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CN111650616B - High-precision Beidou navigation and positioning system navigation and positioning parameter calculation method - Google Patents

High-precision Beidou navigation and positioning system navigation and positioning parameter calculation method Download PDF

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CN111650616B
CN111650616B CN202010397037.8A CN202010397037A CN111650616B CN 111650616 B CN111650616 B CN 111650616B CN 202010397037 A CN202010397037 A CN 202010397037A CN 111650616 B CN111650616 B CN 111650616B
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beidou
positioning
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model
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CN111650616A (en
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林雪原
董云云
张吉松
王美春
孙玉梅
张珊珊
王金虎
陈祥光
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Yantai Nanshan University
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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
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/35—Constructional details or hardware or software details of the signal processing chain
    • G01S19/37—Hardware or software details of the signal processing chain
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/40—Correcting position, velocity or attitude
    • G01S19/41—Differential correction, e.g. DGPS [differential GPS]
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position

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Abstract

The invention discloses a navigation positioning parameter calculation method of a high-precision Beidou navigation positioning system, which comprises the steps of firstly establishing a carrier motion model in a terrestrial coordinate system according to the kinematics principle of a carrier, and establishing a conventional dynamic filtering state equation and a measurement equation of the Beidou navigation positioning system by combining an error model of a Beidou navigation positioning machine; then, a system state equation and a measurement equation of Beidou high-precision navigation in a global coordinate system are established according to the correlation of the system model at the front moment and the rear moment and the independence of pseudo range and pseudo range rate observation of the Beidou navigation positioning receiver; and finally, designing and finishing a system optimal filtering algorithm for Beidou high-precision navigation. The method has moderate calculation amount, can remarkably improve the navigation and positioning accuracy of the Beidou navigation system while ensuring the real-time performance of the system, reduces the navigation and positioning error, and can estimate the acceleration of the carrier with high accuracy.

Description

一种高精度北斗导航定位系统导航定位参数计算方法A method for calculating navigation and positioning parameters of high-precision Beidou navigation and positioning system

技术领域Technical Field

本发明涉及一种高精度北斗导航定位系统导航定位参数计算方法，属于卫星导航技术领域，可用于测绘、航天、航空等领域的导航参数确定。The invention relates to a method for calculating navigation and positioning parameters of a high-precision Beidou navigation and positioning system, belongs to the technical field of satellite navigation, and can be used for determining navigation parameters in the fields of surveying and mapping, aerospace, aviation, etc.

背景技术Background Art

北斗卫星导航系统(BDS)是中国自行研制的全球卫星导航系统，是继GPS、GLONASS之后第三个成熟的卫星导航系统，其主要误差源包括：①卫星测量误差。可分为：卫星时钟误差、星历误差、电离层的附加延时误差、对流层的附加延时误差、多路径误差、接收机本身的噪声。②卫星的几何位置造成的定位误差。由卫星测量误差造成的BDS定位误差可分为两类：一类是随时间、空间快速变化，相关性极弱的随机误差，如接收机噪声，用户、卫星钟噪声，多路径误差，电离层、大气层附加延时的随机变化部分。另一类是随时间、空间缓慢变化，相关性很强的随机偏移误差，如卫星空间位置的误差，卫星钟对BDS时的偏移，用户钟对BDS时的偏移，电离层、对流层的附加延时等。BeiDou Navigation Satellite System (BDS) is a global satellite navigation system independently developed by China. It is the third mature satellite navigation system after GPS and GLONASS. Its main error sources include: ① Satellite measurement error. It can be divided into: satellite clock error, ephemeris error, additional delay error in the ionosphere, additional delay error in the troposphere, multipath error, and noise of the receiver itself. ② Positioning error caused by the geometric position of the satellite. The BDS positioning error caused by satellite measurement error can be divided into two categories: one is the random error that changes rapidly with time and space and has extremely weak correlation, such as receiver noise, user and satellite clock noise, multipath error, and the random change part of the additional delay in the ionosphere and atmosphere. The other is the random offset error that changes slowly with time and space and has a strong correlation, such as the error in the satellite's spatial position, the offset of the satellite clock to the BDS, the offset of the user clock to the BDS, and the additional delay of the ionosphere and troposphere.

为了提高BDS的导航定位精度，已有大量的研究成果，如多星座、载波相位定位中的周跳探测与修复、差分定位、BDS可见星优化选择、组合导航方式等，毋容置疑上述算法为提高BDS的定位精度提供了有效途径，然而上述方法中有的需更多的、价格昂贵的硬件支持，有的无法满足实时性要求。In order to improve the navigation and positioning accuracy of BDS, a large number of research results have been achieved, such as multi-constellation, cycle slip detection and repair in carrier phase positioning, differential positioning, optimal selection of BDS visible stars, combined navigation methods, etc. There is no doubt that the above algorithms provide an effective way to improve the positioning accuracy of BDS. However, some of the above methods require more expensive hardware support, and some cannot meet the real-time requirements.

发明内容Summary of the invention

本发明的目的在于提供了一种高精度北斗导航定位系统导航定位参数计算方法，以提供一种计算简单、易于实现的导航定位解算算法，该算法还能够提高定位解算精度。The purpose of the present invention is to provide a method for calculating navigation and positioning parameters of a high-precision Beidou navigation and positioning system, so as to provide a navigation and positioning solution algorithm that is simple to calculate and easy to implement, and the algorithm can also improve the positioning solution accuracy.

本发明为了实现上述目的，采用如下技术方案：In order to achieve the above object, the present invention adopts the following technical scheme:

本发明基于一种高精度北斗导航定位系统导航定位参数计算方法，包括以下步骤：The present invention is based on a high-precision Beidou navigation and positioning system navigation and positioning parameter calculation method, comprising the following steps:

(1)根据北斗接收机测得的伪距、伪距率计算载体在地球坐标系三个坐标轴上的初始位置及速度分量，在地球坐标系中根据载体的运动学原理建立载体运动模型，建立北斗导航的误差模型，二者模型合并形成动态滤波的常规系统模型；(1) Calculate the initial position and velocity components of the carrier on the three coordinate axes of the earth coordinate system based on the pseudorange and pseudorange rate measured by the Beidou receiver. Establish a carrier motion model in the earth coordinate system based on the carrier's kinematic principle and a Beidou navigation error model. The two models are combined to form a conventional system model of dynamic filtering.

(2)建立北斗导航的观测模型，结合步骤(1)，对系统进行离散化，建立北斗导航动态滤波的常规系统模型；(2) Establishing the observation model of Beidou navigation, combining step (1), discretizing the system, and establishing the conventional system model of Beidou navigation dynamic filtering;

(3)基于步骤(2)建立的北斗导航动态滤波的常规系统模型，考虑到前后两时刻系统状态模型的相关性及北斗导航定位接收机伪距、伪距率观测的独立性，建立地球坐标系下北斗高精度导航的系统状态方程、量测方程；(3) Based on the conventional system model of Beidou navigation dynamic filtering established in step (2), taking into account the correlation of the system state model at two moments and the independence of the pseudorange and pseudorange rate observations of the Beidou navigation positioning receiver, the system state equation and measurement equation of Beidou high-precision navigation in the earth coordinate system are established;

(4)对前后两时刻系统状态模型中相同变量及伪距、伪距率观测量中相同变量进行正交变换，设计并完成了北斗高精度导航的系统最优滤波算法；(4) Orthogonal transformation was performed on the same variables in the system state model at two moments in time and the same variables in the pseudorange and pseudorange rate observations, and the optimal filtering algorithm for the Beidou high-precision navigation system was designed and completed;

(5)进行反正交变换取出滤波结果中当前时刻的系统状态模型，滤波结果能够高精度表达载体在地球坐标系三个轴上的位置、速度分量，还能够对载体的经度、纬度、高度及该三个方向速度的高精度解算，滤波结果同时对北斗接收机进行反馈校正以减小时钟偏差及等效时钟漂移对导航定位精度的影响。(5) An inverse orthogonal transformation is performed to extract the system state model at the current moment from the filtering result. The filtering result can express the position and velocity components of the carrier on the three axes of the earth coordinate system with high precision, and can also calculate the longitude, latitude, altitude and speed of the carrier in these three directions with high precision. The filtering result is also used to perform feedback correction on the Beidou receiver to reduce the impact of clock deviation and equivalent clock drift on navigation positioning accuracy.

