CN103792558A - GNSS carrier phase smoothness pseudo-range processing method - Google Patents

Abstract

The invention belongs to the technical field of a GNSS, and discloses a GNSS carrier phase smoothness pseudo-range processing method. By means of calculating of a smoothing constant, a carrier phase of a current epoch, a coarse code pseudo-range and a carrier phase of the next epoch and a next epoch extrapolation pseudo-range obtained through a carrier phase smoothing pseudo-range initial value, a carrier phase smoothing pseudo-range value of the next epoch is calculated. The preceding processes are repeated, a carrier phase smoothing pseudo-range value of the GNSS is obtained in real time. Carrier phase smoothing pseudo-range precision is improved, and accordingly positioning precision of the GNSS is greatly improved.

Description

A kind of GNSS smoothing the phase of carrier wave pseudorange disposal route

Technical field

The present invention relates to GPS (Global Position System) (GNSS) technical field, relate in particular to a kind of GNSS smoothing the phase of carrier wave pseudorange disposal route.

Background technology

GPS (Global Position System) GNSS positioning principle is: adopt receiver observe the distance observed quantity to receiver of the satellite that obtains, according to known satellite position, adopt the position of geometry intersections calculating receivers.The distance observed quantity that GNSS openly provides for civilian users is thick code pseudorange.

The thick code pseudorange error of GNSS is larger, and the thick code pseudo range measurement error of GNSS receiver output can reach 1m～3m left and right in the time comprising multipath.By contrast, GNSS carrier phase stochastic error is only grade, even if comprised multipath effect, random meausrement error is also less than 1cm.In the time there is no cycle slip, in theory between carrier phase epoch poor (being converted to range difference) and thick code pseudorange is poor should equate.Therefore, can, with the smoothing the phase of carrier wave pseudorange of many epoch, reach the slightly object of code pseudorange error of compression, be called smoothing the phase of carrier wave pseudorange.Smoothing the phase of carrier wave pseudorange is to reduce thick code pseudorange error, improves positioning precision, particularly improves the classical means of difference positioning precision, is widely used in the processing of difference locator data.

Smoothing the phase of carrier wave pseudorange principle is as follows:

The observation equation of GNSS thick code pseudorange and carrier phase can be expressed as:

$\left.\begin{array}{c}P\left(k\right)=R\left(k\right)+I\left(k\right)+C\left(k\right)+{\mathrm{\ϵ}}_P\left(k\right)\\ L\left(k\right)=R\left(k\right)-I\left(k\right)+C\left(k\right)+\mathrm{\λN}+{\mathrm{\ϵ}}_{\mathrm{\φ}}\left(k\right)\end{array}\right\}---\left(1\right)$

Wherein, P represents to observe pseudorange; L represents to be converted to the carrier phase of distance, also claims carrier phase pseudorange; K represents epoch of observation; R represents true geometric distance; I represents ionosphere delay; N represents carrier phase complete cycle number; λ represents carrier wavelength; ε _prepresent the thick code pseudo range measurement error including multipath; ε _lrepresent the carrier phase pseudorange device measuring error including multipath; C represents common error item, comprises ephemeris error, star clock error, tropospheric delay and receiver clock correction.

If, without cycle slip, slightly code pseudorange and carrier phase pseudorange ask respectively difference to be between epoch between adjacent epoch

$\left.\begin{array}{c}P\left(k\right)-P(k-1)=R\left(k\right)-R(k-1)+I\left(k\right)-I(k-1)+{\mathrm{\ϵ}}_P\left(k\right)-{\mathrm{\ϵ}}_P(k-1)\\ L\left(k\right)-L(k-1)=R\left(k\right)-R(k-1)-I\left(k\right)+I(k-1)+{\mathrm{\ϵ}}_{\mathrm{\φ}}\left(k\right)-{\mathrm{\ϵ}}_{\mathrm{\φ}}(k-1)\end{array}\right\}---\left(2\right)$

The time-varying characteristics of ionosphere delay are very slow, therefore can ignore ionosphere delay between epoch and change, and think:

I(k)≈I(k-1) (3)

Can obtain:

$\left.\begin{array}{c}R\left(k\right)-R(k-1)=R\left(k\right)-R(k-1)+{\mathrm{\ϵ}}_{\mathrm{\ρ}}\left(k\right)-{\mathrm{\ϵ}}_P(k-1)\\ L\left(k\right)-L(k-1)=R\left(k\right)-R(k-1)+{\mathrm{\ϵ}}_{\mathrm{\φ}}\left(k\right)-{\mathrm{\ϵ}}_{\mathrm{\φ}}(k-1)\end{array}\right\}---\left(4\right)$

In theory, between carrier phase epoch difference should with poor equating between thick code pseudorange epoch, that is:

R(k)-R(k-1)≈L(k)-L(k-1) (5)

Therefore, can rebuild thick code pseudorange by difference between carrier phase epoch according to formula (4),

$\hat{P}(k-1)=P\left(k\right)-[L\left(k\right)-L(k-1)]---\left(6\right)$

Due to ε _φ< < ε _p, the thick code pseudorange error after reconstruction will be greatly reduced.

Suppose that the carrier phase observed quantity starting epoch from k=0 continues there is no cycle slip, and order

can adopt continuously the observed quantity of follow-up n epoch to rebuild the k=0 thick code pseudorange of epoch according to formula (6),

$\left.\begin{array}{c}{\hat{P}}_0\left(1\right)=P\left(1\right)-[L\left(1\right)-L\left(0\right)]\\ {\hat{P}}_0\left(2\right)=P\left(2\right)-[L\left(2\right)-L\left(0\right)]\\ ...\\ {\hat{P}}_0\left(n\right)=P\left(n\right)-[L\left(n\right)-L\left(0\right)]\end{array}\right\}---\left(7\right)$

Add and ask all various in formula (7), can obtain the k=0 pseudorange smoothing value of epoch:

$P_{\mathrm{sm}}\left(0\right)=\frac{1}{n}\underset{k=1}{\overset{k=n}{\mathrm{\&Sigma;}}}{\hat{P}}_0\left(k\right)=\frac{1}{n}\underset{k=1}{\overset{k=n}{\mathrm{\&Sigma;}}}\{P\left(k\right)-[L\left(k\right)-L\left(0\right)\left]\right\}---\left(8\right)$

In formula, subscript sm represents smooth value.

Further, by P _sm(0) value replaces in formula (7) various

the smooth value that can rebuild each epoch of code pseudorange is as follows:

$P_{\mathrm{sm}}\left(k\right)=\stackrel{-}{P}\left(0\right)+[L\left(k\right)-L\left(0\right)]---\left(9\right)$

Formula (8) and formula (9) are exactly smoothing the phase of carrier wave pseudorange basic model, also referred to as phase differential averaging model.Obviously, phase differential averaging model is not easy to data processing, the recurrence model that adopt based on Hatch filtering in practicality more, and model is as follows:

$\left.\begin{array}{c}{P}_{\mathrm{ex}}\left(k\right)=P_{\mathrm{sm}}(k-1)+[L\left(k\right)-L(k-1)]\\ P_{\mathrm{sm}}\left(k\right)=w\left(k\right)\&times;P\left(k\right)+[1-w\left(k\right)]\&times;P_{\mathrm{ex}}\left(k\right)\\ w\left(k\right)=1/k,k<M\\ w\left(k\right)=1/M,k\&GreaterEqual;M\\ P_{\mathrm{sm}}\left(0\right)=P\left(0\right)\end{array}\right\}---\left(10\right)$

Wherein, P _exrepresent extrapolation pseudorange; W (k) represents the pseudorange weight of k epoch; M is smoothing constant.

Formula (10) is GNSS smoothing the phase of carrier wave recursion formula, and the smoothing pseudo range of each epoch is the weighted sum of observation pseudorange and extrapolation pseudorange, and weight w (k) is inverse epoch, and the minimum value of weights is subject to smoothing constant M restriction simultaneously.Set the reason of restrictive smoothing constant M, be smoothing the phase of carrier wave pseudorange can introduce with epoch k increase ionosphere disperse error.If weight is not limited, ionosphere is dispersed error and finally can be exceeded the compression effectiveness of carrier wave to pseudorange error.

Visible, smoothing constant M is the important parameter that affects smoothing the phase of carrier wave pseudorange precision.If M value is too little, can affect the level and smooth compression effectiveness to pseudorange error; If M value is too large, can introduces insufferable ionosphere and disperse error.At present, smoothing constant M solves by two kinds of approach: the one, artificially specify according to user experience, with very large randomness; The 2nd, pressure is made as M the equivalence value of 100s, is made as the ratio in 100s and data sampling cycle by M.Set all objective means of right and wrong of approach of M for these two kinds, so the smoothing the phase of carrier wave pseudorange that traditional smoothing the phase of carrier wave disposal route obtains exists larger error.

