CN109901206A - A kind of positioning of single star and time service method based on low orbit satellite radio distance-measuring signal - Google Patents
A kind of positioning of single star and time service method based on low orbit satellite radio distance-measuring signal Download PDFInfo
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Abstract
The invention belongs to satellite communications and technical field of satellite navigation, disclose it is a kind of based on low orbit satellite radio distance-measuring signal single star positioning and time service method, the first step, the approximate coordinate and clock deviation of receiver, second step, the then on the basis of first step are solved using a kind of non-iterative method, the user's approximate coordinate and clock deviation parameter solved by the method essence of iteration, equation ill-conditioning problem is solved by the method for regularization, is stablized, the clock jitter of reliable user's three-dimensional coordinate.The present invention can reduce receiver cost and power consumption, applied to Internet of Things, present invention only requires receivers to receive the distance measuring signal from a low orbit satellite multiple moment simultaneously for the location-based service sensor field of the low cost such as search and rescue, so that it may accurately solve the three-dimensional coordinate and receiver clock deviation of user.
Description
Technical field
The invention belongs to satellite communications and technical field of satellite navigation, more particularly to one kind to be based on the wireless electrical measurement of low orbit satellite
The positioning of single star and time service method away from signal.
Background technique
Currently, the immediate prior art:
Low orbit satellite navigation enhancing technology can significantly improve the convergence of GPS (GNSS) precision positioning
Time, thus widely paid close attention in recent years, the Luo Ka No.1 low orbit satellite that Wuhan University develops, which has, broadcasts double frequency survey
Ability away from signal, a possibility that successfully demonstrated low orbit satellite satellite navigation.The swan goose constellation of Aerospace Science and Technology Corporation, space flight
The multimedia LEO satellite communications constellations such as the rainbow cloud constellation of Ke Gong group all by low orbit satellite navigation enhancing be classified as constellation main business it
One.Low rail communication satellite constellation can be divided into two classes: wideband communications service and narrowband internet of things service according to type of service.Wherein object
Networking service also has the demand of positioning.Still further aspect, Communications And Navigation business integration are the development trends of the following navigation, will
Communications And Navigation business, which carries out fusion in signal level, can save frequency spectrum resource, and it is multi-purpose to realize a star, to reduce satellite fortune
Seek cost.
The critical issue of channel integral to be positioned, but is used so that signal of communication has distance measurement function
Low rail communication satellite constellation, which carries out navigation, has a crucial problem to need to solve, and is exactly that communication satellite constellation is typically only capable to guarantee same place
At least receive the signal of 1 telecommunication satellite and GNSS positioning needs at least 4 visible satellites that could position.
Thus, existing GNSS location algorithm is not suitable for low rail telecommunication satellite positioning.It is low there are also using in history
The constellation that rail satellite is positioned, such as predecessor's Transit system of GPS satellite, but these constellations are all based on Doppler
Observation is positioned, rather than positioned using distance measure.The precision of Doppler measurement is relatively low, thus base
It is bad in the Doppler positioning system positioning performance of low orbit satellite, gradually it is substituted.If the signal of low rail telecommunication satellite is simultaneously
Having the function of positioning, Internet of Things will be met, personnel search and rescue, the application of logistic track etc., and reduce positioning cost,
With good development and application prospect.
However how using the distance measuring signal of single telecommunication satellite realize accurate user's three-dimensional coordinate calculate there is not yet
Relevant research.
In conclusion problem of the existing technology is:
The basic principle of satellite positioning is using its distance measuring signal of 4 or 4 or more visible satellite simultaneous observations at present
To determine the three-dimensional coordinate and clock jitter of user.This method is not suitable for low orbit satellite and other terrestrial space aerostatics carry out
Positioning.Since low orbit satellite track is lower, signal cover is small, and the covering of Yao Shixian global signal then needs to emit hundreds of supreme
Thousand satellites, it is with high costs.Low rail communication satellite constellation is only capable of ensureing that ground communication signal substance is covered with, and it is fixed to be unable to satisfy conventional satellite
The location condition of position algorithm.Therefore, it is difficult to carry out navigator fix using the signal of low rail telecommunication satellite.
Existing location technology is positioned using gauss-newton method iterative method, and gauss-newton method has local convergence,
It needs to provide approximate coordinate.For middle high rail satellite, satellite away from 20,000 km of ground, therefore ground receiver position not
Under conditions of knowing, approximate coordinate takes the earth's core to be still able to satisfy convergence demand.And low orbit satellite chooses the earth's core away from ground only several hundred kilometers
Positioning is caused not restrain as approximate coordinate.
