CN108957500B - Method for calculating intersection point of observation sight of sensor and earth surface - Google Patents

Method for calculating intersection point of observation sight of sensor and earth surface Download PDF

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CN108957500B
CN108957500B CN201810491796.3A CN201810491796A CN108957500B CN 108957500 B CN108957500 B CN 108957500B CN 201810491796 A CN201810491796 A CN 201810491796A CN 108957500 B CN108957500 B CN 108957500B
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sensor
sight
intersection point
coordinate system
line
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CN108957500A (en
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刘广
闫世勇
郭华东
张露
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Institute of Remote Sensing and Digital Earth of CAS
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C11/00—Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
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Abstract

The invention discloses a method for calculating an intersection point of a sensor observation sight line and the earth surface. Compared with the prior art, the invention has the advantages that: firstly, the method does not need to carry out multiple times of iterative computation to simultaneously solve a collinear equation and a variable ellipsoidal equation, thereby avoiding the problem of iterative solution of the simultaneous equations; secondly, the method is used for calculating under a geodetic coordinate system, has definite geometric significance and can be well applied under the condition of complex terrain. The method has the advantages of high calculation efficiency, convenient implementation and intuitive result, and has practical value and wide application prospect in the application fields of sensor geometric positioning, remote sensing image correction and the like.

Description

Method for calculating intersection point of observation sight of sensor and earth surface
Technical Field
The invention belongs to the technical field of earth observation, and relates to a method for calculating an intersection point of an observation sight line of a sensor and the earth surface.
Background
With the development of aviation and aerospace technologies, the earth is observed by using optical sensors mounted on platforms such as airplanes and satellites, and the obtained remote sensing images have been widely applied to global changes, territorial resources, disaster monitoring and the like. In order to obtain accurate ground information from the remote sensing image, a ground target corresponding to each pixel of the remote sensing image needs to be obtained, and the accuracy of the position of the target directly determines the accuracy of the obtained information. Generally speaking, the geometric imaging parameters of the sensor are relatively fixed after strict laboratory calibration and on-orbit calibration, but for the conditions of complex terrain and large visual angle, due to the fluctuation of the terrain, a plurality of intersection points exist between the sight direction of the sensor and the earth surface, and the key for obtaining the information of the ground features is how to accurately obtain the actual ground feature target corresponding to the remote sensing pixel.
The intersection point of the observation line of sight of the computing sensor and the earth surface is mainly calculated under the rectangular coordinate system of geocentric earth-solid space at present, for example, Rupter et al in ISPRS conference paper "A program for direct georgerening of airborne and spaceborne lines cameras" 2002, and in 2015 hu 22531of "a large scale"A direct positioning method for an image of an inclination agile imaging satellite, namely a method for solving an intersection point of a sensor observation sight and the earth surface by iteration under a space rectangular coordinate system is designed in CN106403902A by Yinwei, Wangmai and the like, a collinear equation and a variable ellipsoid equation are required to be solved simultaneously for many times in the iteration process, the iterative solution method is related to the iteration initial condition, and a local optimal result rather than a global optimal result sometimes occurs in a region with complex terrain; another is to perform the calculation under a geodetic coordinate system, Karshoglu et al 2006 in the ISPRS conference paper "organization of Monosopic
Figure BDA0001668093770000011
The Images by a New Differential Image retrieval Method' designs a Method for solving intersection points by iteration under a geodetic coordinate system, and the Method assumes that zenith angle and ellipsoid parameters of sight line under the geodetic coordinate system are constants, which is a loose assumption, because the sight line equation under a space rectangular coordinate system is a straight line and is not a straight line in general after being transformed to the geodetic coordinate system.
Disclosure of Invention
The invention mainly establishes a method for calculating the intersection point of the observation sight of the sensor and the earth surface under a geodetic coordinate system. According to the method, when the intersection point of the sensor observation sight line and the earth surface is calculated, a collinear equation and a variable ellipsoid equation do not need to be solved in a simultaneous mode through multiple iterations, the position of the sensor observation sight line under a geodetic coordinate system is compared with the elevation position of the earth surface, and the intersection point of the sensor observation sight line and the earth surface is obtained through calculation.
