CN103364841A - Smooth constellation jump error elimination method in airborne gravity measurement - Google Patents

Abstract

The invention discloses a smooth constellation jump error elimination method in airborne gravity measurement. The method comprises the following steps of: classifying and marking moments when navigation constellation jump occurs on each measuring line, and performing error estimation and compensation according to the jump type; and performing smooth weighting compensation on the position of the calculation position of the epoch before and after the jump, so that the influence of constellation jump on calculation of the carrier position is eliminated so as to obtain a smooth position sequence. The method has the advantages that the principle is simple, the operation is simple and convenient, the jump error can be completely eliminated, and the calculation precision is improved.

Description

A kind of level and smooth removing method for airborne gravimetry constellation saltus step error

Technical field

The present invention is mainly concerned with the airborne gravimetry technical field, refers in particular to a kind of level and smooth removing method for airborne gravimetry constellation saltus step error.

Background technology

Airborne gravimetry is one of important means of obtaining at present near-earth information, and the state parameters such as acceleration of determining aviation carrier self are prerequisite and the keys that realizes that airborne gravity measurement data is processed.At present, generally utilize the high-precision fixed capability of satellite navigation system to carry out the precision measurement of real carrier acceleration, so measurement result is subject to the impact of every GNSS error source, wherein constellation saltus step error is on the larger important errors source of result's impact.

Airborne gravity survey line length can reach several hundred kilometers, and owing to reasons such as elevation angle constraint, signal block, it is inevitable phenomenon that the observability of Navsat changes, and then will adopt different Aerospace Satellite constellations when causing resolve acceleration different epoch.Before and after when epoch, the space reference that resolves changed, the carrier positions of resolving can cause saltus step, this saltus step error will be by gradual magnification in asking for the differential process of acceleration, the gravitational cue that extracts is produced have a strong impact on.

The magnitude of saltus step error is relevant with factors such as the visible satellite at station sum, satellite elevation angle, satellite orbit type, constellation geometric configurations.Research finds, when the measuring error of carrier phase observation data is centimetre-sized, although the saltus step of constellation configuration is grade on the impact of positioning result, but ignore, but the impact of the carrier acceleration that calculus of differences is obtained can reach hundreds of mGal(1mGal=10 ^-5M/s ²) even the impact of thousands of mGal.The magnitude of the gravity anomaly signal that extracts is generally in the 100mGal magnitude, therefore this error will produce the extraction of faint gravitational cue and have a strong impact on, can produce edge effect during low-pass filtering will affect a plurality of GRAVITY ANOMALIES of measuring, generally take following several means to weaken the impact of this error at Data processing at present:

(1) satellite scalping method.Before the survey line data are processed, at first reject the satellite that the observability variation occurs on this survey line.The drawback that the method exists is that available satellite resource reduces, and the precision of calculation result reduces; Data processor is complicated; Be only applicable to shorter survey line.

(2) covariance-weighted method.By the design weighting matrix, low elevation angle satellite will be endowed less weight to reduce the impact on constellation saltus step error.The drawback that the method exists is that the design of weighting matrix lacks theoretical property, can only reduce to a certain extent the impact of saltus step error and can't eliminate fully, and the constellation saltus step error correction that non-low elevation angle reason is caused does not have effect, such as receiver owing to the reason such as be blocked cause to losing lock of high elevation angle satellite etc.

Summary of the invention

The technical problem to be solved in the present invention just is: for the technical matters that prior art exists, the invention provides a kind of principle simple, easy and simple to handle, can eliminate the saltus step error fully, be conducive to improve the level and smooth removing method that is used for airborne gravimetry constellation saltus step error of calculation accuracy.

For solving the problems of the technologies described above, the present invention by the following technical solutions:

A kind of level and smooth removing method for airborne gravimetry constellation saltus step error at first carries out classification and marking to the moment that the navigation constellation saltus step appears in every survey line, and carries out estimation of error and compensation according to the type of saltus step; Then, the position of the calculating location of epoch before and after the saltus step is weighted smooth compensating, the impact of carrier positions being resolved to eliminate the constellation saltus step is to obtain level and smooth position sequence.