Existing location technology requires the space geometry distribution of visible satellite to disperse as far as possible.And for single satellite,
In the course of transit sub-satellite track approximation is in alignment, and geometric configuration is bad, leads to equation morbid state or unusual, and existing positioning is calculated
Method can not directly carry out location Calculation.
Existing low orbit satellite localization method is based on doppler measurement, limit of the doppler measurement by measurement accuracy
System, noise is usually larger, is unable to satisfy the demand of the single star positioning of high-precision.
Existing satellite navigation ground receiver needs to track a satellite channels tens of or even up to a hundred, positioning device simultaneously
Structure is complicated, and power consumption is high, is not suitable for the internet-of-things terminal equipment of low cost miniaturization.
Solve the difficulty of above-mentioned technical problem:
It solves the above problems, needs to design special algorithm aiming at the problem that low orbit satellite list star positions to break through these
Difficult point.The iteration that single star positioning directly calculation there is a problem of do not restrain with equation morbid state, cause positioning result unstable, can not
It leans on, or even can not position.System realizes level, needs to develop special transmitting ranging signals device and is carried on low orbit satellite,
And ground needs design specialized receiver to realize the tracking of distance measuring signal.
Solve the meaning of above-mentioned technical problem:
Realize that user's positioning is to realize multimedia LEO satellite communications navigation integrated design using single low orbit satellite distance measuring signal
Critical issue.Telecommunication satellite only requires that signal substance is covered with, and navigation system then requires signal at least 4 to repeat to cover.The present invention
The localization method being related to be able to use substance coverage signal of communication by range measurement realize user's three-dimensional coordinate determination with
Time service.Multimedia LEO satellite communications constellation is quickly grown both at home and abroad at present, the swan goose constellation of Aerospace Science and Technology Corporation and Aerospace Science and Industry Corporation
Rainbow cloud constellation be made of hundreds of low rail telecommunication satellites.If communication payload is capable of providing ranging information, using low
The positioning and time service of low-orbit satellite communication signal realization terrestrial user.This method even can be integrated with satellite phone etc., realizes side
Side positioning is communicated, there is biggish development and application potential.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of lists based on low orbit satellite radio distance-measuring signal
Star positioning and time service method.The present invention realizes the determination of user's three-dimensional coordinate using single low orbit satellite distance measuring signal, can be used for
It is determined based on the user location of telecommunication satellite signal.
The invention is realized in this way a kind of positioning of single star and time service side based on low orbit satellite radio distance-measuring signal
Method, single star positioning based on low orbit satellite radio distance-measuring signal are solved with time service method using non-iterative approximate coordinate
Method calculates the approximate three-dimensional coordinate and receiver clock-offsets of ground receiver, and the approximate three-dimensional for calculating ground receiver is recycled to sit
The result of mark and receiver clock-offsets is iterated calculating as approximation, solves user's three-dimensional coordinate and receiver clock-offsets；
Further, single star based on low orbit satellite radio distance-measuring signal, which is positioned with time service method, further comprises:
It is calculated using the distance measuring signal of diversified forms, including uses ranging code, pilot code, carrier phase, laser, periodically reproduction
Data frame head and opportunity signal, for realizing range measurement mode between signal projector and receiver.
