CN104792305A - Determination method of kernel function smooth factor of GPS level transformation model - Google Patents
Determination method of kernel function smooth factor of GPS level transformation model Download PDFInfo
- Publication number
- CN104792305A CN104792305A CN201510221938.0A CN201510221938A CN104792305A CN 104792305 A CN104792305 A CN 104792305A CN 201510221938 A CN201510221938 A CN 201510221938A CN 104792305 A CN104792305 A CN 104792305A
- Authority
- CN
- China
- Prior art keywords
- matrix
- level transformation
- kernel function
- transformation model
- smoothing factor
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C5/00—Measuring height; Measuring distances transverse to line of sight; Levelling between separated points; Surveyors' levels
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The invention discloses a method for determining a kernel function smooth factor in a building process of a GPS level transformation model, belonging to the technical field of geodesy and surveying engineering. The GPS level transformation is generally realized through a geoidal surface model; the geoidal surface can be decomposed into the superposition of multiple simple curved surfaces in a certain range, and the simple curved surfaces can be expressed by using the kernel function; a smooth factor in the kernel function is a key parameter. For many years, the smooth factor is subjected to manual trial or empirical formula estimation, while the accuracy of the smooth factor determined in a manual rough way cannot be improved, and the geoidal surface model cannot reach up to be optimal. According to the brand new technical scheme on the determination of the smooth factor, the smooth factor and a model coefficient can be used as unknown parameters at the same time; based on the principle of least squares, by adopting a deterministic searching algorithm, an optimal smooth factor can be accurately calculated in an iterative computation way; the defect that the smooth factor is determined through human experience can be completely solved, and the accuracy of the GPS level transformation model is improved.
Description
Technical field
The present invention is a kind of method determined for GPS level transformation model construction process Kernel Function smoothing factor, belongs to " physical geodesy " technical field in " Geodesy and Survey Engineering " subject.
Background technology
As everyone knows, the conversion of GPS level is realized by geoid's model usually, and geoid surface is the curved surface of very complicated a, continuous and derivable, and this curved surface can resolve into the superposition of many simple surfaces.In the construction process of geoid's model, need to adopt same class function to describe these simple surfaces, this class function is commonly referred to kernel function.Kernel function after determining again by the simple surface superposition corresponding to it, to form a complicated function to describe geoid surface.In the Local Area Geoid Refining basic fundamental regulation of China, specify that kernel function adopts the quadratic function of node and interpolation point coordinate.In order to make node and interpolation point obtain balanced fitting precision, need to add a smoothing factor in kernel function.For many years, China is in geoid surface modeling process, and smoothing factor is all the experience according to technician, is determined, or is estimated by experimental formula, and do not have better technical scheme by artificial tentative calculation.But the method for current this artificial tentative calculation or facile synthesis determination smoothing factor, there are many drawbacks.First be that surface fitting precision is very responsive to smoothing factor, though smoothing factor change ten thousand/ size, fitting result also there will be larger difference, and manually estimate cannot accomplish the precision of smoothing factor to bring up to ten thousand/; Next smoothing factor being artificial experience is determined cannot make geoid surface surface model reach optimum, thus the precision of loss Height Abnormity Model.But lack effective defining method due to kernel function smoothing factor, artificial experience tentative calculation or simple estimation method can only be adopted at present both at home and abroad to determine the technical scheme of smoothing factor.
Patent of the present invention is the brand new technical scheme that GPS level transformation model kernel function smoothing factor that we propose is determined, it is not adopt artificial tentative calculation to determine smoothing factor, but using smoothing factor as unknown parameter, based on the principle of least square, adopt Deterministic searching algorithm by iterative computation, accurately calculate the best smoothing factor of kernel function; Its advantage to be the determination precision of smoothing factor to be brought up to after radix point nine, solves the drawback of artificial experience determination smoothing factor up hill and dale, thus improves the precision of GPS level transformation model.
Summary of the invention
A kind of GPS level transformation model kernel function smoothing factor defining method, its elementary object is the optimal estimation that fine search goes out GPS level transformation model Kernel Function smoothing factor, instead of is determined by artificial experience or approximate formula cursorily.Innovative point of the present invention is: the international precise calculation method proposing kernel function smoothing factor first at home, completely avoid imprecision and the non-optimal of artificial experience or approximate formula, optimum model parameter and GPS level conversion accuracy can be obtained in practical application.
Essential characteristic of the present invention is, for GPS level transformation model, smoothing factor in its kernel function and model weight coefficient matrix are used as unknown parameter simultaneously, under the condition meeting criterion of least squares, adopt iterative algorithm to calculate optimum smoothing factor and model weight coefficient simultaneously, the matching of model and prediction error are minimized.Solve parameter estimation based on the principle of least square, in theory tightly, iterative computation can obtain very high computational accuracy, thus obtains optimum GPS level transformation model.
When GPS level conversion model parameters resolves, owing to being all normalized known point and node coordinate, which kind of coordinate and coordinate figure size regardless of model reach, all by unification to [0,1] between, therefore applicability of the present invention and region have nothing to do, and the GPS level conversion model parameters being applicable to any area resolves.
