CN107167142A - Build the Interpolation Property of Radial Basis Function algorithm of subaqueous gravity assisting navigation ambient field - Google Patents
Build the Interpolation Property of Radial Basis Function algorithm of subaqueous gravity assisting navigation ambient field Download PDFInfo
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- CN107167142A CN107167142A CN201710474963.9A CN201710474963A CN107167142A CN 107167142 A CN107167142 A CN 107167142A CN 201710474963 A CN201710474963 A CN 201710474963A CN 107167142 A CN107167142 A CN 107167142A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
- G01C21/203—Specially adapted for sailing ships
Abstract
The present invention relates to a kind of Interpolation Property of Radial Basis Function algorithm for building subaqueous gravity assisting navigation ambient field, belong to take into account and remove the electronic information technical field that recovery technology builds subaqueous gravity assisting navigation ambient field, including the data based on marine gravity observation, joint building global gravitational field model, the Interpolation Property of Radial Basis Function algorithm for removing recovery technology using taking into account, builds the marine gravity ambient field for meeting subaqueous gravity assisting navigation demand.The present invention includes following technological merit, eliminates the influence of edge effect, improves octuple arithmetic accuracy；The accuracy of algorithm is drastically increased, with prominent substantive distinguishing features and significant progress.
Description
Technical field
The present invention relates to a kind of Interpolation Property of Radial Basis Function algorithm for building subaqueous gravity assisting navigation ambient field, belong to and take into account
Remove the electronic information technical field that recovery technology builds subaqueous gravity assisting navigation ambient field.
Background technology
With the propulsion of national deep-sea strategy, underwater navigation technology is of increased attention.Underwater navigation technology
In most widely used method be inertial navigation, this method has the advantages that precision is high, good reliability, but is carrying out track solution
Systematic error is accumulated over time when calculating with positioning calculation, is such as irregularly resetted, position error can unrestrictedly increase, uncomfortable
Heshui diving device long-time autonomous navigation.Gravity belongs to the intrinsic physical features of the earth, is carried out using marine gravity information and weighed under water
Power assisting navigation, is the effective way for overcoming inertial navigation system position error with the defect of time integral.High Accuracy and High Resolution
The marine gravity ambient field of rate is the premise and necessary condition for carrying out subaqueous gravity assisting navigation, and sea gravity measurement is due to economy
The reason in terms of cost and time cost, can not directly obtain the gravity letter for reaching subaqueous gravity assisting navigation resolution requirement
Breath, seeks to build the high-precision interpolation algorithm of marine gravity ambient field, is the steps necessary for realizing subaqueous gravity assisting navigation.
Interpolation Property of Radial Basis Function method is based on relative distance of the gravity anomaly on locus, in given radial direction base letter
Under conditions of number, optimization is iterated by building response surface model, so that the global optimum for waiting to estimate a gravity anomaly is obtained,
This method has amount of calculation relatively small, the characteristics of computational accuracy is relatively high, in widespread attention in many engineering fields.Ground
Ball gravitation information has its intrinsic physical characteristic, based on Laplace's equation, can be expressed as what is be made up of different orders
The humorous form of ball, the building global gravitational field model using EGM2008 as representative provides the middle long wave gravitation information of 2160 orders, to set up sea
Foreign Gravity Background provides physical characteristic information.Interpolation Property of Radial Basis Function algorithm is only accounted for waiting to estimate a little between observation station
Spatial positional information, to improve the interpolation precision of algorithm, it is necessary to which research takes marine gravity physical characteristic into account and builds subaqueous gravity
The Interpolation Property of Radial Basis Function algorithm of assisting navigation ambient field.
The content of the invention
Take into account it is an object of the invention to provide one kind and remove recovery technology, build subaqueous gravity assisting navigation ambient field
Interpolation Property of Radial Basis Function algorithm, overcomes the deficiencies in the prior art.