Further, single star positioning based on low orbit satellite radio distance-measuring signal is specifically included with time service method:
Step 1, receiver observe n epoch pseudorange perhaps carrier phase observation data and by parse text or
Other modes obtain n epoch corresponding low orbit satellite coordinate and low orbit satellite signal projector clock and reference time system
Between deviation；The coordinate of pseudorange and carrier phase observation data and satellite, input of the clock deviation as algorithm；
Step 2 expresses the form of the observation square of pseudorange and carrier phase are as follows:
(ri-dt)2=| | si-x||2；
R in formulaiIndicate pseudorange and carrier phase observation data；Receiver clock-offsets are indicated for Pseudo-range Observations dt, for carrying
Wave phase observation dt indicates receiver clock-offsets of equal value；Assuming that cycle slip does not occur during positioning, then carrier phase ambiguity parameter
It is constant during positioning；In approximate coordinate solution process, receiver clock-offsets approximatively regard constant, receiver clock-offsets of equal value
Parameter includes not changed clock deviation and carrier phase parameter during positioning；Co-ordinates of satellite is denoted as si=[xi, yi, zi], it uses
Family receiver coordinate is denoted as x=[xr, yr, zr]
Formula (ri-dt)2=| | si-x||2It is expressed as following form:
Define four dimensional vector S of an extensioni=[si, Pi], X=[x, dt]；Define the Lorentz product of two four dimensional vectors
Are as follows:
<XT>=x1y1+x2y2+x3y3-x4y4
So, formulaIt is expressed as vector form below:
Above formula is write a Chinese character in simplified form are as follows:
2AX=en<X·X>+b
E in formulanIt is the vector of n × 1 and its whole element is 1；
Formula 2AX=en<both members of XX>+b all contain unknown parameter vector X, are unable to direct solution；Equation
2AX=en<first item on the right side of XX>+b is the same for all observational equations, is eliminated by difference between observation；Definition
Calculus of differences matrix D=[- en-1, In-1], then formula 2AX=en<XX>+b is indicated are as follows:
2DAX=Db:
Step 3, formula 2DAX=Db are solved using the method for least-squares parameter estimation, parameter to be asked are as follows:
Step 4, using the method for regularization to the position vector X=[x found outr, yr, zr, dt] carry out further essence
Change；
Step 5 obtains stable numerical solution by Biased estimator using the method for regularization；
Step 6, to formulaDerivation obtains estimating for parameter
Value are as follows:
The unit matrix that I is 4 × 4 in formula, L=r-r0；
Step 7 is solved after obtaining stable parameter increase using the method for regularization, utilizes following formula undated parameter:
Xi=Xi-1+dX
Subscript i-1 and i indicate the number of iterations in formula；
Step 8 after the completion of new, judges whether the parameter increase dX solved is less than the limit value of iteration ends, if it is less than repeatedly
The limit value that generation terminates terminates iteration and turns to step 9, return step four is otherwise needed to continue to iterate to calculate；In iterative calculation,
Use the updated parameter of i-th as initial value, restarts approximation r0Calculating, and again solve parameter increase dX；
Step 9 after iteration convergence, exports the parameter X vector acquired as final coordinate and receiver clock-offsets, makees
To position the final result with time service.
Further, in step 4, the method for regularization includes:
Receiver clock-offsets are handled using clock deviation linear model, the parameter vector of clock deviation linear model is expressed asIn formulaFor the changing value of receiver clock error, corresponding equation design matrix are as follows:
T in formula0, t1... tnTo observe the moment.
Further, in step 5, the estimation criterion of Regularization are as follows:
α is regularization parameter in formula；Regularization parameter method for solving is calculated by generalized crossover method of inspection, and calculation method is true
Determine the minimum value of generalized crossover test function, generalized crossover test function indicates are as follows:
In formula, H (α) is the function of regularization parameter, is indicated are as follows:
H (α)=A (ATA+αI)-1AT
The minimum value of generalized crossover test function is obtained by dichotomizing search.
Another object of the present invention is to provide single stars based on low orbit satellite radio distance-measuring signal described in a kind of implementation
Single star based on low orbit satellite radio distance-measuring signal of positioning and time service method positions and time dissemination system, described to be defended based on low rail
Single star of star radio distance-measuring signal is positioned with time dissemination system
The low orbit satellite equipment of signal is broadcast to the ground；Broadcast the ranging code of modulation, pilot code, the data frame repeated
Head characteristic information is used for ranging or time service；
The distance measuring signal of the traceable demodulation low orbit satellite of ground receiver simultaneously carries out single star location Calculation.
Further, the transmitter carrying platform of radio distance-measuring signal includes low orbit satellite, be also possible to unmanned plane or its
His aerostatics platform；
Low orbit satellite signal projector should include the crystal oscillator of high-quality, and crystal oscillator type includes but is not limited to high stability crystal oscillator, core
Chip level atomic clock or atomic clock.
Further, ground receiver is equipped with common crystals XO, the crystal oscillator of temperature compensation type crystal oscillator TCXO or other high stabilities.
Another object of the present invention is to provide single stars based on low orbit satellite radio distance-measuring signal described in a kind of implementation
The global positioning satellite terminal of positioning and time service method.
Another object of the present invention is to provide single stars based on low orbit satellite radio distance-measuring signal described in a kind of implementation
The global positioning satellite network platform of positioning and time service method.
In conclusion advantages of the present invention and good effect are as follows:
The present invention only needs the signal that a satellite is continuously tracked that positioning can be realized, and the radio-frequency front-end of receiver only needs
Support single channel, thus structure is simple, it is low in energy consumption, it is suitble to the internet-of-things terminal equipment of low cost miniaturization.