As a further improvement on the present invention:

The process of described weighting smooth compensating is:

(1) certain calculates constantly t, the position x before the constellation saltus step ^aCan find the solution by least-squares algorithm, and to the solution x after the saltus step ^bEstimate:

x ^b=x ^a+△x

(2) separating x ^aAnd x ^bBetween be weighted average, that is:

$\stackrel{\‾}{x}\left(t\right)=\mathrm{\ω}\left(t\right)x^b+[1-\mathrm{\ω}\left(t\right)]x^a$

In the following formula, 0≤ω (t)≤1 is called smoothing factor, and satisfies:

T is the position sequence jumping moment, T _LPosition sequence length for data smoothing is called smooth window length;

(3) obtain the level and smooth scheme of weighting by above step (1) and step (2):

$\stackrel{\&OverBar;}{x}\left(t\right)=\left\{\begin{array}{cc}{x}^a& t<T\\ \mathrm{\&omega;}\left(t\right)x_t^b+[1-\mathrm{\&omega;}\left(t\right)]x_t^a& T\&le;t\&le;T+T_L\\ x^b& t>T+T_L\end{array}\right..$

As a further improvement on the present invention:

If there is the constellation saltus step current epoch, set saltus step mark then, judge the type of constellation saltus step error:

If be the saltus step of I class, be calculated according to the following formula the size of saltus step: △ x _p=x ₁-x ₂

If be the saltus step of II class, be calculated according to the following formula the size of saltus step: △ x ^p=σ ₀△ GDOP ^p, △ GDOP is the change amount that the constellation configuration changes front and back GDOP value, σ _x=σ ₀GDOP; Then, according to the weighted average scheme shown in the step (3) the position calculation result is carried out smoothing processing.

As a further improvement on the present invention:

The saltus step of described I class is that Navsat increases; Owing to the elevation angle uprises or satellite relocks reason, Navsat appears at the second half section of survey line, and Navsat can see below and cause the bearing accuracy positive transition;

The saltus step of described II class is that Navsat reduces; Owing to elevation angle step-down or the satellite reason that is blocked, Navsat appears at the first half section of survey line, causes the saltus step of bearing accuracy negative sense after Navsat is invisible.

Compared with prior art, the present invention is the optimisation technique based on the satellite navigation constellation, and the position hopping that at first saltus step causes to constellation is estimated, and then by smoothing filter the saltus step error compensated.Than traditional saltus step compensation method, the method has the following advantages:

1, the present invention takes full advantage of the Aerospace Satellite resource.The space reference that Navsat resolves as the carrier acceleration, answer employing as much as possible, be conducive to improve calculation accuracy, the present invention is not owing to need reject the satellite that observability changes, therefore the visible satellite of navigation neceiver all can participate in calculating, and is conducive to obtain the optimum solution of carrier acceleration.

2, treatment scheme of the present invention is simple, and automated procedures easily realize.At the automation algorithm of Data processing utilization based on this method design, do not need human intervention, automaticity is high.

3, the present invention uses rear saltus step error and can eliminate fully.

Description of drawings

Fig. 1 is that position sequence saltus step error is to the schematic diagram of the carrier acceleration action of Difference Calculation.

Fig. 2 is that the present invention is used for the level and smooth removing method of constellation saltus step error at the schematic flow sheet of concrete application example.

Embodiment

Below with reference to Figure of description and specific embodiment the present invention is described in further details.

Finding the solution generally of carrier acceleration in the airborne gravimetry processed afterwards.At first solve the position sequence of carrier, and position sequence is carried out speed, the accekeration of diff to obtain carrier.Therefore, extra error is introduced in the saltus step meeting in the position sequence in differential process.In addition, the carrier acceleration of asking for is measured noise owing to comprising a large amount of randomness, and this just need to suppress high frequency noise by low-pass filter, extracts gravitational cue.Above-mentioned saltus step error also can cause edge effect in low-pass filtering, and then the acceleration sequence generation impact on asking for.

