WO2019218766A1 - Inertial navigation assisted beidou triple-frequency carrier phase whole-cycle ambiguity resolution method - Google Patents
Inertial navigation assisted beidou triple-frequency carrier phase whole-cycle ambiguity resolution method Download PDFInfo
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- WO2019218766A1 WO2019218766A1 PCT/CN2019/077891 CN2019077891W WO2019218766A1 WO 2019218766 A1 WO2019218766 A1 WO 2019218766A1 CN 2019077891 W CN2019077891 W CN 2019077891W WO 2019218766 A1 WO2019218766 A1 WO 2019218766A1
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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
- G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
- G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
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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
- G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
- G01S19/47—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial
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- the invention belongs to the field of positioning and navigation technology of Beidou satellite system (BDS), and particularly relates to a method for solving the full-circumference ambiguity of Beidou tri-frequency carrier phase using inertial guidance.
- BDS Beidou satellite system
- the present invention proposes an inertial navigation aided Beidou tri-frequency carrier phase full-circumference ambiguity solution method.
- An inertial navigation aided Beidou tri-band carrier phase full-circumference ambiguity solving method comprising the following steps:
- the BDS tri-band combined carrier phase double difference and the pseudorange double difference observation model equation are:
- ⁇ 1 , ⁇ 2 , and ⁇ 3 are respectively the carrier phase double difference of the Beidou tri-band B1, B2, and B3, and ⁇ 1 , ⁇ 2 , and ⁇ 3 are respectively B1, B2, B3 pseudo-distance double difference, ⁇ 1 , ⁇ 2 and ⁇ 3 are the wavelengths of B1, B2, and B3, respectively, and k 1 , k 2 , and k 3 are the coefficients of B1, B2, and B3 in the combination, r is the baseline distance, and g is the double-orbiting satellite orbit error, and T is Double-difference tropospheric error, I 1 is the double-difference ionospheric error of B1, with Representing receiver errors associated with carrier phase and pseudorange, respectively;
- N 1 , N 2 , and N 3 are the whole-circumference ambiguity values of B1, B2, and B3, respectively, and the wavelength in the tri-band combination is Combined scale factor is
- the scale factor is ⁇ (k 1 n , k 2 n , k 3 n ) to form a narrow lane combination, wherein the wavelength, the carrier phase double difference, and the whole-circumference ambiguity are respectively ⁇ n .
- step (2) taking A tri-band geometrically independent combination (GF) is obtained, where ⁇ (k 1 , k 2 , k 3 ) takes the value ⁇ g (k 1 g , k 2 g , k 3 g ), and the wavelength and carrier phase are double in the combination.
- the difference and the whole week ambiguity are ⁇ g , ⁇ g , N g respectively ;
- the ambiguities of the whole week are ⁇ i , ⁇ i , N i ;
- the INS position observation equation is among them
- the position estimate for the INS output X is the coordinate position parameter
- I 3 is a 3 ⁇ 3 unit matrix
- n is the observation error.
- the combined observation equations of the carrier phase and pseudorange observation equations in the narrow narrow lane, the wide lane, the ultra wide lane, the ionospheric independent model and the geometrically independent model, and the INS observation equation are as follows:
- ⁇ represents the carrier phase
- ⁇ represents the pseudorange double difference
- r 0 is the initial distance between the satellite and the receiver
- ⁇ represents the receiver noise
- the up/down markers n, w, s, g, i represent the marked Variables are variables in narrow lanes, wide lanes, extra wide lanes, ionospheric independent models, and geometrically independent models
- the position estimate for the INS output X is the coordinate position parameter
- X 0 is the initial position
- I 3 is the 3 ⁇ 3 unit matrix
- n is the observation error.
- the method for obtaining the integer ambiguity N integer solution by using the LAMBDA algorithm is:
- the floating point solution obtained by the integer vector N and step (4) The squared distance is the objective function, and the whole week ambiguity N is searched to make the objective function reach the minimum value, that is,
- the LAMBDA algorithm search space is T:
- the method of the present invention simultaneously introduces inertial navigation information and linear combination information of carrier phase double difference and pseudorange double difference on different frequencies. Since the measured values of the ionospheric-independent combination are not affected by the ionosphere, the geometrically uncorrelated combinations are not affected by the geometric position, and the narrow lane, wide lane, and ultra-wide lane combination have the advantages of low noise and long wavelength, which is more conducive to the whole.
- the inertial navigation is not restricted by environmental factors, and the high precision can be maintained even when the satellite signal is invisible or environmentally disturbed.
- FIG. 1 is a schematic flow chart of the principle of the present invention.
- an inertial navigation assisted Beidou tri-band carrier phase full-circumference ambiguity solving method disclosed in the embodiment of the present invention mainly includes the following steps:
- Step 1 Determine a BDS tri-band combined carrier phase double difference and pseudorange double difference observation model, and obtain pseudorange and carrier phase measurement values from ephemeris information, intermediate frequency data, and the like.
- ⁇ ur ⁇ -1 (r ur (ij) +g ur (ij) +T ur (ij) -I ur (ij) )+N ur (ij) + ⁇ ⁇ ,ur (ij)
- ⁇ ur (ij) r ur (ij) +g ur (ij) +T ur (ij) +I ur (ij) + ⁇ ⁇ ,ur (ij)
- u and r represent the base station and the mobile station receiver, respectively, and i and j represent satellite numbers.
- r ur (ij) is the baseline distance
- g ur (ij) is the double-difference satellite orbit error
- T ur (ij) is the double-difference tropospheric error
- I ur (ij) is the double-difference ionospheric error
- ⁇ is the receiver noise.
- ⁇ 1 ⁇ 1 -1 (r + g + TI 1) + N 1 + ⁇ ⁇ , 1
- ⁇ 2 ⁇ 2 -1 (r+g+TI 2 )+N 2 + ⁇ ⁇ ,2
- ⁇ 3 ⁇ 3 -1 (r+g+TI 3 )+N 3 + ⁇ ⁇ ,3
- ⁇ 1 r+g+T+I 1 + ⁇ ⁇ ,1
- ⁇ 2 r+g+T+I 2 + ⁇ ⁇ ,2
- ⁇ 3 r+g+T+I 3 + ⁇ ⁇ ,3
- ⁇ 1 , ⁇ 2 , and ⁇ 3 are respectively B1, B2, and B3 carrier phase double differences, and ⁇ 1 , ⁇ 2 , and ⁇ 3 are B1, B2, and B3 pseudo-distance double differences, ⁇ 1 , ⁇ 2 , ⁇ 3 is the wavelength of the Beidou tri-band B1, B2, B3, r is the baseline distance, g is the double-difference satellite orbit error, T is the double-difference tropospheric error, I is the double-difference ionospheric error, and ⁇ is the receiver noise.
- the full-circumference ambiguity in the tri-band combination is The wavelength in the tri-band combination is Combined scale factor is
- step 2 different scale factor values are taken, that is, a linear combination of pseudorange observation and carrier phase observation. Different combinations of models are determined based on different baseline lengths, wavelengths, ionospheric magnifications, noise, and the like. Proceed as follows:
- Step 2.1 respectively take the scale factor as ⁇ (k 1 n , k 2 n , k 3 n ), ⁇ (k 1 w , k 2 w , k 3 w ), ⁇ (k 1 s , k 2 s , k 3 s ) constitutes a narrow alley, wide lane, super wide lane combination, simultaneous observation equation.
- the scale factor is (-4,1,4) to form a narrow lane combination
- the wavelength is 4.88m
- the ionosphere is amplified by 0.06 times
- (1,4,-5) constitutes a wide lane combination with a wavelength of 6.37m
- (0, -1, 1) constitutes three combinations of super wide lanes
- the wavelength is 8.1403m
- the ionosphere is amplified by 2.21 times.
- Step 2.2 Three carrier phase observations and three pseudorange observations for narrow lanes, wide lanes and extra wide lanes are processed to obtain a geometrically independent model and an ionospheric independent model.
- ⁇ (k 1 , k 2 , k 3 ) is taken as ⁇ g (k 1 g , k 2 g , k 3 g );
- An ionospherically unrelated combination (IF) is obtained, where ⁇ (k 1 , k 2 , k 3 ) is taken as ⁇ i (k 1 i , k 2 i , k 3 i ).
- Step 3 Estimating the baseline vector geocentric solid coordinates and the corresponding baseline vector matrix by using the inertial output attitude pose matrix, the platform error angle, and the antenna configuration information.
- step 4 a total of 11 BDS double-difference pseudoranges, different lane carrier phases, ionospheric-independent models, and pseudo-ranges under the geometrically independent model, and the position observation equations given by the INS are combined to solve the problem.
- the combined observation equation be as follows:
- ⁇ represents carrier phase in narrow lane, wide lane, extra wide lane, ionospheric independent model and geometrically independent model
- ⁇ represents BD1, BD2, BD3 pseudorange double difference
- A, B are constructed matrices
- N is a whole-circumference ambiguity matrix of different combinations.
- Step 5 using the LAMBDA algorithm to obtain the integer ambiguity N integer solution.
- Integer vector N and floating point solution The squared distance is the objective function, and the whole week ambiguity N is searched to make the objective function reach the minimum value, that is,
- the LAMBDA algorithm search space is T, then the search space for the integer ambiguity N integer solution is:
- the search space defined by the above formula is a multidimensional ellipsoid. Searching within the sphere yields the best integer ambiguity value.
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Abstract
An inertial navigation assisted Beidou triple-frequency carrier phase whole-cycle ambiguity resolution method, comprising: first determining BDS triple-frequency combined carrier phase double-difference and pseudorange double-difference observation models, and obtaining pseudorange and carrier phase observation values; then taking different scale factors to perform linear combination on a pseudo-range observable and a carrier phase observable to obtain narrowlane, widelane and ultra-widelane carrier phase and pseudorange observation equations and carrier phase and pseudorange observation equations under ionospheric-free and geometric-free models, and obtaining an INS observation equation using inertial navigation; and simultaneously establishing the carrier phase and pseudorange observation equations and the INS observation equation, and resolving the equation using a weighted least square method to obtain a float solution of the whole-cycle ambiguity; and finally resolving an integer value of the whole-cycle ambiguity by using the LAMBDA.
Description
本发明属于北斗卫星系统(BDS)定位导航技术领域,特别涉及一种利用惯导辅助的北斗三频载波相位整周模糊度求解方法。The invention belongs to the field of positioning and navigation technology of Beidou satellite system (BDS), and particularly relates to a method for solving the full-circumference ambiguity of Beidou tri-frequency carrier phase using inertial guidance.
载波相位整周模糊度的求解是高精度定位导航技术的关键问题之一。近年来,针对单历元整周模糊度的求解问题,国内外学者提出了很多解决方案。这些方案主要分为两大类:第一,最优线性组合法,通过双频或三频观测量构建窄巷/宽巷/超宽巷等组合观测量,以消除误差对模糊度解算的影响;第二,搜索法,包括最小二乘搜索法,最小二乘模糊度去相关法(LAMBDA法)等。但是由于卫星导航存在信号容易受遮挡等不足,在实际环境中可靠性需进一步提高。Solving the carrier phase ambiguity is one of the key issues in high-precision positioning navigation technology. In recent years, domestic and foreign scholars have proposed many solutions to solve the problem of the ambiguity of the single epoch. These schemes are mainly divided into two categories: first, the optimal linear combination method, which combines the observation of narrow lanes/wide lanes/super wide lanes by dual-frequency or three-frequency observation to eliminate the error to solve the ambiguity. Second, the search method, including the least squares search method, the least squares fuzzy degree decorrelation method (LAMBDA method) and the like. However, due to the lack of occlusion in the satellite navigation, the reliability needs to be further improved in the actual environment.
发明内容Summary of the invention
发明目的:针对北斗导航系统的特点,为克服LAMBDA等方法实时性不高和受环境制约等缺陷,本发明提出一种惯导辅助的北斗三频载波相位整周模糊度求解方法。OBJECTS OF THE INVENTION: In order to overcome the defects of the Beidou navigation system, in order to overcome the shortcomings of LAMBDA and other methods, such as low real-time performance and environmental constraints, the present invention proposes an inertial navigation aided Beidou tri-frequency carrier phase full-circumference ambiguity solution method.
技术方案:为实现上述目的,本发明采用的技术方案如下:Technical Solution: In order to achieve the above object, the technical solution adopted by the present invention is as follows:
一种惯导辅助的北斗三频载波相位整周模糊度求解方法,包括以下步骤:An inertial navigation aided Beidou tri-band carrier phase full-circumference ambiguity solving method, comprising the following steps:
(1)确定BDS三频组合载波相位双差和伪距双差观测模型,获取伪距和载波相位观测值;(1) Determining the BDS tri-band combined carrier phase double difference and pseudorange double difference observation model to obtain pseudorange and carrier phase observation values;
(2)取不同的比例因子值,进行伪距观测量和载波相位观测量线性组合方式,得到窄巷、宽巷和超宽巷载波相位和伪距观测方程,以及电离层无关模型和几何无关模型下的载波相位和伪距观测方程;(2) Taking different scale factor values, performing a linear combination of pseudo-range observation and carrier phase observation, and obtaining carrier phase and pseudo-range observation equations for narrow lane, wide lane and ultra-wide lane, and ion-free layer-independent model and geometry-independent Carrier phase and pseudorange observation equations under the model;
(3)利用惯导,得到INS位置观测方程;(3) Using the inertial navigation, obtain the INS position observation equation;
(4)联立上述窄巷、宽巷、超宽巷、电离层无关模型和几何无关模型下的载波相位和伪距观测方程,和INS观测方程,利用加权最小二乘法进行求解,得到整周模糊度的浮点解;(4) Simultaneously calculate the carrier phase and pseudorange observation equations in the narrow lane, wide lane, extra wide lane, ionosphere-independent model and geometrically independent model, and the INS observation equation, and solve it by weighted least squares method to obtain the whole week. Floating point solution of ambiguity;
(5)利用LAMBDA求解整周模糊度的整数值。(5) Use LAMBDA to solve the integer value of the ambiguity of the whole week.
所述步骤(1)中,BDS三频组合载波相位双差和伪距双差观测模型方程分 别为:In the step (1), the BDS tri-band combined carrier phase double difference and the pseudorange double difference observation model equation are:
其中,φ
1、φ
2、φ
3分别为北斗三频B1、B2、B3载波相位双差值,ρ
1、ρ
2、ρ
3分别为B1、B2、B3伪距双差值,λ
1、λ
2、λ
3分别为B1、B2、B3的波长,k
1、k
2、k
3分别为组合中B1、B2、B3的系数,r为基线距离,g为双差卫星轨道误差,T为双差对流层误差,I
1为B1的双差电离层误差,
和
分别代表与载波相位和伪距相关的接收机误差;
Where φ 1 , φ 2 , and φ 3 are respectively the carrier phase double difference of the Beidou tri-band B1, B2, and B3, and ρ 1 , ρ 2 , and ρ 3 are respectively B1, B2, B3 pseudo-distance double difference, λ 1 , λ 2 and λ 3 are the wavelengths of B1, B2, and B3, respectively, and k 1 , k 2 , and k 3 are the coefficients of B1, B2, and B3 in the combination, r is the baseline distance, and g is the double-orbiting satellite orbit error, and T is Double-difference tropospheric error, I 1 is the double-difference ionospheric error of B1, with Representing receiver errors associated with carrier phase and pseudorange, respectively;
三频组合中的整周模糊度为
其中N
1、N
2、N
3分别为B1、B2、B3的整周模糊度值,三频组合中的波长为
组合比例因子为
The full-circumference ambiguity in the tri-band combination is Where N 1 , N 2 , and N 3 are the whole-circumference ambiguity values of B1, B2, and B3, respectively, and the wavelength in the tri-band combination is Combined scale factor is
所述步骤(2)中,取比例因子为μ(k
1
n,k
2
n,k
3
n)构成窄巷组合,该组合中波长、载波相位双差、整周模糊度分别为λ
n,φ
n,N
n;μ(k
1
w,k
2
w,k
3
w)构成宽巷组合,该组合中波长、载波相位双差、整周模糊度分别为λ
w,φ
w,N
w;μ(k
1
s,k
2
s,k
3
s)构成超宽巷组合,该组合中波长、载波相位双差、整周模糊度分别为λ
s,φ
s,N
s,并针对B1、B2、B3的双差伪距测量值及窄巷、宽巷和超宽巷的载波相位观测值组合,联立方程如下:
In the step (2), the scale factor is μ(k 1 n , k 2 n , k 3 n ) to form a narrow lane combination, wherein the wavelength, the carrier phase double difference, and the whole-circumference ambiguity are respectively λ n . φ n, N n; μ ( k 1 w, k 2 w, k 3 w) configured widelane combination that the wavelength of the carrier phase double-difference integer ambiguity are λ w, φ w, N w ; μ(k 1 s , k 2 s , k 3 s ) constitutes a super wide lane combination in which the wavelength, carrier phase double difference, and whole-circumference ambiguity are λ s , φ s , N s , respectively, and for B1 and B2 , B3 double difference pseudo-range measurement value and carrier phase observation combination of narrow lane, wide lane and super wide lane, the simultaneous equation is as follows:
所述步骤(2)中,取
得到三频几何无关组合(GF),此时μ(k
1,k
2,k
3)取值为μ
g(k
1
g,k
2
g,k
3
g),该组合中波长、载波相位双差、整周模糊度分别为λ
g,φ
g,N
g;取
得到电离层无关组合(IF),此时μ(k
1,k
2,k
3)取值为μ
i(k
1
i,k
2
i,k
3
i),该组合中波长、载波相位双差、整周模糊度分别为λ
i,φ
i,N
i;
In the step (2), taking A tri-band geometrically independent combination (GF) is obtained, where μ(k 1 , k 2 , k 3 ) takes the value μ g (k 1 g , k 2 g , k 3 g ), and the wavelength and carrier phase are double in the combination. The difference and the whole week ambiguity are λ g , φ g , N g respectively ; To give independent ionospheric composition (the IF), this time μ (k 1, k 2, k 3) value of μ i (k 1 i, k 2 i, k 3 i), the wavelength, the double difference carrier phase combination The ambiguities of the whole week are λ i , φ i , N i ;
联立几何无关模型和电离层无关模型,得到方程如下:The simultaneous geometrically independent model and the ionospheric independent model, the equation is as follows:
所述步骤(3)中,INS位置观测方程为
其中
为INS输出的位置估计量,X为坐标位置参数,I
3为3×3单位矩阵,n为观测误差。
In the step (3), the INS position observation equation is among them The position estimate for the INS output, X is the coordinate position parameter, I 3 is a 3 × 3 unit matrix, and n is the observation error.
所述步骤(4)中,联立窄巷、宽巷、超宽巷、电离层无关模型和几何无关模型下的载波相位和伪距观测方程,以及INS观测方程得到的组合观测方程如下:In the step (4), the combined observation equations of the carrier phase and pseudorange observation equations in the narrow narrow lane, the wide lane, the ultra wide lane, the ionospheric independent model and the geometrically independent model, and the INS observation equation are as follows:
其中,φ代表载波相位,ρ代表伪距双差,r
0为卫星到接收机间的初始距离,ε代表接收机噪声,上/下标记n,w,s,g,i分别代表所标记的变量为窄巷、宽巷、超宽巷、电离层无关模型和几何无关模型中的变量;
为INS输出的位置估计量,X为坐标位置参数,X
0为初始位置,I
3为3×3单位矩阵,n为观测误差。
Where φ represents the carrier phase, ρ represents the pseudorange double difference, r 0 is the initial distance between the satellite and the receiver, ε represents the receiver noise, and the up/down markers n, w, s, g, i represent the marked Variables are variables in narrow lanes, wide lanes, extra wide lanes, ionospheric independent models, and geometrically independent models; The position estimate for the INS output, X is the coordinate position parameter, X 0 is the initial position, I 3 is the 3 × 3 unit matrix, and n is the observation error.
由加权最小二乘法求取模糊度浮点解
及协方差阵
Obtaining the ambiguity floating point solution by weighted least squares Covariance matrix
所述步骤(5)中,利用LAMBDA算法求取整周模糊度N整数解的方法为:In the step (5), the method for obtaining the integer ambiguity N integer solution by using the LAMBDA algorithm is:
以整数向量N与步骤(4)获得的浮点解
之间的距离平方为目标函数,搜索整周模糊度N,使这一目标函数达到最小值,即
The floating point solution obtained by the integer vector N and step (4) The squared distance is the objective function, and the whole week ambiguity N is searched to make the objective function reach the minimum value, that is,
LAMBDA算法搜索空间为T:The LAMBDA algorithm search space is T:
在所限定的多维椭球体内进行搜索,得到最佳整数模糊度值。Searching within the defined multidimensional ellipsoid yields the best integer ambiguity value.
有益效果:与现有技术相比,本发明方法同时引入了惯导信息和不同频率上在载波相位双差和伪距双差的线性组合信息。由于电离层无关组合的测量值不受电离层的影响,几何无关组合的测量值不受几何位置影响,窄巷、宽巷、超宽巷组合则具有低噪、长波长等优点,更加利于整周模糊度的求解,惯导则不受环境因素制约,在卫星信号不可见或受到环境干扰情况下,仍可保持高精度。将这些信息联立求解,可克服环境因素的干扰,在任何情况下都能够保证整周模糊度的求解精度,适用于北斗卫星导航系统的高精度定位系统。Advantageous Effects: Compared with the prior art, the method of the present invention simultaneously introduces inertial navigation information and linear combination information of carrier phase double difference and pseudorange double difference on different frequencies. Since the measured values of the ionospheric-independent combination are not affected by the ionosphere, the geometrically uncorrelated combinations are not affected by the geometric position, and the narrow lane, wide lane, and ultra-wide lane combination have the advantages of low noise and long wavelength, which is more conducive to the whole. For the solution of the ambiguity of the week, the inertial navigation is not restricted by environmental factors, and the high precision can be maintained even when the satellite signal is invisible or environmentally disturbed. By solving these information in a simultaneous solution, the interference of environmental factors can be overcome, and the accuracy of the whole-circumference ambiguity can be ensured under any circumstances, and is suitable for the high-precision positioning system of the Beidou satellite navigation system.
图1为本发明的原理流程示意图。FIG. 1 is a schematic flow chart of the principle of the present invention.
下面结合附图和具体实施例对本发明方法进行具体说明。The method of the present invention will be specifically described below in conjunction with the accompanying drawings and specific embodiments.
如图1所示,本发明实施例公开的一种惯导辅助的北斗三频载波相位整周模糊度求解方法,主要包括如下步骤:As shown in FIG. 1 , an inertial navigation assisted Beidou tri-band carrier phase full-circumference ambiguity solving method disclosed in the embodiment of the present invention mainly includes the following steps:
步骤1,确定BDS三频组合载波相位双差和伪距双差观测模型,由星历信息、中频数据等获取伪距和载波相位测量值。Step 1: Determine a BDS tri-band combined carrier phase double difference and pseudorange double difference observation model, and obtain pseudorange and carrier phase measurement values from ephemeris information, intermediate frequency data, and the like.
t时刻的双差伪距的观测方程为The observation equation of the double-difference pseudorange at time t is
φ
ur=λ
-1(r
ur
(ij)+g
ur
(ij)+T
ur
(ij)-I
ur
(ij))+N
ur
(ij)+ε
φ,ur
(ij)
φ ur =λ -1 (r ur (ij) +g ur (ij) +T ur (ij) -I ur (ij) )+N ur (ij) +ε φ,ur (ij)
双差载波相位测量值为Double difference carrier phase measurement
ρ
ur
(ij)=r
ur
(ij)+g
ur
(ij)+T
ur
(ij)+I
ur
(ij)+ε
ρ,ur
(ij)
ρ ur (ij) =r ur (ij) +g ur (ij) +T ur (ij) +I ur (ij) +ε ρ,ur (ij)
其中,u、r分别表示基准站和移动站接收机,i、j表示卫星编号。Where u and r represent the base station and the mobile station receiver, respectively, and i and j represent satellite numbers.
r
ur
(ij)为基线距离,g
ur
(ij)为双差卫星轨道误差,T
ur
(ij)为双差对流层误差,I
ur
(ij)为双差电离层误差,ε为接收机噪声等。
r ur (ij) is the baseline distance, g ur (ij) is the double-difference satellite orbit error, T ur (ij) is the double-difference tropospheric error, I ur (ij) is the double-difference ionospheric error, and ε is the receiver noise. .
将北斗三频B1、B2、B3分别标记为1、2、3,将双差测量值简化上下标,那么在t时刻的三频双差载波相位测量值分别为Marking the Beidou tri-bands B1, B2, and B3 as 1, 2, and 3, respectively, and simplifying the double-difference measurement value, then the three-frequency double-difference carrier phase measurement values at time t are respectively
φ
1=λ
1
-1(r+g+T-I
1)+N
1+ε
φ,1
φ 1 = λ 1 -1 (r + g + TI 1) + N 1 + ε φ, 1
φ
2=λ
2
-1(r+g+T-I
2)+N
2+ε
φ,2
φ 2 =λ 2 -1 (r+g+TI 2 )+N 2 +ε φ,2
φ
3=λ
3
-1(r+g+T-I
3)+N
3+ε
φ,3
φ 3 =λ 3 -1 (r+g+TI 3 )+N 3 +ε φ,3
相应的双差伪距测量值分别为The corresponding double difference pseudorange measurements are
ρ
1=r+g+T+I
1+ε
ρ,1
ρ 1 =r+g+T+I 1 +ε ρ,1
ρ
2=r+g+T+I
2+ε
ρ,2
ρ 2 =r+g+T+I 2 +ε ρ,2
ρ
3=r+g+T+I
3+ε
ρ,3
ρ 3 =r+g+T+I 3 +ε ρ,3
组合测量值的观测方程为:The observed equation for the combined measurements is:
组合伪距观测方程为:The combined pseudorange observation equation is:
其中,φ
1、φ
2、φ
3分别为B1、B2、B3载波相位双差值,ρ
1、ρ
2、ρ
3分别为B1、B2、B3伪距双差值,λ
1、λ
2、λ
3为北斗三频B1、B2、B3的波长,r为基线距离,g为双差卫星轨道误差,T为双差对流层误差,I为双差电离层误差,ε为接收机噪声等。
Where φ 1 , φ 2 , and φ 3 are respectively B1, B2, and B3 carrier phase double differences, and ρ 1 , ρ 2 , and ρ 3 are B1, B2, and B3 pseudo-distance double differences, λ 1 , λ 2 , λ 3 is the wavelength of the Beidou tri-band B1, B2, B3, r is the baseline distance, g is the double-difference satellite orbit error, T is the double-difference tropospheric error, I is the double-difference ionospheric error, and ε is the receiver noise.
三频组合中的整周模糊度为
三频组合中的波长为
组合比例因子为
The full-circumference ambiguity in the tri-band combination is The wavelength in the tri-band combination is Combined scale factor is
步骤2,取不同的比例因子值,即伪距观测量和载波相位观测量线性组合方式。根据不同基线长度、波长、电离层放大倍数、噪声等,确定不同组合的模型。步骤如下:In step 2, different scale factor values are taken, that is, a linear combination of pseudorange observation and carrier phase observation. Different combinations of models are determined based on different baseline lengths, wavelengths, ionospheric magnifications, noise, and the like. Proceed as follows:
步骤2.1,分别取比例因子为μ(k
1
n,k
2
n,k
3
n),μ(k
1
w,k
2
w,k
3
w),μ(k
1
s,k
2
s,k
3
s)构成窄巷、宽巷、超宽巷组合,联立观测方程。本例中取比例因子为(-4,1,4)构成窄巷组合,波长4.88m,电离层放大0.06倍;(1,4,-5)构成宽巷组合,波长为6.37m,电离层放大0.019倍;(0,-1,1)构成超宽巷三种组合,波长8.1403m,电离层放大2.21倍。
Step 2.1, respectively take the scale factor as μ(k 1 n , k 2 n , k 3 n ), μ(k 1 w , k 2 w , k 3 w ), μ(k 1 s , k 2 s , k 3 s ) constitutes a narrow alley, wide lane, super wide lane combination, simultaneous observation equation. In this example, the scale factor is (-4,1,4) to form a narrow lane combination, the wavelength is 4.88m, and the ionosphere is amplified by 0.06 times; (1,4,-5) constitutes a wide lane combination with a wavelength of 6.37m, the ionosphere Magnified 0.019 times; (0, -1, 1) constitutes three combinations of super wide lanes, the wavelength is 8.1403m, and the ionosphere is amplified by 2.21 times.
针对BD1、BD2、BD3的双差伪距测量值及窄巷、宽巷和超宽巷的载波相位观测值组合,联立方程,方程如下:For the double-difference pseudorange measurement of BD1, BD2, BD3 and the carrier phase observation combination of narrow lane, wide lane and super wide lane, the simultaneous equations are as follows:
步骤2.2,对窄巷、宽巷和超宽巷的三个载波相位观测量和三个伪距观测量进行处理,得到几何无关模型和电离层无关模型。Step 2.2: Three carrier phase observations and three pseudorange observations for narrow lanes, wide lanes and extra wide lanes are processed to obtain a geometrically independent model and an ionospheric independent model.
取
得到三频几何无关组合(GF),此时μ(k
1,k
2,k
3)取值记为μ
g(k
1
g,k
2
g,k
3
g);取
得到电离层无关组合(IF),此时μ(k
1,k
2,k
3)取值记为μ
i(k
1
i,k
2
i,k
3
i)。
take Obtaining a tri-band geometrically unrelated combination (GF), where μ(k 1 , k 2 , k 3 ) is taken as μ g (k 1 g , k 2 g , k 3 g ); An ionospherically unrelated combination (IF) is obtained, where μ(k 1 , k 2 , k 3 ) is taken as μ i (k 1 i , k 2 i , k 3 i ).
联立几何无关模型和电离层无关模型,得到方程如下:The simultaneous geometrically independent model and the ionospheric independent model, the equation is as follows:
步骤3,利用惯导输出姿态矩阵、平台误差角和天线配置信息估算基线矢量地心地固坐标及相应的基线矢量矩阵。得到:INS位置观测方程,为
其中
为INS输出的位置估计量,X为坐标位置参数,I
3为3×3单位矩阵,n为观测误差。
Step 3: Estimating the baseline vector geocentric solid coordinates and the corresponding baseline vector matrix by using the inertial output attitude pose matrix, the platform error angle, and the antenna configuration information. Get: INS position observation equation, for among them The position estimate for the INS output, X is the coordinate position parameter, I 3 is a 3 × 3 unit matrix, and n is the observation error.
步骤4,将BDS双差伪距、不同巷载波相位、电离层无关模型和几何无关模型下的伪距、载波相位和INS给出的位置观测方程,共11个,进行组合求解。设组合观测方程如下:In step 4, a total of 11 BDS double-difference pseudoranges, different lane carrier phases, ionospheric-independent models, and pseudo-ranges under the geometrically independent model, and the position observation equations given by the INS are combined to solve the problem. Let the combined observation equation be as follows:
其中,φ代表窄巷、宽巷、超宽巷、电离层无关模型和几何无关模型中的载 波相位,ρ代表BD1、BD2、BD3伪距双差、电离层无关模型和几何无关模型中的伪距,A、B为构造出的矩阵,N为不同组合的整周模糊度矩阵。Where φ represents carrier phase in narrow lane, wide lane, extra wide lane, ionospheric independent model and geometrically independent model, ρ represents BD1, BD2, BD3 pseudorange double difference, ionospheric independent model and pseudo in geometrically independent model Distance, A, B are constructed matrices, and N is a whole-circumference ambiguity matrix of different combinations.