In order to achieve the purpose, the invention is realized by the following technical scheme steps:
step 1: coordinates of a sensor projection center at a certain time in WGS84 space rectangular coordinates based on a sensor mounting matrix measured in a laboratory and auxiliary data such as GPS data of a satellite or an airplane
Figure BDA0001668093770000021
Figure BDA0001668093770000022
And the observed line-of-sight orientation of the sensor
Figure BDA0001668093770000023
Obtaining elevation data of corresponding areas according to the range of the image, and obtaining the lowest elevation value h of the areas1And maximum elevation h2Based on sensor projection center coordinates (x, y, z)wgs84And the observation gaze direction (m, n, q)wgs84Calculating the elevation ha＝h1+hsAnd hb＝h2-hsIntersection point of corresponding ellipsoid and sensor sight line
Figure BDA0001668093770000024
And
Figure BDA0001668093770000025
the method comprises the following specific steps:
Figure BDA0001668093770000026
Figure BDA0001668093770000027
wherein, the product is the dot product,
Figure BDA00016680937700000210
is the Hadamard product (Hadamard product) and | is the modulus of the vector,
Figure BDA0001668093770000028
Figure BDA0001668093770000029
awgs84and bwgs84Respectively, the major half axis and the minor half axis of the WGS84 ellipsoid.
Step 2, coordinates of the intersection point of the ellipsoid obtained in the step 1 and the sensor sight line
Figure BDA0001668093770000033
And
Figure BDA0001668093770000034
the straight line connection is carried out and the N sections are divided according to the requirement of positioning precision, the segmentation method can generally adopt an equal interval segmentation method, and the space rectangular coordinates of the end points of each section are respectively
Figure BDA0001668093770000035
Figure BDA0001668093770000036
Then the space rectangular coordinates of each end point are transformed to the geodetic coordinates
Figure BDA0001668093770000037
The calculation formula for converting the space rectangular coordinate system into the geodetic coordinate system is as follows:
Figure BDA0001668093770000031
wherein
Figure BDA0001668093770000032
Each end point under the geodetic coordinate system after transformation
Figure BDA0001668093770000038
Typically not in the same line.
Step 3, obtaining N +1 longitude and latitude pairs (L, B) in the step 2iInterpolating using regional elevation data to obtain corresponding position
Figure BDA0001668093770000039
Then subtracting the actual elevation data to calculate each longitude and latitude pair (L, B)iCorresponding height difference deltahiAnd sequentially searching for the first height difference deltah from i to 1iA position less than or equal to 0, where i is k, the position is observed by the sensor under the geodetic coordinate systemPosition of intersection of line of sight with earth's surface
Figure BDA00016680937700000310
The invention has the beneficial effects that:
compared with the prior art, the method of the invention has the following advantages: according to the method, simultaneous solution of collinear equations and variable height ellipsoid equations is not required to be performed through repeated iterative calculation, so that the problem of iterative solution of simultaneous equations is solved, local optimization is avoided, and the complexity of calculation is reduced; secondly, the method is used for calculating under a geodetic coordinate system, has definite geometric significance and can be well applied under the condition of complex terrain.
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The foregoing is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and the detailed description.
FIG. 1 is a technical flow diagram of the present invention;
FIG. 2 is a diagram showing elevation profiles of mountain areas north of Chengdu of Sichuan province;
FIG. 3 is a three-dimensional schematic diagram of a connecting line of each end point and a terrain in a geodetic coordinate system;
fig. 4 is a schematic diagram of height difference as a function of position.
Detailed Description
The present invention will be described in detail below with reference to the attached drawings, taking the northern mountain area of Sichuan Chengdu in China as an example, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and thus, the protection scope of the present invention is more clearly and clearly defined.
Referring to fig. 1, the invention discloses a method for calculating the intersection point of the observation sight of a sensor and the earth surface under a geodetic coordinate system, which comprises the following steps:
step one, selecting a mountain area in the northern part of Sichuan Chengdu in China, wherein the longitude of the elevation data scene center is 31 degrees of north latitude, the center latitude is 104 degrees of east longitude, the northwest part is the mountain area, and the southeast part is the plain area. FIG. 2 is a gray scale of topographic data in northern mountainous area of Sichuan Chengdu, wherein the elevations of the terrain are mainly distributed between 500 m and 5000 m.
