CN103235321A - GPS (global positioning system) pseudo-range positioning precision timing method - Google Patents

Abstract

The invention discloses a GPS (global positioning system) pseudo-range positioning precision timing method. A pseudo-range is smoothed by carrier phase on the basis of pseudo-range single-point positioning timing, and is then subjected to single-point positioning. The timing precision is higher than that of the pseudo-range not smoothed. The method includes: firstly, performing pseudo-range single-point positioning by means of least squares so as to calculate a clock correction, and subjecting the clock correction and a precision clock correction issued by IGS (international GPS service) to differential comparison; secondly, smoothing the pseudo-range by a carrier phase value of an observed value, and subjecting the smoothed pseudo-range to single-point positioning again to solve the clock correction, and comparing the clock correction with the precision clock correction; and thirdly, comparing the smoothed clock correction with the unsmoothed clock correction to obtain the fact that the precision is higher after smoothing.

Description

Pseudorange location, the single station of GPS accurate time transmission method

Technical field

The present invention relates to wireless orientation method, particularly the single station of GPS pseudorange location time service method.

Background technology

The high precision time service is most important to the operation of systems such as military affairs, communication, electric power, traffic, and national defence and economic construction aspect are also had widespread usage.Along with the high speed development of modernized society, every profession and trade also improves day by day to the requirement of time service precision.Because the gps system development is comparatively improved and time service precision is higher, the research of GPS time service is increasingly important.

GPS adopts the pseudorange locating accuracy not high, and when adopting the carrier wave location, determining of integer ambiguity is a great problem.

GPS sets up by the one way range measurement principle, and namely the user only needs to receive by receiving equipment the signal of satellite emission, and single way time delay or the phase delay of measured signal propagation, and then the distance between determining from the observation point to the gps satellite.So-called location is exactly at the signal of observation point by some satellites of reception, sets up the range equation of respective numbers, and simultaneous solves the terrestrial coordinates of observation point (user) position correspondence.GPS will measure satellite to the distance of observation point exactly by the time measuring distance, just must make satellite clock and receiver user clock (being called for short user's clock) keep synchronously strict.But this normally is difficult to accomplish, because the normally crystal clock that receiver user is equipped with.Owing to have synchronism deviation between satellite clock and the user's clock, therefore the distance of measuring no longer is actual geometric distance, is referred to as pseudorange here.Just can finish location to the user by the Pseudo-range Equation of setting up right quantity, this location is that the precise time transmission of benchmark realizes when being based on GPS.

Summary of the invention

Goal of the invention: on the basis of pseudorange single-point location time service, propose pseudorange location, the single station of the higher GPS of a kind of precision accurate time transmission method.

Technical scheme:

Pseudorange location, GPS list station accurate time transmission method on the basis of pseudorange single-point location time service, uses carrier phase that pseudorange is carried out smoothly, and the pseudorange after utilization is level and smooth carries out the single-point location again; May further comprise the steps:

Step 1) is gathered the USNO station data, comprises observation file O file, navigate file N file, SP3 file, clk file, carries out pseudorange single-point location by least square method, finds the solution clock correction;

Step 2), use the carrier phase observed quantity that obtains from navigation neceiver that pseudorange is carried out smoothly;

Step 3) is carried out the single-point location again with the pseudorange after level and smooth, finds the solution clock correction;

Step 4) according to step 1) and step 3) gained clock correction, is made comparisons with the accurate clock correction of IGS issue, carries out clock correction error, time service precision analysis.

Wherein, described step 2) with the carrier phase observed quantity pseudorange is carried out carrying out smoothly from pseudorange observed reading P1 and the P2 sign indicating number that navigation neceiver is obtained simultaneously when level and smooth:

$\stackrel{\‾}{p^j\left(t_i\right)}=\frac{1}{i}{p}^j\left(t_i\right)+\frac{i-1}{i}[\stackrel{\‾}{(p^j{(t}_{i-1})}+\mathrm{\δ}{p}^j(t_{i-1},t_i)]$

In the formula, i represents i observation constantly, and the span of i is 1～2880 natural number;

Represent i the phase place smooth value of pseudorange constantly; p ^j(t _i) i pseudorange observed reading constantly of expression;

Represent i-1 the pseudorange value after smoothly constantly; δ p ^j(t _I-1, t _i) expression δ p ^j(t _I-1, t _i) phase difference measurement value between expression (i-1) individual moment and i the moment;

Represent i phase value constantly;

Represent i-1 phase value constantly; λ represents the wavelength value of carrier wave.