Summary of the invention

The technical problem to be solved in the present invention is: a kind of GNSS smoothing the phase of carrier wave pseudorange disposal route is provided.The method makes to adopt smoothing the phase of carrier wave pseudorange to realize more accurate positioning.

For solving the problems of the technologies described above: the present invention proposes a kind of GNSS smoothing the phase of carrier wave pseudorange disposal route, comprise the steps:

Step 1, GNSS receiver be output thick code pseudorange and carrier phase in real time;

The thick code pseudorange of step 2, current epoch of being exported by GNSS receiver, obtains smoothing the phase of carrier wave pseudorange initial value, and be first thick code pseudorange of receiver output described current epoch;

Step 3, obtain according to step 1 current epoch thick code pseudorange and next epoch carrier phase, the smoothing the phase of carrier wave pseudorange initial value with step 2 obtains, obtains the extrapolation pseudorange P of next epoch _ex(k);

Step 4, obtain the smoothing the phase of carrier wave pseudorange value P of next epoch _sm(k)

P _sm(k)＝w(k)×P(k)+[1-w(k)]×P _ex(k)

Wherein, w (k) is the pseudorange weight of front epoch of k, if smoothing constant M value is greater than k epoch, pseudorange weight is got w (k)=1/k, if smoothing constant M value is not more than k epoch, pseudorange weight is got w (k)=1/M;

$M=\mathrm{INT}\left[\frac{1}{2}\sqrt[3]{\frac{{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2}{2T_m^2{I}_d^2}}\right]$

Wherein, M is smoothing constant,

for the slightly variance of the device measuring error of code pseudorange of GNSS, T _mfor data sampling cycle, I _dfor the divergence variations rate of ionosphere delay;

The thick code pseudorange of the current epoch that P (k) is step 1 acquisition, P _ex(k) be the pseudorange of extrapolating for the rapid three current epoch of obtaining;

Step 5, obtain according to step 1 next epoch thick code pseudorange and next epoch carrier phase, with the smoothing the phase of carrier wave pseudorange value that step 4 obtains, obtain the extrapolation pseudorange of lower next epoch;

Step 6, repeating step four and step 5, Real-time Obtaining GNSS smoothing the phase of carrier wave pseudorange value.

The present invention has following beneficial effect:

The object of smoothing the phase of carrier wave pseudorange is to reduce thick code pseudorange error, improves GNSS positioning precision.In smoothing the phase of carrier wave pseudorange disposal route, smoothing constant is the important parameter that affects smoothing the phase of carrier wave pseudorange precision, should and guide smoothing processing according to certain criterion calculated value.The present invention is by analyzing smoothing the phase of carrier wave pseudorange error main composition factor, obtain the mathematical relation between smoothing constant and the variance of measuring equipment error by objective method, adopt Lagrangian extremum method, obtain the disposal route of smoothing constant, this disposal route data strong adaptability, avoid due to the not good even level and smooth problem losing efficacy of the smooth effect of forcing or experience value causes, greatly reduce thick code pseudorange error, suppress ionosphere and dispersed error, improve smoothing the phase of carrier wave pseudorange precision, and then greatly improve GNSS positioning precision, be with a wide range of applications in satellite navigation positioning field.

Accompanying drawing explanation

Fig. 1 is the equivalent low-pass filter schematic diagram of smoothing the phase of carrier wave pseudorange in the present invention.

Fig. 2 adopts the change curve of the smoothing constant that calculates of the inventive method with the device measuring error of the thick code of GNSS pseudorange.

Fig. 3 adopts the smoothing pseudo range of smoothing constant that computing method of the present invention calculate and the difference of raw pseudo range with smoothingtime change curve.

Fig. 4 adopts to be equivalent to the smoothing pseudo range of smoothing constant of 100s smoothingtime and the difference of raw pseudo range with smoothingtime change curve.

Fig. 5 adopts difference between smoothing pseudo range and the raw pseudo range of smoothing constant 710 with smoothingtime change curve

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail; be necessary to be pointed out that at this; following embodiment is only for being further detailed the present invention; can not be interpreted as limiting the scope of the invention, the those of ordinary skill in this field can be made some nonessential improvement and adjustment to the present invention according to foregoing invention content.

