CN107490364A - A kind of wide-angle tilt is imaged aerial camera object positioning method - Google Patents

Abstract

The invention discloses a ground target positioning method for a large-angle oblique imaging aerial camera. Aiming at the problem that the large-angle oblique imaging aerial camera has a long shooting distance and the working distance of a laser ranging device is limited, a direct method that does not rely on a distance measuring device is proposed. Algorithm for ground target location. Based on the aircraft position and attitude information measured by the aircraft POS (Position and Orientation System) and the frame angle position information measured by the position encoder in the aerial camera, the homogeneous coordinate transformation method is used to solve the orientation of the target in the earth coordinate system. Earth ellipsoid model and digital elevation model to determine the latitude and longitude information of the target point. The effectiveness of the target positioning algorithm is verified by flight test data. When the roll angle of the shooting frame is less than 63° at a flight altitude of 18000m, the probability error of the target positioning circle is less than 70m, which can meet the actual needs of the project.

Description

A large-angle oblique imaging aerial camera positioning method for ground targets

technical field

The invention belongs to the technical field of aerial imaging and measurement and control, and in particular relates to a ground target positioning method for a large-angle oblique imaging aerial camera.

Background technique

In addition to high-resolution imaging, the aerial camera also needs to perform high-precision positioning of the target at the same time. At present, most target positioning algorithms are based on distance measurement, and the distance value of the target relative to the airborne optoelectronic equipment needs to be given by the target ranging equipment. The positioning accuracy is better than 15m and 20m respectively; however, when the aerial camera is flying at an altitude of 18,000m and obliquely imaging a target 50km away, the small laser ranging device cannot meet the distance requirements, and the large laser ranging is limited by its size and cannot be used in the aviation field. , At the same time, long-distance laser ranging will also be affected by various factors such as the atmosphere, resulting in a decrease in ranging accuracy, thereby affecting the positioning of the target.

Contents of the invention

In view of this, the object of the present invention is to provide a large-angle oblique imaging aerial camera positioning method for ground targets, which can improve positioning accuracy.

A method for locating a ground target with an imaging aerial camera, comprising the steps of:

Step 0, determine the area where the target is located, extract the digital elevation model DEM corresponding to the area, and determine the highest earth height H _max in the digital elevation model DEM; the average pre-binding height of the earth is h _T = H _max ;

Step 1. The coordinates T _S ' of the target projection position in the camera coordinate system;

Step 2, obtain the coordinates of the projection of any image point of the target on the CCD in the earth coordinate system as:

in, is the conversion matrix from the earth coordinate system to the geographic coordinate system, is the transformation matrix from the geographic coordinate system to the aircraft coordinate system, is the transformation matrix from the aircraft coordinate system to the camera coordinate system; and the origin of the camera coordinate system coincides with the origin of the aircraft coordinate system, and the coordinates of the camera origin are given by the POS system;

Step 3, the coordinates of the target in the earth coordinate system satisfy the equation:

Step 4. The target coordinate position and the parameters of the earth satisfy the following relationship:

Step 5. Solve the coordinates of the target in the earth coordinate system according to the results of steps 3 and 4

Step 6. Use N _i to represent the semi-major axis of the earth obtained in the i-th iteration, H _i to represent the geodetic height obtained in the i-th iteration, and _φi to represent the latitude obtained in the i-th iteration. The iteration formula is as follows:

Among them, the initial value of the target geodetic height is The initial value of latitude is

After continuous iterations, the high precision and latitude precision of the target land converge until they meet the requirements; the longitude λ of the target is obtained directly from the coordinates of the target in the earth coordinate system obtained in step 5:

Among them, when hour, when hour, when hour,

Determined according to the above conditions final destination longitude;

Step 7. Substitute the target longitude and latitude information obtained through the iterative calculation in step 6 into the internationally accepted digital elevation model DEM to obtain the theoretical geodetic height h _i under the current longitude and latitude, and then compare it with the geodetic height H _i calculated in step 6 For comparison, it is to judge whether H _i -h _i is less than 0: if yes, the current target latitude and longitude and geodetic height are the longitude, latitude and geographic height information of the final target to realize the positioning of the target; if not, subtract H _i To tolerate the error ε _h , and assign H _i -ε _h to the average pre-binding height h _T of the target, return to step 1, and use the reassigned h _T to perform steps 1 to 7 until H _i -h _i is satisfied If it is less than 0, output the longitude, latitude and geographic height information of the corresponding target at this time to realize the positioning of the target.