Wherein, clock correction error analysis mode is made difference relatively for the accurate clock correction average that the actual clock correction average that will try to achieve and IGS provide in the described step 4); Described time service precision analysis mode is evaluated for meeting RMS and meet RMS outward in adopting.

Beneficial effect: carry out the clock correction value that pseudorange single-point location Calculation goes out again after the clock correction value that pseudorange single-point location Calculation goes out and carrier phase are level and smooth, make difference with the accurate clock correction of IGS (International GNSS Service: international GPS serves tissue) announcement respectively and obtain error amount, and compare the error amount of the level and smooth front and back of carrier phase.Wherein, the clock correction that single-point location solves is spaced apart 30s, and the accurate clock correction that IGS announces is spaced apart 5min, so both do that difference obtains is the difference of every 5min.By finding that relatively smoothly the error after is littler, namely time service precision is higher.

(United States Naval Observatory: USNO-US Naval Observatory) receiver of website is atomic clock to this method owing to the USNO that adopts, clock correction is highly stable, average with clock correction is worth as reference, meet RMS (Root Mean Square: root-mean-square valve, the i.e. square root of the mean value of one group of statistics quadratic sum) in the relatively poor acquisition between the actual clock correction of finding the solution and the average; The relatively poor acquisition of atomic clock clock correction that the actual clock correction of finding the solution and IGS announce meets RMS outward.

Description of drawings

Fig. 1 is the inventive method process flow diagram;

Fig. 2 is the accurate clock correction data that the USNO website that adopts in the embodiment of the invention is announced by IGS;

Fig. 3 is the clock correction error that find the solution pseudorange single-point location in the embodiment of the invention;

Fig. 4 is the clock correction error that find the solution the single-point location behind the carrier phase smoothing pseudo range in the embodiment of the invention;

Fig. 5 is the clock correction error comparison diagram of the level and smooth front and back of phase place.

Embodiment:

Below in conjunction with accompanying drawing the present invention is done further explanation.

The inventive method is based on the method for the single station of GPS pseudorange location time service, utilizes carrier phase that the pseudorange observed reading is optimized, thereby improves bearing accuracy, makes accurate time transmission more accurate.

For the method for pseudorange location, single station being analyzed and being verified that present embodiment has adopted the observation data in USNO website one day on the 9th April in 2012, data are gathered from IGS station net, comprise observation file O file, navigate file N file, SP3 file, clk file.What USNO station receiver was used is atomic clock, and receiver clock correction is highly stable, and the time service standard of website is provided by precise ephemeris clk file.

As shown in Figure 2, the accurate clock correction data of the USNO that IGS provides, sampling rate is 5min, has 288 epoch, the clock correction mean value of trying to achieve these 288 epoch is 6.241687 * 10 ^-7S.

Concrete grammar comprises the steps:

Step 1) is carried out pseudorange single-point location by least square method, finds the solution clock correction.

At first carry out time service with pseudorange single-point location, utilize broadcast ephemeris to calculate co-ordinates of satellite, list observation equation:

${\mathrm{\ρ}}^{\′}=\sqrt{{[X^j\left(t^j\right)-X_k\left(t_k\right)]}^2+{[Y^j\left(t^j\right)-Y_k\left(t_k\right)]}^2+{[Z^j\left(t^j\right)-Z_k\left(t_k\right)]}^2}+{\mathrm{c\δt}}_k-{\mathrm{c\δt}}^j$

In the formula, ρ ' is pseudo range observed quantity; [X ^j(t ^j), Y ^j(t ^j), Z ^j(t ^j)] be that broadcast ephemeris calculates t ^jThe position of moment satellite; [X _k(t _k), Y _k(t _k), Z _k(t _k)] be the position of receiver; δ t _kBe receiver clock correction; δ t ^jBe satellite clock correction; C represents the light velocity.