It is suitable for all displaced signal sources distance measuring signals that are based on Method And Principle of the present invention and realizes receiver positioning,
It is not only restricted to the modulation system of distance measuring signal, coding structure etc. is also not limited to the movement situation and track of displaced signal sources, low
Rail satellite is its typical case.
Of the present invention to realize the method positioned compared with Doppler positioning technology based on distance measuring signal, positioning accuracy is more
It is high.Due to distance measuring signal can be used phaselocked loop output centimetre even millimeter class precision carrier phase, it can be achieved that meter level is smart
Degree positioning, and the doppler measurement observation noise of frequency-locked loop output is larger, is typically only capable to realize hundred meters of even km magnitudes
Positioning accuracy.
The method of the present invention for realizing positioning based on distance measuring signal, which is able to solve to position caused by initial-value problem, not to be received
The unstable problem of positioning caused by problem and equation morbid state is held back, is provided accurately, continuously, reliable positioning result.
The method of the present invention that positioning is realized based on distance measuring signal and the single-star positioning method phase based on GNSS system
Than primary positioning time is promoted to minute grade by several hours, and it is brilliant to be also reduced to common temperature compensation type to the stability requirement of clock
Vibration, cost is lower, and locating effect is more preferable.
The method of the present invention for realizing positioning based on distance measuring signal can be used for single star time service simultaneously, and time service precision is ten
Nanosecond order, better than the precision based on single GNSS satellite time service.
Detailed description of the invention
Fig. 1 is provided in an embodiment of the present invention for the low orbit satellite list star positioning principle based on distance measuring signal.It is connect in the figure
Same low orbit satellite t can be traced in receipts machine1, t2, t3, t4Etc. the distance measuring signal at more than four moment, then using described herein
Method calculate accurate receiver location.
Geometrical relationship comparison when Fig. 2 is middle high rail satellite and low orbit satellite provided in an embodiment of the present invention positioning.Close
Like coordinate it is unknown under conditions of, if doing approximation using the earth's core, in rail satellite approximate coordinate error and observation ratio
About 6378:20200 ≈ 1:4, and for low orbit satellite, the ratio of approximate coordinate error and observation is about 6378:650
The magnitude that ≈ 10:1, i.e. approximate coordinate error are far longer than observation itself, gauss-newton method iteration can not restrain.
Fig. 3 is the single-star positioning method flow chart provided in an embodiment of the present invention based on low orbit satellite distance measuring signal.
Fig. 4 is the result of localization method simulation calculation provided in an embodiment of the present invention.
Simulation calculation is using Luo Ka No.1 low orbit satellite track and Wuhan as earth station, and the figure illustrates different rangings
Influence of the error level to positioning accuracy.
Fig. 5 is the result that the present invention implements the localization method simulation calculation provided.Simulation calculation uses Luo Ka No.1 satellite
Segmental arc of passing by track carries out user's positioning and time service using carrier phase observation data, in Chinese and neighboring area positioning and awards
Shi Jingdu.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
In the prior art, the determination that user's three-dimensional coordinate is not realized using single low orbit satellite distance measuring signal, causes to use
Family position determines inaccuracy.
To solve the above problems, below with reference to concrete scheme, the present invention is described in detail.
The present invention realizes in positioning function how to use the signal meter of single LEO satellite using low rail telecommunication satellite signal
Calculate the satellite position of user.The basic principle of satellite navigation satellite positioning is to solve user using at least four visible satellites at present
The receiver clock-offsets of three-dimensional coordinate and user.Low rail telecommunication satellite can only guarantee that surface signal substance is covered under normal conditions, nothing
Method meets the primary demand of navigator fix.In order to solve this problem, the invention proposes determine to use using single LEO satellite signal
The method of family three-dimensional coordinate, principle are as shown in Figure 1.The core of single star positioning is the distance measuring signal joint solution using multiple epoch
It calculates, single satellite is used as multi-satellite, with the proviso that can be modeled during observation to receiver clock-offsets.
