CN106019346B - Single-star positioning method based on two-way communication co-located auxiliary - Google Patents
Single-star positioning method based on two-way communication co-located auxiliary Download PDFInfo
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- CN106019346B CN106019346B CN201610517247.XA CN201610517247A CN106019346B CN 106019346 B CN106019346 B CN 106019346B CN 201610517247 A CN201610517247 A CN 201610517247A CN 106019346 B CN106019346 B CN 106019346B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
- G01S19/46—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being of a radio-wave signal type
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Abstract
The present invention proposes a kind of single-star positioning method based on two-way communication co-located auxiliary, it is divided into two parts of single star locating module and co-located module, single star locating module is located at satellite and ground finder, the solution of distance between the main single star positioning calculation for completing ground finder and ground finder, co-located module is located at ground finder, the main co-located completed between ground finder.The obtained self poisoning coordinate of ground finder is sent to position location satellite, the ground finder self poisoning coordinate of position location satellite positioning needed for determines the ground finder of co-located according to a certain distance restrictive condition, and the distance between the ground finder being calculated by satellite and collaboration ground finder information establish weight coefficient, and single star positioning result of each collaboration ground finder is merged so as to reduce influence of the Satellite Orbit Determination error to ground finder position error, and improve positioning accuracy by the coefficient.
Description
Technical field
The present invention is a kind of co-located method for being used for single star alignment system, more particularly to a kind of based on single star positioning system
Two-way communication co-located (the Bi-directional of system (Single satellite position system)
Communication of co-location) auxiliary localization method.
Background technology
With the development and extension of mankind's space exploration, detected, developed on planet and asteroid be the mankind into
Enter the necessary stage in universe.Need to position ground detecting devices when being detected on planet, but established on planet
The satellite constellation navigation such as such as Big Dipper, GPS system can because with high costs and service object is less and without practical feasibility.This
Under satellite navigation constellation missing environment, single star alignment system since cost is low, use, and with rapid fire and can dispose by single star
Positioning service is provided for detection target, so as to instead of constellation type navigation system well in planetary detection.But it is different from star
Seat type navigation system, single star alignment system cause single star to be determined due to lacking mutual ranging amount of restraint and ground base station calibration
The orbit determination accuracy of position system is relatively low, and position error is larger.In addition, in order to increase as far as possible the positioning service time, single star positioning
System uses highly elliptic orbit, and track far point part provides positioning service for positioning target, in track near point part, aeronautical satellite
Quickly through non-service area.But position error can be further amplified in this working method.
Single-star positioning method main at present has the single-star positioning method based on satellite emission signal frequency measurement, is surveyed based on frequency measurement
Away from single-star positioning method, the single-star positioning method based on Doppler frequency shift, based on survey phase angle measurement single-star positioning method and base
In the single-star positioning method of radial acceleration.Wherein, the single-star positioning method based on satellite emission signal frequency measurement is sent out using satellite
The multiple positioning radiating surfaces of frequency measurement information architecture for penetrating signal realize single star positioning, but when radiating surface increases, position error can be fast
Speed increases.Increase ranging information on the basis of single-star positioning method frequency measurement based on frequency measurement ranging and build multiple auditory localization cues realization lists
Star positions, but identical with the single-star positioning method based on satellite emission signal frequency measurement, increases with the distance of auditory localization cues, positioning
Exponential growth is presented in error.The single-star positioning method of Doppler frequency shift is realized single using Doppler frequency shift structure positioning hyperboloid
Star positions, this needs position location satellite to have higher translational speed, and when satellite translational speed is smaller, position error is larger not
It is adapted to single star alignment system of big oval apogee positioning.Satellite orbit is utilized based on the single-star positioning method for surveying phase angle measurement and is determined
Measurement angle between the target of position builds multiple orientational cone-shaped surfaces so as to complete to position, but this required precision to angle measurement is very high.
Based on the single-star positioning method of radial acceleration by building dynamic model to positioning target and being added by the radial direction of dynamic model
Speed completes single star positioning, but this method is higher to the accuracy requirement of dynamic model, when the accuracy of dynamic model is poor,
Position error is larger.
