阅读说明：本技术 一种测码伪距gps绝对定位方法 (Code measurement pseudo range GPS absolute positioning method ) 是由 常占强 钱淑君 王延巧 何兰婷 于 2019-11-22 设计创作，主要内容包括：本发明涉及一种测码伪距GPS绝对定位方法,收集GPS接收机接收到的GPS卫星坐标数据、GPS卫星到接收机的伪距及电离层、对流层延迟；用本发明提供的数学模型估算出接收机概略坐标作为初始坐标,依据各GPS卫星坐标、卫星到接收机的伪距、电离层与对流层延迟组成观测方程组,求解方程组、获取GPS接收机精确坐标；再将上述获取的接收机坐标作为初始坐标,再计算观测方程组系数,求解方程组,以此迭代,获取更精确的接收机坐标。用本发明提供的方法与模型,仅用4颗GPS卫星观测值,在无接收机初始坐标情况下,可精确求取GPS接收机坐标。本发明法克服了常规测码伪距绝对定位方法中需已知接收机初始坐标问题,且较求差解法需观测5颗以上卫星有明显的优势。(The invention relates to a code measurement pseudo range GPS absolute positioning method, which collects GPS satellite coordinate data received by a GPS receiver, pseudo range from the GPS satellite to the receiver, ionosphere delay and troposphere delay; the mathematical model provided by the invention is used for estimating the rough coordinates of the receiver as initial coordinates, an observation equation set is formed according to the coordinates of each GPS satellite, the pseudo distance from the satellite to the receiver, the ionosphere and the troposphere delay, the equation set is solved, and the accurate coordinates of the GPS receiver are obtained; and then taking the acquired receiver coordinates as initial coordinates, calculating the coefficients of the observation equation set, and solving the equation set, so as to iterate and acquire more accurate receiver coordinates. The method and the model provided by the invention can accurately obtain the coordinates of the GPS receiver by only using 4 GPS satellite observation values under the condition of no receiver initial coordinates. The method of the invention overcomes the problem that the conventional code-measuring pseudorange absolute positioning method needs to know the initial coordinate of the receiver, and has obvious advantages compared with a differential solution method which needs to observe more than 5 satellites.)

1. A code measurement pseudorange GPS absolute positioning method is characterized by comprising the following steps:

step 1: acquiring coordinate data of GPS satellites received by a GPS receiver, pseudo distances from each GPS satellite to the GPS receiver and corresponding ionized layer delay and troposphere delay data;

step 2: estimating the initial approximate coordinates of the GPS receiver by using the mathematical model provided by the invention;

and step 3: according to the GPS satellite coordinates, the pseudo distances from each GPS satellite to the GPS receiver, the corresponding ionosphere delay and troposphere delay, calculating the observation equation set coefficients linearized by the Taylor series by taking the GPS receiver approximate coordinates obtained in the step 2 as initial coordinate values, and solving the solution or least square solution of the linear equation set to obtain accurate GPS receiver coordinates;

and 4, step 4: calculating the coefficient of the observation equation set by taking the GPS receiver coordinate obtained from the step 3 as the next initial coordinate of the GPS receiver, and obtaining the solution or least square solution of the linear equation set to obtain more accurate GPS receiver coordinate; and iterating until the coordinate difference of the GPS receiver obtained in the previous and subsequent times meets the precision requirement of the user.

2. The code-measuring pseudorange GPS absolute positioning method according to claim 1, characterized in that: the step 1 is realized by the following specific steps:

(1) real-time ephemeris data of a GPS satellite received by a GPS receiver;

(2) extracting ionosphere delay and troposphere delay from the real-time ephemeris data, and correcting a receiver code measurement pseudo range to obtain the distance from the corrected GPS satellite to the receiver:

in the formula (1), i is a GPS satellite number, and i is 1,2,3, 4; rho_iThe distance from the receiver to the No. i GPS satellite after delay correction of the ionosphere and the troposphere;

(3) obtaining the coordinates of each GPS satellite in a ground-fixed coordinate system, namely X from the GPS real-time ephemeris data_i,Y_i,Z_iAnd the three-dimensional coordinate data are respectively the three-dimensional coordinate data of the No. i GPS satellite.

3. The code-measuring pseudorange GPS absolute positioning method according to claim 1, characterized in that: the step 2 is realized by the following specific steps:

(1) according to the three-dimensional coordinate data of the GPS satellite which can be received by the GPS receiver, the pseudo distance from each GPS satellite to the GPS receiver, and the corresponding ionospheric delay and tropospheric delay, each coefficient in the coefficient matrix is calculated by adopting the following formula:

a_i＝2(X_i+1-X_i) (2)

b_i＝2(Y_i+1-Y_i) (3)

c_i＝2(Z_i+1-Z_i) (4)

a in the formulae (2), (3) and (4)_i，b_i，c_iRespectively coefficient matrix coefficients; l in formula (5)_iIs the free term vector coefficient; the row and column numbers of the i coefficient matrix, i is 1,2 and 3;

(2) the system of equations for solving the initial coordinates of the receiver is formed by the coefficients, and the matrix form is as follows:

(6) wherein A is a coefficient matrix:

(3) solving equation set (6), the receiver initial approximate coordinates are:

all of the above equations provide mathematical models for the present invention,

4. The code-measuring pseudorange GPS absolute positioning method according to claim 1, characterized in that: the step 3 is realized by the following steps:

(1) calculating the coefficients of the observation equation set linearized by the taylor series according to the GPS satellite coordinate values, the pseudoranges of the satellites to the GPS receiver, the corresponding ionospheric and tropospheric delays, and the initial coordinate values of the GPS receiver obtained in step 2:

in the formula (8), the coefficient matrixReceiver coordinate correction vector

(2) solving the equation set (8) to obtain the coordinate correction vector of the GPS receiver

(3) And (3) correcting the initial approximate coordinate of the GPS receiver obtained in the step (2) to obtain the accurate GPS receiver coordinate:

5. the code-measuring pseudorange GPS absolute positioning method according to claim 1, characterized in that: the step 4 is realized by the following steps:

(1) and (3) aiming to acquire more accurate GPS receiver coordinates, and iterating the step (3), wherein the iteration process is as follows:

the precise GPS receiver coordinate obtained in the step 3

and solving the equation set (8) again to obtain a new GPS receiver coordinate correction:

correcting the precise GPS receiver coordinate obtained in the step 3 to obtain a more precise GPS receiver coordinate

(2) And iterating until the coordinate difference of the GPS receiver obtained in the previous and subsequent times meets the precision requirement of the user.

6. The code-measuring pseudorange GPS absolute positioning method according to claim 1, characterized in that: the method is used for acquiring the accurate coordinate value of the GPS receiver under the condition that only 4 GPS satellite observation values exist and the initial coordinate of the GPS receiver does not exist.

Technical Field

The invention can be applied to the fields of vehicle navigation, public security traffic, disaster rescue, travel exploration, geographical investigation, geological survey, resource exploration, cadastral measurement, fine agriculture and the like. The invention provides a method for accurately acquiring a three-dimensional space coordinate of a GPS receiver in the technical field.

Background

The GPS code measurement pseudo-range absolute positioning only needs one GPS receiver, is simple and convenient to operate, low in cost and high in speed, and is widely applied to the fields of vehicle navigation, public security traffic, disaster rescue, travel exploration, geographic investigation, geological survey, resource exploration, cadastral measurement, fine agriculture and the like. In modern large cities, high buildings or structures, or mountainous areas, hilly terrain, mountainous and mountainous peaks of peaks and dense forests, severely block and obscure satellite signals. Therefore, it is very important to research and develop a method for obtaining accurate GPS receiver coordinates when receiving less GPS satellite signals and without initial GPS station coordinates. At present, the code measurement pseudorange GPS absolute single point positioning is mainly realized by the following methods at home and abroad:

method 1. conventional method, otherwise known as general method. The code-measuring pseudo-range from each GPS satellite to the receiver is used as an observed quantity, and a code-measuring pseudo-range absolute positioning observation equation set is listed, so that the relation between the known GPS satellite coordinate and the unknown receiver coordinate is established. Because the GPS code measurement pseudo range single point positioning observation equation is nonlinear, the GPS code measurement pseudo range single point positioning observation equation is generally linearized by Taylor series expansion, and the solution of the observation equation is solved by using a linear least square method, namely the accurate coordinate value of the GPS receiver is obtained. The method for acquiring the coordinates of the GPS receiver needs synchronous observation data of more than 4 GPS satellites, and if the observation data of more than 4 satellites exceeds the observation data of the 4 satellites, the least square solution of an observation equation is solved by using a least square method.