The observational equation positioned using low orbit satellite ranging code and carrier phase can be approximately represented as:
Pi=ρ+c (δ tS-δtR)+∈Pi
Li=ρ+c (δ tS-δtR)+λiNi+∈φi (1)
ρ is geometric distance δ t in formulaSWith δ tRRespectively indicate satellite clock correction and receiver clock-offsets, λlAnd NiIndicate i-th of frequency
The wavelength and carrier phase ambiguity of rate.Formula Satellite coordinate and satellite clock correction can be obtained by ephemeris, receiver clock-offsets and use
Family coordinate can be used as parameter Estimation.In order to express simplicity, satellite orbital error, tropospheric delay, ionosphere delay error and phase
The hardware delay deviation equal error source of pass can correct it using external amendment or empirical model in data processing.Star more epoch
Determine that user location needs to solve two critical issues: due to nonlinearity erron is too big and cause to position iteration not convergence problem and
Equation ill-conditioning problem.
It may be expressed as: to solve user coordinates according to geometric distance
The formula indicates the geometric distance and parameter x to be asked in observationr,yr,zrBetween be non-linear relation, common side
Method is unfolded at approximation using Taylor series, as shown in formula:
Remainder δ indicates linearized stability in formula, this is related with the selection of approximate coordinate and the size of ρ to tie up to user's seat
Mark it is unknown under conditions of, GNSS positioning solved using gauss-newton method, initial coordinate can be set to zero, then pass through 3-4 times
Iteration can converge to meter level positioning magnitude.Since the distance of middle high rail satellite-signal to ground is 20000 kilometers or more, the earth
Radius is about 6400 kilometers.Even if therefore initial value is set as zero, initial position error is also only 1/3 or so of measurement distance.It is right
For low orbit satellite, orbit altitude 500km-1500km, if will be if initial value be set as 0, initial error and measurement
Range error is up to 3-10 times of distance.Gauss-newton method positioning has local convergence, and the excessive condition of initial value error is led
Cause parameter that can not converge near true value.
On the other hand, the ideal conditions for determining user's three-dimensional coordinate is that satellite is uniformly distributed in the sky, and in north, east is high by three
There is certain variation range in a direction, then corresponding coordinate components ornamental is preferable.And the track of low orbit satellite is in a timing
Interior is substantially to move along the same direction, therefore have a directional precision preferable in the in-plane direction, another directional precision
It is relatively poor, or even there is the unusual or ill situation of equation, the positioning accuracy of the direction how is promoted under this condition, is obtained
Stablize, there are certain challenges for reliable positioning result.
Geometrical relationship comparison when Fig. 2 is middle high rail satellite and low orbit satellite provided in an embodiment of the present invention positioning.Close
Like coordinate it is unknown under conditions of, if doing approximation using the earth's core, in rail satellite approximate coordinate error and observation ratio
About 6378:20200 ≈ 1:4, and for low orbit satellite, the ratio of approximate coordinate error and observation is about 6378:650
The magnitude that ≈ 10:1, i.e. approximate coordinate error are far longer than observation itself, gauss-newton method iteration can not restrain.
The present invention provides the positioning of single star and time service method described in a kind of implementation based on low orbit satellite radio distance-measuring signal
Based on low orbit satellite radio distance-measuring signal single star positioning and time dissemination system, it is described based on low orbit satellite radio distance-measuring believe
Number single star position and with time dissemination system include:
The low orbit satellite equipment of signal is broadcast to the ground；Broadcast the ranging code of modulation, pilot code, the data frame repeated
Head characteristic information is used for ranging or time service；
The distance measuring signal of the traceable demodulation low orbit satellite of ground receiver simultaneously carries out single star location Calculation.
The transmitter carrying platform of radio distance-measuring signal includes low orbit satellite, is also possible to unmanned plane or other aerostatics
Platform；
Low orbit satellite signal projector should include the crystal oscillator of high-quality, and crystal oscillator type includes but is not limited to high stability crystal oscillator, core
Chip level atomic clock or atomic clock.
Ground receiver is equipped with common crystals XO, the crystal oscillator of temperature compensation type crystal oscillator TCXO or other high stabilities.
In embodiments of the present invention, the present invention propose a kind of two-step method for single low orbit satellite distance measuring signal positioning with
Time service.The first step is to obtain reliable approximate coordinate using a kind of non-iterative approximate algorithm, then recycles the method for regularization
Pairing approximation coordinate is refined, and high-precision positioning time service result is obtained.Specific implementation step is as shown in Figure 3:
S101: receiver observe n epoch pseudorange perhaps carrier phase observation data and by parse text or its
His mode obtain n epoch corresponding low orbit satellite coordinate and low orbit satellite signal projector clock and reference time system it
Between deviation.The coordinate of pseudorange and carrier phase observation data and satellite, input of the clock deviation as algorithm.