According to the approximate coordinates of point to be located, following formula is carried out linearization, note:

$l_p^i=-\frac{X^i-{\mathrm{<figure-callout\; id="0"\; label="X\; p"\; filenames="HDA00002987468400021.png,HDA00002987468400022.png"\; state="\{\{state\}\}">X</figure-callout>}}_p^{}}{{\mathrm{\&rho;}}_{p,0}^i},$ $m_p^i=-\frac{Y^i-{\mathrm{<figure-callout\; id="0"\; label="Y\; p"\; filenames="HDA00002987468400021.png,HDA00002987468400022.png"\; state="\{\{state\}\}">Y</figure-callout>}}_p^{}}{{\mathrm{\&rho;}}_{p,0}^i},$ $n_p^i=-\frac{Z^i-{\mathrm{<figure-callout\; id="0"\; label="Z\; p"\; filenames="HDA00002987468400021.png,HDA00002987468400022.png"\; state="\{\{state\}\}">Z</figure-callout>}}_p^{}}{{\mathrm{\&rho;}}_{p,0}^i}$

Linearization gets the result:

$l_p^i\mathrm{\&delta;}{X}_p+m_p^i\mathrm{\&delta;}{Y}_p+n_p^i\mathrm{\&delta;}{Z}_p-\mathrm{c\&delta;}{t}_p-R_{p,0}^i+({\mathrm{\&rho;}}_p^i+{\mathrm{c\&delta;t}}^i-{\mathrm{\&delta;\&rho;}}_{\mathrm{trop}}^i-{\mathrm{\&delta;\&rho;}}_{\mathrm{ion}}^i-{\mathrm{\&delta;\&rho;}}_{\mathrm{others}}^i)=0$

In the formula,

Be ionosphere delay error (m); Be tropospheric delay error (m);

Be other errors, as earth rotation, morning and evening tides, relativity influence etc.; [δ X _p, δ Y _p, δ Z _p] represent the x of the receiver location of pseudorange single-point positioning calculation, y, the error of z direction respectively; δ t _pBe receiver clock correction, i.e. the clock correction value of this patent calculating; Expression station star distance, i.e. distance between survey station and the satellite, $R_{p,0}^i=\sqrt{{(X^j-x0)}^2+{(Y^j-y0)}^2+{(Z^j-z0)}^2},$ (X wherein ^j, Y ^j, Z ^j) represent the satellite position coordinate that broadcast ephemeris calculates, (x0, y0 z0) represent ground survey station coordinate.

Being write as matrix form is:

When the satellite number of observation simultaneously equals 4, unique solution δ is arranged _x=A ^-1L, i.e. [δ X _p, δ Y _p, δ Z _p, δ t _p].When observation satellite number during greater than 4, adopt least square method to find the solution, i.e. δ _x=(A ^TA) ^-1A ^TL.

Utilize the broadcast ephemeris file to calculate unknown quantitys such as co-ordinates of satellite and speed, by pseudorange single-point location, the clock correction result who solves should consider the influence of ionosphere, tropospheric delay, earth rotation and relativistic effect.

Wherein ionospheric error adopts the combination of no ionosphere to correct, shown in the following formula:

$p=\frac{{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002987468400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^2{p}_1-{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002987468400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_2^2{p}_2}{{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002987468400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^2-{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002987468400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_2^2}$

In the formula, f ₁And f ₂Be respectively the frequency of P1 sign indicating number and P2 sign indicating number; p ₁And p ₂Be respectively the observation data of P1 sign indicating number P2 sign indicating number.The tropospheric delay error adopts the Hopfield neural network model, and formula is as follows:

Δ ^trop(E)＝Δd ^trop(E)+Δw ^trpp(E)

$\mathrm{\&Delta;}{d}^{\mathrm{trop}}\left(E\right)=\frac{{10}^{-6}}{5}\frac{77.64}{\mathrm{<figure-callout\; id="2"\; label="sin\; E"\; filenames="HDA00002987468400022.png"\; state="\{\{state\}\}">sin</figure-callout>}\sqrt{E^{}}\sqrt{{}^2+6.25}}\frac{p}{T}[40136+148.72(T-273.16)]$

$\mathrm{\&Delta;}{w}^{\mathrm{trop}}\left(E\right)=\frac{{10}^{-6}}{5}\frac{(-12.96T+3.718\&times;{10}^5)}{\sin \sqrt{{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="HDA00002987468400022.png"\; state="\{\{state\}\}">E</figure-callout>}}^2+6.25}}\frac{e}{{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00002987468400022.png"\; state="\{\{state\}\}">T</figure-callout>}}^2}11000$

In the formula, Δ ^Trop(E) be tropospheric delay (m); Δ d ^Trop(E) for doing component delay (m); Δ w ^Trop(E) be wet component delay (m), the correction residual error of wet component only is several centimetres; E be the satellite altitude angle (°); P is air pressure (mbar); T is temperature (kelvin degree); E is the partial pressure (mbar) of water vapor.

Following formula is seen in the correction of earth rotation:

$\left(\begin{array}{c}{X}^{S^{\&prime;}}\\ Y^{S^{\&prime;}}\\ Z^{s^{\&prime;}}\end{array}\right)=\left[\begin{array}{ccc}\cos \mathrm{\&alpha;}& \sin \mathrm{\&alpha;}& 0\\ -\sin \mathrm{\&alpha;}& \cos \mathrm{\&alpha;}& 0\\ 0& 0& 1\end{array}\right]\left(\begin{array}{c}{X}^s\\ Y^s\\ Z^s\end{array}\right)$

In the formula, (X ^s, Y ^s, Z ^s) be co-ordinates of satellite; (X ^s', Y ^s', Z ^s') be the horizontal coordinate after correcting, i.e. NEU (survey station location space rectangular coordinate system) direction coordinate; The angle that α=ω τ, α turn over when propagating for earth signal, ω is rotational-angular velocity of the earth, τ is the satellite-signal travel-time.

The influence of relativistic effect is calculated according to satellite position and velocity, and formula is as follows:

$\mathrm{\&Delta;rela}=-\frac{2}{C}{X}^s\&CenterDot;\stackrel{\&CenterDot;}{X^s}$

In the formula, X ^sBe the satellite position vector;

Be satellite velocity vector.

USNO website accurate clock correction data on the same day that IGS provides as shown in Figure 2, sampling rate is 5min, has 288 epoch, the mean value of trying to achieve clock correction is 6.241687 * 10 ^-7S.

The clock correction mean value of 2880 epoch that pseudorange single-point location solves is 6.268539 * 10 ^-7S, the mean value of the accurate clock correction of the USNO that provides with IGS differs 2.68518ns.

Ask and the accurate clock correction that provides with IGS after the clock correction is provided is compared, wherein the sampling rate of pseudorange single-point is 30s, and precise ephemeris is 5min, so clock correction contrast sampling rate is 5min.The clock correction error of pseudorange single-point location as shown in Figure 3, the mean value of these errors is 3.19ns, substantially in the ns level.

Step 2), use the carrier phase observed quantity that obtains from navigation neceiver that pseudorange is carried out smoothly.

This method is carried out smoothly pseudorange observed reading P1 and the P2 sign indicating number that obtains from navigation neceiver simultaneously.

$\stackrel{\&OverBar;}{p^j\left(t_i\right)}=\frac{1}{i}{p}^j\left(t_i\right)+\frac{i-1}{i}[\stackrel{\&OverBar;}{{(p}^j{(t}_{i-1})}+\mathrm{\&delta;}{p}^j(t_{i-1},t_i)]$

In the formula, i represents i observation constantly, and the span of i is 1～2880 natural number; Represent i the phase place smooth value of pseudorange constantly; p ^j(t _i) i pseudorange observed reading constantly of expression;

Represent i-1 the pseudorange value after smoothly constantly; δ p ^j(t _I-1, t _i) expression δ p ^j(t _I-1, t _i) phase difference measurement value between expression (i-1) individual moment and i the moment;

Represent i phase value constantly;

Represent i-1 phase value constantly; λ represents the wavelength value of carrier wave, and wherein the L1 carrier wavelength is 0.190293672m, and the L2 carrier wavelength is 0.244210213m.

Step 3) is carried out the single-point location again with the pseudorange after level and smooth, finds the solution with least square again, and the clock correction value average that solves is 6.251205 * 10 ^-7S, the average of the accurate clock correction of the USNO that provides with IGS differs 0.95168ns.

The clock correction error of carrier phase smoothing pseudo range as shown in Figure 4, the mean value of these errors is 2.61ns.

As shown in Figure 5, by the error of pseudorange single-point location behind contrast pseudorange single-point location and the carrier phase smoothing pseudo range, find that the level and smooth precision of phase place is than the height of pseudorange single-point.