The principle of the present invention is, only accounts for waiting to estimate sky a little between observation station for Interpolation Property of Radial Basis Function algorithm
Between positional information, the problem of not accounting for earth gravitational field intrinsic physical characteristic, the present invention proposes that one kind is taken into account and removes recovery skill
Art builds the Interpolation Property of Radial Basis Function new algorithm of subaqueous gravity assisting navigation ambient field, i.e., using building global gravitational field model, first
The gravity anomaly model value in gravity anomaly observation is removed, the residual error gravity anomaly at observation station is obtained, then with observation station
Based on the residual error gravity anomaly at place, using Interpolation Property of Radial Basis Function algorithm, obtain waiting estimating at residual error gravity anomaly, finally
A gravity anomaly model value for residual error gravity anomaly at recovering to wait to estimate, obtain waiting estimating at GRAVITY ANOMALIES, structure meets water
The marine gravity ambient field of lower Gravity-aided navigation demand.
The present invention is achieved through the following technical solutions, including the data based on marine gravity observation, joint whole world weight
Force field model, using the Interpolation Property of Radial Basis Function algorithm of removing recovery technology is taken into account, structure meets subaqueous gravity assisting navigation need
The marine gravity ambient field asked.
The Interpolation Property of Radial Basis Function algorithm for building subaqueous gravity assisting navigation ambient field comprises the following steps：
Step 1, the model gravity anomaly removed in gravity anomaly observation, obtain the residual error gravity anomaly at observation station,
δΔgi=Δ gi-ΔgiM
In formula, Δ giIt is gravity anomaly actual measured value at observation station i, Δ giMIt is the observation station calculated by building global gravitational field model
Model gravity anomaly at i, δ Δs giIt is the residual error gravity anomaly at observation station i；
Model gravity anomaly Δ gMCalculation formula be：
In formula, (r, θ, λ) be respectively the earth's core at the point to footpath, colatitude and longitude, a is reference ellipsoid major radius, and GM is universal
The product of gravitational constant and earth gross mass,WithIt is m potential coefficient of standardizing completely of n ranks,For association
Legendre functions, NmaxIt is top step number；
Step 2, using Interpolation Property of Radial Basis Function algorithm, obtain waiting estimating at residual error gravity anomaly,
Interpolation Property of Radial Basis Function is exactly to choose radial function φ (d), utilizes wrench tectonics radial direction baseTo
Fixed gravity anomaly observation data find such as minor function：
Meet S (Xi)=δ Δ g (Xi)
In formula, λiFor real coefficient, X is gravity anomaly observation station position, | | | | it is Euclidean Norm,() is RBF,
The present invention takes multiple quadratic function：
In formula, d is the relative distance that gravity anomaly observation station calculates point to gravity anomaly, and e is the smoothing factor specified, the present invention
Take 2.2 × 10-5, coefficient lambda is easily tried to achieve by known gravity anomaly residual error, so then spatially positional information obtains waiting to estimate a little
Residual error gravity anomaly δ Δs g0；
Step 3, recover the model gravity anomaly waiting to estimate a residual error gravity anomaly, obtain waiting estimating at GRAVITY ANOMALIES
Δg0=δ Δs g0+Δg0M
In formula, Δ g0It is a gravity anomaly calculated value, Δ g at waiting to estimate0MIt is to estimate a little 0 by waiting of calculating of building global gravitational field model
Model gravity anomaly, δ Δs g0It is the residual error gravity anomaly at waiting to estimate.
The present invention includes following technological merit, eliminates the influence of edge effect, improves octuple arithmetic accuracy；Greatly
The accuracy of algorithm is improved, with prominent substantive distinguishing features and significant progress.
Brief description of the drawings
Fig. 1 is the characteristic statisticses figure of gravity abnormal data.
Fig. 2 is the comparison chart of gravity Anomaly standard value.
Fig. 3 is traditional inverse distance weighted interpolation algorithm and the difference value schematic diagram of DTU10 gravity anomaly standard values.