S 102: the form of pseudorange and the observation of carrier phase its square can be expressed as:
(ri-dt)2=| | si-x||2
(4)
R in formulaiIndicate pseudorange and carrier phase observation data.Receiver clock-offsets are indicated for Pseudo-range Observations dt, for carrying
Wave phase observation dt indicates receiver clock-offsets of equal value.Assuming that cycle slip does not occur during positioning, then carrier phase ambiguity parameter
It is constant during positioning.In approximate coordinate solution process, receiver clock-offsets can approximatively regard constant, thus reception of equal value
Machine clock deviation parameter includes the not changed clock deviation during positioning
With carrier phase parameter.Co-ordinates of satellite is denoted as si=[xi, yi, zi], receiver user coordinate is denoted as x=[xr, yr,
zr]
Formula (4) can be expressed as following form:
In order to simplify expression, the present invention defines four dimensional vector S of an extensioni=[si, Pi], X=[x, dt] defines two
The Lorentz product of a four dimensional vector are as follows:
<XY>=x1y1+x2y2+x3y3-x4y4
(6)
So, formula (5) can be expressed as vector form below:
Above formula can be write a Chinese character in simplified form are as follows:
2AX=en<e in XX>+b (8) formulanIt is the vector of n × 1 and its whole element is 1.
The both members of formula (8) all contain unknown parameter vector X, so the equation is unable to direct solution.Lucky
Be, the first item on the right side of equation (8) for all observational equations all, so this can pass through difference between observation
To eliminate.Define calculus of differences matrix D=[- en-1, In-1], then formula (8) can indicate are as follows:
2DAX=Db (9).
S 103: the method that formula (9) can use least-squares parameter estimation solves, parameter to be asked are as follows:
This method is a kind of method for solving of approximate coordinate, can not acquire the optimal solution of user coordinates.But this method
Allow a step to solve user coordinates, do not need iteration, thus can be to avoid iterative divergence the problem of.Under normal conditions, this method
Can be in the hope of several hundred rice to user's approximate coordinate of several kilometers of precision, this approximate solution is for as the first of gauss-newton method iteration
For value, its required precision can satisfy completely.
S 104: the position vector X=[x that then first step is found out using the method for regularizationr, yr, zr, dt] carry out into one
Step is refined.The method flow of regularization is as follows:
Ranging observation is linearized according to Taylor's formula (3), obtains linear system:
V=A × dX- (r-r0) V shows the residual error of parameter Estimation in (11) formula, A is the design matrix of parameter, dX table
Show the increment of parameter X, r indicates the column vector r being made of the pseudorange or carrier phase observation data of n epoch0.Indicate geometry away from
From the approximation with various error sources.The wherein initial value ρ of geometric distance0Be by first step non-iterative method calculate approximate coordinate and
What satellite position calculation obtained, other error sources can be provided by broadcast ephemeris, the calculating such as empirical model.Design matrix A can
It is embodied as:
ρ in formulaiGeometric distance of the expression user to i-th of epoch-making moment co-ordinates of satellite.
For earth surface receiving station, low orbit satellite single transit time is no more than 10 minutes, and to realize user
Three-dimensional localization needs the visible segmental arc long enough of satellite, and preliminary test demonstrates the need for ranging at least continuous observation 300 seconds or so
Signal just can guarantee that three-dimensional coordinate can be solved correctly.Corresponding parameter vector is X=[x in equation (12)r, yr, zr, dt], only
Consider a clock deviation parameter.Its assumed condition defaulted is in this period of time needed for positioning, and the clock deviation of receiver can
It is regarded as a constant.However since receiver is usually using the temperature compensation type crystal oscillator of low cost, frequency stability and frequency are accurate
Degree is not high, therefore many times can introduce biggish clock deviation error using Constant Model estimation clock deviation.For the situation, this hair
Bright to handle receiver clock-offsets problem using clock deviation linear model, the parameter vector of the model is expressed asIn formulaFor the changing value of receiver clock error, corresponding equation design matrix are as follows:
T in formula0, t1... tnTo observe the moment.Parametrization described in the corresponding Regularization of the model and equation (12)
Method solution is identical, but this method accounts for the change rate of receiver clock-offsets, can preferably absorb receiver clock-offsets error.
