CN111998849A - Differential dynamic positioning method based on inertial navigation system - Google Patents

Differential dynamic positioning method based on inertial navigation system Download PDF

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CN111998849A
CN111998849A CN202010881232.8A CN202010881232A CN111998849A CN 111998849 A CN111998849 A CN 111998849A CN 202010881232 A CN202010881232 A CN 202010881232A CN 111998849 A CN111998849 A CN 111998849A
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base station
mobile base
navigation system
positioning
observation
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蔡成林
吴芊
贾伟
刘凌云
张智强
邓钰臻
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Xiangtan University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13Receivers
    • G01S19/24Acquisition or tracking or demodulation of signals transmitted by the system
    • G01S19/25Acquisition or tracking or demodulation of signals transmitted by the system involving aiding data received from a cooperating element, e.g. assisted GPS
    • G01S19/258Acquisition or tracking or demodulation of signals transmitted by the system involving aiding data received from a cooperating element, e.g. assisted GPS relating to the satellite constellation, e.g. almanac, ephemeris data, lists of satellites in view
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13Receivers
    • G01S19/24Acquisition or tracking or demodulation of signals transmitted by the system
    • G01S19/30Acquisition or tracking or demodulation of signals transmitted by the system code related
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining 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
    • G01S19/42Determining position
    • G01S19/45Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
    • G01S19/47Determining 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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Abstract

本发明公开了一种基于惯性导航系统的差分动动定位的方法,通过以下步骤实现移动基站的定位:步骤1、通过伪距单点定位获得初始观测时刻移动基站的位置;步骤2、在每个观测时刻,基于观测方程求解当前观测时刻与上一观测时刻之间移动基站的位置变化量;其中观测方程基于惯性导航系统和卫星导航系统输出的信息建立;步骤3、基于上一观测时刻移动基站的位置与位置变化量,得到当前观测时刻移动基站的位置。基于移动基站的定位结果得到差分校正量,利用差分校正量对流动站的和卫星之间的伪距进行校正,利用校正后的伪距值对流动站进行伪距单点定位,得到流动站的位置坐标。本发明可以提高移动基站和流动站的定位精度。

Figure 202010881232

The invention discloses a method for differential motion positioning based on an inertial navigation system. The positioning of a mobile base station is realized by the following steps: Step 1. Obtain the position of the mobile base station at the initial observation time through pseudo-range single-point positioning; Step 2. At each observation time, the position change of the mobile base station between the current observation time and the last observation time is calculated based on the observation equation; the observation equation is established based on the information output by the inertial navigation system and the satellite navigation system; step 3, based on the last observation time The position and position change of the base station are used to obtain the position of the mobile base station at the current observation time. Based on the positioning result of the mobile base station, the differential correction amount is obtained, the pseudo-range between the rover and the satellite is corrected by the differential correction amount, and the pseudo-range single-point positioning of the rover is performed by using the corrected pseudo-range value, and the rover's pseudo-range is obtained. Position coordinates. The invention can improve the positioning accuracy of the mobile base station and the mobile station.

Figure 202010881232

Description

一种基于惯性导航系统的差分动动定位的方法A Method of Differential Dynamic Positioning Based on Inertial Navigation System

技术领域technical field

本发明涉及一种利用惯性导航与卫星导航相结合的导航定位技术领域,尤其是一种基于惯性导航系统的差分动动定位的方法。The invention relates to the technical field of navigation and positioning using the combination of inertial navigation and satellite navigation, in particular to a differential dynamic positioning method based on an inertial navigation system.

背景技术Background technique

在差分定位中,基准站的位置是已知的,因此基准站和卫星之间的真实距离(站星距)也是已知的。卫星播发的数据中包含伪距信息,伪距是指地面接收机到卫星的大概距离,伪距中包含有许多误差,包括接收机钟差、卫星钟差、电离层和对流层时延误差以及伪距测量噪声,其中卫星钟差可以认为是已知的。如图1所示,差分定位的基本原理主要是依据卫星钟差、卫星星历误差、电离层时延与对流层时延具有空间相关性和时间相关性,即同一地域内的不同接收机的伪距测量值所包含的上述误差成分近似或高度相关。如果将真实精确的站星距与基准站对卫星的距离测量值(伪距)进行比较,二者的差异就等于基准站对这一卫星的测量误差。基准站播发给流动站的测量误差校正量称为差分校正量,流动站可以通过差分校正量来降低甚至是消除测量误差。对于一般的实时动态差分定位(RTK)技术而言,基准站是静止的而流动站是移动的,但是对于某些情况,例如无人机编队、飞机空中加油而言,两个(或多个)目标物体都是运动的,因此需要差分动态对动态定位(简称动动定位)技术来对目标进行导航定位。在动动定位中,与差分定位的原理类似,不同的是基准站也是移动的,称为移动基站。对于动动定位来说,选取的移动基站需要向流动站来播发差分数据来修正流动站的距离测量值来得到流动站更为精确的位置坐标,求得移动基站和流动站之间的基线向量。但是由于移动基站是运动的,其定位精度影响着差分定位的精确度,随着时间(历元)的增加,移动基站的定位误差是越来越大的。如何获取移动基站较为精确的位置信息是一个关键问题。In differential positioning, the location of the base station is known, so the true distance between the base station and the satellite (station star distance) is also known. The data broadcast by the satellite contains pseudorange information. The pseudorange refers to the approximate distance between the ground receiver and the satellite. The pseudorange contains many errors, including receiver clock error, satellite clock error, ionospheric and tropospheric delay errors, and pseudoranges. Distance measurement noise, where satellite clock offsets can be considered known. As shown in Figure 1, the basic principle of differential positioning is mainly based on satellite clock error, satellite ephemeris error, ionospheric delay and tropospheric delay have spatial and temporal correlations, that is, the false detection of different receivers in the same area The above-mentioned error components contained in the measurement values are approximately or highly correlated. If the true and accurate station-to-star distance is compared with the distance measurement (pseudorange) of the reference station to the satellite, the difference between the two is equal to the measurement error of the reference station to this satellite. The measurement error correction broadcast by the base station to the rover is called the differential correction, and the rover can reduce or even eliminate the measurement error through the differential correction. For general real-time kinematic differential positioning (RTK) technology, the base station is stationary and the rover is mobile, but for some situations, such as drone formation, aircraft aerial refueling, two (or more ) The target objects are all moving, so the differential dynamic pairing dynamic positioning (referred to as dynamic positioning) technology is needed to navigate and locate the target. In the dynamic positioning, the principle is similar to the differential positioning, the difference is that the base station is also moving, which is called a mobile base station. For dynamic positioning, the selected mobile base station needs to broadcast differential data to the rover to correct the distance measurement value of the rover to obtain more accurate position coordinates of the rover, and to obtain the baseline vector between the mobile base and the rover. . However, since the mobile base station is moving, its positioning accuracy affects the accuracy of differential positioning. With the increase of time (epoch), the positioning error of the mobile base station becomes larger and larger. How to obtain more accurate location information of a mobile base station is a key issue.

发明内容SUMMARY OF THE INVENTION

本发明所解决的技术问题是,针对现有技术的不足,提供一种基于惯性导航系统的差分动动定位的方法,能够有效提高定位精度。The technical problem solved by the present invention is to provide a method for differential motion positioning based on an inertial navigation system, which can effectively improve the positioning accuracy, aiming at the shortcomings of the prior art.

本发明所提供的技术方案为:The technical scheme provided by the present invention is:

一种基于惯性导航系统的差分动动定位的方法,通过以下步骤实现移动基站的定位:A method for differential motion positioning based on an inertial navigation system, the positioning of a mobile base station is realized through the following steps:

步骤1、通过伪距单点定位获得初始观测时刻移动基站的位置sb(0);Step 1. Obtain the position s b (0) of the mobile base station at the initial observation moment through pseudo-range single-point positioning;

步骤2、在每个观测时刻,基于观测方程求解当前观测时刻k与上一观测时刻k-1之间移动基站的位置变化量[dx dy dz],其中k=1,2,…;其中观测方程基于惯性导航系统和卫星导航系统输出的信息建立;Step 2. At each observation time, based on the observation equation, solve the position change of the mobile base station between the current observation time k and the previous observation time k-1 [dx dy dz], where k=1, 2, ...; where the observation The equations are established based on the information output by the inertial navigation system and the satellite navigation system;

步骤3、基于上一观测时刻移动基站的位置sb(k-1)与位置变化量[dx dy dz],得到当前观测时刻移动基站的位置sb(k)。Step 3: Based on the position s b (k-1) of the mobile base station at the last observation time and the position variation [dx dy dz], obtain the position s b (k) of the mobile base station at the current observation time.

进一步地,所述观测方程为:Further, the observation equation is:

Figure BDA0002654188980000021
Figure BDA0002654188980000021

其中,Lρ为当前观测时刻k移动基站b的伪距观测值,Among them, L ρ is the pseudorange observation value of the mobile base station b at the current observation time k,

Figure BDA0002654188980000022
式中(x(i),y(i),z(i))为当前观测时刻k卫星i的位置坐标,(x,y,z)为惯性导航系统输出的当前观测时刻k移动基站的位置坐标;
Figure BDA0002654188980000022
where (x (i) , y (i) , z (i) ) are the position coordinates of the satellite i at the current observation time k, (x, y, z) are the position of the mobile base station at the current observation time k output by the inertial navigation system coordinate;

H为观测矩阵,其表达式为:H is the observation matrix, and its expression is:

Figure BDA0002654188980000023
Figure BDA0002654188980000023

Figure BDA0002654188980000024
Figure BDA0002654188980000024

Figure BDA0002654188980000025
Figure BDA0002654188980000025

Figure BDA0002654188980000026
Figure BDA0002654188980000026

式中N为移动基站b的接收机可以观测到的卫星个数;where N is the number of satellites that can be observed by the receiver of mobile base station b;

ερ为伪距观测误差,I3×3为3×3维的单位矩阵,εins为观测噪声。ε ρ is the pseudo-range observation error, I 3×3 is a 3×3-dimensional identity matrix, and ε ins is the observation noise.

进一步地,通过最小二乘法求解观测方程,得到:Further, solving the observation equation by the least squares method, we get:

Figure BDA0002654188980000031
Figure BDA0002654188980000031

其中,

Figure BDA0002654188980000032
in,
Figure BDA0002654188980000032

进一步地,通过以下步骤实现流动站的定位:Further, the positioning of the rover is realized through the following steps:

首先,执行步骤1~3,获取当前观测时刻移动基站的位置sb(k);First, perform steps 1 to 3 to obtain the position s b (k) of the mobile base station at the current observation moment;

然后,利用惯性导航系统获得移动基站的速度vb,从而修正移动基站位置:s′b(k)=sb(k)+vbΔt,其中Δt是流动站与移动基站接收到卫星信号的时间差;Then, use the inertial navigation system to obtain the speed v b of the mobile base station to correct the position of the mobile base station: s′ b (k)=s b (k)+v b Δt, where Δt is the difference between the rover and the mobile base station receiving the satellite signal Time difference;

再利用修正后的移动基站的位置s′b(k)计算出移动基站b至卫星i的几何距离

Figure BDA0002654188980000033
从而计算出差分校正量
Figure BDA0002654188980000034
其中ρ(i)为当前观测时刻k移动基站b和卫星i之间的伪距;Then use the corrected position s' b (k) of the mobile base station to calculate the geometric distance from the mobile base station b to the satellite i
Figure BDA0002654188980000033
Thereby, the differential correction amount is calculated
Figure BDA0002654188980000034
where ρ (i) is the pseudorange between the mobile base station b and the satellite i at the current observation time k;

最后,移动基站将差分校正量播发给流动站,利用差分校正量

Figure BDA0002654188980000035
对流动站的和卫星i之间的伪距
Figure BDA0002654188980000036
进行校正,利用校正后的伪距值对流动站进行伪距单点定位,得到流动站的位置坐标。Finally, the mobile base station broadcasts the differential correction to the rover, using the differential correction
Figure BDA0002654188980000035
Pseudorange between rover and satellite i
Figure BDA0002654188980000036
Correction is performed, and the pseudorange single-point positioning of the rover is performed using the corrected pseudorange value to obtain the position coordinates of the rover.

进一步地,伪距单点定位采用精密单点定位。Further, the pseudo-range single-point positioning adopts precise single-point positioning.

利用卫星导航系统对运动目标进行定位时存在定位误差大、收敛时间长的缺陷,但是在动动定位中,进行差分定位对移动基站的定位精度要求较高,因此单纯的卫星导航系统动态单点定位并不能满足移动基站的定位精度要求。为了使流动站能获得较好的差分定位精度就必须提高移动基站的实时定位精度。用户实时动态精密单点定位(PPP)平均在7min内收敛至分米级,收敛后平面精度优于0.1m,高程精度优于0.2m,利用实时动态PPP可以对移动基站进行实时定位,但是定位精度以及收敛速度仍不足以满足作为移动基站的要求。因此,本发明上述技术方仅采用精密单点定位获取初始观测时刻移动基站的位置,后续结合卫星导航系统和惯性导航系统构建观测方程,得到相邻观测时刻移动基站的位置变化量,进而得到移动基站较为精确的位置,提高定位精度以及收敛速度。The use of satellite navigation system to locate moving targets has the defects of large positioning error and long convergence time. However, in dynamic positioning, differential positioning requires high positioning accuracy of mobile base stations. Therefore, the simple dynamic single point of satellite navigation system The positioning cannot meet the positioning accuracy requirements of the mobile base station. In order to make the rover obtain better differential positioning accuracy, it is necessary to improve the real-time positioning accuracy of the mobile base station. The user's real-time dynamic precise point positioning (PPP) converges to the decimeter level within 7 minutes on average. After convergence, the plane accuracy is better than 0.1m, and the elevation accuracy is better than 0.2m. The real-time dynamic PPP can be used to locate the mobile base station in real time, but the positioning Accuracy and convergence speed are still insufficient to meet the requirements of a mobile base station. Therefore, the above technical method of the present invention only uses precise single-point positioning to obtain the position of the mobile base station at the initial observation time, and then combines the satellite navigation system and the inertial navigation system to construct the observation equation to obtain the position change of the mobile base station at the adjacent observation time, and then obtain the mobile base station. The more accurate location of the base station improves the positioning accuracy and convergence speed.

惯性导航系统(INS)是一种自主式导航系统,不易受到外界的干扰。惯导的基本工作原理是以牛顿力学定律为基础,通过测量载体在惯性参考系的加速度,将它对时间进行积分并把它变换到导航坐标系中,就能够得到在导航坐标系中的速度、偏航角和位置等信息。在短时间内惯性导航定位系统可以进行较为精确的定位,得出一个较为精确的位置信息。移动基站在运动过程中,通过惯性导航系统测量移动基站的加速度,并自动进行积分运算,可以获得移动基站瞬时速度和一个较为精确的瞬时位置数据。利用这个位置信息建立观测方程;将该观测方程与通过卫星定位的伪距观测方程联立,可以求解得到移动基站的较为精确的位置坐标。Inertial Navigation System (INS) is an autonomous navigation system that is less susceptible to external interference. The basic working principle of inertial navigation is based on Newton's laws of mechanics. By measuring the acceleration of the carrier in the inertial reference system, integrating it with time and transforming it into the navigation coordinate system, the speed in the navigation coordinate system can be obtained. , yaw angle and position. In a short period of time, the inertial navigation and positioning system can perform relatively accurate positioning and obtain a relatively accurate position information. During the movement of the mobile base station, the acceleration of the mobile base station is measured by the inertial navigation system, and the integral operation is automatically performed to obtain the instantaneous speed of the mobile base station and a relatively accurate instantaneous position data. The observation equation is established by using this position information; the observation equation is combined with the pseudo-range observation equation through satellite positioning, and the relatively accurate position coordinates of the mobile base station can be obtained by solving.

有益效果:Beneficial effects:

本发明提出了一种将卫星导航系统和惯性导航系统结合的定位处理方法,通过惯性导航系统在短时间内能获取移动目标较为精确的位置信息和移动速度的这一特性,将卫星导航系统输出的位置信息和惯性导航系统输出的位置信息融合处理,最后得到一个更为精确的移动基站的位置坐标,提高了移动基站定位精度以及收敛速度,从而使流动站能获得较好的差分定位精度。除此之外,本发明还通过惯性导航系统输出的移动基站的速度来对其位置进行修正,消除移动基站和流动站的时钟差异,进一步提高了流动站的定位精度。The invention proposes a positioning processing method that combines a satellite navigation system and an inertial navigation system. The inertial navigation system can obtain relatively accurate position information and moving speed of a moving target in a short time, and output the satellite navigation system. Finally, a more accurate position coordinate of the mobile base station is obtained, which improves the positioning accuracy and convergence speed of the mobile base station, so that the mobile station can obtain better differential positioning accuracy. In addition, the present invention also corrects the position of the mobile base station through the speed of the inertial navigation system output, eliminates the clock difference between the mobile base station and the mobile station, and further improves the positioning accuracy of the mobile station.

附图说明Description of drawings

图1为差分定位工作原理;Figure 1 shows the working principle of differential positioning;

图2为本发明实施例流程图。FIG. 2 is a flowchart of an embodiment of the present invention.

具体实施方式Detailed ways

以下结合附图和具体实施方式对本发明进行进一步具体说明。The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

如图2所示,本实施例提供了一种基于惯性导航系统的差分动动定位的方法,包括以下步骤:As shown in FIG. 2 , this embodiment provides a method for differential motion positioning based on an inertial navigation system, including the following steps:

第一步,选取一个移动目标作为移动基站b,通过伪距单点定位获得初始观测时刻(观测时刻指移动基站b接收机接收到卫星信号的时刻,即历元)移动基站b的位置sb(0)=(x0,y0,z0),伪距单点定位方程为:The first step is to select a moving target as the mobile base station b, and obtain the initial observation time through pseudo-range single-point positioning (the observation time refers to the time when the receiver of the mobile base station b receives the satellite signal, that is, the epoch) The position s b of the mobile base station b (0)=(x 0 , y 0 , z 0 ), the pseudo-range single-point positioning equation is:

Figure BDA0002654188980000041
Figure BDA0002654188980000041

其中,δtu是移动基站b的接收机钟差,N为移动基站b的接收机可以观测到的卫星个数,ρ(i)为当前观测时刻k移动基站b和卫星i之间的伪距,可以从卫星播发的数据中得到;(x(i),y(i),z(i))为当前观测时刻k卫星i在地心地固坐标系的位置坐标,移动基站b的接收机接收到卫星播发的数据中包含有卫星星历参数,通过星历参数即可计算出(x(i),y(i),z(i));方程组中包含(x0,y0,z0)和δtu4个未知参数,因此至少需要至少4个方程即4颗卫星的观测值才能得到移动基站b的位置坐标和接收机钟差的解;Among them, δt u is the receiver clock difference of mobile base station b, N is the number of satellites that can be observed by the receiver of mobile base station b, ρ (i) is the pseudo-range between mobile base station b and satellite i at the current observation time k , which can be obtained from the data broadcast by the satellite; (x (i) , y (i) , z (i) ) are the position coordinates of the satellite i in the geocentric fixed coordinate system at the current observation time k, and the receiver of the mobile base station b receives The data broadcast to the satellite contains satellite ephemeris parameters, and (x (i) , y (i) , z (i) ) can be calculated through the ephemeris parameters; the equation system contains (x 0 , y 0 , z 0 ) and δt u 4 unknown parameters, so at least 4 equations, that is, the observations of 4 satellites, can be obtained to obtain the solution of the position coordinates of the mobile base station b and the receiver clock error;

第二步,在每个观测时刻,获取惯性导航系统输出的当前观测时刻k移动基站的位置坐标(x,y,z),利用(x,y,z)和当前观测时刻k卫星i在地心地固坐标系的位置坐标(x(i),y(i),z(i))计算出当前观测时刻k移动基站的伪距观测值The second step is to obtain the position coordinates (x, y, z) of the mobile base station at the current observation time k output by the inertial navigation system at each observation time, and use (x, y, z) and the current observation time k to locate the satellite i on the ground. The position coordinates (x (i) , y (i) , z (i) ) of the geocentric fixed coordinate system are used to calculate the pseudorange observation value of the mobile base station at the current observation time k

Figure BDA0002654188980000051
Figure BDA0002654188980000051

建立观测方程并线性化,得到卫星导航系统(包括北斗卫星导航系统BDS)的伪距观测方程为:The observation equation is established and linearized, and the pseudorange observation equation of the satellite navigation system (including the Beidou satellite navigation system BDS) is obtained as:

Figure BDA0002654188980000052
Figure BDA0002654188980000052

其中,ερ为伪距观测误差,[dx dy dz]T为当前观测时刻k与上一观测时刻k-1之间移动基站的坐标变化量;H为观测矩阵,其表达式为:Among them, ε ρ is the pseudo-range observation error, [dx dy dz] T is the coordinate change of the mobile base station between the current observation time k and the previous observation time k-1; H is the observation matrix, and its expression is:

Figure BDA0002654188980000053
Figure BDA0002654188980000053

Figure BDA0002654188980000054
Figure BDA0002654188980000054

Figure BDA0002654188980000055
Figure BDA0002654188980000055

Figure BDA0002654188980000056
Figure BDA0002654188980000056

将惯性导航系统输出的当前观测时刻k移动基站的位置(x,y,z)作为虚拟观测点(参考位置),在此虚拟观测点可以建立如下观测方程:The position (x, y, z) of the mobile base station at the current observation time k output by the inertial navigation system is used as a virtual observation point (reference position), and the following observation equation can be established at this virtual observation point:

Figure BDA0002654188980000057
Figure BDA0002654188980000057

其中,I3×3为3×3维的单位矩阵,εins为观测噪声。Among them, I 3 × 3 is a 3 × 3-dimensional identity matrix, and ε ins is the observation noise.

第三步:联立卫星导航系统和惯性导航系统的观测方程:Step 3: Simultaneous observation equation of satellite navigation system and inertial navigation system:

Figure BDA0002654188980000061
Figure BDA0002654188980000061

通过最小二乘法可以解出将卫星导航系统和惯性导航系统结合的定位结果,具体地:忽略噪声

Figure BDA0002654188980000062
上述观测方程可以简化为B=W·Δx,其中
Figure BDA0002654188980000063
则该观测方程式的最小二乘解为Δx=(WTW)-1WTB;得到移动基站的坐标变化量
Figure BDA0002654188980000064
后,结合上一观测时刻k-1移动基站的位置sb(k-1)就可以计算得到当前观测时刻k移动基站较为精确的位置sb(k),sb(k)=sb(k-1)+[dx dy dz],k=1,2,…。The positioning result combining the satellite navigation system and the inertial navigation system can be solved by the least squares method, specifically: ignoring noise
Figure BDA0002654188980000062
The above observation equation can be simplified to B=W·Δx, where
Figure BDA0002654188980000063
Then the least square solution of the observation equation is Δx=(W T W) -1 W T B; the coordinate change of the mobile base station is obtained
Figure BDA0002654188980000064
Then, combined with the position s b (k-1) of the mobile base station at the previous observation time k-1, the more accurate position s b (k) of the mobile base station at the current observation time k can be calculated, s b (k)=s b ( k-1)+[dx dy dz], k=1, 2, . . .

重复以上处理就可以对移动基站进行实时定位,还保证了移动基站的定位精度。By repeating the above process, the mobile base station can be positioned in real time, and the positioning accuracy of the mobile base station is also ensured.

实现移动基站的精确定位后,进一步通过以下步骤实现流动站的精确定位:After the precise positioning of the mobile base station is achieved, the precise positioning of the rover is further achieved through the following steps:

移动基站和流动站之间的时钟差异通常最多可以达到2ms,不同步的时钟会降低定位的准确度,因此需要修正时钟的差异。利用惯性导航系统获得移动基站的速度vb(可取移动基站或流动站收到卫星信号的时刻移动基站的速度,也可以取平均速度),从而修正移动基站位置:s′b(k)=sb(k)+vbΔt,其中Δt是流动站与移动基站接收到卫星信号的时间差。The clock difference between the mobile base station and the rover can usually be up to 2ms, and the unsynchronized clock will reduce the positioning accuracy, so the clock difference needs to be corrected. Use the inertial navigation system to obtain the speed v b of the mobile base station (the speed of the mobile base station when the mobile base station or the rover receives the satellite signal, or the average speed), so as to correct the position of the mobile base station: s′ b (k)=s b (k)+v b Δt, where Δt is the time difference between the rover and the mobile base station when the satellite signal is received.

利用修正后的移动基站的位置s′b(k)计算出移动基站b至卫星i精确的几何距离

Figure BDA0002654188980000065
(根据两点之间的距离公式进行计算),从而计算出差分校正量
Figure BDA0002654188980000066
差分校正量实际是多个测量误差和偏差量之和。Using the corrected position s' b (k) of the mobile base station to calculate the exact geometric distance from the mobile base station b to the satellite i
Figure BDA0002654188980000065
(calculated according to the distance formula between two points), so as to calculate the difference correction amount
Figure BDA0002654188980000066
The differential correction is actually the sum of multiple measurement errors and deviations.

移动基站可将差分校正量播发给流动站,利用差分校正量

Figure BDA0002654188980000067
对流动站的和卫星i之间的伪距
Figure BDA0002654188980000068
(可以从卫星播发的数据中得到)进行校正,从而获得较为精确的伪距值
Figure BDA0002654188980000069
Figure BDA00026541889800000610
再利用伪距值
Figure BDA00026541889800000611
对流动站进行伪距单点定位,得到流动站精确的位置坐标。The mobile base station can broadcast the differential correction to the rover, and use the differential correction
Figure BDA0002654188980000067
Pseudorange between rover and satellite i
Figure BDA0002654188980000068
(which can be obtained from the data broadcast by the satellite) to be corrected to obtain a more accurate pseudorange value
Figure BDA0002654188980000069
Figure BDA00026541889800000610
Reuse pseudorange values
Figure BDA00026541889800000611
Perform pseudo-range single-point positioning on the rover to obtain the precise position coordinates of the rover.

本实施例利用惯性导航与卫星定位相结合,将惯性导航定位结果和卫星定位结果进行融合处理,可以获取移动基站较为精确的位置信息,提高移动基站的定位精度,以实现其作为基准站的功能,从而有效地提高动动定位的精度,从而达到动动定位的要求。In this embodiment, the inertial navigation and satellite positioning are combined, and the inertial navigation and positioning results and the satellite positioning results are fused to obtain relatively accurate position information of the mobile base station, improve the positioning accuracy of the mobile base station, and realize its function as a reference station. , so as to effectively improve the accuracy of dynamic positioning, so as to meet the requirements of dynamic positioning.

Claims (5)

1.一种基于惯性导航系统的差分动动定位的方法,其特征在于,通过以下步骤实现移动基站的定位:1. a method for differential dynamic positioning based on inertial navigation system, is characterized in that, realizes the positioning of mobile base station by the following steps: 步骤1、通过伪距单点定位获得初始观测时刻移动基站的位置sb(0);Step 1. Obtain the position s b (0) of the mobile base station at the initial observation moment through pseudo-range single-point positioning; 步骤2、在每个观测时刻,基于观测方程求解当前观测时刻k与上一观测时刻k-1之间移动基站的位置变化量[dx dy dz],其中k=1,2,…;其中观测方程基于惯性导航系统和卫星导航系统输出的信息建立;Step 2. At each observation time, based on the observation equation, calculate the position change [dx dy dz] of the mobile base station between the current observation time k and the previous observation time k-1, where k=1, 2, ...; where the observation The equations are established based on the information output by the inertial navigation system and the satellite navigation system; 步骤3、基于上一观测时刻移动基站的位置sb(k-1)与位置变化量[dx dy dz],得到当前观测时刻移动基站的位置sb(k)。Step 3: Based on the position s b (k-1) of the mobile base station at the last observation time and the position variation [dx dy dz], obtain the position s b (k) of the mobile base station at the current observation time. 2.根据权利要求1所述的基于惯性导航系统的差分动动定位的方法,其特征在于,所述观测方程为:2. the method for differential dynamic positioning based on inertial navigation system according to claim 1, is characterized in that, described observation equation is:
Figure FDA0002654188970000011
Figure FDA0002654188970000011
其中,Lρ为当前观测时刻k移动基站b的伪距观测值,Among them, L ρ is the pseudorange observation value of the mobile base station b at the current observation time k,
Figure FDA0002654188970000012
式中(x(i),y(i),z(i))为当前观测时刻k卫星i的位置坐标,(x,y,z)为惯性导航系统输出的当前观测时刻k移动基站的位置坐标;
Figure FDA0002654188970000012
where (x (i) , y (i) , z (i) ) are the position coordinates of the satellite i at the current observation time k, (x, y, z) are the position of the mobile base station at the current observation time k output by the inertial navigation system coordinate;
H为观测矩阵,其表达式为:H is the observation matrix, and its expression is:
Figure FDA0002654188970000013
Figure FDA0002654188970000013
Figure FDA0002654188970000014
Figure FDA0002654188970000014
Figure FDA0002654188970000015
Figure FDA0002654188970000015
Figure FDA0002654188970000016
Figure FDA0002654188970000016
式中N为移动基站b的接收机可以观测到的卫星个数;where N is the number of satellites that can be observed by the receiver of mobile base station b; ερ为伪距观测误差,I3×3为3×3维的单位矩阵,εins为观测噪声。ε ρ is the pseudo-range observation error, I 3×3 is a 3×3-dimensional identity matrix, and ε ins is the observation noise.
3.根据权利要求2所述的基于惯性导航系统的差分动动定位的方法,其特征在于,通过最小二乘法求解观测方程,得到:3. the method for differential dynamic positioning based on inertial navigation system according to claim 2, is characterized in that, solve observation equation by least squares method, obtain:
Figure FDA0002654188970000021
Figure FDA0002654188970000021
其中,
Figure FDA0002654188970000022
in,
Figure FDA0002654188970000022
4.根据权利要求1所述的基于惯性导航系统的差分动动定位的方法,其特征在于,通过以下步骤实现流动站的定位:4. the method for the differential motion positioning based on inertial navigation system according to claim 1, is characterized in that, realizes the positioning of rover through the following steps: 首先,执行步骤1~3,获取当前观测时刻移动基站的位置sb(k);First, perform steps 1 to 3 to obtain the position s b (k) of the mobile base station at the current observation moment; 然后,利用惯性导航系统获得移动基站的速度vb,从而修正移动基站位置:s′b(k)=sb(k)+vbΔt,其中Δt是流动站与移动基站接收到卫星信号的时间差;Then, use the inertial navigation system to obtain the speed v b of the mobile base station to correct the position of the mobile base station: s′ b (k)=s b (k)+v b Δt, where Δt is the difference between the rover and the mobile base station receiving the satellite signal Time difference; 再利用修正后的移动基站的位置s′b(k)计算出移动基站b至卫星i的几何距离
Figure FDA0002654188970000023
从而计算出差分校正量
Figure FDA0002654188970000024
其中ρ(i)为当前观测时刻k移动基站b和卫星i之间的伪距;
Then use the corrected position s' b (k) of the mobile base station to calculate the geometric distance from the mobile base station b to the satellite i
Figure FDA0002654188970000023
Thereby, the differential correction amount is calculated
Figure FDA0002654188970000024
where ρ (i) is the pseudorange between the mobile base station b and the satellite i at the current observation time k;
最后,移动基站将差分校正量播发给流动站,利用差分校正量
Figure FDA0002654188970000025
对流动站的和卫星i之间的伪距
Figure FDA0002654188970000026
进行校正,利用校正后的伪距值对流动站进行伪距单点定位,得到流动站的位置坐标。
Finally, the mobile base station broadcasts the differential correction to the rover, using the differential correction
Figure FDA0002654188970000025
Pseudorange between rover and satellite i
Figure FDA0002654188970000026
Correction is performed, and the pseudorange single-point positioning of the rover is performed using the corrected pseudorange value to obtain the position coordinates of the rover.
5.根据权利要求1~4中任一项所述的基于惯性导航系统的差分动动定位的方法,其特征在于,伪距单点定位采用精密单点定位。5 . The method for differential kinematic positioning based on an inertial navigation system according to claim 1 , wherein the pseudo-range single-point positioning adopts precise single-point positioning. 6 .
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