The content of the invention
For in planetary detection, single star alignment system causes detection target location error larger since Orbit Error is larger
Problem, the present invention devise a kind of single-star positioning method based on two-way communication co-located auxiliary, realize that difficulty is low, be easy to build
It is vertical, the position error of ground finder in single star alignment system can be effectively reduced.It is main fixed comprising single star locating module and collaboration
Position two parts of module.Single star locating module is located at satellite and ground finder, the main single star positioning for completing ground finder
The solution of distance between resolving and ground finder.Co-located module is located at ground finder, mainly completes ground location
Co-located between device.It is of the invention by ground in order to reduce the position error caused by single star positioning system satellite Orbit Error
The obtained self poisoning coordinate of surface detector is sent to position location satellite, and the ground finder of position location satellite positioning needed for is certainly
The body elements of a fix determine the ground finder of co-located according to a certain distance restrictive condition, and be calculated by satellite
The distance between ground finder and collaboration ground finder information establish weight coefficient, and merge each collaboration by the coefficient
Single star positioning result of ground finder improves so as to reduce influence of the Satellite Orbit Determination error to ground finder position error
Positioning accuracy.
The technical scheme is that：
A kind of single-star positioning method based on two-way communication co-located auxiliary, it is characterised in that：Including following step
Suddenly：
Step 1：The initial coordinate estimate of each ground finder is obtained using procedure below：
For i-th of ground finder, single star transmitting signal is received at different moments at three, and obtain three at different moments
The coordinate of lower list star, is obtained between i-th of ground finder and single star using Doppler's frequency meter, when the first moment is with second
The pseudorange at quarter is poor, and poor in the pseudorange at the second moment and the 3rd moment；
According to obtained two pseudoranges difference and the oneself height information of i-th of ground finder, during with reference to three differences
The coordinate of single star is inscribed, the initial coordinate estimate of i-th of ground finder is obtained by least square methodAnd will
The initial coordinate estimate is sent to single star；
Step 2：The coordinate estimate of each ground finder is updated using procedure below iteration：
For i-th of ground finder, its coordinate estimate more new formula is：
WhereinFor coordinate estimate of i-th of ground finder after -1 iteration of kth,For
Coordinate estimate of i-th of ground finder after kth time iteration, n are to be not more than to set with i-th of ground finder air line distance
Determine the ground finder number of threshold value,For j-th of ground finder in n ground finder after -1 iteration of kth to institute
The fusion coefficients of i-th of ground finder are stated, the air line distance between fusion coefficients and corresponding two ground finders is negatively correlated；Estimated coordinates for j-th of ground finder in n ground finder to i-th of ground finder：
For coordinate of j-th of the ground finder in n ground finder certainly after -1 iteration of kth
Estimate,For j-th of ground finder in n ground finder after -1 iteration of kth to described i-th
Component of the air line distance of a ground finder on x, tri- directions of y, z.
Further preferred solution, a kind of single-star positioning method based on two-way communication co-located auxiliary, it is special
Sign is：Fusion coefficientsFor：
WhereinFor j-th of ground finder in n ground finder after -1 iteration of kth to i-th of the ground
The air line distance of surface detector, th are the given threshold.
Beneficial effect
The present invention is provided instead of constellation type navigation system by single star alignment system in planetary detection for ground finder
Positioning service, it is of high cost effectively to solve constellation type navigation system, it is difficult in maintenance the problem of.
The co-located assisted location method based on two-way communication list star alignment system designed by the present invention, passes through collaboration
Positioning assistance module can effectively reduce position error large effect caused by Satellite Orbit Determination error, improve ground location
The positioning accuracy of device.
The additional aspect and advantage of the present invention will be set forth in part in the description, and will partly become from the following description
Obtain substantially, or recognized by the practice of the present invention.
Brief description of the drawings
The above-mentioned and/or additional aspect and advantage of the present invention will become in the description from combination accompanying drawings below to embodiment
Substantially and it is readily appreciated that, wherein：
Fig. 1：Single star alignment system conceptual scheme of the present invention；
LijRepresent the baseline at i-th of moment of satellite to j-th of moment；
RijSatellite is inscribed when representing i-th to the pseudorange between j-th of positioning target；
rijRepresent the ranging between i-th of positioning target and j-th of positioning target；
MiRepresent i-th of positioning target.
