CN104567802B - The survey line formula land-sea height transfer method of integrated boat-carrying gravity and GNSS - Google Patents

Abstract

The present invention relates to the survey line formula land-sea height transfer method of a kind of integrated boat-carrying gravity and GNSS, it utilizes integrated shipboard gravimeter and GNSS to come and go land and island (reef) at a distance once, in a ship comes and goes, carry out sea gravity measurement along ships' routing and GNSS measures, to complete the data acquisition of high accuracy survey line formula height datum over strait transmission, and basic data is modified and noise reduction process, and utilize least square collocation method to be deduced the formula along ocean, the survey line gravimetric data resolving high precision course line deviation of plumb line, and apply astronmical leveling principle, achieve marine survey line formula height datum unification and accurate elevation transmits.The present invention, relative to prior art, has required observation data volume expense relatively fewer, required relatively low；Error is little, precision is high, is suitable to the beneficial effects such as remote elevation transmission over strait.

Description

The survey line formula land-sea height transfer method of integrated boat-carrying gravity and GNSS

Technical field

The present invention relates to a kind of remote height datum transmission method over strait, particularly relate to a kind of integrated boat-carrying gravity and The survey line formula land-sea height transfer method of GNSS.

Background technology

Geospatial information based on elevation, has very important work in the development of the national economy and national defense construction With.

Marine economy, port engineering, sea transport, sea farming, marine fishing, exploration of ocean resources and exploitation, seabed Engineering, littoral zone engineering, marine environmental protection, Oceanic disasters are monitored, island (reef) is developed and protection etc. is required for the height enriched Journey data, needs unified land figure and the vertical reference of sea chart, to build unified land-sea spatial information benchmark.

For universal terrestrial and the height datum on island, land-sea elevation translocation should be carried out.Conventional land-sea elevation translocation side Method has precise leveling, hydrostatic leveling, trigonometric levelling, drive marine method, GPS (Global Positioning System, global positioning system) level method and gravity position method etc..Wherein, although precise leveling is smart Degree height, but survey station sighting distance is shorter, when carrying out across water area survey, front-and rear-view away from difference the biggest, it is impossible to realize distance accurate Leveling across sea is measured.

Static level method is to use communicating pipe to carry out elevation transmission, owing to distance over strait is longer, not only requires that communicating pipe has There is high quality, and in order to keep hydrostatic equilibrium, it is necessary to assure the liquid bubble-free in communicating pipe, also need to consider gas The impact on poised state of the factor such as pressure reduction, density contrast, expense is sufficiently expensive.

Although the height datum on the most multiple island transmits the method that have employed trigonometric levelling, it is known that It is that Trigonometric Leveling can only measure the geometry discrepancy in elevation between any two points, therefore, trigonometric levelling directly inquires into Positive high or GPS survey will comprise that geoid is not parallel and the error that causes, also the most inclined by vertical refraction error, vertical line The impact of difference etc..When distance is more than 10 km, sighting mark error is relatively big, the most even cannot observe.So this method error Greatly, again weather environment is required height, be not suitable for the transmission of distance elevation over strait.

Power level method, i.e. tidal observation method, also referred to as drive marine method, also known as tidal level observation method, its principle is at 2 points Carry out the observation of long-term tidal level, obtain the mean sea level of 2, and then inquired into the positive high of another point or just by the elevation of a bit Chang Gao.This method is owing to needing tidal observation data for many years, and cycle length, cost are high.On the one hand, zone leveling sea level with Geoid has the difference of meter level；On the other hand, there is wind set-up in sea level.

Therefore, the precision that the method is transmitted for remote island (reef) elevation needs to be improved.

The ultimate principle of GPS level method is to simulate region (seemingly) greatly water first with land a large amount of GPS bench mark Quasi-face, then (seemingly) geoid of matching is extrapolated to unknown point, and then the geodetic height combining unknown point obtains positive height/normal Gao Lai.On the one hand region (seemingly) the geoid precision of matching only has decimetre/centimetres, and on the other hand Extrapolation method also carries Carry out error.

The premise of this method is that the GPS bench mark of unknown point and land is at same matching (seemingly) geoid On, gradually can lose its reasonability along with distance increases this premise, this error even can reach when distance is more than 20 km To decimeter grade.It is exactly additionally measurement error and the distribution influence of GPS bench mark of GPS bench mark.The method is to utilize the earth The discrepancy in elevation and (seemingly) geoidal rise elevation transference benchmark, funds in need are less, and the cycle is shorter, convenient and practical.But, this Method error is relatively big, is not suitable for the transmission of distance elevation over strait.

Theoretical according to gravity position, on the basis of based on gravimetric region (seemingly) level Geoid, utilize GNSS Technology can realize the transmission of island (reef) elevation.It is determined by the position being positioned between different land and the base leveling origin of island (reef) Difference, thus unified every country height datum, set up whole world elevation framework, proposes to resolve position by the measurement of the level and gravimetric data Difference, this needs substantial amounts of field process and complicated calculating, is also had a strong impact on by political factor, simultaneously reef on island () also Cannot directly translocation to land.

Geodetic boundary value problem is utilized to resolve, the method that vertical reference connection can be carried out.

Utilizing linearisation to fix Gravimetric Boundary Value Problems to have carried out the elevation in Shenzhen and Hong Kong and compare, precision has reached a centimetre amount Level, on the one hand Shenzhen and Hong Kong are close together, on the other hand have more HIGH-PRECISION GRAVITY DATA.

Can propose to utilize geo-potential difference technology to realize the transmission of land-sea elevation, determine potential difference be one quite time-consuming and complicated Work.

Elevation based on gravity position technology transmits, and needs the gravimetric data under a large amount of unified benchmark and GNSS to measure；

Determine that the solution of the geodetic boundary value problem (GBVP) of potential difference between two places is also applied to elevation unification.Because, weight Force data and landform are strong correlations, and therefore, the residual gravity after deducting reference to gravitational field model can be used for stating earth weight The high fdrequency component in the field of force.

