CN108663697B - A kind of carrier wave correlation intergal improved method for satellite navigation - Google Patents
A kind of carrier wave correlation intergal improved method for satellite navigation Download PDFInfo
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- CN108663697B CN108663697B CN201810790771.3A CN201810790771A CN108663697B CN 108663697 B CN108663697 B CN 108663697B CN 201810790771 A CN201810790771 A CN 201810790771A CN 108663697 B CN108663697 B CN 108663697B
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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
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
- G01S19/29—Acquisition or tracking or demodulation of signals transmitted by the system carrier including Doppler, related
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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
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
- G01S19/30—Acquisition or tracking or demodulation of signals transmitted by the system code related
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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)
- Position Fixing By Use Of Radio Waves (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention discloses a kind of carrier wave correlation intergal improved methods for satellite navigation, comprising the following steps: 1) higher order signal indicates, carrier phase of received signal is carried out Taylor expansion, ranging code phase is not unfolded；2) it is related to reproduction signal progress to receive signal, with reception signal in time interval T after local reproduction signal complex conjugateIInterior correlation；3) carrier wave correlation intergal solves, and the code phase deviation obtained by ranging code correlation intergal loop is adjusted the ranging code phase of local reproduction signal, is directed at the phase of reception signal, reproduction signal ranging code component completely.The present invention not only contains the phase deviation for receiving signal and local reproduction signal in the rotation item phase after correlation intergal, further comprise Doppler frequency shift deviation between the two；In addition, containing influence of the deviation to correlated results of carrier phase all-order derivative in the amplitude of correlation intergal result, in improved model.
Description
Technical field
The invention belongs to technical field of satellite navigation, and in particular to a kind of carrier wave correlation intergal improvement for satellite navigation
Method.
Background technique
Carrier wave only considers phase and its single order amount in satellite navigation signals correlation intergal conventional model.Under normal circumstances,
The a bit of time T of correlation intergalIIt is interior, it is believed that Δ ω is varied less, and this is approximately feasible.But under high dynamic condition or
When person is to satellite navigation emulation signal synthesis accuracy test, then this approximation can bring large error, be unable to satisfy requirement.Document
[1] the ranging code correlation integral function under high dynamic condition is studied, is demonstrated ranging within the correlation intergal period
Code frequency offset as it is constant when will affect the measurement accuracy of pseudorange.
Traditional correlation intergal model analysis
Received satellite-signal passes through the sampled signal s after down coversionr(k) (signal amplitude and text bit are not considered)
It can indicate to determine signal section rr(k) and noise section nrThe sum of (k), i.e.,
sr(k)=rr(k)+nr(k) (3.1)
Determine that signal section is expressed as
rr(k)=c (n0(kTS))exp(iφ0(kTS)) (3.2)
In formula, TSFor system sampling frequency, c () is ranging code data, and exp () is carrier wave plural form, n0(kTS)
And φ0(kTS) indicate relative to integration time period TIThe ranging code phase and carrier phase of k-th interior of sampled point；nr(·)
For the white Gaussian noise of plural form.
Therefore, correlator integrator output is represented by useful signal part and noise section composition
In formula, rlIt (k) is the local signal reappeared inside receiver, TIFor integration period.
It is all traditional correlation intergal model used in most of receivers, i.e. n in formula (3.1)0(k) and φ0(k) it is unfolded
For
In formula, RCOFor the ranging bit rate for receiving signal, n0For the ranging code initial phase for receiving signal, ω0To receive
The carrier phase first derivative of signal, φ0For the carrier wave initial phase for receiving signal.Receipt signal model can in traditional receivers
It is expressed as
rr(k)=c (n0+RCO·kTS)exp(i(φ0+ω0·kTS)) (3.6)
In order to match with receipt signal model, the local signal model that reappears also uses the same model, i.e.,
rl(k)=c (n+RC·kTS)exp(i(φ+ω·kTS)) (3.7)
In formula, RCReappear signal ranging bit rate to be local, n is local reproduction signal ranging code initial phase, and ω is this
Ground reappears signal carrier phase first derivative, and φ is local reproduction signal carrier initial phase.
Therefore, correlator integrator output is represented by
In formula, Δ ω=ω0- ω expression receives signal and locally reappears the deviation of the carrier frequency of signal, and Δ φ=
φ0- φ indicates to receive the deviation of the carrier phase of signal and local reproduction signal.