S105: passing by for satellite single, and sub-satellite track is approximately straight line, therefore is used using single track estimation
There are serious singularitys for the three-dimensional coordinate equation at family, or even close morbid state.The consequence of equation morbid state be parameter Estimation numerical value not
Stablize, small deviation occurs i.e. in observation and will lead to generate biggish unreasonable deviation on parameter estimation.In order to further solve
Certainly numerical problem caused by equation morbid state, the method that the present invention uses regularization obtain stable numerical value by Biased estimator
Solution.The estimation criterion of Regularization are as follows:
α is regularization parameter in formula.Regularization parameter method for solving can pass through, and generalized crossover method of inspection calculates, calculating side
Method is to determine the minimum value of generalized crossover test function, and generalized crossover test function may be expressed as:
In formula, H (α) is the function of regularization parameter, is indicated are as follows:
H (α)=A (ATA+αI)-1AT
(16)
The minimum value of generalized crossover test function can be obtained by dichotomizing search.
S106: the valuation of parameter can be obtained to formula (14) derivation are as follows:
The unit matrix that I is 4 × 4 in formula, L=r-r0Compared with gauss-newton method, this method is more one on the right side of equation
Item α I, this make the pathosis of normal equation obtain the stabilization of the result always, inverted change.
S107: being solved after obtaining stable parameter increase using the method for regularization, using following formula undated parameter:
Xi=Xi-1+dX (18)
Subscript i-1 and i indicate the number of iterations in formula.
S108: after the completion of update, need to judge whether the parameter increase dX solved is less than the limit value of iteration ends, if it is less than
The limit value of iteration ends can then terminate iteration and turn to step 109, return step 104 is otherwise needed to continue to iterate to calculate.In iteration
When calculating, uses the updated parameter of i-th as initial value, restart approximation r0Calculating, and solve parameter again
Increment dX.
S109: after iteration convergence, the parameter X vector that final step is acquired is defeated as final coordinate and receiver clock-offsets
Out, the final result as positioning and time service.
Below with reference to emulation experiment, the invention will be further described.
It is tentatively emulated, the precision of low orbit satellite list star positioning and the precision of observation is carried out using pseudorange and carrier phase
Relationship is as shown in Figure 4.The figure, which is simulated, enhances signal using Luo Ka No.1 satellite navigation, when using Wuhan Railway Station as ground receiver
Positioning accuracy.Under normal circumstances, the measurement accuracy of pseudorange is 0.3-3 meters of corresponding positioning accuracies in tens meters of magnitudes.Carrier wave phase
The measurement accuracy of position is between 0.003-0.03 meters, and corresponding positioning accuracy is in meter level.Traditional low rail based on Doppler is defended
Star positioning method positioning accuracy is usually in km magnitude.Simulation result shows no matter use pseudorange or carrier phase observation data,
No matter method of the present invention uses pseudorange or carrier phase as ranging observation, and the positioning accuracy obtained is remote high
In traditional method using Doppler positioning.
For the correctness for verifying method according to the present invention, the present invention uses Wuhan University's Luo Ka No.1 satellite orbit number
According to using carrier phase observation data information to the positioning of China and neighboring area and time service precision progress simulation calculation.Calculate knot
Fruit is as shown in Figure 5.The figure is shown in the precision of most of zone location all in meter level, and time service precision major part region is received better than 20
Second.Positioning accuracy, which receives ground receiver and the relative geometry position of satellite, to be influenced.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (10)
1. a kind of positioning of single star and time service method based on low orbit satellite radio distance-measuring signal, which is characterized in that described to be based on
Single star positioning of low orbit satellite radio distance-measuring signal calculates ground using non-iterative approximate coordinate method for solving with time service method
The approximate three-dimensional coordinate and receiver clock-offsets of face receiver recycle the approximate three-dimensional coordinate and receiver clock-offsets of ground receiver
Result be iterated calculating as approximation, solve user's three-dimensional coordinate and receiver clock-offsets.
2. single star positioning based on low orbit satellite radio distance-measuring signal and time service method as described in claim 1, feature
It is, single star based on low orbit satellite radio distance-measuring signal, which is positioned with time service method, further comprises: to diversified forms
Distance measuring signal calculated, realize range measurement between signal projector and receiver, the distance measuring signal of diversified forms includes
Use ranging code, pilot code, carrier phase, laser, the data frame head and opportunity signal periodically reappeared.