But, these methods need region elevation (being referred to region height datum), calculated gravity anomaly, gravity reduction Benchmark is the most variant.Theoretical based on gravity position, use the solution of fixed installation hob to carry out height datum unified.Utilize gravity position Method carries out region (seemingly) level Geoid, needs substantial amounts of gravimetric data and complicated algorithm, and cost is high, expense is held high Expensive, the cycle is longer.

Chinese patent application CN101957193B discloses the optimization method of a kind of sea island reef height transmission, and it passes through land Ground, littoral zone, sea island reef gravimetric data highly integrated, the Spatial gravity anomaly data meter that corrected by height datum System level gray correlation Calculate the high accuracy entirety gravity quasi-geoid numerical model that land is consistent with transmitted sea island reef, finally utilize zoning Interior known elevational point, by measuring GPS geodetic height and the GPS geodetic height of sea island reef to be measured point of known elevational point, completes sea The elevation transmission of islands and reefs.

The optimization method of the sea island reef height transmission of technique scheme, owing to it builds gravity quasi-geoid numerical value Model, needs the gravimetric data of comprehensive land, littoral zone and sea island reef, thus required observation data volume is huge, costly, respectively Type data can introduce new error during unifying；More it is essential that this method to build accurate office Portion's gravity quasi-geoid scope is relatively small, say, that it cannot realize the transmission of remote elevation over strait.

Summary of the invention

It is an object of the present invention to provide one realize over strait at a distance, in high precision, the remote height datum over strait of low-cost Transmission method.

The present invention technical issues that need to address for achieving the above object are how to utilize integrated shipboard gravimeter and GNSS Remote come and go land and island (reef) once, in a ship comes and goes, along ships' routing carry out sea gravity measurement and GNSS measures, and to complete the data acquisition of high accuracy survey line formula height datum over strait transmission, and basic data is carried out at computing Reason, to realize remote height datum over strait transmission raising precision, the technical problem of reduction systematic error.

The present invention solves that above-mentioned technical problem be employed technical scheme comprise that, a kind of integrated boat-carrying gravity and the survey of GNSS Wire type land-sea height transfer method, it is characterised in that comprise the following steps:

The first step, it is known that the height datum point A's of land is positive high, measures its geodetic height and use by conventional GNSS method Gravity anomaly measured by gravimeter；

Second step, with integrated shipboard gravimeter and GNSS boat along between land known point A and island (reef) tested point B On course line come and go a voyage, measure process survey line on gravimetric data and GNSS three-dimensional coordinate；

3rd step, uses conventional GNSS method measure its geodetic height and measure weight with gravimeter at island (reef) tested point B Power is abnormal；

4th step, utilizes EGM2008 earth gravity field model, builds the gravity anomaly auto-covariance matrix along ships' routing With gravimetric plumb line deflection Cross-covariance；

It is analyzed to collect along ships' routing gravimetric data and GNSS three-dimensional data and processes, and utilizing GNSS Three-dimensional data and the actual measurement processed, along the gravimetric data of ships' routing, optimize gravity anomaly variance matrix and gravimetric plumb line deflection Difference Cross-covariance；

5th step, the gravimetric data, gravity anomaly variance matrix and the gravity-deviation of plumb line that the 4th step have been processed are assisted mutually Variance matrix, uses least square collocation principle to calculate the deviation of plumb line, result substitutes into astronmical leveling formula, calculate along ship The difference of the geoidal rise between way point and land known point A；

During calculating, need to project on ship line direction the calculated deviation of plumb line, and according to greatly The relation of ground height high, positive and undulation of the geoid calculate along ships' routing measuring point i (i=1,2 ...) put positive high；

6th step, according to the 5th step calculate along ships' routing measuring point i (i=1,2 ...) and put positive high, to the 4th step Processed carries out Spatial gravity anomaly reduction along course line gravimetric data；

Least square collocation is used to recalculate along the course line measuring point deviation of plumb line, result of calculation the gravimetric data after reduction Substitute into astronmical leveling formula, again revise the difference along ships' routing measuring point geoidal rise, and to course line between A, B 2 The difference of all geoidal rises be integrated, obtain the earth water between land known point A and island (reef) tested point B The difference of quasi-face gap；

7th step, the land known point A calculated according to the 6th step and the geoidal rise of island (reef) tested point B it Difference, the A point recorded in conjunction with the first step and the geodetic height of B point, the positive high of unknown point B point can be obtained.

It is preferred that, the survey line formula land-sea height transfer method of above-mentioned integrated boat-carrying gravity and GNSS, it utilizes Integrated shipboard gravimeter and GNSS technology realize the data acquisition of survey line formula elevation over strait transmission；

Utilize EGM2008 earth gravity field model, build gravity anomaly auto-covariance matrix and gravity-deviation of plumb line is assisted mutually Variance matrix；

In conjunction with course line measuring point gravimetric data, utilize least square collocation method, ask for the high accuracy deviation of plumb line；

Finally, astronmical leveling principle is utilized to realize the remote transmission of land-sea height datum.

Further preferably, above-mentioned gravity anomaly covariance matrix also includes noise variance matrix；

Described noise variance matrix is sought acquisition by experiment, is obtained by analog data or empirical data.

