CN105547237B - A kind of shadow location technology based on least square method - Google Patents
A kind of shadow location technology based on least square method Download PDFInfo
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- CN105547237B CN105547237B CN201510924137.0A CN201510924137A CN105547237B CN 105547237 B CN105547237 B CN 105547237B CN 201510924137 A CN201510924137 A CN 201510924137A CN 105547237 B CN105547237 B CN 105547237B
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- shadow
- shadow length
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C1/00—Measuring angles
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- 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)
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Abstract
The present invention relates to shadow location technology of the kind based on least square method, belong to fields of measurement.Localization method of the invention is, record current time and corresponding shadow length at regular intervals first, obtain observation time sequence and observation shadow length sequences, then relational expression of the shadow length about longitude and latitude is established, finally according to principle of least square method, longitude and latitude are determined using observation shadow length and the smallest principle of quadratic sum for calculating gained shadow length difference, are positioned.This method is positioned merely with shadow length, easy to accomplish.
Description
Technical field
The present invention relates to shadow location technology of the kind based on least square method, belong to fields of measurement.
Background technique
It is incomparable important to determine that the longitude and latitude in a certain place plays in terms of exploration, exploration, personnel in other words for positioning
Effect.With the portability of shooting tool, people can take personal video, the photo liked, some videos, photograph everywhere
Piece includes a large amount of information, if it is possible to determine the place of video, photograph taking using shadow therein, can be criminal investigation, feelings
The analysis work of the video datas such as report provides technical support.
Least square method is a kind of mathematical optimization techniques, it finds the best letter of data by minimizing the quadratic sum of error
Number matching.Least square method has a wide range of applications in field of engineering technology, can easily be acquired not using least square method
The parameter known, and the quadratic sum of error is minimum between the data and real data that these are acquired.
Summary of the invention
The purpose of the present invention is establishing the method for determining longitude and latitude using shadow, a kind of simple and practical positioning side is provided
Method.
The method according to the present invention positioned using shadow, using following steps.
1, data acquire
The straight-bar that length is L is stood on into ground O point vertically, note initial time is, shadow length is.When one section
Between record current timeAnd the length of corresponding shadow, obtain time seriesWith corresponding shadow length sequence
Column。
2, the declination angle on calculating observation date
Declination angle is the angle between earth equatorial plane and the sun and the line of earth center, related with the date.If seeing
Survey the day of year on date（The serial number of observation date within the year is counted from New Year's Day）For then declination angle is represented by：
WhereinIndicate day angle, calculation formula is：
。
3, the relationship of shadow length and longitude and latitude is established
If the longitude of observation place is, latitude is, note declination angle is δ, solar elevation h, has relationship between them
Formula：
WhereinIndicate hour angle, t is Beijing time in formula；
If the height of bar is L, then shadow lengthlIt is represented by：
In the length formula of shadow, hour angle T can be by the longitude of observation time t and observation placeIt indicates, declination angle δ can
Expected out by observational day, there was only longitude in formulaAnd latitudeFor unknown parameter.
4, longitude is calculatedEstimated value
In one day, straight-bar shadow length is a symmetrical curve, be at the time of corresponding to the symmetry axis of curve it is local just
The period of the day from 11 a.m. to 1 p.m carves, and according to the difference at the moment and Beijing time, provides longitudeEstimated value.
5, longitude and latitude is determined using least square method
According to shadow length formula, time series is substituted into, calculate corresponding shadow length.According to principle of least square method, required parameterWithCalculated shadow should be made long
DegreeWith the shadow length of observationIt is as close as possible, it enables
MakeReach the smallest parameterWithIt is as required.WithEstimated value as initial value, it is non-using matlab
Linear fit order solves longitudeAnd latitude。
People have had a ways and means of many positioning at present, for example, certain smart phones can by network or
GPS is positioned.However high-tech positioning tool is by the constraint of many conditions, such as power supply, network signal.At certain
Under conjunction, simplest method may be the most useful.Usefulness of the present invention is positioned merely with shadow, is easy real
It is existing.
Specific embodiment
1, on April 18th, 2015 separately begins to 15: 42 to terminate, Mei Gesan in Sanya somewhere from Beijing time 14: 42
Minute measures the shadow for the vertical straight-bar that a length is 1.97 meters, and it is as follows to obtain shadow length data：
=14.7, 14.75, 14.8, 14.85, 14.9, 14.95, 15, 15.05, 15.1, 15.15,
15.2,15.25,15.3,15.35,15.4,15.45,15.5,15.55,15.6,15.65,15.7,=
0.6125, 0.614583, 0.616667, 0.61875, 0.620833, 0.622917, 0.625, 0.627083,
0.629167, 0.63125, 0.633333, 0.635417, 0.6375, 0.639583, 0.641667, 0.64375,
0.645833, 0.647917, 0.65, 0.652083, 0.654167；
0.6125,0.614583,0.616667,0.61875,0.620833,0.622917,0.625,0.627083,
0.629167,0.63125,0.633333,0.635417,0.6375,0.639583,0.641667,0.64375,0.645833,
0.647917,0.65,0.652083,0.654167.
2, April 18 2015 date is observed, by time=2015, day of year N=108 is substituted into
Declination angle can be obtained10.8164 degree.
3, willIt substitutes into
It obtainsThe hour angle at moment, then will10.8164 degree andIt substitutes into
。
4, straight-bar vertex shadow coordinate is fitted and can be obtained using matlab, as t=12.6223, shadow length is most short,
Therefore the difference of longitude of observation point and Beijing timeDegree, therefore, the longitude initial value of observation point can be set as
110.6655 degree.
5, with=110.6655 be initial value, can be found out using matlab nonlinear fitting order " llsqcurvefit ",
Work as longitude=109.8 and latitudeWhen
Reach minimum value.And 109.8 degree of east longitude, 18.5 degree of north latitude exactly Sanya, Hainan longitude and latitude, be true to life.
Claims (1)
1. a kind of method positioned using shadow, it is characterised in that use following steps：
(1) straight-bar that height is L is stood on into ground O point vertically, note initial time is t1, shadow length is l1, at regular intervals
Record current time tiAnd the length l of corresponding shadowi, obtain time series t1, t2…tnWith corresponding shadow length sequences
l1, l2…ln, wherein i and n is positive integer；
(2) the declination angle on calculating observation date：
δ=0.3723+23.2567sin θ+0.1149sin2 θ -0.1712sin3 θ -0.578cos θ+0.3656os2 θ+
0.0201cos3θ
Wherein θ indicates day angle, and calculation formula is：
N indicates the day of year on observation date in formula；
(3) relationship of shadow length and longitude and latitude is established：
If the longitude of observation place is ω, latitude isNote declination angle is δ, solar elevation h, has relational expression between them：
WhereinIndicate hour angle, t is Beijing time in formula；
If the height of bar is L, then shadow length l is represented by：
(4) estimated value of longitude ω is calculated；
It is the local moment at high noon at the time of corresponding to the symmetry axis for the symmetrical curve that straight-bar shadow length is constituted, according to the moment
The estimated value of longitude ω is provided with the difference of Beijing time；
(5) it according to principle of least square method, using the estimated value of ω as initial value, is solved and is passed through using matlab nonlinear fitting order
Spend ω and latitude
According to shadow length formula, time series t is substituted into1, t2…tn, calculate corresponding shadow length
Required parameter ω andIt should make calculated shadow lengthWith the shadow length l of observationiIt is as close as possible, it enables
MakeReach the smallest parameter ω andIt is as required.
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| CN105547237B true CN105547237B (en) | 2018-11-27 |
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Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106895837B (en) * | 2017-01-04 | 2020-04-21 | 重庆三峡学院 | Sun shadow positioning system and positioning method thereof |
| CN107063267A (en) * | 2017-05-08 | 2017-08-18 | 浙江大学城市学院 | A kind of quickly localization method based on sun shadow information |
| CN109813300B (en) * | 2018-12-25 | 2021-01-22 | 维沃移动通信有限公司 | Positioning method and terminal equipment |
| CN109827567A (en) * | 2019-04-03 | 2019-05-31 | 湖南理工学院 | A kind of sunlight is at video display frequency shooting location localization method |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101493322A (en) * | 2009-02-04 | 2009-07-29 | 天津大学 | Latitude and longitude estimation method based on sun shadow track in video |
| CN102568027A (en) * | 2011-12-28 | 2012-07-11 | 浙江工业大学 | Pixelate virtual tree illumination influenced area obtaining method |
| CN103149947A (en) * | 2013-01-08 | 2013-06-12 | 杭州帷盛科技有限公司 | Solar energy tracking method with umbra versa tracking |
-
2015
- 2015-12-14 CN CN201510924137.0A patent/CN105547237B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101493322A (en) * | 2009-02-04 | 2009-07-29 | 天津大学 | Latitude and longitude estimation method based on sun shadow track in video |
| CN102568027A (en) * | 2011-12-28 | 2012-07-11 | 浙江工业大学 | Pixelate virtual tree illumination influenced area obtaining method |
| CN103149947A (en) * | 2013-01-08 | 2013-06-12 | 杭州帷盛科技有限公司 | Solar energy tracking method with umbra versa tracking |
Non-Patent Citations (2)
| Title |
|---|
| 《基于"穷举－非线性拟合"算法下的太阳影子定位分》;郑玉棒 等;《佳木斯大学学报（自然科学版）》;20151130;第33卷(第6期);832-836 * |
| 《太阳影子定位模型的构建》;胡毅华 等;《洛阳师范学院学报》;20151130;第34卷(第11期);13-18 * |
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