Carry out the carrier acceleration when resolving, at first, determining the position sequence of carrier by adopting high precision carrier difference GNSS system (DGNSS), again by twice data difference, obtaining dynamic speed and the acceleration sequence of carrier.

If the GNSS base station is m, the photoplane airboarne receiver is k, and then two poor observation equations can be written as:

$\mathrm{\&lambda;}(\mathrm{\&Delta;}{\&dtri;\mathrm{\&Phi;}}_{m,k}^{p.q}+\mathrm{\&Delta;}\&dtri;N_{m,k}^{p.q})=\mathrm{\&Delta;}\&dtri;R_{m,k}^{p.q}+\mathrm{\&epsiv;}---\left(1\right)$

In the formula (1), subscript p, q represents satellite, subscript m, k represents satellite navigation receiver, " △ ▽ " is two difference operation symbols, and definition

λ is carrier wavelength; Φ is carrier phase observation data; N is at carrier phase ambiguity; R is star ground geometric distance; ε is two difference measurements errors.

Lienarized equation (1) can get two poor normal equations of resolving and is:

A·x=y （2）

In the formula (2): x is carrier positions vector to be asked, and A is observing matrix, and the geometric configuration of reflection Navsat constellation, y are afterwards free term of linearization, and have:

$A=\left[\begin{array}{c}{\left(h_k^{p,1}\right)}^T\\ {\left(h_k^{p,2}\right)}^T\\ .\\ .\\ .\\ {\left(h_k^{p,N}\right)}^T\end{array}\right]---\left(3\right)$

In the formula (3), subscript represents Navsat; N is the population of satellite that base station and airboarne receiver are looked altogether; P is selected reference satellite;

Be called receiver k to the measurement vector of satellite q, and:

$h_k^{p,q}=\left[\begin{array}{c}{e}_{\mathrm{kx}}^q-e_{\mathrm{kx}}^p\\ e_{\mathrm{kq}}^q-e_{\mathrm{ky}}^p\\ e_{\mathrm{kz}}^q-e_{\mathrm{kz}}^p\end{array}\right]---\left(4\right)$

In the formula (4), e is the unit vector of station star observation direction of visual lines, and has:

$e_{\mathrm{kx}}^i=\frac{x^i-x_k}{R_k^i},e_{\mathrm{ky}}^i=\frac{y^i-y_k}{R_k^i},e_{\mathrm{kz}}^i=\frac{z^i-z_k}{R_k^i}---\left(5\right)$

In the formula (5), x ⁱ, y ⁱ, z ⁱBe respectively the location components of Navsat i in the body-fixed coordinate system of the earth's core, can be calculated by the navigation ephemeris.According to least-square principle, the carrier acceleration can resolve into:

$\hat{x}={\left(A^{T}A\right)}^{-1}{A}^{T}y---\left(6\right)$

The precision of carrier positions calculation result can be estimated as:

${\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA00003585073900011.png"\; state="\{\{state\}\}">x</figure-callout>}}^2={\mathrm{\&sigma;}}_0^2\&CenterDot;{\left(A^{T}A\right)}^{-1}---\left(7\right)$

In the formula (7),

Be the variance of phase observations value, then two poor bearing accuracy decay factor GDOP are:

$\mathrm{GDOP}=\sqrt{\mathrm{trace}\left[{\left(A^{T}A\right)}^{-1}\right]}---\left(8\right)$

In the formula (8), trace () is the computing of Matrix Calculating mark.

After calculating the position sequence of carrier, can adopt the single order Central Difference Filter to find the solution the speed of carrier, acceleration, that is:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{x}=\frac{x(t+\mathrm{\&Delta;t})-x(t-\mathrm{\&Delta;t})}{2\mathrm{\&Delta;t}}\\ \stackrel{\&CenterDot;\&CenterDot;}{x}=\frac{\stackrel{\&CenterDot;}{x}(t+\mathrm{\&Delta;t})-\stackrel{\&CenterDot;}{x}(t-\mathrm{\&Delta;t})}{2\mathrm{\&Delta;t}}\end{array}\right.---\left(9\right)$

In the formula (9), △ t is the time interval of the position sequence that resolves.

According to above analysis, the basic reason of the carrier positions generation saltus step of determining based on GNSS is: saltus step occurs in constellation configuration (form with GDOP value embodies), so that bearer rate and acceleration sequence generation that difference is obtained affect.

As shown in Figure 1, be used for the definite navigation constellation configuration of acceleration and at the moment T saltus step occured, and then cause definite carrier positions sequence generation saltus step, this saltus step will be amplified step by step in differential is asked for the process of bearer rate, acceleration and be produced significant impact, for example when △ x=5cm, the saltus step of acceleration impact will reach 5000mGal.

The present invention is divided into following three kinds of situations with the constellation saltus step:

The saltus step of I class: Navsat increases.Owing to the elevation angle uprises or satellite such as relocks at the reason, Navsat appears at the second half section of survey line, and Navsat can see below and cause the bearing accuracy positive transition;

The saltus step of II class: Navsat reduces.Owing to elevation angle step-down or the satellite reason such as be blocked, Navsat appears at the first half section of survey line, causes the saltus step of bearing accuracy negative sense after Navsat is invisible;

The saltus step of III class: Navsat recurs observability in short time interval changes.Owing to reasons such as satellite short time interval are blocked, in certain period in survey line, Navsat recurs observability to be changed, and all can cause navigation accuracy generation saltus step when changing at every turn.

Through type (2) when adopting different constellations to carry out the carrier acceleration when resolving, can cause calculation result there are differences as can be known.Suppose at a time, choose respectively two different navigation constellations, be designated as respectively S1, S2, the Navsat number is respectively N1, N2, and wherein front N visible star is consistent, and then observing matrix can be expressed as respectively:

$\left\{\begin{array}{c}{A}_{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003585073900011.png,HDA00003585073900021.png"\; state="\{\{state\}\}">S</figure-callout>}1}={({\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00003585073900021.png"\; state="\{\{state\}\}">h</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00003585073900011.png,HDA00003585073900021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,...,h_N,...{h_N}_1)}^T\stackrel{\mathrm{\&Delta;}}{=}\left(A\right|A_1)\\ A_{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003585073900011.png"\; state="\{\{state\}\}">S</figure-callout>}2}={({\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00003585073900021.png"\; state="\{\{state\}\}">h</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA00003585073900011.png,HDA00003585073900021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1,...,h_N,...{h_N}_2)}^T\stackrel{\mathrm{\&Delta;}}{=}\left(A\right|A_2)\end{array}\right.---\left(10\right)$

The free term that constellation S1, S2 are corresponding can be designated as respectively:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="L\; S"\; filenames="HDA00003585073900011.png,HDA00003585073900021.png"\; state="\{\{state\}\}">L</figure-callout>}}_S={\left[L\right|L_1]}^{\mathrm{<figure-callout\; id="2"\; label="T\; L\; S"\; filenames="HDA00003585073900011.png"\; state="\{\{state\}\}">T</figure-callout>}}& \\ L_S{2}_{}={\left[L\right|L_2]}^T\end{array}\right.---\left(11\right)$

Can obtain adopting the calculation result of S1, S2 according to formula (6):

$\left\{\begin{array}{c}{x}_1={\left({A_{S1}}^T{A}_{S1}\right)}^{-1}{A_{S1}}^{\mathrm{<figure-callout\; id="1"\; label="T\; L\; S"\; filenames="HDA00003585073900011.png,HDA00003585073900021.png"\; state="\{\{state\}\}">T</figure-callout>}}{L}_S{1}_{}={(A^{T}A+{A_1}^T{A}_1)}^{-1}(A^{T}L+{A_1}^T{L}_1)\\ x_2={\left({A_{S2}}^T{A}_{S2}\right)}^{-1}{A_{S2}}^{\mathrm{<figure-callout\; id="2"\; label="T\; L\; S"\; filenames="HDA00003585073900011.png"\; state="\{\{state\}\}">T</figure-callout>}}{L}_S{2}_{}={(A^{T}A+{A_2}^T{A}_2)}^{-1}(A^{T}L+{A_2}^T{L}_2)\end{array}\right.---\left(12\right)$

According to matrix and Inversion Formula, can obtain:

$\left\{\begin{array}{c}{(A^{T}A+{A_1}^T{A}_1)}^{-1}={\left(A^{T}A\right)}^{-1}-{\left(A^{T}A\right)}^{-1}\left({A_1}^T{A}_1\right){\left(A^{T}A\right)}^{-1}{(I+{A_1}^T{A}_1{\left(A^{T}A\right)}^{-1})}^{-1}\\ {(A^{T}A+{A_2}^T{A}_2)}^{-1}={\left(A^{T}A\right)}^{-1}-{\left(A^{T}A\right)}^{-1}\left({A_2}^T{A}_2\right){\left(A^{T}A\right)}^{-1}{(I+{A_2}^T{A}_2{\left(A^{T}A\right)}^{-1})}^{-1}\end{array}\right.---\left(13\right)$

Obtaining thus calculation result difference is:

$x_1-x_2={\left(A^{T}A\right)}^{-1}(A_1^T{L}_1-A_2^T{L}_2)-[{\left(A^{T}A\right)}^{-1}{A}_1^T{A}_1{x}_1-{\left(A^{T}A\right)}^{-1}{A}_2^T{A}_2{x}_2]---\left(14\right)$

Abbreviation, vertical:

$x_1={(I+{\left(A^{T}A\right)}^{-1}{A_1}^T{A}_1)}^{-1}(I+{\left(A^{T}A\right)}^{-1}{A_2}^T{A}_2)x_2+{(A^{T}A+{A_1}^T{A}_1)}^{-1}({A_1}^T{L}_1-{A_2}^T{L}_2)---\left(15\right)$

Formula (15) has been reacted the calculation result x of different navigation constellation S1, S2 ₁, x ₂Between relation.Calculating x ₂After, can calculate the solution x based on constellation S1 ₁, and then can calculate constellation is changed into calculation result behind the S2 by S1 hop value x ₁-x ₂

Estimation for I class saltus step error:

When the observability of single satellite changes.Suppose that S1 Duos nautical star p, i.e. an A than S2 _S1=[A _S2| h _p], order $G_{s1}={\left(A_{s1}^T{A}_{s1}\right)}^{-1};G_{s2}={\left(A_{s2}^T{A}_{s2}\right)}^{-1},B_{s1}=A_{s1}^T{L}_{s1};B_{s2}=A_{s2}^T{L}_{s2},$ L _S1=[(L _S2) ^Tσ _p] T, have:

$\left\{\begin{array}{c}{x}_1=G_{S1}{B}_{S1}\\ x_2=G_{S2}{B}_{S2}\end{array}\right.---\left(16\right)$

Definition satellite p affects △ x to calculation result _pFor:

△x _p=x ₁-x ₂ （17）

Estimation to II type saltus step error:

II type saltus step error is according to formula (17) when resolving, x ₁Can't try to achieve.Can estimate according to following program, the measuring accuracy of each satellite carrier behavior observed reading of supposing to be used for the carrier acceleration calculation is identical, and then carrier positions determines that precision is:

σ _x=σ ₀·GDOP （18）

When the satellite constellation configuration changed, saltus step can occur in the amount GDOP that describes its geometric configuration, and then caused that saltus step occurs in determined position, and satellite p on the impact of calculation result is:

△x ^p=σ ₀·△GDOP ^p （19）

In the formula (19), △ GDOP is the change amount that the constellation configuration changes front and back GDOP value.Single satellite p can be calculated as the impact of GDOP in the constellation:

$\mathrm{\&Delta;GDO}{P}^p=\mathrm{trace}\left(\frac{A_n{h}_p^T{h}_p{A}_n}{1-h_p{A}_n{h}_p^T}\right)---\left(20\right)$

In the formula (20), A _nBe observing matrix corresponding to a constellation n satellite; h _pMeasurement vector for satellite p; Trace is for asking trace function.

Estimation to III type saltus step error:

III type saltus step error can be decomposed into I type saltus step error and II type saltus step error, then estimates according to formula (17) and formula (19) respectively.