The present invention has following beneficial effect:

Aiming at the problem of long shooting distance of large-angle oblique imaging aerial camera and limited range of laser ranging equipment, a direct ground target positioning algorithm independent of distance measuring equipment is proposed. Based on the aircraft position and attitude information measured by the aircraft POS (Position and Orientation System) and the frame angle position information measured by the position encoder in the aerial camera, the method of homogeneous coordinate transformation is used to solve the orientation of the target in the earth coordinate system. Ellipsoid model and digital elevation model to determine the latitude and longitude information of the target point. The effectiveness of the target positioning algorithm is verified by flight test data. When the roll angle of the shooting frame is less than 63° at a flight altitude of 18000m, the probability error of the target positioning circle is less than 70m, which can meet the actual needs of the project.

Description of drawings

Fig. 1 is the target projection schematic diagram on CCD of the present invention;

Fig. 2 is a schematic diagram of the coordinate relationship of each point of the present invention under the earth coordinate system;

Fig. 3 is a target positioning iterative process diagram of the present invention;

Fig. 4 is a block diagram of the ground target positioning algorithm based on the digital elevation model of the present invention.

detailed description

The present invention will be described in detail below with reference to the accompanying drawings and examples.

Target positioning is to obtain the geographical location information of the target area in the captured image, so as to effectively evaluate and analyze the target area. The airborne POS system is composed of GPS (Global Positioning System) and IMU (Inertial Measurement Unit). It integrates the advantages of GPS and IMU, greatly improves the performance and reliability, and can accurately measure the position and attitude of the aircraft. information.

use Represents the transformation matrix from the A coordinate system to the B coordinate system.

Among them, [x _A y _A z _A ] ^T and [x _B y _B z _B ] ^T are the coordinates of the same point in the A coordinate system and the B coordinate system.

Four basic coordinate systems are needed in the target positioning process, the earth coordinate system, the geographic coordinate system, the aircraft coordinate system and the camera coordinate system.

1. The earth coordinate system (ECEF) EX _E Y _E Z _E , the origin is at the earth's center of mass, the EX _E axis points to the intersection of the prime meridian and the equator, the EZ _E axis points to the geographic North Pole, and the EY _E and other two axes form a right-handed coordinate system.

2. Geographic coordinate system (NED) A-NED, AN and AE coordinate axes point to true north and true east respectively, and AD axis is perpendicular to the tangent of the local reference ellipsoid to point to the center of the earth. Assuming that the coordinates of any point in the earth's Cartesian coordinate system are (x, y, z), the spherical coordinates are (λ, φ, h), λ is the longitude, φ is the latitude, and h is the height of the earth, then:

x=(R _N +h)cosφcosλ

y=(R _N +h)cosφsinλ

z＝(R _N (1-ε) ² +h) sinφ

The transformation matrix from the earth coordinate system to the geographic coordinate system is:

in is the radius of curvature of the unitary surface, R _E is the semi-major axis of the ellipsoid, R _P is the semi-minor axis of the ellipsoid, is the eccentricity, is the flatness of the earth.

3. (AC) AX _A Y _A Z _A of the aircraft coordinate system, AX _A is the direction of the nose of the carrier aircraft, AY _A is the direction of the right wing, and AZ _A is vertical to the carrier aircraft downward in the longitudinal symmetry plane of the carrier aircraft. During the shooting process of the aerial camera, the attitude changes of the carrier aircraft are heading angle Ψ, pitch angle θ, roll angle In the aircraft coordinate system, the AX _A axis is generally called the Roll Axis, the AY _A axis is called the Pitch Axis, and the AZ _A axis is called the Yaw Axis. The attitude angle of an aircraft is generally defined in the form of generalized Euler angles. The aircraft coordinate system can be obtained by rotating the geographic coordinate system in the order of Euler angles.

4. The camera coordinate system (S) SX _S Y _S Z _S , the origin is at the center of the aerial camera optical system, and the S–Z _S axis is the direction of the viewing axis. When the inner and outer frame angles of the camera are both 0, the camera coordinate system and the aircraft coordinate The system is completely overlapped. When the camera takes an image, the outer and inner frame angles are at β and α, respectively. Then there are:

The positioning method of the present invention specifically includes the following steps, as shown in Figure 4:

Step 0, determine the area where the target is located, extract the digital elevation model DEM corresponding to the area, and determine the highest earth height H _max in the digital elevation model DEM; the average pre-binding height of the earth is h _T = H _max ;

Step 1. The coordinates T _S ' of the target projection position in the camera coordinate system are:

Among them, f is the focal length of the camera, the CCD pixel size is α, the number of pixels is M×N, the projected point of the target on the CCD is (i, j), i is the number of rows, and j is the number of columns;