In formula, Δ τ=n0(kTS)-n(kTS) indicate to receive the deviation of the ranging code phase of signal and local reproduction signal
Value, R () are ranging code auto-correlation function.
By that can be obtained in formula (3.10), only phase and one that the navigation signal model in traditional correlation intergal model provides
The function of order derivative is only related to the two variables in integral result, it is clear that under high dynamic condition, to introduce error.
In some documents and materials, the carrier track model of high state has been established, but observed quantity still uses traditional phase
Close integral model as a result, only reflecting and the approximation relation of phase state amount.
Pseudo-code correlation properties and its Changsha application study [D] under document [1] Li Chunxia high dynamic condition: defence science skill
Art university, 2005.
Summary of the invention
The purpose of the present invention is to provide a kind of carrier wave correlation intergal improved methods for satellite navigation.
The present invention adopts the following technical scheme that realize:
A kind of carrier wave correlation intergal improved method for satellite navigation, comprising the following steps:
1) higher order signal indicates
Carrier phase of received signal is subjected to Taylor expansion, ranging code phase is not unfolded, and obtains receiving the expression of signal high-order
rr(kTS):
In formula, φ0、ω0、AndCorrelation intergal cycle T is corresponded to receive signalIInterior carrier wave initial phase and one
Rank, two, three order derivatives, TSFor system sampling frequency, c () is ranging code data, and exp () is carrier wave plural form, n0
(kTS) it is to receive signal to correspond to correlation intergal cycle TIInterior kTSMoment point ranging code initial phase, εφr(kTS) it is to receive signal
Carrier phase Taylor expansion remainder error；
It is corresponding to obtain local high-order reproduction signal rl(kTS):
In formula, φ, ω,AndCorrelation intergal cycle T is corresponded to for local reproduction signalIInterior carrier wave initial phase and its
Single order, two, three order derivatives, n (kTS) it is that local reproduction signal corresponds to correlation intergal cycle TIInterior kTSMoment point ranging code is initial
Phase, εφ(kTS) it is the local carrier phase Taylor expansion remainder error for reappearing signal；
2) it is related to reproduction signal progress to receive signal
With reception signal in time interval T after local reproduction signal complex conjugateIInterior correlation can obtain
In formula, Δ φ, Δ ω,AndIt indicates to receive signal and reappears the state difference and n of signal initial time0
(kTS) it is respectively local reproduction signal and the correspondence correlation intergal cycle T for receiving signalIInterior kTSMoment point ranging code initial phase
Position；φ0、ω0、AndCorrelation intergal cycle T is corresponded to receive signalIInterior carrier wave initial phase and its single order, two, three ranks
Derivative；
3) carrier wave correlation intergal solves
The code phase deviation obtained by ranging code correlation intergal loop carries out the ranging code phase of local reproduction signal
Adjustment is directed at the phase of reception signal, reproduction signal ranging code component completely, i.e. n0(kTS)=n (kTS), c (n0(kTS))c
(n(kTS))=1, then formula (3.19) is expressed as
In the initial stage, when receiving signal and reappearing the state difference Δ ω ≠ 0 of signal initial time, formula (3.20) are carried out
It calculates, approximation can obtain
As the correlation intergal period constantly carries out, when receiving signal and reproduction signal condition difference Δ ω=0, formula (3.20)
Approximation can obtain
A further improvement of the present invention lies in that the concrete methods of realizing of step 3) is as follows:
301) it is according to the maximum dynamic of emulation signal | ω |≤3.962 × 106rad/s、 Carrier phase two is obtained in formula (3.15) to Fourth-Derivative
Boundary condition TI=1ms:
For small angle theta, plural exp (i θ) carries out Taylor expansion, and is expanded to 2 ranks, 4 ranks respectively:
Boundary condition in formula (3.16) is substituted into formula (3.17) and formula (3.18), the side of Taylor expansion approximate error is obtained
Dividing value: 1.571 × 10–6–i8.018×10–5、3.216×10–10–i2.462×10–8；
302) formula (3.15) is decomposed into
303) the code phase deviation and then by ranging code correlation intergal loop obtained is to the local ranging code for reappearing signal
Phase is adjusted, and is directed at the phase of reception signal, reproduction signal ranging code component completely, i.e. n0(kTS)=n (kTS), c
(n0(kTS))c(n(kTS))=1.
The present invention has following beneficial technical effect:
1, the phase for receiving signal and local reproduction signal is not only contained in the rotation item phase after correlation intergal
Deviation further comprises Doppler frequency shift deviation between the two；
2, the deviation of carrier phase all-order derivative is contained in the amplitude of correlation intergal result, in improved model to correlation
As a result influence.
3, in high dynamic, the phase error of the cumulative model of correlation is by the 2.901 × 10 of conventional model–2It falls to and changes
The 1.057 × 10 of positive model–5(maximum absolute value point in emulated motion interval), precision improves 2700 times (34dB).
Detailed description of the invention
Fig. 1 is the carrier phase deviation map of traditional correlation intergal model.
Fig. 2 is the carrier phase deviation map for improving carrier wave correlation intergal model.
Specific embodiment
The present invention is made further instructions below in conjunction with attached drawing.
For specific careful analysis carrier wave correlation model, the Taylor expansion and noise of ranging code phase are put aside here
Influence, i.e. received signal is expressed as
In formula, φ0、ω0、AndCorrelation intergal cycle T is corresponded to receive signalIInterior carrier wave initial phase and one
Rank, two, three order derivatives, TSFor system sampling frequency, c () is ranging code data, and exp () is carrier wave plural form, n0
(kTS) it is to receive signal to correspond to correlation intergal cycle TIInterior kTSMoment point ranging code initial phase, εφr(kTS) it is to receive signal
Carrier phase Taylor expansion remainder error.
It is corresponding to it, the local signal that reappears also has corresponding form:
In formula, φ, ω,AndCorrelation intergal cycle T is corresponded to for local reproduction signalIInterior carrier wave initial phase and its
Single order, two, three order derivatives, n (kTS) it is that local reproduction signal corresponds to correlation intergal cycle TIInterior kTSMoment point ranging code is initial
Phase, εφ(kTS) it is the local carrier phase Taylor expansion remainder error for reappearing signal.
With reception signal in time interval T after local reproduction signal complex conjugateIInterior correlation can obtain
In formula, Δ φ, Δ ω,AndIt indicates to receive signal and reappears the state difference and n of signal initial time0
(kTS) it is respectively local reproduction signal and the correspondence correlation intergal cycle T for receiving signalIInterior kTSMoment point ranging code initial phase
Position；φ0、ω0、AndCorrelation intergal cycle T is corresponded to receive signalIInterior carrier wave initial phase and its single order, two, three ranks
Derivative.It is according to the maximum dynamic of emulation signal | ω |≤3.962 × 106rad/s、Carrier phase two to quadravalence is led in available formula (3.15)
Several boundary condition (TI=1ms):
For small angle theta, plural exp (i θ) carries out Taylor expansion, and is expanded to 2 ranks, 4 ranks respectively:
Boundary condition in formula (3.16) is substituted into formula (3.17) and formula (3.18), the side of Taylor expansion approximate error is obtained
Dividing value: 1.571 × 10–6–i8.018×10–5、3.216×10–10–i2.462×10–8。
Formula (3.15) is decomposed into
It is aligned completely assuming that receiving ranging code signal in signal and reproduction signal, i.e. n0(kTS)=n (kTS), c (n0
(kTS))c(n(kTS))=1.Then formula (3.19) can be expressed as
As Δ ω ≠ 0, formula (3.20) is calculated, approximation can obtain
As Δ ω=0, formula (3.20) approximation can be obtained
Contrast (3.21) and formula (3.8) are it is found that relative to traditional correlation intergal model, improved carrier wave correlation intergal
Model mainly has two o'clock different:
(1) phase for receiving signal and local reproduction signal is not only contained in the rotation item phase after correlation intergal
Deviation further comprises Doppler frequency shift deviation between the two；
(2) deviation of carrier phase all-order derivative is contained in the amplitude of correlation intergal result, in improved model to phase
Close the influence of result.
Fig. 1 and Fig. 2 is respectively traditional correlation intergal model and improvement phase in different acceleration and acceleration
Close integral model acquired results and true reception, reproduction signal correlation intergal result phase difference.