Key technical feature of the present invention and flow process comprise following content:
(A) known GPS leveling point and node coordinate are normalized;
(B) kernel function smoothing factor and model coefficient matrix are used as unknown parameter to solve simultaneously, unknown parameter initial value is set;
(C) according to GPS level transformation model expression formula, partial derivative is asked to unknown parameter, obtain Jacobi matrix
;
(D) according to Jacobi matrix and model error, Hessian matrix and error matrix is tried to achieve
;
(E) based on the principle of least square, the correction obtaining kernel function smoothing factor and model coefficient is resolved;
(F) according to iterative strategy, calculate new model parameter and carry out next round iteration, if meet stopping criterion for iteration, then termination of iterations, and obtain final GPS level transformation model;
Accompanying drawing explanation
Fig. 1 GPS level transformation model kernel function smoothing factor defining method process flow diagram
Embodiment
A kind of GPS level transformation model kernel function smoothing factor defining method, is characterized in that, comprise the following steps in concrete enforcement:
L) GPS level transformation model known point Unitary coordinate, adopts normalization computing formula,
,
, wherein
,
minimum in known point respectively
,
coordinate;
,
maximum in known point respectively
,
coordinate; Unitary coordinate is by the known point in model reach
between coordinate naturalization to [0,1];
2) according to the quantity of known point quantity determination node, the quantity of node should be less than known point quantity, and node can be known point, also can be unknown point, and node should balancedly be distributed in the square graticule mesh of rule, and its coordinate is normalization coordinate
;
3) kernel function of GPS level transformation model
form be
, wherein
for smoothing factor to be asked;
4) GPS level transformation model
expression formula is:
, wherein
for node number,
for weight matrix to be asked;
5) smoothing factor is set
initial value be 0.5, setting weight matrix
initial value be
;
6) Jacobi matrix is calculated
, wherein
,
for the number of known point,
;
7) Hessian matrix is calculated according to Jacobi matrix
;
8) height anomaly of known GPS leveling point is
, and by GPS level transformation model
the height anomaly calculating this point is
, then model error matrix
, calculate according to Jacobi matrix and error matrix
matrix
;
9) according to Hessian matrix
with
matrix, by the correction of iterative computation smoothing factor and weight matrix
:
, wherein
,
,
for unit matrix;
10) establish
,
,
, then when
time,
; When
time,
;
11) if residual error after iteration
, then upgrade fol-lowing values:
,
,
,
, enter next round iteration; Otherwise change
value after enter next round iteration;
12) if residual error after iteration
reach appointment permissible accuracy, or iterative computation reaches the number of times of specifying, then stop iteration, now obtain kernel function smoothing factor
optimal value, simultaneously also obtain weight matrix
value;
13) according to the optimum smoothing factor that iterative computation obtains
and weight matrix
value, and point coordinate
by GPS level transformation model
calculate the height anomaly of this point.
Claims (2)
1. a GPS level transformation model kernel function smoothing factor defining method, is characterized in that, comprise the following steps:
L () GPS level transformation model known point Unitary coordinate, adopts normalization computing formula,
,
, wherein,
be respectively minimum in known point
,
coordinate;
,
be respectively maximum in known point
,
coordinate;
,
for the original coordinates before normalization, Unitary coordinate is by the known point in model reach
between coordinate naturalization to [0,1];
(2) according to the quantity of known point quantity determination node, the quantity of node should be less than known point quantity, and node can be known point, also can be unknown point, and node should balancedly be distributed in the square graticule mesh of rule, and its coordinate is normalization coordinate
;
(3) kernel function of GPS level transformation model
form be
, wherein
for smoothing factor to be asked;
(4) GPS level transformation model
expression formula is:
, wherein
for node number,
for weight matrix to be asked;
(5) smoothing factor is set
initial value be 0.5, setting weight matrix
initial value be
;
(6) Jacobi matrix is calculated
, wherein
,
for the number of known point,
;
(7) Hessian matrix is calculated according to Jacobi matrix
;
(8) height anomaly of known GPS leveling point is
, and by GPS level transformation model
the height anomaly calculating this point is
, then model error matrix
, calculate according to Jacobi matrix and error matrix
matrix
;
(9) according to Hessian matrix
with
matrix, by the correction of iterative computation smoothing factor and weight matrix
:
, wherein
,
,
for unit matrix;
(10) establish
,
,
, then when
time,
; When
time,
;
(11) if residual error after iteration
, then upgrade fol-lowing values:
,
,
,
, enter next round iteration; Otherwise change
value after enter next round iteration;
(12) if residual error after iteration
reach appointment permissible accuracy, or iterative computation reaches the number of times of specifying, then stop iteration, now obtain kernel function smoothing factor
optimal value, simultaneously also obtain weight matrix
value;
(13) according to the optimum smoothing factor that iterative computation obtains
and weight matrix
value, and point coordinate
by GPS level transformation model
calculate the height anomaly of this point.