Step 2. The coordinates of the projection of any image point of the target on the CCD in the earth coordinate system are:

in, is the conversion matrix from the earth coordinate system to the geographic coordinate system, is the transformation matrix from the geographic coordinate system to the aircraft coordinate system, is the transformation matrix from the aircraft coordinate system to the camera coordinate system; and the origin of the camera coordinate system coincides with the origin of the aircraft coordinate system, and the coordinates of the camera origin are given by the POS system;

Step 3, the coordinates of the target in the earth coordinate system satisfy the equation

Step 4. The target coordinate position and the parameters of the earth satisfy the following relationship:

Step 5. Solve the coordinates of the target in the earth coordinate system according to the results of steps 3 and 4

If the earth is a standard ellipsoid, all variables in the formula are known quantities.

Step 6. The longitude and latitude information of the target is obtained through its coordinates in the geodetic coordinate system. Since the earth ellipsoid model given by WGS-84 is used, its latitude and geodetic height information cannot be accurately obtained. For this reason, the iterative method is used to solve the geodetic height and latitude. The iterative process of target positioning is shown in Figure 3, in which it is stipulated that the latitude of the northern hemisphere is positive, and the latitude of the southern hemisphere is negative; the east longitude is positive, and the west _longitude is negative. The semi-major axis of the earth obtained by the i iteration, H _i represents the earth height obtained by the i iteration, φ _i represents the latitude obtained by the i iteration, and the iteration formula is as follows:

Among them, the initial value of the semi-major axis of the earth used in the first iteration is N ₀ = R _E , and the initial value of the target geodetic height is The initial value of latitude is

After continuous iteration, the high precision and latitude precision of the target land converge until they meet the requirements. Generally, iterates 4 times to ensure that the high precision of the target land converges to within 0.001m, and the latitude converges to 0.00001″. The longitude λ of the target can be directly obtained according to the coordinates of the target obtained in step 5 in the earth coordinate system:

Among them, when hour, when hour, when hour,

Determined according to the above conditions The final destination longitude.

Step 7. Substitute the target longitude and latitude information obtained through the iterative calculation in step 6 into the internationally accepted digital elevation model DEM to obtain the theoretical geodetic height h _i under the current longitude and latitude, and then compare it with the geodetic height H _i calculated in step 6 For comparison, it is to judge whether H _i -h _i is less than 0: if yes, the current target latitude and longitude and geodetic height are the longitude, latitude and geographic height information of the final target to realize the positioning of the target; if not, subtract H _i To tolerate the error ε _h , in order to obtain more accurate geographical information ε _h generally takes 5m, and assign H _i -ε _h to the average pre-binding height h _T of the target earth, return to step 1, and execute with the reassigned h _T From step 1 to step 7, until H _i -h _i is less than 0, output the longitude, latitude and geographic height information of the corresponding target at this time, so as to realize the positioning of the target.

To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (1)

1. A method for positioning a ground target of an imaging aerial camera is characterized by comprising the following steps:

step 0, determining an area where the target is located, extracting a digital elevation model DEM corresponding to the area, and determining the highest earth height H in the digital elevation model DEM_max(ii) a The average pre-binding height value of the earth is h_T＝H_max；

Step 1, coordinate T of target projection position in camera coordinate system_S'；

Step 2, the coordinates of the projection of the target on any image point of the CCD under the terrestrial coordinate system are as follows:

<mrow> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <msubsup> <mi>x</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>y</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>z</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msubsup> <mi>C</mi> <mrow> <mi>N</mi> <mi>E</mi> <mi>D</mi> </mrow> <mrow> <mi>E</mi> <mi>C</mi> <mi>E</mi> <mi>F</mi> </mrow> </msubsup> <msubsup> <mi>C</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> <mrow> <mi>N</mi> <mi>E</mi> <mi>D</mi> </mrow> </msubsup> <msubsup> <mi>C</mi> <mi>S</mi> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msubsup> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <msubsup> <mi>T</mi> <mi>S</mi> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>

wherein,is a transformation matrix from a terrestrial coordinate system to a geographical coordinate system,is a transformation matrix of the geographic coordinate system to the aircraft coordinate system,is a transformation matrix from the airplane coordinate system to the camera coordinate system; and the origin of the camera coordinate system is coincident with the origin of the carrier coordinate system, and the coordinates of the camera origin areGiven by the POS system;

step 3, coordinates of the target under the terrestrial coordinate systemSatisfies the equation:

<mrow> <mfrac> <mrow> <msubsup> <mi>x</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>T</mi> <mi>E</mi> </msubsup> </mrow> <mrow> <msubsup> <mi>x</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>S</mi> <mi>E</mi> </msubsup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>y</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>-</mo> <msubsup> <mi>y</mi> <mi>T</mi> <mi>E</mi> </msubsup> </mrow> <mrow> <msubsup> <mi>y</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>-</mo> <msubsup> <mi>y</mi> <mi>S</mi> <mi>E</mi> </msubsup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>z</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>-</mo> <msubsup> <mi>z</mi> <mi>T</mi> <mi>E</mi> </msubsup> </mrow> <mrow> <msubsup> <mi>z</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>-</mo> <msubsup> <mi>z</mi> <mi>S</mi> <mi>E</mi> </msubsup> </mrow> </mfrac> <mo>;</mo> </mrow>

and 4, enabling the target coordinate position and the parameters of the earth to meet the following relation:

<mrow> <mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <mo>+</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>+</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <mo>+</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>P</mi> </msub> <mo>+</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <mo>=</mo> <mn>1</mn> </mrow>

step 5, solving the coordinates of the target under the terrestrial coordinate system according to the results of the steps 3 and 4

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mi>x</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>=</mo> <mi>f</mi> <mo>(</mo> <msubsup> <mi>x</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>x</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>y</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>y</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>z</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>z</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>,</mo> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>,</mo> <msub> <mi>R</mi> <mi>P</mi> </msub> <mo>,</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>y</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>=</mo> <mi>g</mi> <mo>(</mo> <msubsup> <mi>x</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>x</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>y</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>y</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>z</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>z</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>,</mo> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>,</mo> <msub> <mi>R</mi> <mi>P</mi> </msub> <mo>,</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>z</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>=</mo> <mi>p</mi> <mo>(</mo> <msubsup> <mi>x</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>x</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>y</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>y</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>z</mi> <mi>S</mi> <mi>E</mi> </msubsup> <mo>,</mo> <msubsup> <mi>z</mi> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>E</mi> </msubsup> <mo>,</mo> <msub> <mi>R</mi> <mi>E</mi> </msub> <mo>,</mo> <msub> <mi>R</mi> <mi>P</mi> </msub> <mo>,</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced>

Step 6, using N_iRepresents the semimajor axis of the earth, H, obtained at the ith iteration_iIndicating the geodetic height, phi, obtained in the ith iteration_iAnd expressing the latitude obtained by the ith iteration, wherein the iteration formula is as follows:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>N</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>E</mi> </msub> <msqrt> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>&amp;epsiv;</mi> <mn>2</mn> </msup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <msub> <mi>&amp;phi;</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </msqrt> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>H</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mrow> <msub> <mi>cos&amp;phi;</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>-</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;phi;</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mi>tan</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <msubsup> <mi>z</mi> <mi>T</mi> <mi>E</mi> </msubsup> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mi>T</mi> <mi>E</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msup> <mi>&amp;epsiv;</mi> <mn>2</mn> </msup> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>H</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

wherein the target geodetic height is initially set toInitial value of latitude is

Continuously iterating to make the high precision and latitude precision of the target converge to meet the requirement; the longitude λ of the target is directly obtained according to the coordinates of the target in the terrestrial coordinate system obtained in the step 5:

<mrow> <mi>&amp;lambda;</mi> <mo>=</mo> <msup> <mi>tan</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mfrac> <msubsup> <mi>y</mi> <mi>T</mi> <mi>E</mi> </msubsup> <msubsup> <mi>x</mi> <mi>T</mi> <mi>E</mi> </msubsup> </mfrac> <mo>)</mo> </mrow> </mrow>

wherein whenWhen the temperature of the water is higher than the set temperature,when in useWhen the temperature of the water is higher than the set temperature,when in useWhen the temperature of the water is higher than the set temperature,

determined according to the above conditionsA final target longitude;

and 7, substituting the target longitude and latitude information obtained by the iterative operation in the step 6 into an international universal digital elevation model DEM to obtain the theoretical geodetic height h under the current longitude and latitude_iAnd then the ground height H obtained by calculation in the step 6_iMaking a comparison, i.e. judging H_i-h_iWhether or not less than 0: if so, the current longitude and latitude and geodetic height of the target are the final longitude, latitude and geographical height information of the target, and the target is positioned; if not, the step H is carried out_iMinus tolerance error_hAnd is combined with H_i-_hEarth mean pre-set height h assigned to target_TReturning to the step 1, adopting the h after reassignment_TExecuting the steps 1 to 7 until H is satisfied_i-h_iAnd if the current time is less than 0, outputting the longitude, latitude and geographical altitude information of the corresponding target at the time to realize the positioning of the target.