CN105549052B - A kind of indoor orientation method and method for improving accuracy based on GNSS repeaters - Google Patents

A kind of indoor orientation method and method for improving accuracy based on GNSS repeaters Download PDF

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CN105549052B
CN105549052B CN201510932905.7A CN201510932905A CN105549052B CN 105549052 B CN105549052 B CN 105549052B CN 201510932905 A CN201510932905 A CN 201510932905A CN 105549052 B CN105549052 B CN 105549052B
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CN105549052A (en
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李秀魁
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Dalian University of Technology
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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
    • G01S19/421—Determining position by combining or switching between position solutions or signals derived from different satellite radio beacon positioning systems; by combining or switching between position solutions or signals derived from different modes of operation in a single system
    • G01S19/423—Determining position by combining or switching between position solutions or signals derived from different satellite radio beacon positioning systems; by combining or switching between position solutions or signals derived from different modes of operation in a single system by combining or switching between position solutions derived from different satellite radio beacon positioning systems
    • 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
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/03—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers
    • G01S19/10—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing dedicated supplementary positioning signals
    • G01S19/11—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing dedicated supplementary positioning signals wherein the cooperating elements are pseudolites or satellite radio beacon positioning system signal repeaters

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radio Relay Systems (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)

Abstract

The invention belongs to electronics, communication and automation field, it is related to the user that can not directly obtain under the navigation satellite signal environment positioning based on GNSS repeaters.It is proposed by the present invention to realize that the method for indoor positioning does not need GNSS repeater synchronizations based on GNSS repeaters, it is not required that repeater is sequentially exchanged repeater satellite signal and is connected with same GNSS antenna with fixed length cables.In the methods of the invention, each GN SS repeaters can Consecutive forwarding navigation satellite signal, and the repeater of the given satellite-signal of the recognizable forwarding of receiver.Receiver calculates each repeater to the distance of receiver, and using the repeater and co-ordinates of satellite of identification using the code phase of measurement, further calculates its position coordinates.In addition, the soft method of sampling of signal proposed by the invention can further improve customer location precision.Present invention arrangement cost in practical application is low and installs easy, and can obtain higher positioning accuracy.

Description

A kind of indoor orientation method and method for improving accuracy based on GNSS repeaters
Technical field
The invention belongs to electronics, communication and automation field, it is related to user's positioning based on aeronautical satellite, especially relates to And it is fixed to the user that can not directly obtain under navigation satellite signal environment based on GNSS (GPS) repeater Position.
Background technology
In building or in other environment that can not directly obtain navigation satellite signal, user typically can not directly utilize Navigation satellite signal obtains positioning.There is multiple indoor location technology at present.Indoor orientation method based on GNSS repeaters is main It is to be amplified navigation satellite signal using repeater and there is provided carry out navigator fix to indoor reception machine after forwarding.Propose at present The indoor orientation method based on GNSS repeaters typically require to realize between repeater it is synchronous, while several in forward signal Repeater needs sequentially to exchange forwarding the signal to avoid repeater from forwarding to interfere with each other, and is also beneficial to receiver and judges forwarding Signal is which repeater come from.All repeaters need to be connected with an outdoor GNSS antenna jointly in addition.Connection cable It is required that length is fixed and accurately measured.Indoor orientation method based on pseudo satellite, pseudolite is realized synchronously between also requiring that pseudo satellite, pseudolite.Knot The indoor orientation method for closing pseudo satellite, pseudolite and GNSS repeater techniques utilizes both advantages, it is not necessary to synchronous, while can be to relaying Device realizes accurate measurement to distance between receiver.But this method also requires that all repeaters use cable and an outdoor respectively Antenna is connected, and the accurate measurement of cable length requirement.Determine that satellite is believed by measuring by the different caused delays of cable length Number come from which repeater.If cable length measurement is not accurate enough, repeater identification will be caused to judge by accident, so as to cause Position error.Other this law cost is relatively also higher.