Fig. 4 is inventive algorithm and the difference value schematic diagram of DTU10 gravity anomaly standard values.
Embodiment
The present invention be it is a kind of take into account remove recovery technology build subaqueous gravity assisting navigation ambient field RBF insert
It is worth new method, including the data based on marine gravity observation, combines building global gravitational field model, recovery skill is removed using taking into account
The Interpolation Property of Radial Basis Function algorithm of art, builds the marine gravity ambient field for meeting subaqueous gravity assisting navigation demand.
The Interpolation Property of Radial Basis Function algorithm for building subaqueous gravity assisting navigation ambient field comprises the following steps：
Step 1, the model gravity anomaly removed in gravity anomaly observation, obtain the residual error gravity anomaly at observation station,
δΔgi=Δ gi-ΔgiM
In formula, Δ giIt is gravity anomaly actual measured value at observation station i, Δ giMIt is the observation station calculated by building global gravitational field model
Model gravity anomaly at i, δ Δs giIt is the residual error gravity anomaly at observation station i；
Model gravity anomaly Δ gMCalculation formula be：
In formula, (r, θ, λ) be respectively the earth's core at the point to footpath, colatitude and longitude, a is reference ellipsoid major radius, and GM is universal
The product of gravitational constant and earth gross mass,WithIt is m potential coefficient of standardizing completely of n ranks,For association
Legendre functions, NmaxIt is top step number；
Step 2, using Interpolation Property of Radial Basis Function algorithm, obtain waiting estimating at residual error gravity anomaly,
Interpolation Property of Radial Basis Function is exactly to choose radial function φ (d), utilizes wrench tectonics radial direction baseTo
Fixed gravity anomaly observation data find such as minor function：
Meet S (Xi)=δ Δ g (Xi)
In formula, λiFor real coefficient, X is gravity anomaly observation station position, | | | | it is Euclidean Norm,() is RBF,
The present invention takes multiple quadratic function：
In formula, d is the relative distance that gravity anomaly observation station calculates point to gravity anomaly, and e is the smoothing factor specified, the present invention
Take 2.2 × 10-5, coefficient lambda is easily tried to achieve by known gravity anomaly residual error, so then spatially positional information obtains waiting to estimate a little
Residual error gravity anomaly δ Δs g0；
Step 3, recover the model gravity anomaly waiting to estimate a residual error gravity anomaly, obtain waiting estimating at GRAVITY ANOMALIES
Δg0=δ Δs g0+Δg0M
In formula, Δ g0It is a gravity anomaly calculated value, Δ g at waiting to estimate0MIt is to estimate a little 0 by waiting of calculating of building global gravitational field model
Model gravity anomaly, δ Δs g0It is the residual error gravity anomaly at waiting to estimate.
For the objects, technical solutions and advantages of the present invention are more clearly understood, illustrate below and detailed is made to present invention
Describe in detail bright.Design data is tested based on DTU10 gravity anomaly numerical models, and the model is combined by Denmark University of Science and Technology
Many resolution ratio for Altimetry Data calculating are 1 ' × 1 ' global marine site gravitational field numerical model.Using 2160 orders
EGM2008 gravity field models are used as the reference field for removing recovery technology.3 ° × 3 ° blocks be have selected as main experimental area
Carry out numerical computations, the DTU10 GRAVITY ANOMALIESs in the marine site, EGM2008 gravity anomalies model value and residual error GRAVITY ANOMALIES
Characteristic statisticses are shown in Fig. 1：Characteristic statisticses table/mGal of trial zone gravity anomaly data.
