CN110082800B - Differential positioning method - Google Patents
Differential positioning method Download PDFInfo
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- CN110082800B CN110082800B CN201910387787.4A CN201910387787A CN110082800B CN 110082800 B CN110082800 B CN 110082800B CN 201910387787 A CN201910387787 A CN 201910387787A CN 110082800 B CN110082800 B CN 110082800B
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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
- G01S19/40—Correcting position, velocity or attitude
- G01S19/41—Differential correction, e.g. DGPS [differential GPS]
-
- 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
Abstract
Disclosed is a differential positioning method, comprising: a mobile terminal receiver receives space satellite signals in an area; and calculating the position coordinate according to a formula, calculating the distances from the mobile terminal receiver to the plurality of satellites, substituting the distances into the formula to calculate new N, and continuously solving the position of the mobile terminal receiver through multiple iterations. The method can effectively eliminate the influence caused by linear errors and Gaussian errors. Through iteration, the positioning error can be controlled within 1 m; the results are distributed around the origin; this results in a differential positioning method with a smaller error range and more aggregated results.
Description
Technical Field
The invention belongs to the technical field of satellite positioning; relates to a differential positioning method.
Background
China has wide range of members, and 960 ten thousand square kilometers of land area is only needed. In addition, the oceans in China include Bohai sea, yellow sea, east sea and south sea, and the ocean area also has millions of square kilometers. In order to meet the requirements of high-precision positioning and navigation in the field of sea, land and air, the Beidou navigation system is independently and autonomously developed in China. The satellite positioning system consists of 5 stationary orbit satellites and 30 non-stationary orbit satellites; wherein, 27 medium orbit satellites are evenly distributed on 3 orbit planes which form an angle of 120 degrees with each other. From the overall view, in the position of a middle-low latitude area, any one satellite signal receiver can receive more than 4 satellite signals, then the arrival time difference from the satellite to the receiver is obtained by using the accurate position of each satellite and navigation information generated by an atomic clock on the satellite, the distance from the satellite to the receiver is obtained by multiplying the arrival time difference by the light speed, and then an equation group is formed by using a distance formula of a three-dimensional space coordinate to obtain the position of an observation point.
Satellite receivers are ubiquitous in the sea, land and air, and are closely related to the productive life of everyone. The most widely applied fields comprise airplane navigation, vehicle-mounted electronic maps, mineral exploration, meteorological forecasting, missile guidance, emergency rescue and the like.
However, in practical applications, the distance from the surface of the earth due to the navigation satellite is between 215000 and 36000 km. During signal propagation, the distance measurement between the receiver and the satellite has large errors due to multiple refractions and reflections. In addition, the satellite clock adopts a high-precision rubidium atomic clock, a clock difference exists between the receiver and the satellite clock, and the clock difference is multiplied by the light speed to cause a large distance measurement error, so that the positioning precision is reduced. This will result in inaccurate coarse positioning results of the original satellite navigation ephemeris text and the observed pseudorange directly acquired by the receiver, and the positioning results will deviate from the actual position.
In order to improve the positioning accuracy of the receiver, people mainly improve the positioning accuracy of the receiver through several methods, including a least square method, a particle filtering method, a kalman filtering method and a differential positioning method. Among them, the differential positioning method is currently the most widely used method.
The method comprises three modes of position difference, pseudo range difference and carrier phase difference. Three modes all use two receivers, including a base station receiver and a mobile end receiver, and the distance between them has a decisive influence on the accuracy. In contrast, the data information and the calculation method they receive have their own features. In general, the position difference mode is the simplest to calculate, but the improvement degree of the positioning precision is the worst; the carrier phase differential mode requires resolution of the integer ambiguity problem, and requires higher hardware. The pseudo-range differential mode algorithm has moderate complexity and can ensure proper positioning precision.
However, the error range of the general differential positioning method is large, which is about tens of meters, and the result is more divergent, and the positioning accuracy still needs to be improved. In view of the above disadvantages, it is desirable to provide a differential positioning method with smaller error range and more aggregated results.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a differential positioning method with smaller error range and more aggregated results.
In order to achieve the above object, the present invention provides a differential positioning method, which is characterized by comprising the following steps:
setting a base station receiver and a mobile terminal receiver 1;
the receiver can receive space satellite signals in the area and select a plurality of satellites with the highest signal ratios;
assuming that the coordinates of the mobile terminal receiver 1 are (x, y, z), D _ jk represents the distance difference between the mobile terminal receiver 1 and the satellites j and k, and a plurality of sets of equations as shown below are obtained:
2x(xk-xj)+2y(yk-yj)+2z(zk-zj)
＝D_jk2+(xk 2+yk 2+zk 2)-(xj 2+yj 2+zj 2)+2D_jk·dk
(10)
wherein the content of the first and second substances,
the sets of equations are written in matrix form, as shown below, according to j-1, k-2, m-3, n-4, and so on:
2θX＝M+N
(11)
measuring distance P by using mobile terminal according to actual distance represented by root number itemi jCalculating; thus, the position calculation formula of the mobile terminal receiver is as follows:
and (3) calculating the distance from the mobile terminal receiver 1 to the satellite according to the position coordinates (x, y, z) calculated by the formula (13), substituting the distance into the formula (13) to calculate new N, and continuously solving the position of the mobile terminal receiver 1 through multiple iterations.
The differential positioning method according to the present invention is characterized in that the position of the base station receiver is set as the origin of coordinates by spatial coordinate transformation.
According to the differential positioning method of the present invention, the distance between the mobile terminal receiver and the base station receiver is within 15 km.
According to the differential positioning method of the present invention, the distance between the mobile terminal receiver and the base station receiver is within 10 km.
The differential positioning method according to the present invention is characterized in that four satellites j, k, m and m with the highest signal ratios, which may be called satellites 1 to 4, are selected, and the position information of the satellites 1 to 4 is obtained as (x)1，y1，z1)，(x2，y2，z2)，(x3，y3，z3) And (x)4，y4，z4)。
The differential positioning method according to the present invention is characterized in that θ ═ x, y, z,
the differential positioning method according to the present invention is characterized in that the actual distance represented by the root number term is measured by using the mobile terminal-measured distance Pi jCalculation, N translates to the following formula:
wherein, Pi jRepresenting the observation distance of receiver i to satellite j, and so on.
The differential positioning method according to the present invention is characterized in that the distances from the mobile terminal receiver 1 to the four satellites j, k, m and m are calculated and then substituted into the formula (13) to calculate a new N.
The differential positioning method according to the present invention is characterized in that the number of iterations is at least three.
The differential positioning method according to the present invention is characterized in that the number of iterations is at least five.
Compared with the prior art, the invention has the following beneficial technical effects:
according to the differential positioning method, the influence caused by linear errors and Gaussian errors can be effectively eliminated. After three times of iteration processing, the positioning error can be controlled within 2 m; further, through five times of iteration processing, the positioning error can be controlled within 1 m; and the result is basically distributed around the origin, linear noise increase does not influence positioning, and the position of the mobile terminal receiver does not become dispersed due to the existence of Gaussian error.
In addition, the positioning method disclosed by the invention is low in calculation complexity, easy to popularize and high in practical value.
Detailed Description
Hereinafter, the present invention will be explained in detail with reference to specific embodiments.
First, a base station receiver and a mobile terminal receiver are provided, wherein the position of the base station receiver is determined. Advantageously, the position of the base station receiver is set to the origin of coordinates by a spatial coordinate transformation.
The base station receiver and the mobile terminal receiver receive a signal of the space satellite j and output observation distance information between the satellite j and the base station receiver (or the mobile terminal receiver), and a measured pseudorange of the base station receiver (or the mobile terminal receiver) is as follows:
wherein, Pi jDenotes the observation distance, ρ, from the receiver i (base station receiver or mobile terminal receiver) to the satellite ji jRepresenting the actual distance of the receiver i from the satellite j,
and
representing the time effects, deltat, of the ionosphere and troposphereiAnd δ tjRespectively, the effects of receiver i-clock differences and satellite clock differences.
The pseudorange equations measured by the receiver 1 for the satellites j and k are as follows:
in one specific embodiment, the mobile terminal receiver is the receiver 1, and the base station receiver is the receiver 2, with a distance of 5km between them. It can be considered that the spatial errors of the receiver 1 and the receiver 2 have correlation. According to the actual measurement research, when the distance between the receiver 1 and the receiver 2 is within 10km, the spatial error correlation between the two is high; as the distance between the receivers 1 and 2 increases to 15km, the spatial error correlation decreases significantly, thereby affecting the error range more strongly, resulting in a lower and lower positioning accuracy. In general, when the distance between the two is within 10km, the spatial error hasHighly correlated, i.e.
And
both are approximately the same.
Subtracting the formula (3) from the formula (2) yields the following formula:
similarly, for the receiver 2, the same processing is performed, resulting in the following formula:
further, equation (5) is subtracted from equation (4) to obtain the following equation:
the receiver can receive the space satellite signals in the area and select the four satellites j, k, m and m with the highest signal ratio, which can be referred to as satellites 1-4. Each receiver is capable of acquiring four observed pseudorange information. First, a difference process is performed between the receivers and then between the satellites, resulting in three sets of equations as shown below:
wherein the content of the first and second substances,
a difference operator is represented twice as many times as,
showing that the receiver 1 and the receiver 2 simultaneously observe the satellites j and k, the receiver 1 and the receiver 2 firstly perform one inter-satellite differential processing between the simultaneously observed satellite j and the satellite k, and then perform one inter-station differential processing between the receiver 1 and the receiver 2.
Since the receiver 2 is used as a base station receiver and the position is determined, the distance between the coordinates and the satellite coordinates is determined to obtain the precise distance between the satellite and the base station receiver. Then, equation (7) is transformed to calculate the determined distance from the base station receiver to the satellite, and the distance is shifted to the left of the equation, resulting in the following equation:
where D _ jk represents the distance difference between the mobile-end receiver 1 and the satellites j and k.
Let the coordinates of satellites j and k be (x), respectivelyj，yj，zj) And (x)k，yk，zk) The coordinates of the mobile receiver (i.e., receiver 1) are (x, y, z), and this is substituted for equation (8), which yields the following equation:
further, moving the last square root in the above formula to the left for squaring, and simplifying the process, the following formula is obtained:
2x(xk-xj)+2y(yk-yj)+2z(zk-zj)
＝D_jK2+(xk 2+yk 2+zk 2)-(xj 2+yj 2+zj 2)+2D_jk·dk(10) wherein the content of the first and second substances,
further, in the case where four satellites j, k, m, and m (numbered 1 to 4, respectively) are observed, three equations of equation (10) can be obtained, written in the form of a matrix, as shown below:
2θX＝M+N
(11)
where θ is (x, y, z),
in the above matrix, since the position of the spatial satellite coordinates is already known when the satellite navigation message is extracted, only the position information of the mobile-end receiver is unknown in the entire equation set. In N, an iterative method can be adopted for solving, and the actual distance represented by the root number item is used for measuring the distance P by using the mobile terminali jCalculation, therefore, N can be converted to the following formula:
thus, the position calculation formula of the mobile terminal receiver is as follows:
in the above matrix formula, since the actual distance is replaced by the observation distance, the replacement has an error, the distances from the mobile terminal receiver to the four satellites j, k, m and m (the numbers are 1 to 4 respectively) are calculated according to the position coordinates (x, y, z) calculated by the formula (13), and then the distances are substituted into the formula (13) to calculate new N, and the position of the mobile terminal receiver is continuously solved through multiple iterations.
According to the above calculation formula, when the coordinate positions of the four satellites j, k, m and m are (0,0,2000), (1500,1500,5000), (0,20000,0) and (20000,0,0) respectively and the base station receiver is located at the origin of coordinates (0,0,0), it is assumed that noise errors due to the ionosphere and the troposphere are linearly distributed, the noise errors are increased by 100m at a time, and other noise errors are gaussian distributed with a variance of 100 db. The result accuracy is calculated according to the method and the single-point positioning method respectively.
The result shows that the error range of more than 30m exists by adopting the single-point positioning method, and the position of the mobile terminal receiver deviates from the original point along with the increasing of the linear error, so that the positioning accuracy is greatly reduced. The Gaussian error causes the position of the receiver at the mobile terminal to be scattered and cannot be focused into an anchor point. That is, the single-point positioning accuracy is greatly affected by noise, and the positioning accuracy is low.
According to the differential positioning method, the influence caused by linear errors and Gaussian errors can be effectively eliminated. After three times of iteration processing, the positioning error can be controlled within 2 m; further, through five times of iteration processing, the positioning error can be controlled within 1 m; and the result is basically distributed around the origin, linear noise increase does not influence positioning, and the position of the mobile terminal receiver does not become dispersed due to the existence of Gaussian error.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.
Claims (6)
1. A differential positioning method is characterized by comprising the following steps:
setting a base station receiver and a mobile terminal receiver 1;
the base station receiver and the mobile terminal receiver 1 receive space satellite signals in an area, select four satellites j, k, m and m with the highest signal ratios, which may be called satellites 1 to 4, and acquire position information of the satellites 1 to 4, which are (x) respectively1，y1，z1)，(x2，y2，z2)，(x3，y3，z3) And (x)4，y4，z4)；
Assuming that the coordinates of the mobile terminal receiver 1 are (x, y, z), D _ jk represents the distance difference between the mobile terminal receiver 1 and the satellites j and k, and a plurality of sets of equations as shown below are obtained:
2x(xk-xj)+2y(yk-yj)+2z(zk-zj)＝D_jk2+(xk 2+yk 2+zk 2)-(xj 2+yj 2+zj 2)+2D_jk·dk (10)
wherein the content of the first and second substances,
the sets of equations are written in matrix form, as shown below, according to j-1, k-2, m-3, n-4, and so on:
2θX＝M+N (11)
measuring distance P by using mobile terminal according to actual distance represented by root number itemi jCalculating; thus, the position calculation formula of the mobile terminal receiver is as follows:
wherein θ is (x, y, z),
measuring distance P by using mobile terminal according to actual distance represented by root number itemi jCalculation, N translates to the following formula:
wherein, Pi jRepresents the observation distance from the receiver i to the satellite j, and so on;
and (3) calculating the distances from the mobile terminal receiver 1 to the four satellites i, k, m and m according to the position coordinates (x, y and z) calculated by the formula (13), substituting the distances into the formula (13) to calculate new N, and continuously solving the position of the mobile terminal receiver 1 through multiple iterations.
2. The differential positioning method as claimed in claim 1, characterized in that the position of the base station receiver is set to the origin of coordinates by spatial coordinate transformation.
3. The differential positioning method as claimed in claim 1, wherein the distance between the mobile-side receiver and the base-station receiver is within 15 km.
4. The differential positioning method as claimed in claim 3, wherein the distance between the mobile terminal receiver and the base station receiver is within 10 km.
5. The differential positioning method of claim 1, wherein the number of iterations is at least three.
6. The differential positioning method of claim 5, wherein the number of iterations is at least five.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TW502123B (en) * | 2000-09-14 | 2002-09-11 | Ching-Fang Lin | Real-time integrated vehicle positioning method and system with differential GPS |
| CN103837879A (en) * | 2012-11-27 | 2014-06-04 | 中国科学院光电研究院 | Method for realizing high-precision location based on Big Dipper system civil carrier phase combination |
| EP2902804A1 (en) * | 2014-02-03 | 2015-08-05 | Honeywell International Inc. | Systems and methods to monitor for false alarms from ionosphere gradient monitors |
| CN105242292A (en) * | 2015-10-30 | 2016-01-13 | 中国电子科技集团公司第二十研究所 | Pseudo-range differential positioning method of long base line |
| CN107229061A (en) * | 2017-07-18 | 2017-10-03 | 武汉大学 | A kind of star based on low orbit satellite ground difference real-time accurate localization method |
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| TWI424183B (en) * | 2011-01-26 | 2014-01-21 | Ind Tech Res Inst | Method for positioning and apparatus thereof |
| TWM502123U (en) * | 2015-01-31 | 2015-06-01 | Hung-Kai Chuang | Temperature display device with evaporation and dissipation |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TW502123B (en) * | 2000-09-14 | 2002-09-11 | Ching-Fang Lin | Real-time integrated vehicle positioning method and system with differential GPS |
| CN103837879A (en) * | 2012-11-27 | 2014-06-04 | 中国科学院光电研究院 | Method for realizing high-precision location based on Big Dipper system civil carrier phase combination |
| EP2902804A1 (en) * | 2014-02-03 | 2015-08-05 | Honeywell International Inc. | Systems and methods to monitor for false alarms from ionosphere gradient monitors |
| CN105242292A (en) * | 2015-10-30 | 2016-01-13 | 中国电子科技集团公司第二十研究所 | Pseudo-range differential positioning method of long base line |
| CN107229061A (en) * | 2017-07-18 | 2017-10-03 | 武汉大学 | A kind of star based on low orbit satellite ground difference real-time accurate localization method |
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