By Fig. 1 and Fig. 2 as it can be seen that in high dynamic, the phase error of the cumulative model of correlation is by the 2.901 of conventional model
×10–2Fall to the 1.057 × 10 of correction model–5(maximum absolute value point in emulated motion interval), precision improves 2700
Again (34dB).
Key point of the invention and point to be protected:
Carrier wave correlation intergal modular form (3.21) and (3.22) are innovative point, this is result under two conditions.
Advantages of the present invention:
(1) phase for receiving signal and local reproduction signal is not only contained in the rotation item phase after correlation intergal
Deviation further comprises Doppler frequency shift deviation between the two；
(2) deviation of carrier phase all-order derivative is contained in the amplitude of correlation intergal result, in improved model to phase
Close the influence of result.
(3) in high dynamic, the phase error of the cumulative model of correlation is by the 2.901 × 10 of conventional model–2It falls to
The 1.057 × 10 of correction model–5(maximum absolute value point in emulated motion interval), precision improves 2700 times (34dB).
Claims (1)
1. a kind of carrier wave correlation intergal improved method for satellite navigation, which comprises the following steps:
1) higher order signal indicates
Carrier phase of received signal is subjected to Taylor expansion, ranging code phase is not unfolded, and obtains receiving signal high-order expression rr
(kTS):
In formula, φ0、ω0、AndCorrelation intergal cycle T is corresponded to receive signalIInterior carrier wave initial phase and its single order,
Two, three order derivative, TSFor system sampling frequency, c () is ranging code data, and exp () is carrier wave plural form, n0(kTS) be
It receives signal and corresponds to correlation intergal cycle TIInterior kTSMoment point ranging code initial phase, εφr(kTS) it is the carrier wave for receiving signal
Phase Taylor expansion remainder error；
It is corresponding to obtain local high-order reproduction signal rl(kTS):
In formula, φ, ω,AndCorrelation intergal cycle T is corresponded to for local reproduction signalIInterior carrier wave initial phase and its single order,
Two, three order derivative, n (kTS) it is that local reproduction signal corresponds to correlation intergal cycle TIInterior kTSMoment point ranging code initial phase,
εφ(kTS) it is the local carrier phase Taylor expansion remainder error for reappearing signal；
2) it is related to reproduction signal progress to receive signal
With reception signal in time interval T after local reproduction signal complex conjugateIInterior correlation can obtain
In formula, Δ φ, Δ ω,AndIt indicates to receive signal and reappears the state difference and n of signal initial time0(kTS) point
The correspondence correlation intergal cycle T that local Wei not reappear signal and receive signalIInterior kTSMoment point ranging code initial phase；φ0、
ω0、AndCorrelation intergal cycle T is corresponded to receive signalIInterior carrier wave initial phase and its single order, two, three order derivatives；
3) carrier wave correlation intergal solves
The code phase deviation obtained by ranging code correlation intergal loop is adjusted the ranging code phase of local reproduction signal,
It is directed at the phase of reception signal, reproduction signal ranging code component completely, i.e. n0(kTS)=n (kTS), c (n0(kTS))c(n
(kTS))=1, then formula (3.19) is expressed as
In the initial stage, when receiving signal and reappearing the state difference Δ ω ≠ 0 of signal initial time, formula (3.20) is counted
It calculates, approximation can obtain
As the correlation intergal period constantly carries out, when receiving signal and reproduction signal condition difference Δ ω=0, formula (3.20) is approximate
It can obtain
The concrete methods of realizing of step 3) is as follows:
301) it is according to the maximum dynamic of emulation signal | ω |≤3.962 × 106rad/s、 Carrier phase two is obtained in formula (3.15) to the boundary condition T of Fourth-DerivativeI=1ms:
For small angle theta, plural exp (i θ) carries out Taylor expansion, and is expanded to 2 ranks, 4 ranks respectively:
Boundary condition in formula (3.16) is substituted into formula (3.17) and formula (3.18), Taylor's exhibition is obtained
Open the boundary value of approximate error: 1.571 × 10–6–i8.018×10–5、3.216×10–10–i2.462×10–8；
302) formula (3.15) is decomposed into
303) the code phase deviation and then by ranging code correlation intergal loop obtained is to the local ranging code phase for reappearing signal
It is adjusted, is directed at the phase of reception signal, reproduction signal ranging code component completely, i.e. n0(kTS)=n (kTS), c (n0
(kTS))c(n(kTS))=1.
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