Testing program is that gridization encrypts application, that is, sets original grid data resolution and be unsatisfactory for subaqueous gravity auxiliary
The demand of navigation application is, it is necessary to carry out grid encryption to obtain the marine gravity anomaly ambient field of higher resolution.By DTU10
Gravity anomaly numerical model vacuates into 5' × 5' grid data, is then encrypted to resolution ratio using gridding method for 1'
× 1' grid data.Reference pair the inventive method is used as by the use of the DTU10 gravity anomalies data for having neither part nor lot in gridization calculating
Obtained result of calculation carries out precision evaluation, in order to eliminate the influence of edge effect, participates in the data area center of precision evaluation
2 ° × 2 ° of region.For the validity of comparative analysis inventive algorithm, the conventional radial that recovery technology is removed without application is introduced
Basic function interpolation algorithm carries out grid calculating.Fig. 2 gives the result of calculation and DTU10 gravity anomaly marks of two kinds of interpolation methods
The comparison result of quasi- value.It can be seen that with reference to Fig. 3, Fig. 4, the subaqueous gravity assisting navigation ambient field precision that inventive algorithm is built is
0.227mGal, better than the 1.835mGal of conventional radial basic function interpolation algorithm precision, improves octuple arithmetic accuracy, checking
The advance of inventive algorithm, the marine site background field energy built based on inventive algorithm effectively meets subaqueous gravity assisting navigation
Demand.
Claims (2)
1. the Interpolation Property of Radial Basis Function algorithm of subaqueous gravity assisting navigation ambient field is built, including using marine gravity observation as base
Plinth data, combine building global gravitational field model, and using the Interpolation Property of Radial Basis Function algorithm of removing recovery technology is taken into account, structure meets water
The marine gravity ambient field of lower Gravity-aided navigation demand.
2. according to the Interpolation Property of Radial Basis Function algorithm of the structure subaqueous gravity assisting navigation ambient field described in claim 1, including with
Lower step：
Step 1, the model gravity anomaly removed in gravity anomaly observation, obtain the residual error gravity anomaly at observation station,
δΔgi=Δ gi-ΔgiM
In formula, Δ giIt is gravity anomaly actual measured value at observation station i, Δ giMIt is the observation station calculated by building global gravitational field model
Model gravity anomaly at i, δ Δs giIt is the residual error gravity anomaly at observation station i；
Model gravity anomaly Δ gMCalculation formula be：
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In formula, (r, θ, λ) be respectively the earth's core at the point to footpath, colatitude and longitude, a is reference ellipsoid major radius, and GM is universal
The product of gravitational constant and earth gross mass,WithIt is m potential coefficient of standardizing completely of n ranks,For association
Legendre functions, NmaxIt is top step number；
Step 2, using Interpolation Property of Radial Basis Function algorithm, obtain waiting estimating at residual error gravity anomaly,
Interpolation Property of Radial Basis Function is exactly to choose radial function φ (d), utilizes wrench tectonics radial direction baseTo given
Gravity anomaly observation data find such as minor function：
Meet S (Xi)=δ Δ g (Xi)
In formula, λiFor real coefficient, X is gravity anomaly observation station position, | | | | it is Euclidean Norm,For RBF, sheet
Invention takes multiple quadratic function：
In formula, d is the relative distance that gravity anomaly observation station calculates point to gravity anomaly, and e is the smoothing factor specified, the present invention
Take 2.2 × 10-5, coefficient lambda is easily tried to achieve by known gravity anomaly residual error, so then spatially positional information obtains waiting to estimate a little
Residual error gravity anomaly δ Δs g0；
Step 3, recover the model gravity anomaly waiting to estimate a residual error gravity anomaly, obtain waiting estimating at GRAVITY ANOMALIES Δ g0=δ
Δg0+Δg0M
In formula, Δ g0It is a gravity anomaly calculated value, Δ g at waiting to estimate0MIt is to estimate a little 0 by waiting of calculating of building global gravitational field model
Model gravity anomaly, δ Δs g0It is the residual error gravity anomaly at waiting to estimate.