(see [1] Lissajou. GPS principle and application [ M ], 21 st college textbook, scientific Press, 2003; [2] Liuji residue. GPS satellite navigation positioning principle and method [ M ], scientific Press, 2003 ]; [3] Zhouyomi plan, Yijijun, Zhouyi. GPS satellite measurement principle and application [ M ], surveying and mapping Press, 1997 ]; [4] Elliott Kaplan, ChristopherHegarty, Understand GPS: printies and applications [ M ], Secondedition 2006ARTH HOUSE, INCORPORATION)

Method 2. difference method. Different from the method 1, the method does not carry out linearization on code measurement pseudo-range observation equations, but carries out difference solving on each observation equation so as to eliminate nonlinear terms in the observation equations, and then solves the observation equations to directly solve the three-dimensional rectangular coordinates of the GPS receiver.

(see [5] Liu Dale, et al. principles and data processing of Global Positioning System (GPS) [ M ]. Shanghai: Tongji university Press, 1996; [6] Guoqiying, et al. several algorithms for absolute positioning of GPS code-measuring pseudoranges, survey and drawing science, 2005,30(5):26-28)

In the method 1, the initial coordinates of the GPS receiver need to be known, and then the accurate coordinates of the GPS receiver are obtained by solving the observation equation set. This method cannot be implemented without the GPS receiver initial coordinates. Even if the initial coordinate of the GPS receiver is known, if the deviation between the initial value and the accurate value of the coordinate of the observation station is large, the model error of the secondary tiny amount is omitted, the calculation result is influenced by the model error which cannot be ignored, and even the accurate coordinate cannot be obtained through iterative divergence.

Method 2 should be noted that this method needs to receive more than 5 GPS satellite signals at the same time to list more than 5 pseudorange observation equations, so as to ensure the linear independence of the equations after the difference processing between the observation equations. This clearly limits the range of application of the method, especially in urban areas, high building groups, structures, mountainous and hilly lands, mountainous and mountainous peaks and peaks over peaks terrains and dense forests, which can obscure the GPS signals seriously and in many cases, it is impossible to receive more than 5 GPS satellite signals at the same time.

From the above, it is known that: how to obtain the accurate three-dimensional space coordinate of a GPS receiver under the condition of receiving less GPS satellite signals (without increasing the number of GPS observation satellites) and without an initial GPS coordinate value is one of the core contents and research hotspot directions of code measurement pseudorange GPS single-point positioning.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, and provides a code-measuring pseudorange GPS absolute positioning method to obtain the accurate three-dimensional space coordinate of a GPS receiver under the condition of receiving less GPS satellite signals and having no GPS initial coordinate value.

The technical scheme for solving the problems is as follows:

a code measurement pseudorange GPS absolute positioning method comprises the following steps:

step 1: data collection: collecting coordinate data of GPS satellites received by a GPS receiver, pseudo distances from each GPS satellite to the GPS receiver and corresponding ionosphere delay and troposphere delay data;

step 2: the mathematical model provided by the invention utilizes the data acquired in the step 1 to estimate the approximate coordinates of the GPS receiver, and provides data support for the step 3;

and step 3: and (2) calculating the coefficients of the observation equation set after the Taylor series linearization by taking the approximate coordinates of the GPS receiver obtained in the step (2) as initial coordinate values according to the coordinates of the GPS satellites, the pseudo distances from the GPS satellites to the GPS receiver, and the corresponding ionospheric delay and tropospheric delay, and solving the solution (or least square solution) of the linear equation set to obtain accurate coordinates of the GPS receiver. Simultaneously providing data support for the step 4;

and 4, step 4: and (3) aiming to obtain more accurate GPS receiver coordinates, taking the GPS receiver coordinate values obtained from the step (3) as initial coordinates of the next GPS receiver, calculating the coefficients of the observation equation set, obtaining the solution (least square solution) of the linear equation set, and obtaining more accurate GPS receiver coordinates. And iterating until the coordinate difference of the GPS receiver obtained in the previous and subsequent times meets the precision requirement of the user.

The step 1 is realized by the following specific steps:

(1) real-time ephemeris data of a GPS satellite received by a GPS receiver;

(2) extracting ionosphere delay and troposphere delay from the real-time ephemeris data, and correcting a receiver code measurement pseudo range to obtain the distance from the corrected GPS satellite to the receiver:

in the formula (1), i is a GPS satellite number, and i is 1,2,3, 4; rho_iAfter the delay of the ionosphere and the troposphere is corrected from the receiver to the No. i GPS satelliteThe distance of (d);

the pseudo range from the satellite measured by the No. i GPS receiver to the measuring station; delta I_iAnd δ T_iDelay data for the corresponding ionosphere and troposphere;

(3) obtaining the coordinates of each GPS satellite in a ground-fixed coordinate system, namely X from the GPS real-time ephemeris data_i,Y_i,Z_iAnd the three-dimensional coordinate data are respectively the three-dimensional coordinate data of the No. i GPS satellite.

The step 2 is realized by the following specific steps:

(1) according to the three-dimensional coordinate data of the GPS satellite which can be received by the GPS receiver, the pseudo distance from each GPS satellite to the GPS receiver, and the corresponding ionospheric delay and tropospheric delay, each coefficient in the coefficient matrix is calculated by adopting the following formula:

a_i＝2(X_i+1-X_i) (2)

b_i＝2(Y_i+1-Y_i) (3)

c_i＝2(Z_i+1-Z_i) (4)

a in the formulae (2), (3) and (4)_i，b_i，c_iRespectively coefficient matrix coefficients; l in formula (5)_iIs the free term vector coefficient; the row and column numbers of the i coefficient matrix, i is 1,2 and 3;

(2) the system of equations for solving the initial coordinates of the receiver is formed by the coefficients, and the matrix form is as follows:

(6) wherein A is a coefficient matrix:

for the initial coordinate vector of the receiver,

l is a vector of the free terms,

(3) solving equation set (6), the receiver initial approximate coordinates are:

all of the above equations provide mathematical models for the present invention,

i.e. the calculated initial approximate coordinates of the GPS receiver.

The step 3 is realized by the following steps:

(1) calculating the coefficients of the observation equation set linearized by the taylor series according to the GPS satellite coordinate values, the pseudoranges of the satellites to the GPS receiver, the corresponding ionospheric and tropospheric delays, and the initial coordinate values of the GPS receiver obtained in step 2:

in the formula (8), the coefficient matrix

Receiver coordinate correction vector

δ X, δ Y, δ Z are correction amounts in the direction X, Y, Z, respectively; free term vector

Wherein:

c is the speed of light, and c is 299792.458 km/s;

(2) solving the equation set (8) to obtain the coordinate correction vector of the GPS receiver

(3) And (3) correcting the initial approximate coordinate of the GPS receiver obtained in the step (2) to obtain the accurate GPS receiver coordinate:

in order to correct the exact GPS receiver coordinates after correction,

the step 4 is realized by the following steps:

(1) and (3) aiming to acquire more accurate GPS receiver coordinates, and iterating the step (3), wherein the iteration process is as follows:

the precise GPS receiver coordinate obtained in the step 3

As initial coordinates for the next GPS receiver, i.e.

Will be provided with

Substituting into step 3 to obtain k_i、m_i、n_iAnd a new coefficient matrix B is obtained,

and solving the equation set (8) again to obtain a new GPS receiver coordinate correction:

correcting the precise GPS receiver coordinate obtained in the step 3 to obtain a more precise GPS receiver coordinate

(2) And iterating until the coordinate difference of the GPS receiver obtained in the previous and subsequent times meets the precision requirement of the user.

The method is used for acquiring the accurate coordinate value of the GPS receiver under the condition that only 4 GPS satellite observation values exist and no initial coordinate of the GPS receiver exists.

Compared with the prior art, the invention has the beneficial effects that:

(1) compared with the prior method 1, the invention can accurately obtain the coordinate value of the GPS receiver by using 4 GPS satellite observation values under the condition of no initial coordinate of the GPS receiver. Whereas method 1 must know the initial coordinates of the GPS receiver. In addition, if the initial coordinates are too different from the actual coordinates, the iterative divergence cannot acquire accurate coordinate values.

(2) Compared with the prior method 2, under the condition of no initial coordinate of the GPS receiver, the invention can accurately obtain the coordinate value of the GPS receiver by only using 4 observation values of the GPS satellites. Whereas method 2 requires more than 5 GPS satellite observations.

In practical application, the method of the present invention is suitable for GPS code measurement pseudorange absolute positioning navigation in urban areas, high building groups, structures, mountainous and hilly mountainous and mountainous. In these cases, the GPS signals are severely blocked, and in many cases, more than 5 GPS satellite signals cannot be received at the same time.

Drawings

Fig. 1 is a flowchart of a code measurement pseudorange GPS absolute positioning method according to the present invention.

Detailed Description

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

As shown in fig. 1, the present invention provides a flowchart of a code measurement pseudorange GPS absolute positioning method, which comprises the following specific steps:

step 1: data collection: collecting coordinate data of GPS satellites received by a GPS receiver, pseudo distances from each GPS satellite to the GPS receiver, corresponding data such as ionospheric delay, tropospheric delay and the like;

(1) collecting real-time ephemeris data of a GPS satellite received by a GPS receiver;

(2) extracting ionosphere delay and troposphere delay from the real-time ephemeris data, and correcting a receiver code measurement pseudo range to obtain the distance from the corrected GPS satellite to the receiver:

in the formula (1), i is a GPS satellite number, and i is 1,2,3, 4; rho_iThe distance from the receiver to the No. i GPS satellite after delay correction of the ionosphere and the troposphere;

the pseudo range from the satellite measured by the No. i GPS receiver to the measuring station; delta I_iAnd δ T_iCorresponding ionospheric and tropospheric delays.

(3) Obtaining the coordinates of each GPS satellite in a ground-fixed coordinate system, namely X from the GPS real-time ephemeris data_i,Y_i,Z_iThree-dimensional coordinate components of the i-th GPS satellite, respectively.

Step 2: the mathematical model provided by the invention is used for estimating the approximate coordinates of the GPS receiver, and data support is provided for the step 3;

(1) calculating each coefficient in the coefficient matrix by the following formula according to the coordinate data of the GPS satellite which can be received by the GPS receiver, the pseudo distance from each GPS satellite to the GPS receiver, and the corresponding ionospheric delay and tropospheric delay:

a_i＝2(X_i+1-X_i) (2)

b_i＝2(Y_i+1-Y_i) (3)

c_i＝2(Z_i+1-Z_i) (4)

a in the formulae (2), (3) and (4)_i，b_i，c_iRespectively coefficient matrix coefficients; l in formula (5)_iIs the free term vector coefficient; i is the row and column number of the coefficient matrix, i is 1,2, 3.

(2) The system of equations for solving the initial coordinates of the receiver is formed by the coefficients, and the matrix form is as follows:

in equation (6), a is a coefficient matrix:

for the initial coordinate vector of the receiver,

l is a vector of the free terms,

(3) solving the equation set (6) to obtain the initial coordinates of the receiver as:

and step 3: and (2) calculating the coefficients of the observation equation set after the Taylor series linearization by taking the approximate coordinates of the GPS receiver obtained in the step (2) as initial coordinate values according to the coordinates of the GPS satellites, the pseudo distances from the GPS satellites to the GPS receiver, and the corresponding ionospheric delay and tropospheric delay, and solving the solution (or least square solution) of the linear equation set to obtain accurate coordinates of the GPS receiver. Simultaneously providing data support for the step 4;

(1) calculating the coefficients of the observation equation set linearized by the taylor series according to the GPS satellite coordinate values acquired by the GPS receiver, the pseudoranges of the satellites to the GPS receiver, the corresponding ionospheric and tropospheric delays, and the initial coordinate values of the GPS receiver obtained in step 2:

k in the formulae (8), (9) and (10)_i,m_i,n_iRespectively coefficient matrix coefficients; w in formula (11)_iAre the free term vector coefficients, wherein,

i is the row and column number of the coefficient matrix, i is 1,2,3, 4.

(2) The above coefficients form an observation equation set to obtain the accurate coordinate of the GPS receiver, and the matrix form is as follows:

in the formula (12), B is a coefficient matrix,

wherein c is the speed of light, and c is 299792.458 km/s;

the vector is corrected for the receiver coordinates and,δ X, δ Y, δ Z are correction amounts in the direction X, Y, Z, respectively; w is a free term vector

(3) Solving the system of linear equations (12) to obtain the GPS receiver coordinate correction vector:

(4) and (3) correcting the initial approximate coordinate of the GPS receiver obtained in the step (2) to obtain the accurate GPS receiver coordinate:

in order to correct the exact GPS receiver coordinates after correction,

and 4, step 4: more accurate GPS receiver coordinates are to be acquired.

(1) Using the GPS receiver coordinate value obtained from step 3 as the next GPS receiver initial coordinateThen, the coefficients B and W of the observation equation set are calculated according to the step 3, and the solution (least square solution) of the linear equation set is solved

More accurate GPS receiver coordinates can be obtained.

(2) And iterating until the coordinate difference of the GPS receiver obtained in the two times meets the precision requirement of the user.

Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.