具体方程为:The specific equation is:
由加权最小二乘法求取模糊度浮点解矩阵
以及协方差阵
Obtaining the ambiguity floating point solution matrix by weighted least squares Covariance matrix
步骤5,利用LAMBDA算法求取整周模糊度N整数解。Step 5, using the LAMBDA algorithm to obtain the integer ambiguity N integer solution.
以整数向量N与浮点解
之间的距离平方为目标函数,搜索整周模糊度N,使这一目标函数达到最小值,即
Integer vector N and floating point solution The squared distance is the objective function, and the whole week ambiguity N is searched to make the objective function reach the minimum value, that is,
LAMBDA算法搜索空间为T,则关于整周模糊度N整数解的搜索空间为:The LAMBDA algorithm search space is T, then the search space for the integer ambiguity N integer solution is:
上式所限定的搜索空间是一个多维椭球体。在该球体内进行搜索,得到最佳整数模糊度值。The search space defined by the above formula is a multidimensional ellipsoid. Searching within the sphere yields the best integer ambiguity value.
Claims (7)
- 一种惯导辅助的北斗三频载波相位整周模糊度求解方法,其特征在于,包括以下步骤:An inertial navigation aided Beidou tri-band carrier phase whole-circumference ambiguity solving method, characterized in that the method comprises the following steps:(1)确定BDS三频组合载波相位双差和伪距双差观测模型,获取伪距和载波相位观测值;(1) Determining the BDS tri-band combined carrier phase double difference and pseudorange double difference observation model to obtain pseudorange and carrier phase observation values;(2)取不同的比例因子值,进行伪距观测量和载波相位观测量线性组合方式,得到窄巷、宽巷和超宽巷载波相位和伪距观测方程,以及电离层无关模型和几何无关模型下的载波相位和伪距观测方程;(2) Taking different scale factor values, performing a linear combination of pseudo-range observation and carrier phase observation, and obtaining carrier phase and pseudo-range observation equations for narrow lane, wide lane and ultra-wide lane, and ion-free layer-independent model and geometry-independent Carrier phase and pseudorange observation equations under the model;(3)利用惯导,得到INS位置观测方程;(3) Using the inertial navigation, obtain the INS position observation equation;(4)联立上述窄巷、宽巷、超宽巷、电离层无关模型和几何无关模型下的载波相位和伪距观测方程,和INS观测方程,利用加权最小二乘法进行求解,得到整周模糊度的浮点解;(4) Simultaneously calculate the carrier phase and pseudorange observation equations in the narrow lane, wide lane, extra wide lane, ionosphere-independent model and geometrically independent model, and the INS observation equation, and solve it by weighted least squares method to obtain the whole week. Floating point solution of ambiguity;(5)利用LAMBDA求解整周模糊度的整数值。(5) Use LAMBDA to solve the integer value of the ambiguity of the whole week.
- 根据权利要求1所述的一种惯导辅助的北斗三频载波相位整周模糊度求解方法,其特征在于,所述步骤(1)中,BDS三频组合载波相位双差和伪距双差观测模型方程分别为:The method for solving the Beidou tri-band carrier phase full-circumference ambiguity according to claim 1, wherein in the step (1), the BDS tri-band combined carrier phase double difference and pseudo-range double difference The observed model equations are:其中,φ 1、φ 2、φ 3分别为北斗三频B1、B2、B3载波相位双差值,ρ 1、ρ 2、ρ 3分别为B1、B2、B3伪距双差值,λ 1、λ 2、λ 3分别为B1、B2、B3的波长,k 1、k 2、k 3分别为组合中B1、B2、B3的系数,r为基线距离,g为双差卫星轨道误差,T为双差对流层误差,I 1为B1的双差电离层误差, 和 分别代表与载波相位和伪距相关的接收机误差; Where φ 1 , φ 2 , and φ 3 are respectively the carrier phase double difference of the Beidou tri-band B1, B2, and B3, and ρ 1 , ρ 2 , and ρ 3 are respectively B1, B2, B3 pseudo-distance double difference, λ 1 , λ 2 and λ 3 are the wavelengths of B1, B2, and B3, respectively, and k 1 , k 2 , and k 3 are the coefficients of B1, B2, and B3 in the combination, r is the baseline distance, and g is the double-orbiting satellite orbit error, and T is Double-difference tropospheric error, I 1 is the double-difference ionospheric error of B1, with Representing receiver errors associated with carrier phase and pseudorange, respectively;三频组合中的整周模糊度为 其中N 1、N 2、N 3分 别为B1、B2、B3的整周模糊度值,三频组合中的波长为 组合比例因子为 The full-circumference ambiguity in the tri-band combination is Where N 1 , N 2 , and N 3 are the whole-circumference ambiguity values of B1, B2, and B3, respectively, and the wavelength in the tri-band combination is Combined scale factor is
- 根据权利要求2所述的一种惯导辅助的北斗三频载波相位整周模糊度求解方法,其特征在于,所述步骤(2)中,取比例因子为μ(k 1 n,k 2 n,k 3 n)构成窄巷组合,该组合中波长、载波相位双差、整周模糊度分别为λ n,φ n,N n;μ(k 1 w,k 2 w,k 3 w)构成宽巷组合,该组合中波长、载波相位双差、整周模糊度分别为λ w,φ w,N w;μ(k 1 s,k 2 s,k 3 s)构成超宽巷组合,该组合中波长、载波相位双差、整周模糊度分别为λ s,φ s,N s,并针对B1、B2、B3的双差伪距测量值及窄巷、宽巷和超宽巷的载波相位观测值组合,联立方程如下: The method according to claim 2, wherein the step (2) takes a scaling factor of μ(k 1 n , k 2 n). , k 3 n ) constitutes a narrow lane combination in which the wavelength, carrier phase double difference, and full-circumference ambiguity are respectively λ n , φ n , N n ; μ(k 1 w , k 2 w , k 3 w ) Wide lane combination, the wavelength, carrier phase double difference, and full-circumference ambiguity of the combination are λ w , φ w , N w ; μ(k 1 s , k 2 s , k 3 s ) constitute a super wide lane combination, The combined wavelength, carrier phase double difference, and full-circumference ambiguity are λ s , φ s , N s , and the double-difference pseudo-range measurement values for B1, B2, and B3, and the carriers of narrow lane, wide lane, and ultra-wide lane The phase observation combination, the simultaneous equation is as follows:
- 根据权利要求2所述的一种惯导辅助的北斗三频载波相位整周模糊度求解方法,其特征在于,所述步骤(2)中,取 得到三频几何无关组合(GF),此时μ(k 1,k 2,k 3)取值记为μ g(k 1 g,k 2 g,k 3 g),该组合中波长、载波相位双差、整周模糊度分别记为λ g,φ g,N g;取 得到电离层无关组合(IF),此时μ(k 1,k 2,k 3)取值记为μ i(k 1 i,k 2 i,k 3 i),该组合中波长、载波相位双差、整周模糊度分别记为λ i,φ i,N i; The method for solving the Beidou tri-frequency carrier phase full-circumference ambiguity of the INS according to claim 2, wherein in the step (2), A tri-band geometrically independent combination (GF) is obtained, where μ(k 1 , k 2 , k 3 ) is taken as μ g (k 1 g , k 2 g , k 3 g ), and the wavelength and carrier phase of the combination The double difference and the whole week ambiguity are respectively recorded as λ g , φ g , N g ; Obtaining an ionospheric-independent combination (IF), where μ(k 1 , k 2 , k 3 ) is taken as μ i (k 1 i , k 2 i , k 3 i ), and the wavelength and carrier phase are double in the combination. The difference and the whole week ambiguity are respectively recorded as λ i , φ i , N i ;联立几何无关模型和电离层无关模型,得到方程如下:The simultaneous geometrically independent model and the ionospheric independent model, the equation is as follows:
- 根据权利要求1所述的一种惯导辅助的北斗三频载波相位整周模糊度求解方法,其特征在于,所述步骤(3)中,INS位置观测方程为 其中 为INS输出的位置估计量,X为坐标位置参数,I 3为3×3单位矩阵,n为观测误差。 The method for solving the Beidou tri-frequency carrier phase full-circumference ambiguity according to claim 1 is characterized in that, in the step (3), the INS position observation equation is among them The position estimate for the INS output, X is the coordinate position parameter, I 3 is a 3 × 3 unit matrix, and n is the observation error.
- 根据权利要求2所述的一种惯导辅助的北斗三频载波相位整周模糊度求解方法,其特征在于,所述步骤(4)中,联立窄巷、宽巷、超宽巷、电离层无关模型和几何无关模型下的载波相位和伪距观测方程,以及INS观测方程得到的组合观测方程如下:The method for solving the Beidou tri-frequency carrier phase full-circumference ambiguity according to claim 2, wherein in the step (4), the narrow lane, the wide lane, the ultra-wide lane, and the ionization The carrier phase and pseudorange observation equations under the layer-independent model and the geometrically independent model, and the combined observation equations obtained from the INS observation equation are as follows:其中,φ代表载波相位,ρ代表伪距双差,r 0为卫星到接收机间的初始距离,ε代表接收机噪声,上/下标记n,w,s,g,i分别代表所标记的变量为窄巷、宽巷、超宽巷、电离层无关模型和几何无关模型中的变量; 为INS输出的位置估计量,X为坐标位置参数,X 0为初始位置,I 3为3×3单位矩阵,n为观测误差。 Where φ represents the carrier phase, ρ represents the pseudorange double difference, r 0 is the initial distance between the satellite and the receiver, ε represents the receiver noise, and the up/down markers n, w, s, g, i represent the marked Variables are variables in narrow lanes, wide lanes, extra wide lanes, ionospheric independent models, and geometrically independent models; The position estimate for the INS output, X is the coordinate position parameter, X 0 is the initial position, I 3 is the 3 × 3 unit matrix, and n is the observation error.
- 根据权利要求1所述的一种惯导辅助的北斗三频载波相位整周模糊度求解方法,其特征在于,所述步骤(5)中,利用LAMBDA算法求取整周模糊度N整数解的方法为:The method for solving the Beidou tri-frequency carrier phase full-circumference ambiguity according to claim 1 is characterized in that, in the step (5), the LAMBDA algorithm is used to obtain the integer-degree ambiguity N integer solution. The method is:以整数向量N与步骤(4)获得的浮点解 之间的距离平方为目标函数,搜 索整周模糊度N,使这一目标函数达到最小值,即 The floating point solution obtained by the integer vector N and step (4) The squared distance is the objective function, and the whole week ambiguity N is searched to make the objective function reach the minimum value, that is,LAMBDA算法搜索空间为T:The LAMBDA algorithm search space is T:在所限定的多维椭球体内进行搜索,得到最佳整数模糊度值。Searching within the defined multidimensional ellipsoid yields the best integer ambiguity value.
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