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108898252A (en) * | 2018-07-02 | 2018-11-27 | 河南师范大学 | A kind of prediction technique of whole nation troposphere Atmosphere Refractivity Profile |
| CN109085656A (en) * | 2018-09-19 | 2018-12-25 | 中国船舶重工集团公司第七0七研究所 | A kind of high-precision gravity figure building of Feature Oriented and interpolation method |
| CN111506871A (en) * | 2020-03-06 | 2020-08-07 | 中国人民解放军92859部队 | Radial basis function grid method for constructing sea area perpendicular deviation model based on frequency domain characteristics |
| CN112229403A (en) * | 2020-08-31 | 2021-01-15 | 中国空间技术研究院 | Method for improving marine gravity reconstruction precision based on geodetic level three-dimensional correction principle |
| CN112229404A (en) * | 2020-08-31 | 2021-01-15 | 中国空间技术研究院 | Method for improving ocean gravity field interpolation precision based on three-dimensional optimization principle of submarine topography |
| CN112949049A (en) * | 2021-02-08 | 2021-06-11 | 中国人民解放军92859部队 | Method for calculating gravity anomaly low-order radial derivative by using band-limiting thought |
| CN112965124A (en) * | 2021-02-08 | 2021-06-15 | 中国人民解放军92859部队 | Method for calculating abnormal vertical gradient of external gravity by considering local guarantee conditions |
| CN112965125A (en) * | 2021-02-08 | 2021-06-15 | 中国人民解放军92859部队 | Method for calculating eastern component of external disturbance gravity based on gravity anomaly |
-
2017
- 2017-06-21 CN CN201710474963.9A patent/CN107167142A/en not_active Withdrawn
Non-Patent Citations (1)
| Title |
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| 李姗姗: "水下重力辅助惯性导航的理论与方法研究", 《中国博士学位论文全文数据库基础科学辑》 * |
Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108898252A (en) * | 2018-07-02 | 2018-11-27 | 河南师范大学 | A kind of prediction technique of whole nation troposphere Atmosphere Refractivity Profile |
| CN109085656A (en) * | 2018-09-19 | 2018-12-25 | 中国船舶重工集团公司第七0七研究所 | A kind of high-precision gravity figure building of Feature Oriented and interpolation method |
| CN111506871A (en) * | 2020-03-06 | 2020-08-07 | 中国人民解放军92859部队 | Radial basis function grid method for constructing sea area perpendicular deviation model based on frequency domain characteristics |
| CN112229403A (en) * | 2020-08-31 | 2021-01-15 | 中国空间技术研究院 | Method for improving marine gravity reconstruction precision based on geodetic level three-dimensional correction principle |
| CN112229404A (en) * | 2020-08-31 | 2021-01-15 | 中国空间技术研究院 | Method for improving ocean gravity field interpolation precision based on three-dimensional optimization principle of submarine topography |
| CN112229404B (en) * | 2020-08-31 | 2024-02-09 | 中国空间技术研究院 | Method for improving interpolation accuracy of ocean gravity field based on submarine topography three-dimensional optimization principle |
| CN112229403B (en) * | 2020-08-31 | 2024-02-20 | 中国空间技术研究院 | Method for improving ocean gravity reconstruction accuracy based on three-dimensional correction principle of ground level |
| CN112949049A (en) * | 2021-02-08 | 2021-06-11 | 中国人民解放军92859部队 | Method for calculating gravity anomaly low-order radial derivative by using band-limiting thought |
| CN112965124A (en) * | 2021-02-08 | 2021-06-15 | 中国人民解放军92859部队 | Method for calculating abnormal vertical gradient of external gravity by considering local guarantee conditions |
| CN112965125A (en) * | 2021-02-08 | 2021-06-15 | 中国人民解放军92859部队 | Method for calculating eastern component of external disturbance gravity based on gravity anomaly |
| CN112965125B (en) * | 2021-02-08 | 2022-08-05 | 中国人民解放军92859部队 | Method for calculating eastern component of external disturbance gravity based on gravity anomaly |
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