GNSS smoothing the phase of carrier wave pseudorange disposal route of the present invention, comprises the steps:

Step 1, GNSS receiver are exported thick code pseudorange and the carrier phase of each epoch in real time.

The thick code pseudorange of step 2, current epoch of being exported by GNSS receiver, obtains smoothing the phase of carrier wave pseudorange initial value P _sm(0); Be first thick code pseudorange of receiver output described current epoch.

P _sm(0)＝P(0)

Step 3, obtain according to step 1 current epoch thick code pseudorange and next epoch carrier phase, the smoothing the phase of carrier wave pseudorange initial value with step 2 obtains, obtains the extrapolation pseudorange P of next epoch _ex(k).

Step 4, obtain the smoothing the phase of carrier wave pseudorange value P of next epoch _sm(k).

P _sm(k)＝w(k)×P(k)+[1-w(k)]×P _ex(k)

Wherein, w (k) is the pseudorange weight of front epoch of k, if smoothing constant M value is greater than k epoch, pseudorange weight is got w (k)=1/k, if smoothing constant M value is not more than k epoch, pseudorange weight is got w (k)=1/M;

$M=\mathrm{INT}\left[\frac{1}{2}\sqrt[3]{\frac{{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2}{2T_m^2{I}_d^2}}\right],$

Wherein,

for the slightly variance of the device measuring error of code pseudorange of GNSS, the m of unit ²;

it is equipment thermonoise and the multipath effect equivalent range error after by thick code delay locking ring (DLL).This parameter both can be obtained by device parameter, also can obtain by pseudorange stochastic error statistics.The thick code of GNSS pseudo range data stochastic error statistical method is referring to (the Appendix B that GJB5830-2006 guided missile, spacecraft testing GPS measuring system off-line data processing method are.T _mfor the data sampling cycle, the s of unit.I _dfor the divergence variations rate of ionosphere delay, the m/s of unit, gets mid latitudes ionosphere divergence speed representative value upper bound 0.1m/min conventionally, amounts to 0.0017m/s.M is smoothing constant.

The thick code pseudorange of the current epoch that P (k) is step 1 acquisition, P _ex(k) be the pseudorange of extrapolating for the rapid three current epoch of obtaining.

Step 5, obtain according to step 1 next epoch thick code pseudorange and next epoch carrier phase, with the smoothing the phase of carrier wave pseudorange value that step 4 obtains, obtain the extrapolation pseudorange of lower next epoch;

Step 6, repeating step four and step 5, Real-time Obtaining GNSS smoothing the phase of carrier wave pseudorange value.

The concrete derivation of smoothing constant M of the present invention is as follows:

One, the main composition of analytical smoothing error on continuous time

According to aforementioned background art introduction, level and smooth ultimate principle is that smoothing process can equivalence be considered as the low-pass filtering for thick code pseudorange and carrier phase pseudorange difference, as shown in Figure 1 by poor error epoch of the thick code of the differential pressure contracting epoch pseudorange of carrier phase.

Filter time constant is τ, and the difference single order of thick code pseudorange and the carrier phase pseudorange continuous model that surely gains can be expressed as

$P_{\mathrm{sm}}=\frac{1}{\mathrm{\&tau;s}+1}(P-L)+L---\left(1\right)$

Wherein: P represents thick code pseudorange, P _smrepresent smoothing pseudo range; L represents carrier phase pseudorange, the complex variable that s is laplace transform.

Further, slightly code pseudorange and carrier phase pseudorange decompose, and are expressed as

$\left.\begin{array}{c}P=R+I+\mathrm{\&epsiv;}\\ L=R-I\end{array}\right\}---\left(2\right)$

Wherein, R represents geometric distance, ephemeris error, star clock error and tropospheric delay sum; I represents ionosphere delay; ε represents thick code pseudorange device measuring error.Formula (13) has been ignored carrier phase pseudorange device measuring error, and this is reasonably, because carrier phase pseudorange device measuring error is far smaller than ε.

