 ，t 1 ，…t n Is the observation time. The regularization solution corresponding to the model is the same as the parameterization solution described in equation (12), but the method considers the change rate of the receiver clock error and can better absorb the receiver clock error.
S105: for a single transit of a satellite, the track of a point under the satellite is approximately a straight line, so that the three-dimensional coordinate equation of a user estimated by using a single track has serious singularities and even approaches to a pathological state. The result of the equation morbidity is that the parameter estimation value is unstable, and small deviations in the observed value can lead to larger unreasonable deviations in the parameter estimation value. In order to further solve the numerical problem caused by equation pathology, the invention adopts a regularization method to obtain a stable numerical solution through biased estimation. The estimation criteria for the regularization solution are:
where α is a regularization parameter. The regularization parameter solving method can be calculated by a generalized cross checking method, wherein the calculating method is used for determining the minimum value of a generalized cross checking function, and the generalized cross checking function can be expressed as:
where H (α) is a function of the regularization parameter α, expressed as:
H(α)＝A(A T A+αI) -1 A T
(16)
the minimum value of the generalized cross-checking function can be found by a dichotomy search.
S106: the estimate of the derivative available parameter for equation (14) is:
wherein I is a 4×4 identity matrix, l=r-r 0 Compared with Gauss Newton method, the method has one more term alpha I on the right side of the equation, which leads the pathogenicity of the equation of the method to be always obtained, and the inversion result to be stable.
S107: after the stable parameter increment is obtained by solving by using a regularization method, the parameters can be updated by using the following formula:
X i ＝X i-1 +dX (18)
where subscripts i-1 and i represent the number of iterations.
S108: after the updating is completed, it is determined whether the solved parameter increment dX is smaller than the limit value of iteration termination, if so, the iteration can be terminated to step 109, otherwise, the step 104 is required to be returned to continue the iterative calculation. In iterative calculation, the parameter updated by the ith time is used as an initial value, and the approximation r is restarted 0 And solving again for the parameter delta dX.
S109: after iteration convergence, the parameter X vector obtained in the last step is used as a final coordinate and receiver clock error to be output as a final result of positioning and timing.
The invention is further described in connection with simulation experiments.
Through preliminary simulation, the relationship between the precision of the low-orbit satellite single-star positioning by using the pseudo-range and the carrier phase and the precision of the observed value is shown in fig. 4. The figure simulates the positioning accuracy when the satellite navigation enhancement signal of Lopa nationality first is utilized and the Wuhan station is taken as a ground receiver. Typically, the measurement accuracy of the pseudo-range is in the order of tens of meters with a corresponding positioning accuracy of 0.3-3 meters. The measuring precision of the carrier phase is between 0.003 and 0.03 meters, and the corresponding positioning precision is in the meter level. The positioning accuracy of conventional doppler-based low-orbit satellite positioning methods is typically on the order of kilometers. Simulation results show that no matter the pseudo range or the carrier phase observation value is used, the positioning accuracy obtained by the method of the invention is far higher than that obtained by the traditional method adopting Doppler positioning no matter the pseudo range or the carrier phase is used as the ranging observation value.
In order to verify the correctness of the method, satellite orbit data of the first-order satellite of the Lopa of the university of Wuhan is adopted, and carrier phase observation value information is adopted to carry out simulation calculation on the positioning and timing precision of the China and the surrounding area. The calculation result is shown in fig. 5. The figure shows that the positioning accuracy is in the order of meters in most areas, and the time service accuracy is superior to 20 nanoseconds in most areas. The relative geometrical position of the positioning accuracy terrestrial receiver and the satellite is affected.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (9)
1. The single-star positioning and time service method based on the low-orbit satellite radio range signal is characterized in that the single-star positioning and time service method based on the low-orbit satellite radio range signal utilizes a non-iterative approximate coordinate solving method to calculate the approximate three-dimensional coordinate of a ground receiver and the clock difference of the receiver, and then utilizes the result of the approximate three-dimensional coordinate of the ground receiver and the clock difference of the receiver as an approximate value to carry out iterative calculation to solve the three-dimensional coordinate of a user and the clock difference of the receiver;
the single-star positioning and time service method based on the low-orbit satellite radio range signal specifically comprises the following steps:
firstly, a receiver observes pseudo-range or carrier phase observation values of n epochs, and obtains low-orbit satellite coordinates corresponding to the n epochs, deviation between a clock of a low-orbit satellite signal transmitter and a reference time system, the pseudo-range and carrier phase observation values and coordinates of satellites by analyzing a telegram;
expressing the square of the observed values of the pseudo range and the carrier phase:
(r i -dt) 2 ＝‖s i -x‖ 2 ；
wherein r is i Representing pseudorange and carrier phase observations; the pseudorange observations dt represent the receiver clock differences, and the carrier phase observations dt represent the equivalent receiver clock differences;satellite sitting mark s i ＝[x i ,y i ,z i ]The user receiver coordinates are noted as x= [ x ] r ,y r ,z r ]The method comprises the steps of carrying out a first treatment on the surface of the Formula (r) i -dt) 2 ＝‖s i -x‖ 2 The expression is as follows:
defining a differential operation matrix D= [ -e n-1 ,I n-1 ]2 ax=e n <X·X>+b is expressed as:
2DAX＝Db；
step three, equation 2 dax=db is solved by using a least square parameter estimation method, and the parameters to be solved are:
step four, adopting a regularization method to calculate a position vector X= [ X ] r ,y r ,z r ,dt]Performing further refinement;
fifthly, obtaining a stable numerical solution through biased estimation by adopting a regularization method;
step six, opposite type
Deriving an estimate of the parameter:
wherein I is a 4×4 identity matrix, l=r-r 0 ；
Step seven, after solving by using a regularization method to obtain stable parameter increment, updating parameters by using the following formula:
X i ＝X i-1 +dX；
wherein subscripts i-1 and i represent the number of iterations;
step eight, after updating, judging whether the solved parameter increment dX is smaller than the limit value of iteration termination, if so, terminating the iteration to a step nine, otherwise, returning to the step four to continue the iteration calculation; in iterative calculation, the parameter updated by the ith time is used as an initial value, and the approximation r is restarted 0 And solving the parameter increment dX again;
and step nine, outputting the obtained parameter X vector as a final coordinate and receiver clock error after iteration convergence, and taking the final coordinate and receiver clock error as a final result of positioning and timing.
2. The single-star positioning and timing method based on low-orbit satellite radio range signal according to claim 1, wherein the single-star positioning and timing method based on low-orbit satellite radio range signal further comprises: and calculating various ranging signals, including ranging codes, pilot codes, carrier phases, lasers, periodically recurring data frame heads and opportunistic signals, so as to realize the distance measurement between the signal transmitter and the receiver.
3. The single-star positioning and timing method based on low-orbit satellite radio ranging signal according to claim 1, wherein in the fourth step, the regularization method comprises: processing receiver clock using a clock linear model, the parameter vector of which is expressed as
In->
For the receiver clock rate of change, the corresponding equation design matrix is: />
T is in 0 ,t 1 ,…t n Is the observation time.
4. The single-star positioning and timing method based on low-orbit satellite radio ranging signals according to claim 1, wherein in the fifth step, the estimation criterion of the regularization method is as follows:
alpha in the formula is regularization parameter; the regularization parameter solving method is calculated through a generalized cross checking method, the minimum value of a generalized cross checking function is determined through the calculating method, and the generalized cross checking function is expressed as:
where H (α) is a function of the regularization parameter α, expressed as:
H(α)＝A(A T A+αI) -1 A T ；
the minimum value of the generalized cross checking function is obtained by a dichotomy search.
5. A low-orbit satellite radio range signal based single-star positioning and timing system for implementing the low-orbit satellite radio range signal based single-star positioning and timing method according to claim 1, comprising:
a signal transmitter for broadcasting radio ranging signals to the ground, wherein the signal transmitter is carried on a low-orbit satellite platform or a space vehicle platform;
and the ground receiver is used for tracking and demodulating the ranging signals of the low-orbit satellites and performing single-star positioning calculation.
6. The single-star positioning and timing system based on low-orbit satellite radio ranging signals according to claim 5, wherein the transmitter-mounted platform of the radio ranging signals comprises a low-orbit satellite, or is an unmanned aerial vehicle or an aerostat platform;
the signal transmitter includes a crystal oscillator including, but not limited to, a high stability crystal oscillator, a chip-scale atomic clock or an atomic clock.
7. The single star positioning and timing system based on low-orbit satellite radio ranging signals according to claim 5, wherein the ground receiver is equipped with a normal crystal oscillator XO, a temperature compensated crystal oscillator TCXO or a high stability crystal oscillator.
8. A global positioning satellite terminal for implementing the single-star positioning and timing method based on low-orbit satellite radio ranging signals as claimed in claim 1.
9. A global positioning satellite network platform implementing the low-orbit satellite radio range signal based single-star positioning and timing method of claim 1.
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| CN110289903B (en) * | 2019-06-26 | 2020-04-14 | 清华大学 | Satellite network autonomous time synchronization method and system based on link measurement |
| CN110557191B (en) * | 2019-09-05 | 2021-05-11 | 东南大学 | Terminal positioning method and device in low-earth-orbit satellite mobile communication system |
| CN111398999A (en) * | 2020-03-25 | 2020-07-10 | 中国科学院微小卫星创新研究院 | User terminal and search and rescue system based on low-orbit communication constellation |
| CN111398994B (en) * | 2020-04-26 | 2020-10-30 | 清华大学 | Method and device for positioning and time service of medium-orbit communication satellite |
| CN113267797B (en) * | 2021-05-18 | 2023-02-24 | 中国联合网络通信集团有限公司 | Positioning method and electronic equipment |
| CN115268252B (en) * | 2022-08-05 | 2024-07-19 | 腾讯科技（深圳）有限公司 | Time management method, apparatus, computer, readable storage medium, and program product |
| CN117092588B (en) * | 2023-10-20 | 2024-01-09 | 中国科学院深海科学与工程研究所 | Method for estimating clock deviation of underwater sound positioning system |
| CN117970775B (en) * | 2024-04-01 | 2024-06-11 | 中国科学院国家授时中心 | Standard time timing method and system combining GNSS and LEO satellites |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103149571A (en) * | 2013-02-18 | 2013-06-12 | 桂林电子科技大学 | GNSS (Global Navigation Satellite System)-based signal aided time frequency difference comprehensive correction method |
| CN103197335A (en) * | 2013-03-22 | 2013-07-10 | 哈尔滨工程大学 | Method using improved regularization method to restrain difference global positioning system (DGPS) integer ambiguity ill-condition |
| CN106569241A (en) * | 2016-09-27 | 2017-04-19 | 北京航空航天大学 | Single frequency high precision positioning method based on GNSS |
| CN106842256A (en) * | 2016-12-12 | 2017-06-13 | 西安空间无线电技术研究所 | A kind of navigation locating method of the mono- star signals of utilization GNSS |
| CN107153209A (en) * | 2017-07-06 | 2017-09-12 | 武汉大学 | A kind of low rail aeronautical satellite real-time accurate orbit determination method of short arc segments |
| CN107490800A (en) * | 2017-08-07 | 2017-12-19 | 桂林电子科技大学 | A kind of satellite navigation method for rapidly positioning, device and satellite navigation receiver |
| CN108415050A (en) * | 2018-06-04 | 2018-08-17 | 北京未来导航科技有限公司 | A kind of PPP-RTK localization methods enhancing system based on low rail constellation navigation |
| CN108508468A (en) * | 2018-03-20 | 2018-09-07 | 安徽理工大学 | Medium-long baselines single epoch Ambiguity Solution Methods, system, equipment, storage medium |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7362265B2 (en) * | 2005-04-12 | 2008-04-22 | Magellan Systems Japan Inc. | Process for accurate location determination in GPS positioning system |
-
2019
- 2019-04-01 CN CN201910258127.6A patent/CN109901206B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103149571A (en) * | 2013-02-18 | 2013-06-12 | 桂林电子科技大学 | GNSS (Global Navigation Satellite System)-based signal aided time frequency difference comprehensive correction method |
| CN103197335A (en) * | 2013-03-22 | 2013-07-10 | 哈尔滨工程大学 | Method using improved regularization method to restrain difference global positioning system (DGPS) integer ambiguity ill-condition |
| CN106569241A (en) * | 2016-09-27 | 2017-04-19 | 北京航空航天大学 | Single frequency high precision positioning method based on GNSS |
| CN106842256A (en) * | 2016-12-12 | 2017-06-13 | 西安空间无线电技术研究所 | A kind of navigation locating method of the mono- star signals of utilization GNSS |
| CN107153209A (en) * | 2017-07-06 | 2017-09-12 | 武汉大学 | A kind of low rail aeronautical satellite real-time accurate orbit determination method of short arc segments |
| CN107490800A (en) * | 2017-08-07 | 2017-12-19 | 桂林电子科技大学 | A kind of satellite navigation method for rapidly positioning, device and satellite navigation receiver |
| CN108508468A (en) * | 2018-03-20 | 2018-09-07 | 安徽理工大学 | Medium-long baselines single epoch Ambiguity Solution Methods, system, equipment, storage medium |
| CN108415050A (en) * | 2018-06-04 | 2018-08-17 | 北京未来导航科技有限公司 | A kind of PPP-RTK localization methods enhancing system based on low rail constellation navigation |
Non-Patent Citations (3)
| Title |
|---|
| 一种全球定位系统接收机单点定位的新算法及数值试验;黄思训等;《物理学报》;20061212;第55卷(第12期);第6720-6726页 * |
| 单星导航HEO卫星初轨确定算法;李涛护等;《北京航空航天大学学报》;20120615;第38卷(第06期);第755-759页 * |
| 基于位置信息的低轨卫星上行时钟同步方法;姚广济等;《计算机应用》;20180610;第38卷(第6期);第1732-1736页 * |
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