Obtaining a carrier position (x, y, z) at an observation time based on GPS dataGPSFor a near-earth vehicle such as an airplane or satellite, the carrier position is typically given in earth-fixed coordinates. Then installing the matrix according to the sensor
Figure BDA0001668093770000041
Offset of GPS coordinate system origin and body coordinate system origin
Figure BDA0001668093770000042
Sensor pixel vector (x, y, z)losObtaining the coordinates of the projection center of the sensor under the space rectangular coordinate of WGS84 at a certain moment:
Figure BDA0001668093770000043
and the observed line-of-sight orientation of the sensor
Figure BDA0001668093770000044
In this example
Figure BDA0001668093770000045
Figure BDA0001668093770000046
Obtaining the lowest elevation value h of the area according to the elevation data of the example area1382 m and maximum elevation h25273 m, and setting the safety height hs100 m, ha＝h1+hs5373 m, hb＝h2-hs282 meters based on sensor projection center coordinates
Figure BDA0001668093770000053
And observing gaze direction
Figure BDA0001668093770000054
Calculate h in this regionaAnd hbIntersection point of corresponding ellipsoid and sensor sight line
Figure BDA0001668093770000055
And
Figure BDA0001668093770000056
the method comprises the following specific steps:
Figure BDA0001668093770000051
Figure BDA0001668093770000052
wherein, the product is the dot product,
Figure BDA0001668093770000057
is the Hadamard product, | is the modulus of the vector, awgs846378137.000 m and bwgs846356752.314 m are respectively the major and minor half-axes of a WGS84 ellipsoid, in this example
Figure BDA0001668093770000058
Figure BDA0001668093770000059
And the numerator adopts addition when the two intersection points are calculated.
The calculated coordinates are respectively
Figure BDA00016680937700000510
And
Figure BDA00016680937700000511
step 2, coordinates of the intersection point of the ellipsoid obtained in the step 1 and the sensor sight line
Figure BDA00016680937700000512
And
Figure BDA00016680937700000513
making a straight connection, assuming positioning accuracyThe requirement is 10 meters, then the division is according to the accuracy requirement
Figure BDA00016680937700000514
The segment and segmentation method can generally adopt an equal-interval segmentation method, and the spatial rectangular coordinates of the end points of each segment are respectively
Figure BDA00016680937700000515
Then the space rectangular coordinates of each end point are transformed to the geodetic coordinates
Figure BDA00016680937700000516
The calculation formula for converting the space rectangular coordinate system into the geodetic coordinate system is as follows:
Figure BDA0001668093770000061
wherein
Figure BDA0001668093770000062
Each end point under the geodetic coordinate system after transformation
Figure BDA0001668093770000063
Typically not in the same line.
Fig. 3 is a three-dimensional schematic diagram of the connection line of each end point and the terrain in the geodetic coordinate system in this example, and it can be seen that the line of sight of the sensor is not a straight line in the geodetic coordinate system and that there are multiple intersections with the earth's surface.