3. single star positioning based on low orbit satellite radio distance-measuring signal and time service method as described in claim 1, feature
It is, single star positioning based on low orbit satellite radio distance-measuring signal is specifically included with time service method:
Step 1, receiver observes the pseudorange or carrier phase observation data of n epoch, and obtains n by parsing text
Deviation, pseudorange between epoch corresponding low orbit satellite coordinate and low orbit satellite signal projector clock and reference time system
And the coordinate of carrier phase observation data and satellite；
Step 2, to expressing for the observation square of pseudorange and carrier phase:
(ri-dt)2=| | si-x||2；
R in formulaiIndicate pseudorange and carrier phase observation data；Pseudo-range Observations dt indicates receiver clock-offsets, carrier phase observation data dt
Indicate receiver clock-offsets of equal value；Co-ordinates of satellite is denoted as Si=[xi, yi, zi], receiver user coordinate is denoted as x=[xr, yr, zr]；
Formula (ri-dt)2=| | si-x||2Expression are as follows:
Define calculus of differences matrix D=[- en-1, In-1], formula 2AX=en<XX>+b is indicated are as follows:
2DAX=Db；
Step 3, formula 2DAX=Db are solved using the method for least-squares parameter estimation, parameter to be asked are as follows:
Step 4, using the method for regularization to the position vector X=[x found outr, yr, zr, dt] further refined；
Step 5 obtains stable numerical solution by Biased estimator using the method for regularization；
Step 6, to formulaDerivation obtains estimating for parameter
Value:
The unit matrix that I is 4 × 4 in formula, L=r-r0；
Step 7 is solved after obtaining stable parameter increase using the method for regularization, utilizes following formula undated parameter:
Xi=Xi-1+dX；
Subscript i-1 and i indicate the number of iterations in formula；
Step 8 after the completion of update, judges whether the parameter increase dX solved is less than the limit value of iteration ends, if it is less than iteration
The limit value of termination terminates iteration and turns to step 9, return step four is otherwise needed to continue to iterate to calculate；In iterative calculation, make
It uses the updated parameter of i-th as initial value, restarts approximation r0Calculating, and again solve parameter increase dX；
Step 9 after iteration convergence, is exported the parameter X vector acquired as final coordinate and receiver clock-offsets, as fixed
The final result of position and time service.
4. single star positioning based on low orbit satellite radio distance-measuring signal and time service method as claimed in claim 3, feature
It is, in step 4, the method for regularization includes: to handle receiver clock-offsets using clock deviation linear model, clock deviation linear model
Parameter vector is expressed as X=[xr, yr, zr, dt, dt]；Dt is the changing value of receiver clock error, corresponding equation design matrix in formula
Are as follows:
T in formula0, t1... tnTo observe the moment.
5. single star positioning based on low orbit satellite radio distance-measuring signal and time service method as claimed in claim 3, feature
It is, in step 5, the estimation criterion of Regularization are as follows:
α is regularization parameter in formula；Regularization parameter method for solving is calculated by generalized crossover method of inspection, and calculation method determines wide
Justice crosscheck functional minimum value, generalized crossover test function indicate are as follows:
In formula, H (α) is the function of regularization parameter, is indicated are as follows:
H (α)=A (ATA+αI)-1AT；
The minimum value of generalized crossover test function is obtained by dichotomizing search.
6. a kind of base for single star positioning and time service method implemented described in claim 1 based on low orbit satellite radio distance-measuring signal
In single star positioning of low orbit satellite radio distance-measuring signal and time dissemination system, which is characterized in that described wireless based on low orbit satellite
Single star of electric distance measuring signal is positioned with time dissemination system
The signal projector of radio distance-measuring signal is broadcast to the ground, and signal projector is mounted in low orbit satellite platform or space
On aircraft platforms；
Ground receiver, for trace demodulation low orbit satellite distance measuring signal and carry out single star location Calculation.
7. single star positioning based on low orbit satellite radio distance-measuring signal and time dissemination system as claimed in claim 6, feature
It is, the transmitter carrying platform of radio distance-measuring signal includes low orbit satellite, or is unmanned plane or aerostatics platform；
Signal projector includes crystal oscillator, and crystal oscillator includes but is not limited to high stability crystal oscillator, chip-scale atomic clock or atomic clock.
8. single star positioning based on low orbit satellite radio distance-measuring signal and time dissemination system as claimed in claim 6, feature
It is, ground receiver is equipped with common crystals XO, the crystal oscillator of temperature compensation type crystal oscillator TCXO or high stability.
9. a kind of single star positioning implemented described in claim 1 based on low orbit satellite radio distance-measuring signal is complete with time service method
Ball satellite positioning-terminal.
10. a kind of single star positioning implemented described in claim 1 based on low orbit satellite radio distance-measuring signal and time service method
The global positioning satellite network platform.
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