Fig. 2：Single star alignment system position error comparison curves；
Wherein, 3 target cooperative of single-star positioning method that the co-located auxiliary of the present invention is represented with diamond indicia solid line is determined
The position error curve of position；4 target of the single-star positioning method association of the co-located auxiliary of the present invention is represented with circular mark solid line
With the position error curve of positioning；The single-star positioning method 5 of the co-located auxiliary of the present invention is represented with five-pointed star mark solid line
The position error curve of target cooperative positioning；The positioning that Doppler frequency shift single-star positioning method is represented with triangular marker solid line misses
Poor curve；Band square marks solid line represents radial acceleration single-star positioning method.
Embodiment
The embodiment of the present invention is described below in detail, the example of the embodiment is exemplary, it is intended to for explaining this
Invention, and be not considered as limiting the invention.
Co-located assisted location method proposed by the present invention based on two-way communication list star alignment system combines single star
The advantages of the advantages of alignment system is easy to build and co-located can effectively reduce ground finder position error.The present invention is built
Vertical single star alignment system come replace constellation type navigation system realize planetary detection position, solve constellation type navigation system cost
Height, it is difficult in maintenance the problem of, and reduce single star alignment system Satellite Orbit Error using co-located supplementary module and made
Into ground finder error it is larger the problem of.
The basic principle of the present invention is as follows：
A, the satellite emission signal and corresponding satellite orbit position that planet ground finder receives on Fixed Time Interval
Put, the pseudorange difference between the ground finder and satellite that are obtained using Doppler's frequency meter.
B, using 2 obtained pseudorange differences of a and oneself height information, with reference to the satellite orbital position at corresponding moment,
The estimate of the planet ground finder coordinate at current time is obtained by least square method, and the estimate is sent to and is defended
Star.
C, for the ground finder M for needing progress co-located1, satellite is with ground finder M1Coordinate centered on,
Selection and M1The ground finder that the distance of coordinate is less than setting thresholding carries out co-located and calculates all ground in the range of this
Detector is to ground finder M1Air line distance, and ground finder M is obtained by fusion function using the air line distance1's
Fusion coefficients.
D, the ground finder for carrying out co-located obtains current time and ground finder M using ranging angle-measuring equipment1
The distance between information and directional information, and estimate to obtain ground finder M with reference to own coordinate1Coordinate position and transmission
Give ground finder M1。
E, in ground finder M1On, by the estimated coordinates combination c of the ground finder transmission of other progress co-positioneds
Obtained fusion coefficients, are merged and update ground finder M1Coordinate.
F, step c is utilized to the coordinate of all ground finders, d, e are estimated and update coordinate position.
Whole list star alignment system be by an aeronautical satellite, single star locating module of several planet ground finders and
Co-located module is formed.
Based on above-mentioned principle, the system structure of the present embodiment as shown in Figure 1, planet ground finder in Fixed Time Interval
The satellite emission signal of upper reception and corresponding satellite orbital position, and calculate the ground finder in each time interval and defend
Pseudorange between star is poor.The seat of the planet ground finder at current time is obtained by least square method by multiple pseudorange differences
Cursor position.And obtained coordinate position is estimated to improve positioning accuracy using co-located, comprise the following steps that：
Step 1：The initial coordinate estimate of each ground finder is obtained using procedure below：
For i-th of ground finder, single star transmitting signal is received at different moments at three, and obtain three at different moments
The coordinate of lower list star, is obtained between i-th of ground finder and single star using Doppler's frequency meter, when the first moment is with second
The pseudorange at quarter is poor, and poor in the pseudorange at the second moment and the 3rd moment；
According to obtained two pseudoranges difference and the oneself height information of i-th of ground finder, during with reference to three differences
The coordinate of single star is inscribed, the initial coordinate estimate of i-th of ground finder is obtained by least square methodAnd will
The initial coordinate estimate is sent to single star.
As shown in fig. 1, set i-th of moment of satellite to the distance between j-th ground finder be Rij, for positioning
Target floor detector M1, the pseudorange difference d that is chosen at respectively between the first moment of satellite flight position and the second moment position12=
R21-R11Pseudorange difference d between the second moment of satellite flight position and the 3rd moment position23=R31-R21Structure positioning target M1
Two positioning hyperboloids.Wherein, the coordinate of satellite can be calculated by satellite ephemeris, and setting satellite is i-th of moment
Coordinate be Xi,Yi,Zi, ground finder M1Two positioning hyperboloids represent it is as follows：
In formula, x1,y1,z1Represent ground finder M to be solved1Coordinate.Recycle ground finder M1The height of itself
Information architecture location sphere is spent, is represented as follows：
In formula, h1Represent ground finder M1Elevation information.Simultaneous (1), (2) and (3) can be obtained using least square method
To ground finder M1Initial coordinate estimateSimilarly, other ground finders M can be obtainediInitial coordinate
EstimateAnd the coordinate estimate of all ground finders is issued into satellite.
Step 2：The coordinate estimate of each ground finder is updated using procedure below iteration：
For i-th of ground finder, its coordinate estimate more new formula is：
WhereinFor coordinate estimate of i-th of ground finder after -1 iteration of kth,For
Coordinate estimate of i-th of ground finder after kth time iteration, n are to be not more than to set with i-th of ground finder air line distance
Determine the ground finder number of threshold value,For j-th of ground finder in n ground finder after -1 iteration of kth to institute
The fusion coefficients of i-th of ground finder are stated, the air line distance between fusion coefficients and corresponding two ground finders is negatively correlated, melts
Syzygy number can use a variety of distribution modes such as normal distribution, exponential distribution, and the form of exponential distribution is used in the present embodiment, is melted
Syzygy numberFor：
WhereinFor j-th of ground finder in n ground finder after -1 iteration of kth to i-th of the ground
The air line distance of surface detector, th are the given threshold；Visited for j-th of ground in n ground finder
Survey estimated coordinates of the device to i-th of ground finder：
For coordinate of j-th of the ground finder in n ground finder certainly after -1 iteration of kth
Estimate,For j-th of ground finder in n ground finder after -1 iteration of kth to described i-th
Component of the air line distance of a ground finder on x, tri- directions of y, z.
In the present embodiment, for the ground finder M for needing progress co-located1, satellite is with ground finder M1's
Centered on coordinate, selection and ground finder M1The ground finder that the distance of coordinate is less than setting thresholding carries out co-located simultaneously
All ground finders are calculated in the range of this to ground finder M1Air line distance, and using the air line distance by merging letter
Number obtains ground finder M1Fusion coefficients.
With ground finder M1Exemplified by, the ground finder M of co-positionediNeed to meet：
In formula, th is the thresholding whether ground finder participates in this co-located.The ground received by satellite
Surface detector MiCoordinate estimateIt can obtain participating in the ground finder M of co-locatediTo ground finder M1
Air line distance rsi,1：
Pass through air line distance rsi1, ground finder M can be obtainediTo ground finder M1Fusion coefficients λi,1.
During the fusion coefficients solve, a variety of distribution modes such as normal distribution, exponential distribution can be used, the present embodiment uses exponential distribution
Form, fusion coefficients λi,1It is as follows：
Then carry out the ground finder M of co-locatediCurrent time and ground location are obtained using ranging angle-measuring equipment
Device M1The distance between information and directional information, and estimate to obtain ground finder M with reference to own coordinate1Coordinate position simultaneously
It is sent to ground finder M1。
Ground finder MiTo ground finder M1Estimated coordinatesIt is as follows
In formula,Represent ground finder MiEstimated coordinates, Δ xi,1,Δyi,1,Δzi,1For ground finder Mi
With ground finder M1The distance between component of the information in all directions, and the above results are sent to ground finder M1。
In ground finder M1On, the estimated coordinates that the ground finder of other progress co-positioneds is sent are combined and are obtained
Fusion coefficients, merged and update ground finder M1Coordinate.This process is iterative process, kth time iteration
Ground finder M afterwards1Coordinate be：
The coordinate of all ground finders can be estimated as procedure described above and update coordinate position.
Performance evaluation
In simulation analysis, selection perigee is 300km, apogee 36000km, and recursion period is big ellipse when small for 24
Circular orbit satellite, puts region and provides positioning for positioning target in distant.In simulations, the single satellite positioning time is 300 seconds, association
It it is 10 seconds with the list star positioning distance measuring information updating cycle, the maximum iteration for cooperateing with single star positioning is 10 times, cooperates with single star to determine
The position Doppler shift measurement cycle is 10 seconds, and radial acceleration measurement period is 10 seconds, and Satellite Orbit Determination error value range is to defend
Spaceborne wave frequency rate is 2.4GHz, and the number of co-located target is 4, satellite other conditions for ideally simulation result such as
Shown in Fig. 2.
From figure 2 it can be seen that when Orbit Error is zero, the position error of three kinds of single-star positioning methods is 10-6Km,
In this ideal case, position error mainly has caused by the carrier frequency resolution of satellite emission signal.Work as satellite
When rail error is 0.1km, the positioning of single-star positioning method and Doppler frequency shift single-star positioning method based on radial acceleration misses
Difference is 10m, and the position error of the single-star positioning method proposed by the invention based on two-way communication co-located auxiliary is 1m,
When Satellite Orbit Determination error is 1km, single-star positioning method and Doppler frequency shift single-star positioning method based on radial acceleration
Position error will be respectively 1.7km and 2km, and the position error of method proposed by the invention is only 0.8km.This is because this hair
Bright proposed single-star positioning method carries out co-located auxiliary using the ranging information of located in connection target, reduces satellite
Influence of the rail error to positioning target, so as to reduce position error.
Although the embodiment of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is impossible to limitation of the present invention is interpreted as, those of ordinary skill in the art are not departing from the principle of the present invention and objective
In the case of above-described embodiment can be changed within the scope of the invention, change, replace and modification.
Claims (2)
- A kind of 1. single-star positioning method based on two-way communication co-located auxiliary, it is characterised in that：Comprise the following steps：Step 1：The initial coordinate estimate of each ground finder is obtained using procedure below：For i-th of ground finder, single star transmitting signal is received at different moments at three, and obtain three and place an order at different moments The coordinate of star, was obtained between i-th of ground finder and single star using Doppler's frequency meter, at the first moment and the second moment Pseudorange is poor, and poor in the pseudorange at the second moment and the 3rd moment；According to obtain two pseudoranges difference and i-th of ground finder oneself height information, with reference to three at different moments under The coordinate of single star, the initial coordinate estimate of i-th of ground finder is obtained by least square methodIt is and this is first Beginning coordinate estimate is sent to single star；Step 2：The coordinate estimate of each ground finder is updated using procedure below iteration：For i-th of ground finder, its coordinate estimate more new formula is：<mrow> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> <mi>k</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>&lambda;</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>&lambda;</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow><mrow> <msubsup> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>i</mi> <mi>k</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>&lambda;</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>i</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>&lambda;</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow><mrow> <msubsup> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>i</mi> <mi>k</mi> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>&lambda;</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <msubsup> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>i</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>&lambda;</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mover> <mi>z</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow>WhereinFor coordinate estimate of i-th of ground finder after -1 iteration of kth,For i-th Coordinate estimate of the ground finder after kth time iteration, n are no more than setting threshold with i-th of ground finder air line distance The ground finder number of value,For j-th of ground finder in n ground finder after -1 iteration of kth to described The fusion coefficients of i ground finder, the air line distance between fusion coefficients and corresponding two ground finders are negatively correlated；Estimated coordinates for j-th of ground finder in n ground finder to i-th of ground finder：<mrow> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>j</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>&Delta;x</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow><mrow> <msubsup> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>j</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>&Delta;y</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow><mrow> <msubsup> <mover> <mi>z</mi> <mo>^</mo> </mover> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mover> <mi>z</mi> <mo>^</mo> </mover> <mi>j</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>&Delta;z</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow>Estimate for j-th of ground finder in n ground finder from the coordinate after -1 iteration of kth Value,For j-th of ground finder in n ground finder after -1 iteration of kth to i-th of the ground Component of the air line distance of surface detector on x, tri- directions of y, z.
- A kind of 2. single-star positioning method based on two-way communication co-located auxiliary according to claim 1, it is characterised in that： Fusion coefficientsFor：<mrow> <msubsup> <mi>&lambda;</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msubsup> <mi>rs</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </mfrac> </mrow> </msup> </mrow>WhereinFor j-th of ground finder in n ground finder after -1 iteration of kth to i-th of ground location The air line distance of device, th are the given threshold.
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