Based on above-mentioned principle and analysis, level and smooth removing method for airborne gravimetry constellation saltus step error of the present invention is: the moment that at first the navigation constellation saltus step is appearred in every survey line is carried out classification and marking, and carries out estimation of error and compensation according to the type of saltus step; Then, the position of the calculating location of epoch before and after the saltus step is weighted smooth compensating, the impact of carrier positions being resolved to eliminate the constellation saltus step obtaining level and smooth position sequence, and then is tried to achieve the optimum calculation result of acceleration.

Particularly, adopt in the present invention following level and smooth removing method:

Certain calculates constantly t, the position x before the constellation saltus step ^aCan find the solution by the least-squares algorithm shown in the following formula (6); And the solution x after the saltus step ^bBut association type (19) is estimated:

x ^b=x ^a+△x （21）

Smoothing method of the present invention is exactly to separate x ^aAnd x ^bBetween be weighted average, that is:

$\stackrel{\&OverBar;}{x}\left(t\right)=\mathrm{\&omega;}\left(t\right)x^b+[1-\mathrm{\&omega;}\left(t\right)]x^a---\left(22\right)$

In the formula (22), 0≤ω (t)≤1 is called smoothing factor, and the present invention adopts following scheme to calculate this smoothing factor:

$\mathrm{\&omega;}\left(t\right)=\frac{t-T}{T_L},(T\&le;t\&le;T+T_L)---\left(23\right)$

In the formula (23), T is the position sequence jumping moment, T _LPosition sequence length for data smoothing is called smooth window length.Know thus:

$\mathrm{\&omega;}\left(t\right)=\left\{\begin{array}{cc}0& \mathrm{if\; t}=\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00003585073900011.png,HDA00003585073900021.png"\; state="\{\{state\}\}">T</figure-callout>}\\ 1& \mathrm{if\; t}=T+T_L\end{array}\right.---\left(24\right)$

The level and smooth scheme of weighting: according to formula (22) and formula (23), can get the level and smooth scheme of following weighting:

$\stackrel{\&OverBar;}{x}\left(t\right)=\left\{\begin{array}{cc}{x}^a& t<T\\ \mathrm{\&omega;}\left(t\right)x_t^b+[1-\mathrm{\&omega;}\left(t\right)]x_t^a& T\&le;t\&le;T+T_L\\ x^b& t>T+T_L\end{array}\right.---\left(25\right)$

Further, the smooth effect of the inventive method is assessed: smoothing algorithm should be eliminated the impact of position sequence saltus step error, does not produce or produce insignificant impact and simultaneously other acceleration are constantly extracted.By following formula (25) as can be known, smoothing algorithm is to t＜T or t〉T+T _LPosition-order train value in period is impact not, and as T≤t≤T+T _LThe time, second-order differential can get:

$\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&OverBar;}{x}}\left(t\right)={\stackrel{\&CenterDot;\&CenterDot;}{x}}_t^a+\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&omega;}}\left(t\right)\&CenterDot;(x_t^b-x_t^a)---\left(26\right)$

According to formula (23), can calculate:

$\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&omega;}}\left(t\right)=0,(T\&le;t\&le;T+T_L)---\left(27\right)$

As from the foregoing, smoothing operator is on not impact of the extraction of carrier acceleration, and saltus step occurs at t=T place the position sequence before level and smooth, and the saltus step at this place is completely eliminated smoothly, thereby proved validity of the present invention.

As shown in Figure 2, be the concrete application example of the inventive method.Wherein, the data of airborne gravity constellation saltus step error are processed and are specifically comprised following steps:

(1) GNSS receiver observation data is downloaded and pre-service;

After airborne gravimetry finishes, should from base station navigation receiving equipment, airborne navigation receiving equipment, derive the GNSS Satellite Observations, carry out necessary data pre-service, as reject wild value, Carrier Phase Ambiguity Resolution etc.

(2) airborne gravimetry survey line segmentation;

According to actual airborne gravimetry process survey line is carried out segmentation, should not comprise the turning process of survey aircraft in the general every survey line.

(3) the beginning data are processed, and set initial parameter;

Begin data from the survey line initial time and process, and set corresponding initial parameter, replacement saltus step compensation mark.As, set initial time and saltus step mark, t=0; Flag=0.

(4) utilize location algorithm to determine carrier positions (t constantly); Carrying out carrier positions according to the least-squares algorithm shown in the formula (6) resolves.

(5) adopt method of the present invention to carry out saltus step error smooth compensating.

If there is the constellation saltus step current epoch, set saltus step mark is then judged the type of constellation saltus step error, if be I class saltus step error, according to the size of formula (17) calculating saltus step; If be the saltus step of II class then calculate the size of saltus step according to formula (19), then according to the weighted average scheme shown in the formula (25) the position calculation result is carried out smoothing processing.The carrier acceleration that adopts diff to ask for after survey line calculates end can be avoided the impact of saltus step type error.

Below only be preferred implementation of the present invention, protection scope of the present invention also not only is confined to above-described embodiment, and all technical schemes that belongs under the thinking of the present invention all belong to protection scope of the present invention.Should be pointed out that for those skilled in the art, the some improvements and modifications not breaking away under the principle of the invention prerequisite should be considered as protection scope of the present invention.

Claims (4)

1. a level and smooth removing method that is used for airborne gravimetry constellation saltus step error is characterized in that, the moment that at first the navigation constellation saltus step is appearred in every survey line is carried out classification and marking, and carries out estimation of error and compensation according to the type of saltus step; Then, the position of the calculating location of epoch before and after the saltus step is weighted smooth compensating, the impact of carrier positions being resolved to eliminate the constellation saltus step is to obtain level and smooth position sequence.

2. the level and smooth removing method for airborne gravimetry constellation saltus step error according to claim 1 is characterized in that, the process of described weighting smooth compensating is:

(1) certain calculates constantly t, the position x before the constellation saltus step ^aCan find the solution by least-squares algorithm, and to the solution x after the saltus step ^bEstimate:

x ^b=x ^a+△x

(2) separating x ^aAnd x ^bBetween be weighted average, that is:

$\stackrel{\&OverBar;}{x}\left(t\right)=\mathrm{\&omega;}\left(t\right)x^b+[1-\mathrm{\&omega;}\left(t\right)]x^a$

In the following formula, 0≤ω (t)≤1 is called smoothing factor, and satisfies:

T≤t≤T+T wherein _L, T is the position sequence jumping moment, T _LPosition sequence length for data smoothing is called smooth window length;

(3) obtain the level and smooth scheme of weighting by above step (1) and step (2):

$\stackrel{\&OverBar;}{x}\left(t\right)=\left\{\begin{array}{cc}{x}^a& t<T\\ \mathrm{\&omega;}\left(t\right)x_t^b+[1-\mathrm{\&omega;}\left(t\right)]x_t^a& T\&le;t\&le;T+T_L\\ x^b& t>T+T_L\end{array}\right..$

3. the level and smooth removing method for airborne gravimetry constellation saltus step error according to claim 2 is characterized in that, if there is the constellation saltus step current epoch, and set saltus step mark then, judge the type of constellation saltus step error:

If be the saltus step of I class, be calculated according to the following formula the size of saltus step: △ x _p=x ₁-x ₂

If be the saltus step of II class, be calculated according to the following formula the size of saltus step: △ x ^p=σ ₀△ GDOP ^p, △ GDOP is the change amount that the constellation configuration changes front and back GDOP value, σ _x=σ ₀GDOP; Then, according to the weighted average scheme shown in the step (3) the position calculation result is carried out smoothing processing.

4. the level and smooth removing method for airborne gravimetry constellation saltus step error according to claim 3 is characterized in that:

The saltus step of described I class is that Navsat increases; Owing to the elevation angle uprises or satellite relocks reason, Navsat appears at the second half section of survey line, and Navsat can see below and cause the bearing accuracy positive transition;

The saltus step of described II class is that Navsat reduces; Owing to elevation angle step-down or the satellite reason that is blocked, Navsat appears at the first half section of survey line, causes the saltus step of bearing accuracy negative sense after Navsat is invisible.

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