2. GPS level transformation model kernel function smoothing factor defining method according to claim 1, it is characterized in that, the method can be applicable in the calculating of GPS level transformation model weight matrix.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510221938.0A CN104792305B (en) | 2015-05-05 | 2015-05-05 | Determination method of kernel function smooth factor of GPS level transformation model |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510221938.0A CN104792305B (en) | 2015-05-05 | 2015-05-05 | Determination method of kernel function smooth factor of GPS level transformation model |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104792305A true CN104792305A (en) | 2015-07-22 |
| CN104792305B CN104792305B (en) | 2017-01-18 |
Family
ID=53557305
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510221938.0A Expired - Fee Related CN104792305B (en) | 2015-05-05 | 2015-05-05 | Determination method of kernel function smooth factor of GPS level transformation model |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104792305B (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6492934B1 (en) * | 2001-08-06 | 2002-12-10 | Rockwell Collins | Method of deriving ground speed for descending aircraft |
| CN101839710A (en) * | 2010-06-12 | 2010-09-22 | 中国测绘科学研究院 | Method for optimizing quasi-geoid calculation |
| CN102944220A (en) * | 2012-11-30 | 2013-02-27 | 长沙理工大学 | Gravity level surface and global position system (GPS) level difference decomposition and fusion method |
-
2015
- 2015-05-05 CN CN201510221938.0A patent/CN104792305B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6492934B1 (en) * | 2001-08-06 | 2002-12-10 | Rockwell Collins | Method of deriving ground speed for descending aircraft |
| CN101839710A (en) * | 2010-06-12 | 2010-09-22 | 中国测绘科学研究院 | Method for optimizing quasi-geoid calculation |
| CN102944220A (en) * | 2012-11-30 | 2013-02-27 | 长沙理工大学 | Gravity level surface and global position system (GPS) level difference decomposition and fusion method |
Non-Patent Citations (5)
| Title |
|---|
| 管真 等: "多面函数法在丘陵区GPS水准拟合中的应用研究", 《测绘与空间地理信息》 * |
| 贾翔: "GPS水准拟合模型的误差分析与研究", 《中国优秀硕士学位论文全文数据库 基础科学辑 （月刊）》 * |
| 陆艳华 等: "多面函数光滑因子对GPS高程转换精度影响分析", 《矿山测量》 * |
| 马洪滨 等: "多面函数GPS水准高程拟合中光滑因子求定方法", 《东北大学学报(自然科学版)》 * |
| 高伟 等: "GPS高程分区拟合转换正常高的研究", 《武汉大学学报·信息科学版》 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104792305B (en) | 2017-01-18 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106570867B (en) | Movable contour model image fast segmentation method based on gray scale morphology energy method | |
| CN107332240B (en) | Method for searching static voltage stability domain boundary of power system based on optimization model | |
| CN104867136B (en) | A kind of workpiece point cloud matching algorithm minimum based on distance variance | |
| CN105115573B (en) | A kind of bearing calibration of flood discharge forecast and device | |
| CN108804382B (en) | Parameter automatic reverse calculation method and device | |
| JP2016509271A5 (en) | ||
| CN107016489A (en) | A kind of electric power system robust state estimation method and device | |
| WO2017088328A1 (en) | Surface water depth information based ground irrigation control method | |
| CN112884237A (en) | Power distribution network prediction auxiliary state estimation method and system | |
| CN112257722B (en) | Point cloud fitting method based on robust nonlinear Gaussian-Hermer model | |
| CN102982250B (en) | Based on the probabilistic stochastic response of random response face estimated parameter | |
| CN104102836B (en) | A kind of quick robust state estimation method of electric system | |
| CN104066179B (en) | A kind of improved adaptive iteration UKF WSN node positioning methods | |
| JP2014215822A (en) | State estimating apparatus, method, and program | |
| CN107025609B (en) | Singular value decomposition CDKF-based power system dynamic state estimation method | |
| CN109188481A (en) | A kind of new method being fitted GPS height anomaly | |
| CN105356456A (en) | Boundary-node-equivalence-based combined power flow calculation method of power transmission network and distribution network | |
| CN103237320A (en) | Hybrid quantization Kalman fusion based target tracking method of wireless sensor network | |
| CN109359360B (en) | Structural stress processing method based on local features | |
| CN104792305A (en) | Determination method of kernel function smooth factor of GPS level transformation model | |
| CN107452064A (en) | A kind of three-dimensional building entity space levelling implementation method, device and storage device | |
| CN105226644B (en) | Belt restraining equivalence method based on active volume uniformity | |
| CN106600038A (en) | Load interval prediction method based on Markov model | |
| CN106887844B (en) | A kind of fast decoupled power distribution network three-phase state estimation method based on sparse recovery | |
| CN110968931A (en) | Method for calculating time-varying reliability and sensitivity of axial compression short column |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| EXSB | Decision made by sipo to initiate substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20170118 Termination date: 20190505 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |