CN105716603B - Change the method positioned to object according to the sun shadow of object in video - Google Patents

Change the method positioned to object according to the sun shadow of object in video Download PDF

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CN105716603B
CN105716603B CN201610066710.3A CN201610066710A CN105716603B CN 105716603 B CN105716603 B CN 105716603B CN 201610066710 A CN201610066710 A CN 201610066710A CN 105716603 B CN105716603 B CN 105716603B
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shadow
model
sun
video
latitude
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CN105716603A (en
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金新元
连新泽
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Wenzhou University of Technology
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Wenzhou University Oujiang College
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/02Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20Instruments for performing navigational calculations

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Abstract

The present invention relates to a kind of sun shadows according to object in video to change the method positioned to object, including step 1: building model one and solution, construct pilot object shadow length variation mathematical model: for influence shadow length variation correlated variables: solar elevation, the longitude and latitude in location, location moment time, establish nonlinear model, and for solar elevation, the triangle relation of shadow length and object height, equation is established, model is applied to specific data and draws the change curve of sun shadow length;Step 2: the model established with step 1 carries out nonlinear fitting to the sun shadow delta data of object in video, obtains the longitude and latitude of object in video.Technical solution of the present invention, location technology effect can be carried out to object according to the sun shadow variation of object in video by having.

Description

Change the method positioned to object according to the sun shadow of object in video
Technical field
The present invention relates to a kind of sun shadows according to object in video to change the method positioned to object.
Background technique
Society of today is in the information age, and interaction and the transmitting of information are particularly important.Wherein, sun shadow is fixed Position technology will constantly apply among masses.Sun shadow location technology changes according to the length of the sun shadow of object, accurately Judgment object geographical location, not only save the time, but have accuracy, for gradually relying on the people of electronic product, this The development of technology has huge potentiality.
Summary of the invention
In view of the deficiencies of the prior art, the present invention intends to provide a kind of sun shadow according to object in video The method that son variation positions object.
To achieve the above object, the present invention provides the following technical scheme that a kind of sun shadow according to object in video Change the method positioned to object, including step 1: the shadow length of building model one and solution, building pilot object becomes The mathematical model of change: for the correlated variables for influencing the variation of shadow length: solar elevation, the longitude and latitude in location, location Moment time, establish nonlinear model, and for solar elevation, shadow is long and the triangle relation of object height, establish equation, Model is applied to specific data and draws the change curve of sun shadow length;Step 2: the model established with step 1, it is right The sun shadow delta data of object carries out nonlinear fitting in video, obtains the longitude and latitude of object in video.
The present invention is further arranged to: the step 1 is solved with step 2 with MATLAB, and MATLAB program is set It sets the upper and lower of latitude and is limited to 0 ° -90 °, the upper and lower of longitude is limited to 0 ° -180 °.
The present invention is further arranged to: solar elevation geographic logitude described in step 1, hour angle and solar declination Approximate representation:
Wherein, α is solar elevation, and φ is local latitude, and n1 is time of this year apart from January 1, t1For specific north Capital time, λ are local longitude;
The long relationship with object height of object shadow can be expressed as
Wherein 1 is long for shadow, and h is object height.
The present invention is further arranged to: establishing the following objective function peace treaty of model according to least square method in the step 2 Beam condition:
Objective function:
Constraint condition:
, φ ∈ (- 90 °, 90 °), λ ∈ (0 °, 180 °),
Wherein, n2It is this year apart from the time on January 1, t2For specific Beijing time,For known measurement point straight-bar Sun shadow length.
The present invention is further arranged to: establishing the following objective function peace treaty of model according to least square method in the step 2 Beam condition:
Objective function:
Constraint condition:
, φ ∈ (- 90 °, 90 °), λ ∈ (0 °, 180 °), n ∈ (1,365),
Wherein, n3It is this year apart from the time on January 1, t3 is specific Beijing time,For known measurement point straight-bar Sun shadow length.
By using above-mentioned technical proposal, the estimation in geographical location itself is not only an extremely important problem, special Also unpredictable help can be brought to other problems.For example, as it is known that certain criminal of kidnapping has sent out the photo or video of a victim To aggrieved members, the police can use sun shadow location technology, by the analysis of sun shadow length, estimate victim place Position, more rapidly, more effective must succour victim.Sun shadow location technology is studied herein, although the experimental results showed that too Positive shadow location technology has good effect, but there are many more needs of work to carry out, and wishes this research work herein only It is a beginning of geography informatization computer age.
The invention will be further described below in conjunction with the accompanying drawings.
Detailed description of the invention
Fig. 1 is the program solution flow chart of model of the embodiment of the present invention one;
Fig. 2 is the sun shadow length change curve of the embodiment of the present invention;
Fig. 3 is the program solution flow chart of the model two of the embodiment of the present invention;
Fig. 4 is that two numerical value of model of the embodiment of the present invention substitutes into the fitted figure after model;
Fig. 5 is that three numerical value of model of the embodiment of the present invention substitutes into the fitted figure after model;
Fig. 6 is that four numerical value of model of the embodiment of the present invention substitutes into the fitted figure after model.
Specific embodiment
Problem one: establishing the mathematical model of shadow length variation, analyzes changing rule of the shadow length about parameters, And the model of application foundation draws the change curve of the sun shadow length of certain high straight-bar in 3 meters of the Tian'anmen Square of period.
Problem two: sun shadow vertex coordinates data of the straight-bar on level ground, founding mathematical models are fixed according to certain Determine place locating for straight-bar.And model is applied to the shadow vertex coordinates data provided, provide several possible places.
Problem three: sun shadow vertex coordinates data of the straight-bar on level ground, founding mathematical models are fixed according to certain Determine place locating for straight-bar and date.And model is applied to the shadow vertex coordinates data of problem two, providing several can The place of energy and date.
Problem four: the mathematical model for determining video capture place is established, and application model provides several possible shootings Place.If shooting date is unknown, shooting location and date are determined according to video.
The present embodiment testee is preferably straight-bar,
Symbol description:
T: local time,
φ: local latitude,
λ: local longitude,
H: the length of straight-bar,
x1: the x-axis coordinate of some point,
y1: the y-axis coordinate of some point,
ti: the Beijing time in particular problem,
Lyinzi: the sun shadow length of straight-bar,
: the sun shadow length of known measurement point straight-bar,
Gi: the angle that shadow coordinate generates, i=1,2,
δ: latitude angle, also known as solar declination, i.e. direct sunlight latitude,
N: time of this year apart from January 1;I.e. duration on January 1 is 1, and January 2, value was 2,
ω: hour angle starts to calculate with 12 points of high noon for 0 degree, and each hour is 15 degree, and be negative in the morning is positive afternoon, i.e., and 10 points With 14 points be respectively -30 degree and 30 degree,
α: solar elevation is the sun relative to horizontal elevation angle, is with the geometric center and reason in sun optic disk face Think angle folded by horizon,
αi: specific solar elevation, i=1,2,
One, one model construction of problem and solution
The mathematical model of shadow length variation is constructed, we will find the parameters for influencing shadow length and variation rule Rule.Calculating first according to wikipedia about solar elevation obtains solar elevation α, solar hour angle, solar declination δ, Local latitude φ, there are following functional relations:
Equation (1): sin α=sin φ .sin δ+cos φ .cos δ .cos ω
Equation (2): solar declination:
Equation (3): hour angle:
ω=15* (t-12) (t=0,2...24, t ∈ Z)
Equation (4): shadow length:
Equation (1), equation (2) and equation (3) are substituted into equation (4), shadow can be obtained
Sub- length model:
By formula (1) it is found that solar elevation is determined by geographic latitude and longitude, hour angle and solar declination.When known Beijing Between 9:00 it is whole, and Beijing time measurement position be 120 ° of east longitude.Known straight-bar measurement position is 116 degree 23 points of east longitude 29 seconds, then The time of straight-bar present position is poor there are certain time with Beijing time, so we first have to be modified the time.Due to It is that earth rotation influences the time difference, every 360 ° of rotation in 24 hours, then 15 ° of rotation per hour.The longitude and latitude of known straight-bar measurement position It is 39 degree 54 points of north latitude 26 seconds, 3 degree 26 points is differed with Beijing time measurement position 31 seconds.Time revision is carried out to equation (3), it should Expression formula may be expressed as: when the place of test point
Equation (5):
(-180≤λ≤180)
t1For the test point Beijing time;
Equation (4), which brings equation (3) into, can obtain revised hour angle, the hour angle expression formula of the revised test point are as follows:
Equation (6)
By equation (4) it is found that the time of straight-bar present position differs with Beijing timeWhen, i.e., when local than Beijing Between it is earlyHour, then the real time of straight-bar present position beWhen.
Equation (1), (2) and (5) can show that solar elevation can use geographic logitude, hour angle and solar declination approximation table Show:
Equation (7):
n1The date is measured apart from the specific time on January 1 for the problem,
Shadow is long to grow up to trigonometric function with solar elevation and bar, then the relationship of the long 1 and high h of bar of shadow can be stated are as follows:
Equation (8):
As known to problem data:
Geographic latitude: φ=39.91 °
Geographic logitude: λ=116.39 °
Beijing time: 9:00~15:00
Time: n1=295
By above-mentioned specific value, following matlab software program joint equation (7) and equation (8), the journey of model one are utilized Sequence solves process referring to attached drawing 1, directly calculates the sun shadow length of straight-bar, the change curve drafting pattern of sun shadow length It is formed " bathtub curve ", referring to attached drawing 2.
Establish the program of the change curve model of the sun shadow length of straight-bar:
T=9:05:15
Phi=39.907222222222222222224;
Jd=116.3913888888888;
N=295;
Delta=23.45*sin (2*pi* (284+n)/365);
W=15* (t- (120-jd)/15-12);
Alpha=asind (sind (phi) .*sind (delta)+cosd (phi) .*cosd (delta) .*cosd (w))
Yinzi=3./tand (alpha)
Plot (t, yinzi)
Program operation result
9.5000 10.0000 10.5000 11.0000 11.5000 12.000012.5000 of t=9.0000 13.0000 13.5000 14.0000 14.5000 15.0000
25.5075 29.3512 32.6160 35.192736.9764 37.8831 37.8655 of alpha=21.1878 36.9246 35.1093 32.504729.2161 25.3526
6.2875 5.3348 4.6881 4.25393.9845 3.8560 3.8585 3.9920 of 1=7.7394 4.2671 4.70825.3643 6.3315
" bathtub curve " (also known as U-shaped curve) is an essential term, is changed over time for describing semiconductor product The master curve of instantaneous failure rate.Although the physical fault rate curve of specific semiconductor product is widely different, this master curve It is still the useful example of some general-purpose attributes.These are the samples based on general data in the worst cases.Exist as shown in Figure 2 When 9 o'clock sharp to 15 o'clock sharp Beijing time, the sun shadow length longest of 9 o'clock sharps.Morning time, sun shadow are gradually become by growing Short, by short progressively longer, meet the objective changing rule of shadow in one day in the afternoon.According to the drafting of the chart, the observable measurement The shadow at each moment of point is long.Wherein 9 points of sun shadow length is 7.7394 meters, and 15 points of sun shadow length is 6.3315 The meter Ying Zi length shortest time about after 12 points, before 12 thirty.With the observation of 30 minute time intervals, certain can be obtained out The solar elevation and shadow length of the high straight-bar in 3 meters of the Tian'anmen Square of period, are as follows:
Table 1: the solar elevation and shadow length of specific time
Two, the building and solution of two model of problem
The sun shadow vertex coordinates data of the problem of being provided according to topic two one, since coordinate system is original with straight-bar bottom end Point, level ground are x/y plane.The shadow length and xy reference axis of the straight-bar perpendicular to ground can be obtained by the formation basic theory of shadow Meet Pythagorean theorem, the long l of shadow is represented by
Equation (9):
The sun shadow length released for the topic by vertex data.
Is determined by elevation angle positive known to problem one by geographic latitude and longitude, hour angle and solar declination, and solar elevation with Bar is long to determine that shadow is long.There are three unknown independents variable, respectively the longitude φ, latitude λ and bar of the test point long 1 in the problem.Root The following objective function of model and constraint condition are established according to least square method.
Objective function:
Equation (10):
Constraint condition:
φ ∈ (- 90 °, 90 °),
λ ∈ (0 °, 180 °),
The relational expression between three unknown parameters, which can be obtained, by equation (7) and equation (8) again is
Equation (11):
t2It is April 18 by the testing time for the shooting time on the ground, then n=108.Least square is carried out to model Method estimation fits the occurrence of unknown parameter, that is, determines several possible places locating for the straight-bar in problem two, and benefit Occurrence is solved with following matlab software program.Wherein the problem program flow chart of program is referring to attached drawing 3.
To the solver of three unknown quantitys in problem two:
clc
X0=[(rand () -0.5) * 180, (rand () -0.5) * 360rand () * 10] %Starting guess
[x, resnorm]=lsqnonlin (@myfunB2, x0, [0,0,0.1], [90,180,10]);%Invoke optimizer
X, resnorm
Fid=fopen (' xy.txt ', ' r ');
Xy=fscanf (fid, ' %f ', [2,21]) ';
fclose(fid);
T=14.7:0.05:15.7;
Yinzi=sqrt (xy (:, 1) .^2+xy (:, 2) .^2) ';
Phi=x (1)/180*pi;
Delta=23.45*sin (2*pi* (108+284)/365)/180*pi;
W=15* ((t- (120-x (2))/15) -12)/180*pi;
Alpha=asin (sin (phi) .*sin (delta)+cos (phi) .*cos (delta) .*cos (w));
F=x (3) ./tan (alpha);
Plot (t, F)
hold on
Plot (t, yinzi, ' r0 ')
Legend (' calculated value ', ' exact value ', ' Location ', ' SouthEast ')
Xlabel (' time t ')
Ylabel (' shadow length ')
Function file
Function F=myfunB2 (a)
Fid=fopen (' xy.txt ', ' r ');
Xy=fscanf (fid, ' %f ', [2,21]) ';
fclose(fid);
T=14.7:0.05:15.7;
Phi=a (1)/180*pi;
Delta=23.45*sin (2*pi* (108+284)/365)/180*pi;
W=15* ((t- (120-a (2))/15) -12)/180*pi;
Alpha=asin (sin (phi) .*sin (delta)+cos (phi) .*cos (delta) .*cos (w));
F=(a (3) ./tan (alpha)-sqrt (xy (:, 1) .^2+xy (:, 2) .^2) ') * 10;
TXT document
1.1637 3.336
1.2212 3.3299
1.2791 3.3242
1.3373 3.3188
1.396 3.3137
1.4552 3.3091
1.5148 3.3048
1.575 3.3007
1.6357 3.2971
1.697 3.2937
1.7589 3.2907
1.8215 3.2881
1.8848 3.2859
1.9488 3.284
2.0136 3.2824
2.0792 3.2813
2.1457 3.2805
2.2131 3.2801
2.2815 3.2801
2.3508 3.2804
2.4213 3.2812
Two program operation result of problem:
X0=-2.5232140.86767.6210
Maximum number of function evaluations exceeded;
increase options.MsxFunEvals
X=25.1331 95.6678 2.9730
Resnorm=0.0024
Different longitude and latitude bounds, which is arranged, to program according to topic can change the occurrence after unknown parameter is fitted, simultaneously Influence the goodness of fitting.By being constantly trying to, discovery set latitude it is upper and lower be limited to 0 ° -90 °, longitude it is upper and lower be limited to 0 ° - At 180 °, fitting degree is best.Obtain fitted figure referring to attached drawing 4.
Due to using least square method, when global error is greater than certain value, program exports automatically meets the smallest totality Error amount finds out the shadow vertex coordinates data change that can be able to satisfy one model of problem so we pass through the upper limit for changing error The specific measurement point and bar changed are long.
Table 2: possible place and bar are long
Since linear fit error is no more than 0.05, so retain the 1st, 2 group of geographical location, therefore, the in table one 1,2 groups of geographical locations are possible position locating for straight-bar in problem two.1st group of location is Hainan Province Li Autonomous County of ledong, 2nd group of location is Dai-Jingpo Autonomous Prefecture of Dehong of Yunnan Province Lianghe County.3rd group of location is Indonesia.
Three, the building and solution of three model of problem
According to the variation of sun shadow length of the fixed straight-bar on level ground, we can continue to use the mould of problem two Type, and upper introducing unknown quantity date n on the basis of this model.Just there are four unknown independents variable, the respectively test in the problem The long 1 and date n of longitude, latitude, bar of point.It is available by equation (7)
Equation (12):
t3For the shooting time on the ground.
Equation (13):
Equation (14):
Equation (15):
Equation (16):
It in same quadrant, is obtained (14) by (13) formula, and is generated accordingly by shadow coordinate, while substituting into formula In sub (16), so that there are the solar elevations of large error for exclusion, to reduce the range of undetermined coefficient probable value.
Problem three is with only providing sun shadow vertex coordinates data in problem two.In order to estimate shadow length, need to upper Formula carries out nonlinear fitting in MATLAB, fits the occurrence of unknown parameter, that is, determines locating for the straight-bar in problem three Several possible places and date, wherein problem program flow chart such as Fig. 3 of program.
Equation (17):
Undetermined coefficient is assumed to be to longitude, latitude, bar tetra- variables of long h and date n of the test point, is carried out in MATLAB Middle carry out nonlinear fitting.t4For the shooting time on the ground.The following objective function of model and constraint are established according to least square method Condition.
Objective function:
Equation (18):
Constraint condition:
φ ∈ (- 90 °, 90 °),
λ ∈ (0 °, 180 °),
N ∈ (1.365),
According to the data in problem two, in MATLAB, carry out nonlinear fitting, it is known that place locating for fixed straight-bar and Date may be
Table 3: possible place and bar are long
Due to needing to screen the lesser data of linear fit error, so retaining above 6 groups of the geographical location, therefore, table 1-6 group geographical location in two is possible position locating for straight-bar in problem two.1st group of location is that Xinjiang Uygur is autonomous Hotan Prefecture of area Moyu County, measurement date are July 27.2nd group of location is Xinjiang Uygur Autonomous Regions's Kyzyl Su Keer Ke Zi autonomous prefecture Wuqia County, measurement date are May 18.3rd group of location is Hotan Prefecture of Xinjiang Uygur Autonomous Regions in field County, measurement date are July 22.4th group of location is Gu Erbaijia Sericulture in Karnataka nation, and the measurement date is March 2.5th Group location is Xinjiang Uygur Autonomous Regions Aksu Prefecture Shaya County, and the measurement date is July 2.6th group of location is to breathe out Sa Bolkestein, measurement date are June 10.
Choose above-mentioned 1st group as a result, do code amendment, obtain fitted figure referring to attached drawing 5.
It finds that fitting degree is good by attached drawing 5, predicts that the specified place position angle obtained, confidence level are higher.
Four, the building and solution of four model of problem
Solve video shooting location, clearly to inscribe given in data and unknown quantity number.It first has to decompose video, obtain The coordinate of shadow length out, key step are as follows:
1, shadow variation view of the moment straight-bar under the sun is read using VideoReader function in MATLAB software Frequently: VideoReader (' Appendix.avi '), one picture of extraction in three minutes every to video, the picture reflect shadow Specific location.
2, picture, imwrite (img, filename) are saved.
3, imread function is called to read each frame picture, imgRgb=Imread (filename).
4, color image is converted to gray scale picture with img2gray function, rgb2gray (imgRgb), gray scale is shown The bright-dark degree of image pixel.
5, it to the gray level image of every page, places it in (x, y) plane, divides the image into uniform coordinate, in order to Find the vertex of shadow and coordinate in picture.
Since real straight-bar length is 2 meters, according to the proportionate relationship of practical straight-bar length and picture straight-bar length:
It obtains practical shadow length, obtains the related data of time Yu sun shadow length by processing:
Table 5: time and treated practical sun shadow length
The shooting time of known video determines to include two unknown quantitys, solves the geographical location of shooting, solves with problem two It is similar, data are substituted into the model in problem two, nonlinear fitting is carried out, estimates shadow length, if fitting effect is better, Shadow length and practical shadow error in length after indicating fitting is smaller, then geographical location is more excellent.It knows in video locating for straight-bar Place may are as follows:
Table 6: the longitude and latitude and error of the specified place of model four
The shooting time of unknown video determines to include three unknown quantitys, date and the geographical location of shooting is solved, with problem Three solutions are similar, and data are substituted into the model in problem three, carry out nonlinear fitting.The shooting time and place for knowing video can Can be
Table 7: possible place and time
Since linear fit error is no more than 0.05, so retaining the 1st, 2,3,4 group of geographical location.Therefore, in table three The the 1st, 2,3 group of geographical location be possible position locating for straight-bar in problem two.1st group of location is Inner Mongolia Autonomous Region packet header City Guyang County, shooting date are May 21.2nd group of location is Hohhot City ,Inner Mongolia Autonomous Region Wuchuan County, shooting date For June 7.3rd group of location is Hebei province Baoding Yi County, and shooting date is July 4.4th group of location is the Shandong Province Weihe River Mill city Linqu County, shooting date are August 22nd.
Code amendment is carried out to it simultaneously, is drawn a diagram, fitting degree is preferable.Fitted figure is referring to attached drawing 6.

Claims (2)

1. a kind of sun shadow according to object in video changes the method positioned to object, it is characterised in that: including step Rapid one: building model one and solution, the mathematical model of the shadow length variation of building pilot object: for influence shadow length change The correlated variables of change: solar elevation, the longitude and latitude in location, location moment time, establish nonlinear model, and be directed to The triangle relation of solar elevation, shadow length and object height, establishes equation, and model is applied to specific data and draws sun shadow The change curve of sub- length;Step 2: the model established with step 1 carries out the sun shadow delta data of object in video Nonlinear fitting obtains the longitude and latitude of object in video;
The step 1 is solved with step 2 with MATLAB, and MATLAB program setting the upper and lower of latitude is limited to 0 ° -90 °, The upper and lower of longitude is limited to 0 ° -180 °;
Solar elevation geographic logitude described in step 1, hour angle and solar declination approximate representation:
Wherein, α is solar elevation, and φ is local latitude, and n1 is this year apart from the time on January 1, when t1 is specific Beijing Between, λ is local longitude;
The long relationship with object height of object shadow is stated are as follows:
Wherein l is that shadow is long, and h is object height;
The following objective function of model and constraint condition are established according to least square method in the step 2:
Objective function:
Constraint condition:
φ ∈ (- 90 °, 90 °), λ ∈ (0 °, 180 °),
Wherein, n2 is this year apart from the time on January 1, and t2 is specific Beijing time,For known measurement point straight-bar Sun shadow length.
2. a kind of sun shadow according to object in video changes the method positioned to object, it is characterised in that: including step Rapid one: building model one and solution, the mathematical model of the shadow length variation of building pilot object: for influence shadow length change The correlated variables of change: solar elevation, the longitude and latitude in location, location moment time, establish nonlinear model, and be directed to The triangle relation of solar elevation, shadow length and object height, establishes equation, and model is applied to specific data and draws sun shadow The change curve of sub- length;Step 2: the model established with step 1 carries out the sun shadow delta data of object in video Nonlinear fitting obtains the longitude and latitude of object in video;
The step 1 is solved with step 2 with MATLAB, and MATLAB program setting the upper and lower of latitude is limited to 0 ° -90 °, The upper and lower of longitude is limited to 0 ° -180 °;
Solar elevation geographic logitude described in step 1, hour angle and solar declination approximate representation:
Wherein, α is solar elevation, and φ is local latitude, and n1 is this year apart from the time on January 1, when t1 is specific Beijing Between, λ is local longitude;
The long relationship with object height of object shadow is stated are as follows:
Wherein l is that shadow is long, and h is object height;
The following objective function of model and constraint condition are established according to least square method in the step 2:
Objective function:
Constraint condition:
φ ∈ (- 90 °, 90 °), λ ∈ (0 °, 180 °), n ∈ (1,365),
Wherein, n3 is this year apart from the time on January 1, and t3 is specific Beijing time,For known measurement point straight-bar Sun shadow length.
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