Technique scheme, by the positive height of the height datum point A of known land, measures it by conventional GNSS method Geodetic height and measure gravity anomaly with gravimeter；With integrated shipboard gravimeter and GNSS boat along land known point A and island On course line between (reef) tested point B come and go a voyage, measure process survey line on gravimetric data and GNSS three-dimensional sit Mark；Its geodetic height and gravity anomaly is measured by conventional GNSS method at island (reef) tested point B；Utilize EGM2008 earth weight Force field model, builds the gravity anomaly variance matrix along ships' routing and gravimetric plumb line deflection Cross-covariance；To being adopted Collect to be analyzed along ships' routing gravimetric data and GNSS three-dimensional data and process, and utilize GNSS three-dimensional data and process The actual measurement crossed, along the gravimetric data of ships' routing, optimizes gravity anomaly variance matrix and gravimetric plumb line deflection Cross-covariance Deng the employing of series technique means, what it directly brought has the technical effect that

1, twice measurement has been carried out with integrated shipboard gravimeter and GNSS boat altogether along course line round trip, can be by altogether Line adjustment is effectively improved data precision, and its low cost and data acquisition cover face width, thus are suitable for remote island (reef) elevation The collection accurately determining basic data, and the acquisition cost of basic data is low；

2, EGM2008 earth gravity field model Gravity coefficients standard deviation is utilized to build gravity anomaly variance matrix and weight Power-deviation of plumb line Cross-covariance；Boat-carrying actual measurement gravimetric data is carried out denoising and adjustment processing, its precision can be improved；

3, the gravimetric data correction gravity anomaly variance matrix after utilization processes and gravity-deviation of plumb line covariance matrix； Finally, utilize least square collocation principle, the high accuracy deviation of plumb line can be calculated, it is ensured that marine survey line formula height datum system One and accurate elevation transmission, the exactly determined needs of off-lying sea island (reef) elevation can be met；

It should be understood that

In technique scheme, owing to carrying out Ocean Surveying under the dynamic environment of ocean, by ship attitude, acceleration, The impact of Etvs effect, noise of instrument etc., it is therefore necessary to the gravimetric data collected and geodetic height data are carried out noise filtering Process.

In technique scheme, build gravity anomaly variance matrix and gravimetric plumb line deflection Cross-covariance exactly It it is the basis of the resolving high precision deviation of plumb line.Only calculate the high-precision deviation of plumb line, astronmical leveling principle could be applied Among elevation over strait transmits, build gravity anomaly variance matrix and gravimetric plumb line deflection Cross-covariance the most accurately It it is a most crucial step.

In technique scheme, EGM2008 earth gravity field model Gravity coefficients standard deviation is utilized to build gravity anomaly Variance matrix and gravity-deviation of plumb line Cross-covariance；

Boat-carrying actual measurement gravimetric data is carried out denoising and adjustment processing to improve its precision；

Gravimetric data correction gravity anomaly variance matrix after utilization process and gravity-deviation of plumb line covariance matrix；

Finally, the least square collocation principle resolving high precision deviation of plumb line is utilized.

Wherein:

1, gravity-deviation of plumb line Cross-covariance process is built as follows:

The derivation of the spheric harmonic expansion formula of (a) gravity anomaly and the deviation of plumb line

Can obtain according to Bruns formula:

The spheric harmonics expansion of disturbing potential:

$T(r,\mathrm{\θ},\mathrm{\λ})=\frac{GM}{r}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(cos\mathrm{\θ}\right)---\left(2\right)$

It is that earth gravitational field cuts normal ellipsoid gravity position Coefficient.

Local derviation is asked to obtain earth radius disturbing potential:

$\begin{array}{c}-\frac{\∂T}{\∂r}=-\[-\frac{GM}{r^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(\cos \mathrm{\θ}\right)\\ -\frac{GM}{r^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}n{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(\cos \mathrm{\θ}\right)\]\\ =\frac{GM}{r^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}(n+1){\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(\cos \mathrm{\θ}\right)\end{array}---\left(3\right)$

Formula (3) is substituted into formula (1) obtain:

$\mathrm{\Δ}g=\frac{GM}{r^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}(n-1){\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(cos\mathrm{\θ}\right)---\left(4\right)$

Obtain according to the relation between disturbing potential and the deviation of plumb line:

$\left\{\begin{array}{c}\mathrm{\ξ}=\frac{1}{\mathrm{\γ}r}\frac{\∂T}{\∂\mathrm{\θ}}\\ \mathrm{\η}=-\frac{1}{\mathrm{\γ}r\sin \mathrm{\θ}}\frac{\∂T}{\∂\mathrm{\λ}}\end{array}\right.---\left(5\right)$

Local derviation is asked to obtain disturbing potential:

$\begin{array}{c}\mathrm{\ξ}=\frac{1}{\mathrm{\γ}r}\frac{\∂T}{\∂\mathrm{\θ}}=\frac{1}{\mathrm{\γ}r}\·\frac{GM}{r}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ})\frac{d\left({\stackrel{\‾}{P}}_{nm}\right(\cos \mathrm{\θ}\left)\right)}{d\mathrm{\θ}}\\ =\frac{GM}{{\mathrm{\γr}}^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ})\frac{d\left({\stackrel{\‾}{P}}_{nm}\right(\cos \mathrm{\θ}\left)\right)}{d\mathrm{\θ}}\end{array}---\left(6\right)$

$\begin{array}{c}\mathrm{\η}=-\frac{1}{\mathrm{\γ}r\sin \mathrm{\θ}}\frac{\∂T}{\∂\mathrm{\λ}}=-\frac{1}{\mathrm{\γ}r\sin \mathrm{\θ}}\frac{GM}{r}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}m(-{\stackrel{\‾}{C}}_{nm}^{*}\sin m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\cos m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(\cos \mathrm{\θ}\right)\\ =\frac{GM}{{\mathrm{\γr}}^2\sin \mathrm{\θ}}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}m({\stackrel{\‾}{C}}_{nm}^{*}\sin m\mathrm{\λ}-{\stackrel{\‾}{S}}_{nm}\cos m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(\cos \mathrm{\θ}\right)\end{array}---\left(7\right)$

B Legendre function is launched to substitute into gravity anomaly and the spheric harmonic expansion formula of the deviation of plumb line by ()

Legendre function expansion is:

${\stackrel{\‾}{P}}_{nm}\left(cos\mathrm{\θ}\right)=\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(cos\mathrm{\θ}\right)}^{n-m-2k}---\left(8\right)$

Local derviation is asked to obtain formula (8):

$\begin{array}{c}\frac{d\left({\stackrel{\‾}{P}}_{nm}\right(\cos \mathrm{\θ}\left)\right)}{d\mathrm{\θ}}=\frac{d\left({\stackrel{\‾}{P}}_{nm}\right(\cos \mathrm{\θ}\left)\right)}{d\left(\cos \mathrm{\θ}\right)}\frac{d\left(\cos \mathrm{\θ}\right)}{d\mathrm{\θ}}\\ =(\frac{1}{2^n}\frac{m}{2}\frac{{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}}{1-{\cos }^2\mathrm{\θ}}\left(-2\cos \mathrm{\θ}\right)\underset{k=0}{\overset{n}{\Σ}}{\left(-1\right)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}\\ +\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{n}{\Σ}}{\left(-1\right)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}\frac{(n-m-2k)}{\cos \mathrm{\θ}}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k})(-\sin \mathrm{\θ})\\ =\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{\left(-1\right)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}(m\cot \mathrm{\θ}-(n-m-2k\left)\tan \mathrm{\θ}\right)\end{array}---\left(9\right)$

Formula (8) is substituted into formula (4) and formula (7), formula (9) substitution formula (6) is obtained gravity anomaly, vertical line inclined Difference is about longitude and latitude and terrestrial gravitation potential coefficientWithExpansion form:

$\begin{array}{c}\mathrm{\Δ}g=\frac{GM}{r^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}(n-1){\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(\cos \mathrm{\θ}\right)\\ =\frac{GM}{r^2}\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}(n-1){\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(\cos \mathrm{\θ}\right)\\ =\frac{GM}{r^2}\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}(n-1){\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ})\frac{1}{2^n}{\left(1-{\cos }^2\mathrm{\θ}\right)}^{\frac{m}{2}}\\ \underset{k=0}{\overset{q}{\Σ}}{\left(-1\right)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}\end{array}---\left(10\right)$

$\begin{array}{c}\mathrm{\ξ}=\frac{GM}{{\mathrm{\γr}}^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}({\stackrel{\‾}{C}}_{nm}^{*}\cos m\mathrm{\λ}+{\stackrel{\‾}{S}}_{nm}\sin m\mathrm{\λ})\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\\ \underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}(m\cot \mathrm{\θ}-(n-m-2k\left)\tan \mathrm{\θ}\right)\end{array}---\left(11\right)$

$\begin{array}{c}\mathrm{\η}=\frac{GM}{{\mathrm{\γr}}^2\sin \mathrm{\θ}}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}m({\stackrel{\‾}{C}}_{nm}^{*}\sin m\mathrm{\λ}-{\stackrel{\‾}{S}}_{nm}\cos m\mathrm{\λ}){\stackrel{\‾}{P}}_{nm}\left(\cos \mathrm{\θ}\right)\\ =\frac{GM}{{\mathrm{\γr}}^2\sin \mathrm{\θ}}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{\left(\frac{a}{r}\right)}^n\underset{m=0}{\overset{n}{\Σ}}m({\stackrel{\‾}{C}}_{nm}^{*}\sin m\mathrm{\λ}-{\stackrel{\‾}{S}}_{nm}\cos m\mathrm{\λ})\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\\ \underset{k=0}{\overset{q}{\Σ}}{\left(-1\right)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}\end{array}---\left(12\right)$

C () utilizes EGM2008 earth gravity field model, structure gravity anomaly-deviation of plumb line covariance:

Formula (10)～(12) are changed into following form:

$\begin{array}{c}\mathrm{\Δ}g=\frac{GM}{r^2}\{\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}\[(n-1){\left(\frac{a}{r}\right)}^n\cos m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}\·{\stackrel{\‾}{C}}_{nm}^{*}\]+\\ \underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}\[(n-1){\left(\frac{a}{r}\right)}^n\sin m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}\·{\stackrel{\‾}{S}}_{nm}\]\}\end{array}---\left(13\right)$

$\begin{array}{c}\mathrm{\ξ}=\frac{GM}{{\mathrm{\γr}}^2}\{\underset{n=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}\[{\left(\frac{a}{r}\right)}^n\cos m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}(m\cot \mathrm{\θ}-\left(n-m-2k\right)\tan \mathrm{\θ}\·{\stackrel{\‾}{C}}_{nm}^{*}\]+\\ \underset{n=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}\[{\left(\frac{a}{r}\right)}^n\sin m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}(m\cot \mathrm{\θ}-\left(n-m-2k\right)\tan \mathrm{\θ}\·{\stackrel{\‾}{S}}_{nm}\]\}\end{array}---\left(14\right)$

$\begin{array}{c}\mathrm{\η}=\frac{GM}{{\mathrm{\γr}}^2\sin \mathrm{\θ}}\{\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}\[{\left(\frac{a}{r}\right)}^{n}m\·\sin m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}\·{\stackrel{\‾}{C}}_{nm}^{*}\]-\\ \underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}\[{\left(\frac{a}{r}\right)}^{n}m\·\cos m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(\cos \mathrm{\θ}\right)}^{n-m-2k}\·{\stackrel{\‾}{S}}_{nm}\]\}\end{array}---\left(15\right)$

Order

$(n-1){\left(\frac{a}{r}\right)}^n\sin m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(cos\mathrm{\θ}\right)}^{n-m-2k}=B_{nm}$

${\left(\frac{a}{r}\right)}^n\cos m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(cos\mathrm{\θ}\right)}^{n-m-2k}(m\cot \mathrm{\θ}-\left(n-m-2k\right)tan\mathrm{\θ}=D_{nm}$

${\left(\frac{a}{r}\right)}^n\sin m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(cos\mathrm{\θ}\right)}^{n-m-2k}(m\cot \mathrm{\θ}-\left(n-m-2k\right)tan\mathrm{\θ}=E_{nm}$

${\left(\frac{a}{r}\right)}^{n}m\·\sin m\mathrm{\λ}\·\frac{1}{2^n}{(1-{\cos }^2\mathrm{\θ})}^{\frac{m}{2}}\underset{k=0}{\overset{q}{\Σ}}{(-1)}^k\frac{1}{k!(n-k)!}\frac{(2n-2k)!}{(n-m-2k)!}{\left(cos\mathrm{\θ}\right)}^{n-m-2k}=M_{nm}$

Obtain:

$\mathrm{\Δ}g=\frac{GM}{r^2}(\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{A}_{nm}\·{\stackrel{\‾}{C}}_{nm}^{*}+\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{B}_{nm}\·{\stackrel{\‾}{S}}_{nm})---\left(16\right)$

$\mathrm{\ξ}=\frac{GM}{{\mathrm{\γr}}^2}(\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{D}_{nm}\·{\stackrel{\‾}{C}}_{nm}^{*}+\underset{n=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{E}_{nm}\·{\stackrel{\‾}{S}}_{nm})---\left(17\right)$

$\mathrm{\η}=\frac{GM}{{\mathrm{\γr}}^{2}sin\mathrm{\θ}}(\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{M}_{nm}\·{\stackrel{\‾}{C}}_{nm}^{*}-\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{N}_{nm}\·{\stackrel{\‾}{S}}_{nm})---\left(18\right)$

If P, Q are two points on ground, its gravity anomaly Δ g^P、Δg^QWith deviation of plumb line Δ ξ^P、Δξ^Q、Δη^P、Δη^QPoint Not:

${\mathrm{\Δg}}^P=\frac{GM}{r_P^2}(\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{A}_{nm}^P\·{\stackrel{\‾}{C}}_{nm}^{*}+\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{B}_{nm}^P\·{\stackrel{\‾}{S}}_{nm})---\left(19\right)$

${\mathrm{\Δg}}^Q=\frac{GM}{r_Q^2}(\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{A}_{nm}^Q\·{\stackrel{\‾}{C}}_{nm}^{*}+\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{B}_{nm}^Q\·{\stackrel{\‾}{S}}_{nm})---\left(20\right)$

${\mathrm{\ξ}}^P=\frac{GM}{{\mathrm{\γ}}_P{r}_P^2}(\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{D}_{nm}^P\·{\stackrel{\‾}{C}}_{nm}^{*}+\underset{n=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{E}_{nm}^P\·{\stackrel{\‾}{S}}_{nm})---\left(21\right)$

${\mathrm{\ξ}}^Q=\frac{GM}{{\mathrm{\γ}}_P{r}_P^2}(\underset{n=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{D}_{nm}^Q\·{\stackrel{\‾}{C}}_{nm}^{*}+\underset{n=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{E}_{nm}^Q\·{\stackrel{\‾}{S}}_{nm})---\left(22\right)$

${\mathrm{\η}}^P=\frac{GM}{{\mathrm{\γ}}_P{r}_P^2{\mathrm{sin\θ}}_P}(\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{M}_{nm}^P\·{\stackrel{\‾}{C}}_{nm}^{*}-\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{N}_{nm}^P\·{\stackrel{\‾}{S}}_{nm})---\left(23\right)$

${\mathrm{\η}}^Q=\frac{GM}{{\mathrm{\γ}}_Q{r}_Q^2{\mathrm{sin\θ}}_Q}(\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{M}_{nm}^Q\·{\stackrel{\‾}{C}}_{nm}^{*}-\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{N}_{nm}^Q\·{\stackrel{\‾}{S}}_{nm})---\left(24\right)$

Obtaining gravity potential of earth system errors standard deviation according to EGM2008 earth gravity field model isWithRoot The covariance matrix between two points of P, Q can be obtained according to law of propagation of errors:

$COV({\mathrm{\Δg}}^P,{\mathrm{\Δg}}^Q)=\frac{GM}{r_P^2}\frac{GM}{r_Q^2}(\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{A}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{C}}_{nm}}^2\·A_{nm}^Q+\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{B}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{S}}_{nm}}^2{B}_{nm}^Q)---\left(25\right)$

$COV({\mathrm{\ξ}}^P,{\mathrm{\ξ}}^Q)=\frac{GM}{{\mathrm{\γ}}_P{r}_P^2}\frac{GM}{{\mathrm{\γ}}_Q{r}_Q^2}(\underset{n=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{D}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{C}}_{nm}}^2{D}_{nm}^Q+\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{E}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{S}}_{nm}}^2{E}_{nm}^Q)---\left(26\right)$

$COV({\mathrm{\η}}^P,{\mathrm{\η}}^Q)=\frac{GM}{{\mathrm{\γ}}_P{r}_P^2{\mathrm{sin\θ}}_P}\frac{GM}{{\mathrm{\γ}}_Q{r}_Q^2{\mathrm{sin\θ}}_Q}(\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{D}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{C}}_{nm}}^2\·M_{nm}^Q+\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{N}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{S}}_{nm}}\·N_{nm}^Q)---\left(27\right)$

$COV({\mathrm{\Δg}}^P,{\mathrm{\ξ}}^Q)=\frac{GM}{r_P^2}\frac{GM}{{\mathrm{\γ}}_Q{r}_Q^2}(\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{A}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{C}}_{nm}}^2\·D_{nm}^Q+\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{B}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{S}}_{nm}}^2{E}_{nm}^Q)---\left(28\right)$

$COV({\mathrm{\Δg}}^P,{\mathrm{\η}}^Q)=\frac{GM}{r_P^2}\frac{GM}{{\mathrm{\γ}}_Q{r}_Q^2{\mathrm{sin\θ}}_Q}(\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{A}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{C}}_{nm}}^2\·D_{nm}^Q-\underset{n=2}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}{B}_{nm}^P\·{\mathrm{\σ}}_{{\stackrel{\‾}{S}}_{nm}}^2{E}_{nm}^Q)---\left(29\right)$

2, ask along the survey line measuring point deviation of plumb line according to least square collocation method

After gathering and processing is Δ g along survey line boat-carrying gravimetric data₁,Δg₂,…Δg_i..., the deviation of plumb line tried to achieve Meridional component and fourth of the twelve Earthly Branches component at the tenth of the twelve Earthly Branches are respectively ξ₁,ξ₂,…ξ_i... and η₁,η,…η_i..., least square collocation principle is:

$S=C_{sl}(C_{ll}^{-1}+D)L---\left(30\right)$

In formula:

OrOr

$\begin{array}{cc}{C}_{sl}=\left[\begin{array}{ccccc}COV({\mathrm{\Δg}}^1,{\mathrm{\η}}^1)& COV({\mathrm{\Δg}}^1,{\mathrm{\η}}^2)& \mathrm{...}& COV({\mathrm{\Δg}}^1,{\mathrm{\η}}^i)& \mathrm{...}\\ COV({\mathrm{\Δg}}^2,{\mathrm{\η}}^1)& COV({\mathrm{\Δg}}^2,{\mathrm{\η}}^2)& \mathrm{...}& COV({\mathrm{\Δg}}^2,{\mathrm{\η}}^i)& \mathrm{...}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ COV({\mathrm{\Δg}}^i,{\mathrm{\η}}^1)& COV({\mathrm{\Δg}}^i,{\mathrm{\η}}^2)& \mathrm{...}& COV({\mathrm{\Δg}}^i,{\mathrm{\η}}^i)& \mathrm{...}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\end{array}\right]& L=\left[\begin{array}{c}{\mathrm{\Δg}}_1\\ {\mathrm{\Δg}}_2\\ \mathrm{...}\\ {\mathrm{\Δg}}_i\\ \mathrm{...}\end{array}\right]\end{array}$

D is noise variance matrix.

Relational expression between the deviation of plumb line and meridional component fourth of the twelve Earthly Branches component at the tenth of the twelve Earthly Branches is:

μ_i=ξ cosA_i+ηsinA_i (31)

A_iFor ship along survey line i, i+1 two geodetic azimuth of measuring point.

In sum, the present invention, relative to prior art, has required observation data volume expense phase relatively fewer, required To relatively low；Error is little, precision is high, is suitable to the beneficial effects such as remote elevation transmission over strait.

Accompanying drawing explanation

Fig. 1 survey line formula elevation over strait transmission data general technical route schematic diagram；

Fig. 2 astronmical leveling elevation transfer principle figure.

Detailed description of the invention

Below in conjunction with the accompanying drawings, the present invention is described in detail.

The integrated boat-carrying gravity of the present invention and the survey line formula land-sea height transfer method of GNSS, utilize integrated shipboard gravimeter Realizing, with GNSS technology, the data acquisition that survey line formula elevation over strait transmits, it comprises the following steps:

The first step, it is known that the highest h of the height datum point A of land_A, measure its geodetic height H by conventional GNSS method_A Gravity anomaly Δ g is measured with gravimeter_A；

Second step, with integrated shipboard gravimeter and GNSS boat along between land known point A and island (reef) tested point B On course line come and go a voyage, measure process survey line on gravimetric data Δ g_i(i=1,2 ...) and GNSS three-dimensional coordinate

3rd step, measures its geodetic height H at island (reef) tested point B by conventional GNSS method_BMeasure with gravimeter Gravity anomaly Δ g_B；

As it is shown in figure 1, the survey line formula land-sea height transfer method of the integrated boat-carrying gravity of the present invention and GNSS, number therein It is divided into three bulks according to process:

1, shipborne gravimetric data flow chart of data processing: under the dynamic environment of ocean, is placed in gravimeter on ship, carries out ocean Gravity measurement, is affected by ship attitude, acceleration, Etvs effect, noise of instrument etc., is processed boat-carrying gravimetric data To improve boat-carrying gravity precision.Boat-carrying its Correction of Errors of gravity survey data handling process includes: the effect correction that lags, zero point are floated Move correction, the correction of Vertical disturbing acceleration lingering effect, the correction of horizontal disturbance acceleration lingering effect, Etvs effect correction etc.. Carry out course line measuring point Spatial gravity anomaly after calculating sea height to correct.Correcting the method related to has the gaussian filtering along course line to calculate Method and conllinear error compensation method etc..

2, sea, course line height calculation process: correct include Attitude Correction, lag correction and by draft model and floating The altitude correction that sub-GNSS determines.Sea height deducted DTU10 mean recovery time and obtained sea high residual error epoch, used Gauss method Residual error sea height is filtered.The integrated approach using satellite to survey height+tidal observation+tidal model carries out sea, course line high accuracy and tests Card.

Boat-carrying GNSS processes and uses single epoch accurate one-point positioning method.

First, build boat-carrying GNSS data quality evaluation and control system.

Secondly, boat-carrying GNSS data is carried out pretreatment, carries out cycle-slip detection and repair and time synchronized.Carry out initial Change, determine fuzziness.Using NCEP, ECMWF or UCAR model calculating tropospheric delay as initial value, utilize GNSS precise ephemeris, Unknown parameter includes position, receiver clock-offsets and tropospheric delay residual error, carries out least square batch processing.Distributing boat-carrying rationally In GNSS receiver and antenna foundation, resolve position accurate epoch, speed, acceleration and ship appearance.

When GNSS precise ephemeris cannot be obtained, use history precise ephemeris and broadcast ephemeris, build ephemeris residual sequence, Using spectral analysis method, set up residual error ephemeris forecasting model, real-time broadcast ephemeris replaces precision plus residual error ephemeris forecasting model Ephemeris.

3, along the deviation of plumb line in course line: with EGM2008 for reference to gravitational field, use Remove-restore technology, utilize along course line Gravity residual error data by least square collocation method resolve the deviation of plumb line.

Processed by shipborne gravimetric data data, it is possible to determine along course line gravimetric data variance matrix and noise matrix.

According to the functional relationship between the deviation of plumb line and gravity anomaly and potential coefficient, EGM2008 model set up vertical line inclined Cross-covariance between difference and gravity, is processed by measured data and analyzes, constantly improving this Cross-covariance.

The idiographic flow of above-mentioned data processing method, comprises the following steps:

The first step, utilizes EGM2008 earth gravity field model, builds the gravity anomaly covariance matrix along ships' routing cov(Δg_i,Δg_j) and gravity-deviation of plumb line Cross-covariance cov (Δ g_i,ξ_j) and cov (Δ g_i,η_j)；

Second step, to being analyzed along ships' routing gravimetric data and GNSS three-dimensional geodetic coordinates data of being collected and Process；Actual measurement boat-carrying gravimetric data is carried out denoising and adjustment processing to improve its precision；Boat-carrying GNSS measures by ship appearance, ship Impact such as draft, wind and wave field etc., builds corresponding correction model, uses float GNSS technology, carries out single epoch accurate one-point Location/relative localization, improves sea high accuracy by conllinear adjustment and filtering method；Distribute boat-carrying GNSS rationally, build boat-carrying GNSS data quality evaluation and control system, it is achieved that the single epoch relative localization/Static Precise Point Positioning under marine environment, reach The high-acruracy survey of position, speed, acceleration and attitude；Utilize and accurately measure the survey line measuring point sea geodetic height obtained and drinking water The degree of depth carries out free air correction to shipborne gravimetric data data, checks and assesses sea gravimetric data and precision；

3rd step, utilizes GNSS three-dimensional data with the actual measurement processed along the gravimetric data of ships' routing, optimizes gravity different Often covariance matrix cov (Δ g_i,Δg_j) and gravity-deviation of plumb line Cross-covariance cov (Δ g_i,ξ_j) and cov (Δ g_i, η_j)；

4th step, uses Remove-restore technology, with EGM2008 gravity field model as reference, according to the actual measurement after processing GNSS three-dimensional geodetic coordinates data resolve model gravity anomaly Δ g_i ^modelWith the model deviation of plumb line (ξ^model _i,η^model _i)；According to place Real gravity anomaly data Δ g after reason_iWith model gravity anomaly Δ g_i ^modelCalculate residual gravity anomaly Δ g_i ^res,

Δg_i ^res=Δ g_i-Δg_i ^model (32)

5th step, the residual gravity data Δ g that the 4th step has been processed_i ^res, gravity anomaly covariance matrix cov (Δ g_i,Δg_j) and gravity-deviation of plumb line Cross-covariance cov (Δ g_i,ξ_j) and cov (Δ g_i,η_j), substitute into least square collocation Formula (30) calculates the remaining deviation of plumb line (ξ^res _i,η^res _i)；The model deviation of plumb line (ξ^model _i,η^model _i) and the remaining deviation of plumb line (ξ^res _i,η^res _i) recover the deviation of plumb line (ξ along survey line measuring point_i,η_i)；

${\mathrm{\ξ}}_i={\mathrm{\ξ}}_i^{res}+{{\mathrm{\ξ}}_i}^{\mathrm{mod}el}$

${\mathrm{\η}}_i={\mathrm{\η}}_i^{res}+{{\mathrm{\η}}_i}^{\mathrm{mod}el}---\left(33\right)$

By the deviation of plumb line (ξ_i,η_i) result of calculation substitution formula (31) calculating deviation of plumb line μ_i；

6th step, according to the ultimate principle of astronmical leveling, has two somes a, b of infinite approach, as in figure 2 it is shown, on a point n₁n₁' represent reference ellipsoid normal, a₁a₁' represent geoid normal, i.e. gravity direction, the sky on ab direction Literary composition the earth deviation of plumb line component is μ_ab。

dN_abRepresent 2 differences relative to the geoidal rise of reference ellipsoid of ab, represent between ab 2 with ds Distance.

dN_ab=-μ_abds (34)

The then difference Δ N of the geoidal rise between land known point A and island (reef) tested point B_ABIt is represented by:

${\mathrm{\ΔN}}_{AB}=-{\∫}_A^B{\mathrm{\μ}}_{i}ds---\left(35\right)$

Above formula discrete representation is,

${\mathrm{\ΔN}}_{AB}=-\underset{i=1}{\overset{n}{\Σ}}{\mathrm{\μ}}_i{\mathrm{\Δs}}_i---\left(36\right)$

By the 5th step deviation of plumb line μ_iResult of calculation substitutes into astronmical leveling formula formula (35), calculates along ships' routing i (i =1,2 ...) difference of geoidal rise between point and land known point A

The relation of geodetic height, positive height and undulation of the geoid is:

H_i=h_i+N_i (37)

During calculating, need to project on ship line direction the calculated deviation of plumb line, and according to greatly The relation of ground height high, positive and undulation of the geoid calculates the positive high of ships' routing i point；

7th step, the ship calculated according to the 6th step along ships' routing measuring point i (i=1,2 ...) and put positive high, to the 4th Step processed along course line gravimetric data Δ g_i ^resCarry out Spatial gravity anomaly reduction；

Residual gravity data application least square collocation after reduction is recalculated along course line measuring point i (i=1,2 ...) The remaining deviation of plumb line of point, and again recover the deviation of plumb line, result of calculation substitutes into astronmical leveling formula, again revises along ships' routing Measuring point i (i=1,2 ...) difference of some geoidal rise, and to all geoidal rises in course line between A, B 2 Difference be integratedObtain the geoidal rise between land known point A and island (reef) tested point B it Difference Δ N_BA；

8th step, the land known point A calculated according to the 7th step and the geoidal rise of island (reef) tested point B it Difference, the A point recorded in conjunction with the first step and the geodetic height of B point, the positive high of unknown point B point can be obtained,

The positive discrepancy in elevation between A, B 2 is,

$\begin{array}{c}{h}_{AB}=-H_A+N_A+(H_B-N_B)={\mathrm{\ΔH}}_{AB}-{\mathrm{\ΔN}}_{AB}\\ ={\mathrm{\ΔH}}_{AB}+\underset{i=1}{\overset{n}{\Σ}}{\mathrm{\μ}}_i{\mathrm{\Δs}}_i\end{array}---\left(38\right)$

Unknown point B point the most a height of:

$h_B=h_A+h_{AB}=h_A+H_B-H_A+\underset{i=1}{\overset{n}{\Σ}}{\mathrm{\μ}}_i{\mathrm{\Δs}}_i---\left(39\right)$

Above-mentioned height datum transmission method over strait, is preferably, and utilizes integrated shipboard gravimeter and GNSS technology to realize surveying The data acquisition of wire type elevation over strait transmission；

High-precision deviation of plumb line data are the basic datas of height transfer method, on boat-carrying gravimetric data processing basis On, set up gravimetric data variance matrix and gravity-deviation of plumb line side of association mutually by EGM2008 earth gravitational field potential coefficient standard deviation Difference matrix, optimizes covariance matrix, by least square collocation method resolving high precision along course line in conjunction with actual measurement gravimetric data The deviation of plumb line；

As in figure 2 it is shown, last, utilize astronmical leveling principle to realize the remote transmission of land-sea height datum；

The survey line formula land-sea height transfer method of above-mentioned integrated boat-carrying gravity and GNSS, it is also possible to be preferably, described Gravity anomaly covariance matrix also includes noise variance matrix；In order to further improve the precision that data process, permissible In gravity anomaly covariance matrix, add noise variance matrix, be modified；

The acquisition of described noise variance matrix can be sought by experiment, it is possible to is obtained by analog data or empirical data Arrive；

It should be noted that owing to effect of noise has randomness and occasionality, its size to data influence, need Explored by experiment and verify.

Claims (3)

1. the survey line formula land-sea height transfer method of an integrated boat-carrying gravity and GNSS, it is characterised in that comprise the following steps:

The first step, it is known that the highest h of the height datum point A of land_A, measure its geodetic height H by conventional GNSS method_AWith with Gravity anomaly Δ g measured by gravimeter_A；

Second step, with integrated shipboard gravimeter and GNSS boat along the course line between land known point A and island (reef) tested point B Upper come and go a voyage, measure process survey line on gravimetric data Δ g_iWith GNSS three-dimensional coordinate

3rd step, measures its geodetic height H at island (reef) tested point B by conventional GNSS method_BDifferent with measuring gravity with gravimeter Often Δ g_B；

4th step, utilizes EGM2008 earth gravity field model, builds the gravity anomaly auto-covariance matrix along ships' routing and weight Power deviation of plumb line Cross-covariance；

It is analyzed to collect along ships' routing gravimetric data and GNSS three-dimensional data and processes, and utilizing GNSS three-dimensional Data and the actual measurement processed, along the gravimetric data of ships' routing, optimize gravity anomaly auto-covariance matrix and gravimetric plumb line deflection Difference Cross-covariance；

5th step, the gravimetric data, gravity anomaly auto-covariance matrix and the gravity-deviation of plumb line that the 4th step have been processed are assisted mutually Variance matrix, uses least square collocation principle to calculate the deviation of plumb line, result substitutes into astronmical leveling formula, calculate along ship The difference of the geoidal rise between course line measuring point i point and land known point A

Calculate during, need to project on ship line direction the calculated deviation of plumb line, and according to geodetic height, The highest and undulation of the geoid relation calculates the positive height along ships' routing measuring point i point；

6th step, the positive height along ships' routing measuring point i point calculated according to the 5th step, processed the 4th step is heavy along course line Force data carries out Spatial gravity anomaly reduction；

Gravimetric data after reduction is used least square collocation recalculate along the course line measuring point deviation of plumb line, and result of calculation substitutes into Astronmical leveling formula, revises the difference along ships' routing measuring point geoidal rise again, and to the institute in course line between A, B 2 The difference having geoidal rise is integratedObtain between land known point A and island (reef) tested point B The difference Δ N of geoidal rise_BA；

7th step, the land known point A calculated according to the 6th step and the difference of the geoidal rise of island (reef) tested point B, The A point recorded in conjunction with the first step and the geodetic height of B point, can obtain the positive high of unknown point B point；

Above-mentioned i=1,2 ....

The survey line formula land-sea height transfer method of integrated boat-carrying gravity the most according to claim 1 and GNSS, its feature exists In, utilize integrated shipboard gravimeter and GNSS technology to realize the data acquisition of survey line formula elevation over strait transmission；

Utilize EGM2008 earth gravity field model, build gravity anomaly auto-covariance matrix and gravity-deviation of plumb line cross covariance Matrix；

Utilize actual measurement along the gravimetric data of ships' routing, optimize gravity anomaly auto-covariance matrix and gravimetric plumb line deflection is assisted mutually Variance matrix；

In conjunction with course line measuring point gravimetric data, utilize least square collocation method, ask for the high accuracy deviation of plumb line；

Finally, astronmical leveling principle is utilized to realize the remote transmission of land-sea height datum.

The survey line formula land-sea height transfer method of integrated boat-carrying gravity the most according to claim 1 and GNSS, its feature exists In, described gravity anomaly covariance matrix also includes noise variance matrix；

Described noise variance matrix is sought acquisition by experiment, is obtained by analog data or empirical data.