The content of the invention
Involved in the present invention realizes that the method for indoor positioning does not need GNSS repeaters same first based on GNSS repeaters Step, it is not required that repeater sequentially exchanges forwarding and is connected with same GNSS antenna with fixing cable length.In present invention side In method, each GNSS repeaters can Consecutive forwarding navigation satellite signal, simply require at least two or two with aeronautical satellite pair Repeater is visible.At any one time, no matter being measured with which satellite-signal, the distance from repeater to a receiver is constant 's.Using this characteristic, by being compared with that different satellite-signals measure from a repeater to the distance of receiver, user Receiver can determine that a given satellite-signal is come from which repeater forwarding.The position coordinates of repeater can shift to an earlier date Obtain.So, using the assigned repeaters of measurement to the distance and repeater location coordinate of receiver, receiver can just calculate Its own position is drawn, so as to realize that indoor navigation is positioned.
(1) customer location coordinate is calculated
Application claims arrangement 4 in top of building or other open environments (navigation satellite signal can be directly received) The individual or GNSS repeaters of more than 4, while require that at least 2 aeronautical satellites are visible to these repeaters, namely all GNSS Repeater can directly receive the navigation satellite signal of 2 or more than 2 simultaneously.Repeater is by the navigation satellite signal to receiving It is amplified and forwards.Each repeater will postpone before forward signal to signal, if repeater riDuring to signal delay Between be Δi, then require | Δi-Δj|>tc(i≠j,tcIt is a chip delay of spreading code used in navigation satellite signal), and | Δi|<min{1/fu,ts, wherein fuIt is receiver location renewal frequency, and tsIt is one of spreading code used in navigation satellite signal The code length time.
In receiver end, the satellite-signal received carries out associative operation with local CA codes (spreading code).When with CA codes Ci When carrying out associative operation, 4 larger correlation peaks and corresponding code phase can be obtained, and this 4 larger correlation peaks divide It is not the satellite s of 4 repeater forwardingsiSignal produce.By the code phase of acquisition, receiver can calculate satellite si Signal is from satellite siThe time that repeater is forwarded to required for receiver again is issued to, is designated asWherein subscript k represents this Time is calculated by the corresponding code phase of k-th of correlation peak and obtained.But produce the signal of this k-th of correlation peak be by Which further determined that the need for repeater forwarding.It is represented by,
Wherein,It is signal from repeater rjTime to needed for indoor reception machine；δtcIt is receiver clock error；It is the propagated error that signal is undergone to receiver again from satellite to repeater, andIt is processing of the signal in repeater Time (reaches the time needed for repeater antenna leaves antenna to after having handled from signal).Formula (1), which can be arranged further, is：
Using formula (2), for different satellite-signals, 4 matrix M can be formedi, i=1,2,3,4,
For some repeater rjFor, different satellite-signal propagated errorsIt is contemplated that near Patibhaga-nimitta etc..In addition, because all repeaters all have identical hardware and software, processing timeTo all repeaters For be equal.Work as satellite siWhen signal is forwarded by 4 repeaters, in receiver end signal and local CA codes CiCarry out related 4 larger correlation peaks will occur in operation, and one of peak value will be by repeater rjRepeater satellite siSignal is produced 's.At the same measurement moment, for the signal of any satellite, as long as pass through repeater rjForwarding, then formula (2) right-hand member All it is approximately equalised.Because either the signal of which satellite is from repeater rjIt is forwarded to receiver, repeater to receiver Distance be all it is constant (It is constant).So, it is considered to repeater r1, matrix M1Some element of the first row will be with matrix M2Some element approximately equal of the first row, also will be with matrix M3With matrix M4Some element approximately equal of the first row.Also It is to say,
Pass through comparator matrix M1、M2、M3And M4Element in the first row, i1,j1,k1,l1It can be determined.So,To be satellite s respectively1,s2,s3,s4Signal after satellite launch to repeater r1It is forwarded to again Time required for receiver.It is similar, by being respectively compared matrix M1、M2、M3And M4In second row, the third line and fourth line Element, it may be determined that WithAnd these times are satellite s1,s2,s3,s4Signal arrive separately at after satellite launch After device r2、r3And r4The time required for receiver is forwarded to again.Utilize formula (1), it can be deduced that
Allow Obtained by the above method, andIt is satellite s1To the time of repeater, repeater and satellite s can be passed through1Coordinate calculate.So,It can be expressed as follows：
It is by satellite s1Signal measure, it represents satellite s1Signal is from repeater rmTo needed for receiver Time, including propagated error, clock correction and processing time.It is similar, satellite s can be passed through2,s3And s4Signal obtainWithTo reduce measurement error, signal is from repeater rmIt can be averaged to receiver required time, Namely：Meanwhile, allowSo, formula (6) may be updated as：
Because all repeaters are relatively near apart,May be considered it is equal (if there is compared with Small error, it may be considered that be included inMeasurement error in).In addition, the signal processing time of each repeaterIt is also equal.Therefore, according to formula (7), can further it obtain：
AllowWherein (xu,yu,zu) WithIt is receiver user and repeater r respectivelyiCoordinate.So, formula (8) can be write as：
WhereinRepresent from repeater riTo receiver when Between.According to formula (9), customer location coordinate (x can be obtainedu,yu,zu) closed solutions.
Because bi(i=1,2,3) may be 0, so closed solutions need to be directed to different bi(i=1,2,3) it is equal to 0 situation Discuss.Generally, if biSome in (i=1,2,3) is 0, or two are 0, or is all 0, can be passed through Formula (9) solves (xu,yu,zu).If bi(i=1,2,3) is not 0, then (xu,yu,zu) closed solutions are as follows:
Allow first
Wherein,WithIt is repeater rjCoordinate.
Allow again
So, (xu,yu,zu) last solution be：
Wherein,WithzuThere may be two non-equivalence zu1And zu2, by (xu,yu,zu1) and (xu,yu,zu2) respectively Longitude and latitude and height above sea level expression are converted into, then that group of relatively low data of height above sea level will be used as customer location coordinate.
(2) positioning performance improves method
For the building of many floors, the height above sea level of each layer of any location point can be measured accurately.Because one As for the area of each floor will not be very big, it is possible to be used as the layer with the average value of this layer of all location point height above sea levels Height above sea level.Because the range measurement from repeater to receiver has error, the customer location obtained by the above method (xu,yu,zu) possible and inaccurate, in some instances it may even be possible to contain larger error.But if the height above sea level of each floor is measured in advance Learn, then by the customer location coordinate transformation of acquisition be longitude and latitude and height above sea level expression way after, will can measure User's height above sea level is compared with the height above sea level of each floor.If user's height above sea level measurement error be not more than two floors it Between height half, then compared by this, it is possible to determine user be located at which floor, then further determine that user essence True height above sea level (i.e. the height above sea level of floor where it).
Using accurate height above sea level after this correction, customer location precision can be further improved.Sample rate is low to be After one of device to the error source of range measurement between receiver user.General solution is to improve sample rate, but can increase and connect Receipts machine processing data amount.So admissible method is that first signal is sampled with lower frequency, after rough code phase is obtained (being used to calculate the distance from repeater to receiver), then determine that a time window is adopted again to primary signal with upper frequency Sample.This time window determines that method is as follows：Signal is sampled with low frequency at the beginning, and associative operation is being carried out with local CA codes Afterwards, acquirable code phase δcp.Because code phase error is not over the half in sampling period, true code phase should beIn the range of this.So, primary signal can be entered with upper frequency in this time range Row resampling is to obtain high-precision code phase.But this method for resampling can cause receiver signal complex disposal process, and Practical operation Feasible degree is relatively low.Therefore, the present invention proposes a kind of method of soft sampling.