(13) are updated to (12), can obtain

$P_{\mathrm{sm}}=R+\frac{1}{\mathrm{\&tau;s}+1}\mathrm{\&epsiv;}+\frac{1-\mathrm{\&tau;s}}{1+\mathrm{\&tau;s}}I---\left(3\right)$

Analytical formula (14), there is following characteristics in known pseudorange after level and smooth:

(1) the 1st R of the right formula of formula (14), shows that geometric distance, ephemeris error, star clock error and tropospheric delay are not smoothly affected;

(2) the 2nd of the right formula of formula (14)

show that thick code pseudorange device measuring error ε is low pass filtering, smoothing the phase of carrier wave pseudorange can reduce receiver device thermonoise and multipath delay error, and this part error is DLL tracking error;

(3) the 3rd of the right formula of formula (14)

show that smoothing the phase of carrier wave pseudorange can cause ionosphere delay item to change.Make Δ I represent instantaneous ionosphere delay and level and smooth rear postpone poor, and increase time independent variable t, that is:

$\mathrm{\&Delta;I}\left(t\right)=I-\frac{1-\mathrm{\&tau;s}}{1+\mathrm{\&tau;s}}I---\left(15\right)$

The reason that occurs Δ I (f) is that ionosphere delay is dispersed in time: the one, and phase retardation and group delay opposite direction, the 2nd, postpone to have time-varying characteristics.Δ I (t) is the new error term of being introduced by smoothing process, is called the level and smooth ionosphere of phase place and disperses error.

Two, the DLL tracking error variance estimation equation of derivation smoothing the phase of carrier wave pseudorange.

Analytical formula (12), the discrete equation of equal value with formula (12) is:

$P_{\mathrm{sm}}\left(k\right)=\mathrm{\&alpha;}\&times;P\left(k\right)+(1-\mathrm{\&alpha;})\&times;P_{\mathrm{sm}}(k-1),\mathrm{\&alpha;}=1-e^{-\frac{T_m}{\mathrm{\&tau;}}}---\left(16\right)$

Wherein: α represents index weight; T _mrepresent the data sampling cycle, k is epoch of observation.

Be considered as independent sequence by approximate continuous pseudo range observed quantity, ignored ionosphere delay completely and dispersed error.The stable state variance that can be obtained smoothing the phase of carrier wave pseudorange by formula (16) is:

${\mathrm{\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}^2={\mathrm{\&alpha;}}^2\&times;{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2+{(1-\mathrm{\&alpha;})}^2\&times;{\mathrm{\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}^2---\left(17\right)$

Wherein:

for the DLL tracking error variance of smoothing pseudo range;

for the DLL tracking error variance of thick code pseudorange.

Make n=τ/T _m, separate

can obtain:

${\mathrm{\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}^2=\frac{\mathrm{\&alpha;}}{2-\mathrm{\&alpha;}}{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2=\frac{1-e^{-\frac{1}{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HSA0000100299880000011.png"\; state="\{\{state\}\}">n</figure-callout>}}}}{1+e^{-\frac{1}{n}}}{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2---\left(18\right)$

carry out series expansion, and ignore higher order term,

substitution formula (18):

${\mathrm{\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}^2\&ap;\frac{1-1+\frac{1}{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HSA0000100299880000011.png"\; state="\{\{state\}\}">n</figure-callout>}}}{1+1-\frac{1}{n}}{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2=\frac{1}{2n-1}{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2\&ap;\frac{{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2}{2n}=\frac{T_m}{2\mathrm{\&tau;}}{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2---\left(19\right)$

Formula (19) is the DLL tracking error variance estimation equation of smoothing the phase of carrier wave pseudorange.

Three, error variance estimation equation is dispersed in the ionosphere that derivation smoothing the phase of carrier wave pseudorange is introduced

Ionosphere delay slowly changes in time, can be decomposed into a constant deviation and a time dependent slope deviation, that is:

I(t)＝I ₀+I _dt (20)

Wherein: I _drepresent ionosphere delay rate of change.I ₀for initial ionization layer postpones, by formula (20) substitution formula (15), can obtain ionosphere and disperse error delta I (t) and be

$\mathrm{\&Delta;I}\left(t\right)=I-\frac{1-\mathrm{\&tau;s}}{1+\mathrm{\&tau;s}}I=\frac{2\mathrm{\&tau;s}}{\mathrm{\&tau;s}+1}[I_0+I_{d}t]---\left(21\right)$

In the time that filtering enters stable state, application Laplace transform final-value theorem, can obtaining ionosphere, to disperse steady-state error as follows:

${\mathrm{\&Delta;I}}_{\mathrm{ss}}\left(t\right)=\underset{s\&RightArrow;0}{\lim }s\&CenterDot;\left[\frac{2\mathrm{\&tau;s}}{\mathrm{\&tau;s}+1}(\frac{I_0}{s}+\frac{I_d}{s^2})\right]=2\mathrm{\&tau;}{I}_d---\left(22\right)$

Formula (22) shows: due to ionosphere delay temporal evolution (I _d≠ 0), therefore smoothing the phase of carrier wave pseudorange can be introduced ionosphere and disperses error, its value and smoothingtime constant r and ionosphere delay rate of change I _dproduct be directly proportional.Statistical research shows (Patricia H etc., The Spatial and Temporal Variations in Ionospheric Range Delay, ION GPS97), the sun in when low active degree, the common Normal Distribution of mid latitudes ionosphere divergence variations rate, and magnitude is no more than 0.1m/min conventionally.

Obviously, the smoothingtime constant τ under continuous state, and meet between k level and smooth epoch under discrete case:

τ=kT _m (23)

By squared to formula (23) substitution formula (22) both sides, error variance estimation formula is dispersed in the ionosphere that can obtain smoothing the phase of carrier wave pseudorange:

${\mathrm{\&sigma;}}_{\mathrm{\&Delta;I}}^2\left(k\right)=k^2{T}_m^2---\left(24\right)$

Four, derivation smoothing the phase of carrier wave pseudorange total error variance estimation equation

According to propagation of error Computing Principle, by formula (19) and formula (24) summation, can provide the variance of smoothing the phase of carrier wave pseudorange total error

estimation equation:

${\mathrm{\&sigma;}}_{\mathrm{sm}}^2\left(k\right)={\mathrm{\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}^2\left(k\right)+{\mathrm{\&sigma;}}_{\mathrm{\&Delta;I}}^2\left(k\right)---\left(25\right)$

Take smoothing the phase of carrier wave pseudorange the recursive calculative formula (10) into account, complete estimation equation is:

$\left.\begin{array}{c}{\mathrm{\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}^2\left(0\right)={\mathrm{\&sigma;}}_{\mathrm{DLL}}^2\\ {\mathrm{\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}^2\left(k\right)=\frac{1}{2k}{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2+{4k}^2{T}_m^2{I}_d^2,k<M\\ {\mathrm{\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}^2\left(k\right)=\frac{1}{2M}{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2+{4M}^2{T}_m^2{I}_d^2,k\&GreaterEqual;M\end{array}\right\}---\left(26\right)$

Five, obtain smoothing constant M _bestcomputing formula

According to the 3rd formula of formula (26) ${\mathrm{\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}^2\left(k\right)=\frac{1}{2M}{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2+4M^2{T}_m^2{I}_d^2,k\&GreaterEqual;M$ If, known σ _dLL, T _mand I _d, find M optimal value M _beststandard be exactly the total error σ that makes smoothing the phase of carrier wave pseudorange _sm(k) minimum.Adopt Lagrange to ask extreme value algorithm: to M differentiate, and to make the expression formula after differentiate equal 0 formula (26) the 3rd formula, that is:

$\frac{{\mathrm{d\&sigma;}}_{\mathrm{DLL},\mathrm{sm}}}{\mathrm{dM}}=0---\left(27\right)$

By formula (26) the 3rd formula substitution, that is:

$-\left(\frac{{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2}{2}\right)M^{-2}+{8T}_m^2{I}_d^{2}M=0---\left(28\right)$

After solution formula (28), can obtain M optimal value M _bestcalculating formula:

$M_{\mathrm{best}}=\frac{1}{2}\sqrt[3]{\frac{{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2}{2T_m^2{I}_d^2}}---\left(29\right)$

That is:

Illustrate:

Example 1: when receiver output frequency is 1Hz, 10Hz and 20Hz, the smoothing constant M that adopts the inventive method to calculate _bestwith the device measuring error σ of the thick code of GNSS pseudorange _dLLchange curve as shown in Figure 2, the divergence variations rate I of ionosphere delay in figure _d, get mid latitudes ionosphere divergence variations rate representative value upper bound 0.1m/min.Fig. 2 shows, along with the device measuring error σ of the thick code of GNSS pseudorange _dLLdifferent with receiver output frequency, smoothing constant is also more big changes, and specifies arbitrarily smoothing constant or smoothing constant is forced to be made as the equivalence value of 100s improper.

Example 2: a GPS receiver 14000 epoch observation data smoothing the phase of carrier wave process contrast.

(1) data known parameters is: defending asterisk is 11, and the sampling period is T _m=0.25s, the DLL tracking error of thick code pseudorange is

, I _dget mid latitudes ionosphere divergence speed representative value upper bound 0.1m/min.

(2) select comparison other: select three smoothing constants object as a comparison:

(a) smoothing constant that adopts computing method of the present invention to obtain is

(b) 100s equivalence smoothing constant is

M _100s＝100／0.25＝400

(c) an artificial smoothing constant of specifying, specifies 10 times that this smoothing constant value is smoothing constant, i.e. M ₇₁₀=710

(3) compare object: relatively adopt three smoothing constants, carry out after smoothing the phase of carrier wave according to formula (10), smoothing error is situation over time.

(4) comparative approach: original thick code pseudorange is asked to poor and ask poor with smoothing the phase of carrier wave value: if smooth effect is good, ask difference sequence should show as the random error characteristics of 0 average; If smooth effect is poor, introduce excessive ionosphere and dispersed error, can show as mutual deviation sequence and depart from gradually 0 average.As shown in Figure 3, adopt the present invention calculate smoothing constant time smooth effect normal.As shown in Figure 4, while adopting 100s equivalence smoothing constant, curve progressively departs from 0 axis, shows that having introduced ionosphere in level and smooth disperses error, and maximum can reach 2m magnitude.Because the DLL tracking error that error has exceeded thick code pseudorange is dispersed in the ionosphere of introducing, smoothing the phase of carrier wave is dispersed, and adopts smoothing the phase of carrier wave pseudorange to realize the meaning of location so lost.As shown in Figure 5, while adopting an artificial smoothing constant of specifying, curve progressively departs from 0 axis, shows that having introduced ionosphere in level and smooth disperses error, and maximum can reach 3m magnitude.Because the DLL tracking error that error has exceeded thick code pseudorange is dispersed in the ionosphere of introducing, smoothing the phase of carrier wave is dispersed, and adopts smoothing the phase of carrier wave pseudorange to realize the meaning of location so lost.

Claims (1)

1. a GNSS smoothing the phase of carrier wave pseudorange disposal route, is characterized in that: comprise the steps:

Step 1, GNSS receiver be output thick code pseudorange and carrier phase in real time;

The thick code pseudorange of step 2, current epoch of being exported by GNSS receiver, obtains smoothing the phase of carrier wave pseudorange initial value, and be first thick code pseudorange of receiver output described current epoch;

Step 3, obtain according to step 1 current epoch thick code pseudorange and next epoch carrier phase, the smoothing the phase of carrier wave pseudorange initial value with step 2 obtains, obtains the extrapolation pseudorange P of next epoch _ex(k);

Step 4, obtain the smoothing the phase of carrier wave pseudorange value P of next epoch _sm(k)

P _sm(k)＝w(k)×P(k)+[1-w(k)]×P _ex(k)

Wherein, w (k) is the pseudorange weight of front epoch of k, if smoothing constant M value is greater than k epoch, pseudorange weight is got w (k)=1/k, if smoothing constant M value is not more than k epoch, pseudorange weight is got w (k)=1/M;

$M=\mathrm{INT}\left[\frac{1}{2}\sqrt[3]{\frac{{\mathrm{\&sigma;}}_{\mathrm{DLL}}^2}{2T_m^2{I}_d^2}}\right]$

Wherein, M is smoothing constant,

for the slightly variance of the device measuring error of code pseudorange of GNSS, T _mfor data sampling cycle, I _dfor the divergence variations rate of ionosphere delay;

The thick code pseudorange of the current epoch that P (k) is step 1 acquisition, P _ex(k) be the pseudorange of extrapolating for the rapid three current epoch of obtaining;

Step 5, obtain according to step 1 next epoch thick code pseudorange and next epoch carrier phase, with the smoothing the phase of carrier wave pseudorange value that step 4 obtains, obtain the extrapolation pseudorange of lower next epoch;

Step 6, repeating step four and step 5, Real-time Obtaining GNSS smoothing the phase of carrier wave pseudorange value.

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