Pseudorange single-point location and phase place smoothly after again in the pseudorange single-point analysis of Positioning Error, not only to consider the clock correction precision of algorithm, also need to evaluate the stability of clock.In the interpretation of result of embodiment, owing to only evaluate the time service in time field and the precision of clock correction, meet RMS and meet RMS outward in considering to adopt and evaluate.Because the receiver of the USNO website that adopts is atomic clock, clock correction is highly stable, can be with the average of clock correction as with reference to value, in meet RMS just can be by the relatively poor acquisition between the actual clock correction of finding the solution and the average; Meet the relatively poor acquisition of atomic clock clock correction that RMS is announced by the actual clock correction of finding the solution and IGS outward.

$\mathrm{RMS}=\sqrt{\frac{{\mathrm{\&Delta;}}^T\mathrm{P\&Delta;}}{n}}$

In the formula, Δ is relatively poor, and n is clock correction sequence samples sum, and P is the power battle array.

The calculating that meets RMS outward is poor by the accurate clock correction of the actual clock correction of finding the solution and IGS announcement earlier, obtains one group of data, calculates the square root of the mean value of these data quadratic sums then, i.e. the outer RMS value that meets; In meet RMS calculating be earlier poor by the actual clock correction of finding the solution and their mean value, obtain one group of data, calculate the square root of the mean value of these data quadratic sums then, meet the RMS value in namely.

Ratio of precision between the two is more as shown in table 1.

Table 1. precision index

By the calculating to two kinds of method for solving, the outer RMS of meeting of pseudorange single-point is 9.27ns, in to meet RMS be 10.22ns.Be 7.32ns through the carrier phase level and smooth outer RMS of meeting, in to meet RMS be 7.64ns.

By relatively, the pseudorange single-point location after carrier phase is level and smooth is outer meet RMS with in meet RMS to compare pseudorange single-point locating accuracy higher, better effects if.

Step 2) and the clock correction error of step 3), the time service precision analysis can computational analysis together after step 3) is finished wherein.

The above only is preferred implementation of the present invention; should be pointed out that for those skilled in the art, under the prerequisite that does not break away from the principle of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (3)

1.GPS pseudorange location, list station accurate time transmission method is characterized in that: on the basis of pseudorange single-point location time service, use carrier phase that pseudorange is carried out smoothly, the pseudorange after utilization is level and smooth carries out the single-point location again; May further comprise the steps:

Step 1) is gathered the USNO station data, comprises observation file O file, navigate file N file, precise ephemeris SP3 file, clock correction file clk file, carries out pseudorange single-point location by least square method, finds the solution clock correction;

Step 2), use the carrier phase observed quantity that obtains from navigation neceiver that pseudorange is carried out smoothly;

Step 3) is carried out the single-point location again with the pseudorange after level and smooth, finds the solution clock correction;

Step 4) according to step 1) and step 3) gained clock correction, is made comparisons with the accurate clock correction of IGS issue, carries out clock correction error, time service precision analysis.

2. the single station of GPS according to claim 1 pseudorange location accurate time transmission method is characterized in that: described step 2) with the carrier phase observed quantity pseudorange is carried out simultaneously pseudorange observed reading P1 and P2 sign indicating number from the navigation neceiver acquisition being carried out smoothly when level and smooth:

$\stackrel{\&OverBar;}{p^j\left(t_i\right)}=\frac{1}{i}{p}^j\left(t_i\right)+\frac{i-1}{i}[\stackrel{\&OverBar;}{(p^j\left(t_{i-1}\right)}+\mathrm{\&delta;}{p}^j(t_{i-1},t_i)]$

In the formula, i represents i observation constantly, and the span of i is 1～2880 natural number; Represent i the phase place smooth value of pseudorange constantly; p ^j(t _i) i pseudorange observed reading constantly of expression;

Represent i-1 the pseudorange value after smoothly constantly; δ p ^j(t _I-1, t _i) phase difference measurement value between expression (i-1) individual moment and i the moment;

Represent i phase value constantly;

Represent i-1 phase value constantly; λ represents the wavelength value of carrier wave.

3. the single station of GPS according to claim 1 pseudorange location accurate time transmission method is characterized in that: the accurate clock correction average that clock correction error analysis mode provides for the actual clock correction average that will try to achieve and IGS in the described step 4) is made difference and is compared; Described time service precision analysis mode is evaluated for meeting RMS and meet RMS outward in adopting.

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