Step 3, obtaining N +1 longitude and latitude pairs (L, B) in the step 2iInterpolating using regional elevation data to obtain corresponding position
Figure BDA0001668093770000064
Then subtracting the actual elevation data to calculate each longitude and latitude pair (L, B)iCorresponding height difference deltahiAnd sequentially searching for the first height difference deltah from i to 1iThe position less than or equal to 0, i being 3599 in the example found, and the height difference is shown in fig. 4The schematic diagram changes along with the position, and the position is the intersection point position of the observation sight of the sensor and the earth surface under the geodetic coordinate system
Figure BDA0001668093770000065
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (4)

1. A method for calculating the intersection point of a sensor observation sight line and the earth surface is characterized by comprising the following steps: the method is characterized in that the intersection point of the observation sight of the sensor and the earth surface is calculated based on the geodetic coordinate system, iterative calculation is not needed, and the situation that the sensor falls into local optimum is avoided, and the method specifically comprises the following steps:
step 1: obtaining coordinates of a sensor projection center at a certain time under WGS84 space rectangular coordinates based on a sensor installation matrix measured by a laboratory and GPS position auxiliary data of a satellite or an airplane
Figure FDA0002766653100000011
And the observed line-of-sight orientation of the sensor
Figure FDA0002766653100000012
Wherein m, n and q are coordinate components of the observation sight line pointing to the directions of x, y and z under the space rectangular coordinate of WGS84 respectively; simultaneously acquiring the elevation data of the corresponding area and obtaining the lowest elevation value h of the area1And maximum elevation h2Setting a safety height hsBased on sensor projection center coordinates (x, y, z)wgs84And the observation gaze direction (m, n, q)wgs84Calculating the elevation ha＝h1+hsAnd hb＝h2-hsIntersection point of corresponding ellipsoid and sensor sight line
Figure FDA0002766653100000013
And
Figure FDA0002766653100000014
step 2, coordinates of the intersection point of the ellipsoid obtained in the step 1 and the sensor sight line
Figure FDA0002766653100000015
And
Figure FDA0002766653100000016
the straight line connection is carried out and the connection is divided into N sections according to the precision requirement, and the space rectangular coordinates of the end points of each section are respectively
Figure FDA0002766653100000017
Then the space rectangular coordinates of each end point are transformed to the geodetic coordinates
Figure FDA0002766653100000018
L, B, H, wherein L, B, H is the longitude, latitude and altitude of each segment end point under the geodetic coordinate system;
step 3, obtaining longitude and latitude pairs (L, B) corresponding to the N +1 endpoints in the step 2iWherein (L, B)iLongitude L in (1) is step 2
Figure FDA0002766653100000019
L in (1), (L, B)iThe latitude B in (1) is that in step 2
Figure FDA00027666531000000110
B, interpolating by using the regional height data to obtain the corresponding position
Figure FDA00027666531000000111
H is the elevation corresponding to longitude L and latitude B in a geodetic coordinate system; then calculate each longitude and latitude pair (L, B)iCorresponding height difference deltahi＝Hi-hiAnd sequentially searching for the first height difference deltah from i to 1iA position less than or equal to 0, where i is k, where k is the position number of the intersection point of the line of sight observed by the sensor and the earth surface, and the position is the intersection point position of the line of sight observed by the sensor and the earth surface
Figure FDA00027666531000000112
2. The method for calculating the intersection point of the observation line of sight of the sensor and the earth's surface according to claim 1, wherein the intersection points of the ellipsoid and the line of sight of the sensor in the step 1 are respectively:
Figure FDA00027666531000000113
Figure FDA0002766653100000021
wherein, the product is the dot product,
Figure FDA00027666531000000210
is the Hadamard product, | | | | | is the modulus of the vector,
Figure FDA0002766653100000022
awgs84and bwgs84The major half axis and the minor half axis of the WGS84 ellipsoid are respectively, and the plus and minus signs in the formula are selected to be operation signs enabling the numerator to be small.
3. The method as claimed in claim 1, wherein the step 2 of calculating the intersection point of the sensor observation line of sight and the earth's surface is performed by using the intersection point coordinate system in the rectangular spatial coordinate system
Figure FDA0002766653100000023
And
Figure FDA0002766653100000024
the straight line connection is carried out, and the calculation formula for converting the space rectangular coordinate system into the geodetic coordinate system is as follows:
Figure FDA0002766653100000025
wherein
Figure 1
Each end point under the geodetic coordinate system after transformation
Figure FDA0002766653100000027
Typically not in the same line.
4. The method of claim 1, wherein the step 3 is performed by a height difference Δ hi：
Δhi＝Hi-hi (4)
Wherein HiIs composed of
Figure FDA0002766653100000028
Height H, H ofiIs composed of
Figure FDA0002766653100000029
Height h in (1).
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CN102243074A (en) * 2010-05-13 2011-11-16 中国科学院遥感应用研究所 Method for simulating geometric distortion of aerial remote sensing image based on ray tracing technology
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