The soft method of sampling herein refers to not sample to signal really, also without associative operation to obtain new code Phase, and only assume that signal existsInterior to be sampled with upper frequency, like that, new code phase is just Can beIn any one value, it is resampling rate to the low sampling of original that wherein N, which can contemplate, The ratio of rate.This mode carries out resampling new code phase is substantially equivalent to obtain with real, not unique except new code phase Property.Accordingly, it would be desirable to recalculate repeater to the distance of receiver using each new code phase, then computed user locations seat Mark.Then position coordinates is converted into longitude and latitude and height above sea level again to express, and by the user's height above sea level and building of acquisition Every layer of height above sea level accurately measured in advance is compared, to determine the code phase closest to actual value.This method can not only subtract Few sampling error, while the measurement error caused by other error sources can also be reduced.
By comparing height above sea level, it may be determined that closest to the code phase of actual value.Although but the code phase may be minimum Change height above sea level error, but not necessarily can guarantee that the longitude and latitude error of customer location minimum (longitude and latitude and height above sea level are together It can determine that customer location).Therefore need further to improve customer location precision by the following method：(1) receiver utilizes code phase δcp(utilizing the signal after being sampled with lower frequency to obtain, precision is relatively low) is calculated it and calculated to the distance of repeater, and then Draw customer location (x0,y0,z0).By the position (x0,y0,z0) it is converted into longitude and latitude and height above sea level expression Whereinλ0,h0It is latitude, longitude and height above sea level respectively.Again by height above sea level h0Compared with each floor height above sea level, can be with Floor where determining user, then determines its true height above sea level hα.So, customer location (x0,y0,z0) height above sea level miss Difference is：δh,0=h0-hα.Calculate influence of this difference in height to customer location coordinate：
Wherein, a=6378137, b=6356752.31424518,Allow (xξ,yξ,zξ)=(x0,y0,z0)-(δx,δy,δz).So, user True location coordinate will be close to (xξ,yξ,zξ).(2) obtained after multiple new code phases, recycled using the above-mentioned soft method of sampling Each new code phase recalculates repeater to the distance of receiver, can then calculate a new customer location (xκ,yκ, zκ).Calculate γk=| | (xξ,yξ,zξ)-(xκ,yκ,zκ) | | andMeanwhile, receive It is confidential by new position coordinate (xκ,yκ,zκ) it is converted into longitude and latitude and height above sea level expressionAnd calculate height above sea level Poor δh,κ=hκ-hα.So, for the multiple customer locations obtained using multigroup new code phase, wherein energy minimization δh,κAnd γk And ensure φ simultaneouslyκLess than one given threshold phiκ,0Customer location will be used as the final position of user.φκ,0Size will Influence customer location error range, but φκ,0It can not be made too small, otherwise may result in customer location without solution.
Indoor orientation method proposed by the present invention based on GNSS repeaters, can improve user's positioning precision, while Arrangement cost is low during practical application and installs easy.

Claims (2)

1. a kind of indoor orientation method based on GNSS repeaters, it is characterised in that comprise the following steps：
(a) in top of building or other directly receive in navigation satellite signal place in the arrangement GNSS of 4 or more than 4 After device, at least 2 aeronautical satellites are visible to these repeaters；Repeater will be amplified simultaneously to the navigation satellite signal received Forwarding；Each repeater will postpone before forward signal to signal, if repeater riIt is Δ to signal delay timei, then Ask | Δi-Δj|>tc, i ≠ j；tcIt is a chip delay of spreading code used in navigation satellite signal, and | Δi|<min{1/fu, ts, wherein fuIt is receiver location renewal frequency, and tsIt is the code length time of spreading code used in navigation satellite signal；
(b) in receiver end, the satellite-signal received carries out associative operation with local CA codes；When with CA codes CiCarry out related behaviour When making, 4 larger correlation peaks and corresponding code phase can be obtained, this 4 larger correlation peaks are 4 repeaters respectively The satellite s of forwardingiSignal produce；By the code phase of acquisition, receiver calculates satellite siSignal is from satellite siSend Time required for being forwarded to receiver again to repeater, it is designated asWherein subscript k represents that this time is by k-th The corresponding code phase of correlation peak calculates what is obtained；It is expressed as,
<mrow> <msubsup> <mi>&amp;Delta;T</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mi>j</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mi>j</mi> </msub> </msub> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein,It is signal from repeater rjTime to needed for indoor reception machine；δtcIt is receiver clock error； It is the propagated error that signal is undergone to receiver again from satellite to repeater, andIt is processing time of the signal in repeater； Formula (1) is further arranged：
<mrow> <msubsup> <mi>&amp;Delta;T</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mi>j</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <msub> <mi>i</mi> <mo>,</mo> </msub> </msub> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mi>j</mi> </msub> </msub> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
(c) using formula (2), for different satellite-signals, 4 matrix M are formedi, i=1,2,3,4,
<mrow> <msub> <mi>M</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "|" close = "|"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>1</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>2</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>3</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>4</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>1</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>2</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>3</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>4</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>1</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>3</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>2</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>3</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>3</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>3</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>4</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>3</mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>1</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>4</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>2</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>4</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>3</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>4</mn> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mn>4</mn> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mi>i</mi> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>4</mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
(d) repeater r is considered1, matrix M1Some element of the first row will be with matrix M2The approximate phase of some element of the first row Deng also will be with matrix M3With matrix M4Some element approximately equal of the first row, i.e.,
<mrow> <msubsup> <mi>&amp;Delta;T</mi> <msub> <mi>i</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>&amp;ap;</mo> <msubsup> <mi>&amp;Delta;T</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>2</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>&amp;ap;</mo> <msubsup> <mi>&amp;Delta;T</mi> <msub> <mi>k</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>&amp;ap;</mo> <msubsup> <mi>&amp;Delta;T</mi> <msub> <mi>l</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mn>4</mn> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Pass through comparator matrix M1、M2、M3And M4Element in the first row, i1,j1,k1,l1It is determined； To be satellite s respectively1,s2,s3,s4Signal after satellite launch to repeater r1The time required for receiver is forwarded to again； It is similar, by being respectively compared matrix M1、M2、M3And M4Element in second row, the third line and fourth line, it is determined thatWithAnd these Time is satellite s1,s2,s3,s4Signal repeater r is arrived separately at after satellite launch2、r3And r4Receiver institute is forwarded to again The time needed；
(e) using formula (1), draw
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <msub> <mi>i</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>1</mn> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <msub> <mi>i</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>2</mn> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>2</mn> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <msub> <mi>i</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>3</mn> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>3</mn> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <msub> <mi>i</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>4</mn> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>4</mn> </msub> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Allow Obtained by the above method, andIt is Satellite s1To the time needed for repeater, pass through repeater and satellite s1Coordinate calculate；
(f) m=1,2,3,4；It can be expressed as follows：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>1</mn> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>2</mn> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>3</mn> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&amp;Delta;T</mi> <mrow> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>s</mi> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </msub> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>4</mn> </msub> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
(g)It is by satellite s1Signal measure, it represents satellite s1Signal is from repeater rmNeeded for receiver when Between, including propagated error, clock correction and processing time；It is similar, pass through satellite s2,s3And s4Signal obtainWithTo reduce measurement error, signal is from repeater rmAveraged to receiver required time, namely：Meanwhile, allowM=1,2,3,4；According to formula (6), obtain：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <mi>&amp;delta;</mi> <msub> <mover> <mi>t</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>s</mi> <mo>,</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>1</mn> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <mi>&amp;delta;</mi> <msub> <mover> <mi>t</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>s</mi> <mo>,</mo> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>2</mn> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <mi>&amp;delta;</mi> <msub> <mover> <mi>t</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>s</mi> <mo>,</mo> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>3</mn> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <mi>c</mi> </msub> <mo>+</mo> <mi>&amp;delta;</mi> <msub> <mover> <mi>t</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>s</mi> <mo>,</mo> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;delta;t</mi> <msub> <mi>r</mi> <mn>4</mn> </msub> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
(h) according to formula (7), can further it obtain：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>-</mo> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>-</mo> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>3</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>-</mo> <mi>&amp;Delta;</mi> <msub> <mover> <mi>T</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;delta;t</mi> <mrow> <msub> <mi>r</mi> <mn>4</mn> </msub> <mo>,</mo> <mi>u</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
(i) i=1 is allowed, 2,3,Wherein (xu,yu,zu) andIt is receiver user and repeater r respectivelyiCoordinate；Formula (8) is write as：
WhereinRepresent from repeater riTo the distance of receiver；
(j) according to formula (9), customer location coordinate (x is obtainedu,yu,zu) closed solutions；For i=1,2,3, because biMay be 0, so closed solutions need to be directed to different biSituation equal to 0 is discussed, generally, if biIn some be 0, or Two are 0, or are all 0, all solve (x by formula (9)u,yu,zu)；If biIt is not 0, then (xu,yu,zu) closed solutions are such as Under:
Allow
Wherein,WithIt is repeater rjCoordinate；
Allow again
(xu,yu,zu) last solution is：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mrow> <mi>u</mi> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <mi>B</mi> <mo>&amp;PlusMinus;</mo> <msqrt> <mrow> <msup> <mi>B</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <mi>A</mi> <mi>C</mi> </mrow> </msqrt> </mrow> <mrow> <mn>2</mn> <mi>A</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mi>u</mi> </msub> <mo>=</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> <msub> <mi>z</mi> <mi>u</mi> </msub> <mo>+</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mi>u</mi> </msub> <mo>=</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <msub> <mi>z</mi> <mi>u</mi> </msub> <mo>+</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
Wherein,With zuThere may be two non-equivalence zu1And zu2, by (xu,yu,zu1) and (xu,yu,zu2) it is separately converted to longitude and latitude and height above sea level table Reach, then that group of relatively low data of height above sea level will be used as customer location coordinate.
2. the customer location obtained by a kind of indoor orientation method based on GNSS repeaters described in claim 1 carries out precision The method of raising, is comprised the following steps that：
(a) for the building of many floors, the height above sea level of the multiple location points of each layer is accurately measured, and these location points are extra large The average value for degree of lifting as this layer height above sea level；
(b) receive signal to be sampled with lower frequency at the beginning, carried out with local CA codes after associative operation, obtain code phase δcp； Receiver utilizes code phase δcpIt is calculated to the distance of repeater, and further calculates customer location (x0,y0,z0)； By the position coordinates (x0,y0,z0) it is converted into longitude and latitude and height above sea level expressionWhereinλ0,h0It is latitude respectively Degree, longitude and height above sea level；Again by height above sea level h0Compared with each floor height above sea level, determine floor where user, then really Its fixed true height above sea level degree hα；Customer location (x0,y0,z0) height above sea level error be：δh,0=h0-hα；Calculate this difference in height pair The influence of customer location coordinate：
Wherein, a=6378137, b=6356752.31424518,
(c) (x is allowedξ,yξ,zξ)=(x0,y0,z0)-(δx,δy,δz), the true location coordinate of user will be close to (xξ,yξ,zξ)；
(d) obtain new code phase to recalculate repeater to the distance of receiver using the soft method of sampling；The soft method of sampling Refer to the really sampling not carried out to signal, new code phase is also obtained without associative operation, and only assume that signal existsIt is interior by with upper frequency resampling, new code phase would is thatIn any one value, wherein N consider be ratio of the resampling rate to former low sampling rate； Repeater is recalculated to the distance of receiver using each new code phase of acquisition, then calculates a new customer location (xκ,yκ,zκ)；Calculate γk=| | (xξ,yξ,zξ)-(xκ,yκ,zκ) | | andTogether When, receiver is by new position coordinate (xκ,yκ,zκ) it is converted into longitude and latitude and height above sea level expressionAnd calculate height above sea level Difference in height δh,κ=hκ-hα；
(e) for the multiple customer locations obtained using multigroup new code phase, wherein energy minimization δh,κAnd γkAnd ensure simultaneously φκLess than one given threshold phiκ,0Customer location will be used as the final position of user；φκ,0Size will influence user position Put error range, but φκ,0It can not be made too small, otherwise can cause customer location without solution.
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