本发明与现有技术相比，利用数据处理手段取代北斗导航接收机内部对伪距伪距率的求解过程，消除了大部分的随机误差，构建了一种高精度北斗导航定位系统导航定位参数计算方法，它具有如下优点：(1)该方法构建的滤波方法在地球坐标系三个坐标轴上是解耦的，计算量与单独求解伪距、伪距率方程相当，但求解精度高；(2)相对于现有的提高北斗定位精度的技术而言，不需额外的硬件成本，如：相对于差分技术不需要基准站及数据通讯装置，不受差分技术所面临的信号作用范围的限制；(3)该方法能够与现有的提高北斗定位精度的技术方法相互协作，能够进一步提高北斗定位精度。Compared with the prior art, the present invention utilizes data processing means to replace the internal solution process of the Beidou navigation receiver for pseudorange and pseudorange rate, thereby eliminating most of the random errors and constructing a high-precision Beidou navigation and positioning system navigation and positioning parameter calculation method, which has the following advantages: (1) The filtering method constructed by the method is decoupled on the three coordinate axes of the earth coordinate system, and the calculation amount is equivalent to that of solving the pseudorange and pseudorange rate equations separately, but the solution accuracy is high; (2) Compared with the existing technology for improving Beidou positioning accuracy, no additional hardware cost is required, such as: compared with the differential technology, no base station and data communication device are required, and it is not subject to the signal action range limitation faced by the differential technology; (3) The method can cooperate with the existing technical methods for improving Beidou positioning accuracy, and can further improve Beidou positioning accuracy.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为本发明的原理框图。FIG1 is a block diagram of the principle of the present invention.

图2为利用伪距方程直接求解的地球坐标系x轴方向的位置误差曲线。FIG2 is a position error curve in the x-axis direction of the earth coordinate system directly solved by the pseudorange equation.

图3为利用常规滤波方法求解的地球坐标系x轴方向的位置误差曲线。FIG3 is a position error curve in the x-axis direction of the earth coordinate system solved by a conventional filtering method.

图4为利用本发明方法求解的地球坐标系x轴方向的位置误差曲线。FIG. 4 is a position error curve in the x-axis direction of the earth coordinate system solved by the method of the present invention.

图5为利用伪距率方程直接求解的地球坐标系x轴方向的速度误差曲线。FIG5 is a velocity error curve in the x-axis direction of the earth coordinate system directly solved by using the pseudo-range rate equation.

图6为利用常规滤波方法求解的地球坐标系x轴方向的速度误差曲线。FIG6 is a velocity error curve in the x-axis direction of the earth coordinate system solved by the conventional filtering method.

图7为利用本发明方法求解的地球坐标系x轴方向的速度误差曲线。FIG. 7 is a velocity error curve in the x-axis direction of the earth coordinate system solved by the method of the present invention.

图8为利用常规滤波方法求解的地球坐标系x轴方向的加速度误差曲线。FIG8 is an acceleration error curve in the x-axis direction of the earth coordinate system solved by a conventional filtering method.

图9为利用本发明方法方法求解的地球坐标系x轴方向的加速度误差曲线。FIG. 9 is an acceleration error curve in the x-axis direction of the earth coordinate system solved by the method of the present invention.

具体实施方式DETAILED DESCRIPTION

下面结合附图对本发明的技术方案进行详细说明：The technical solution of the present invention is described in detail below with reference to the accompanying drawings:

本发明的原理如图1所示：首先根据北斗接收机测得的伪距、伪距率计算载体在地球坐标系三个坐标轴上的初始位置及速度分量，并在地球坐标系中根据载体的运动学原理建立载体运动模型，结合北斗导航定位机的误差模型，进而建立北斗导航定位系统动态滤波常规状态方程及量测方程；然后分别根据前后两时刻系统模型的相关性及北斗导航定位接收机伪距、伪距率观测的独立性，建立地球坐标系下北斗高精度导航的系统状态方程与量测方程；最后设计并完成了北斗高精度导航的系统最优滤波算法，滤波结果能够直接作为载体在地区坐标系下三个轴方向的位置速度解，还能够用于载体的经度、纬度、速度、及与此方向对应速度的高精度解算，并对北斗接收机的时钟偏差、等效时钟漂移进行信息校正。具体实施方法如下：The principle of the present invention is shown in Figure 1: First, the initial position and velocity components of the carrier on the three coordinate axes of the earth coordinate system are calculated based on the pseudorange and pseudorange rate measured by the Beidou receiver, and the carrier motion model is established in the earth coordinate system according to the kinematic principle of the carrier, combined with the error model of the Beidou navigation and positioning machine, and then the conventional state equation and measurement equation of the Beidou navigation and positioning system dynamic filtering are established; then, according to the correlation of the system model at the previous and next moments and the independence of the pseudorange and pseudorange rate observations of the Beidou navigation and positioning receiver, the system state equation and measurement equation of the Beidou high-precision navigation in the earth coordinate system are established; finally, the optimal filtering algorithm of the Beidou high-precision navigation system is designed and completed, and the filtering result can be directly used as the position and velocity solution of the carrier in the three axis directions in the regional coordinate system, and can also be used for the high-precision solution of the longitude, latitude, velocity, and the velocity corresponding to this direction of the carrier, and the clock deviation and equivalent clock drift of the Beidou receiver are corrected for information. The specific implementation method is as follows:

一、根据北斗接收机测得的伪距、伪距率计算载体在地球坐标系三个坐标轴上的初始位置及速度分量1. Calculate the initial position and velocity components of the carrier on the three coordinate axes of the earth coordinate system based on the pseudorange and pseudorange rate measured by the Beidou receiver

根据北斗接收机测得的四个伪距量测量ρi(i＝1,2,3,4)：According to the four pseudo-range measurements measured by the BeiDou receiver, ρ i (i = 1, 2, 3, 4) is:

Figure GDA0003972715100000031
Figure GDA0003972715100000031

利用泰勒级数展开法计算载体在地球坐标系三个轴方向上的位置。其中：载体的真实位置为XU＝[x y z c·Δtu]T或XU＝[x y z lu]T，第i颗卫星的真实位置为XSi＝[xsiysi zsi]T，er代表各项测距误差。The Taylor series expansion method is used to calculate the position of the carrier in the three axis directions of the earth coordinate system. Among them: the real position of the carrier is Xu = [xyzc·Δt u ] T or Xu = [xyzl u ] T , the real position of the i-th satellite is XSi = [ xsi ysi zsi ] T , and er represents various ranging errors.

根据北斗接收机测得的四个伪距率量测量

Figure GDA0003972715100000032
Based on the four pseudo-range rate measurements measured by the BeiDou receiver
Figure GDA0003972715100000032

Figure GDA0003972715100000033
Figure GDA0003972715100000033

利用泰勒级数展开法计算载体在地球坐标系三个轴方向上的速度。其中：

Figure GDA0003972715100000034
代表用户时钟频率误差对应的距离率，err代表测量误差，载体真实速度为
Figure GDA0003972715100000035
以及卫星真实速度为
Figure GDA0003972715100000036
The Taylor series expansion method is used to calculate the velocity of the carrier in the three axis directions of the earth coordinate system. Among them:
Figure GDA0003972715100000034
represents the distance rate corresponding to the user clock frequency error, err represents the measurement error, and the actual speed of the carrier is
Figure GDA0003972715100000035
And the true speed of the satellite is
Figure GDA0003972715100000036

二、根据载体的运动学原理建立载体运动模型，建立北斗导航的误差模型，二者模型合并形成动态滤波的常规系统模型2. According to the kinematic principle of the carrier, the carrier motion model is established, and the Beidou navigation error model is established. The two models are combined to form a conventional system model of dynamic filtering.

在地球坐标系中根据载体的运动学原理建立载体运动模型，载体运动状态取为：In the earth coordinate system, the carrier motion model is established according to the kinematic principle of the carrier, and the carrier motion state is taken as:

Figure GDA0003972715100000037
Figure GDA0003972715100000037

其中状态变量x，

Figure GDA0003972715100000038
y，
Figure GDA0003972715100000039
z，
Figure GDA00039727151000000310
分别为载体在地球坐标系下x，y，z三个坐标轴上的位置、速度和加速度分量，由此建立系统的运动模型：The state variable x is
Figure GDA0003972715100000038
y,
Figure GDA0003972715100000039
z,
Figure GDA00039727151000000310
They are the position, velocity and acceleration components of the carrier on the three coordinate axes x, y and z in the earth coordinate system, and the motion model of the system is established:

Figure GDA00039727151000000311
Figure GDA00039727151000000311

其中：

Figure GDA00039727151000000312
in:
Figure GDA00039727151000000312

Figure GDA00039727151000000313
Figure GDA00039727151000000313

W1＝[0 0 wx 0 0 wy 0 0 wz]T，τi(i＝x,y,z)分别为对应三个坐标轴的相关时间常数，wi(i＝x,y,z)为高斯白噪声，

Figure GDA00039727151000000314
分别为三个坐标轴上的加速度分量的均值。W 1 ＝[0 0 w x 0 0 w y 0 0 w z ] T , τ i (i＝x, y, z) are the relevant time constants corresponding to the three coordinate axes, w i (i＝x, y, z) is Gaussian white noise,
Figure GDA00039727151000000314
are the means of the acceleration components on the three coordinate axes.

北斗导航定位接收机的误差取为：The error of Beidou navigation and positioning receiver is taken as:

Figure GDA00039727151000000315
Figure GDA00039727151000000315

其中：XG(t)＝[δl δlf]T，δl为与时钟偏置对应的距离误差，δlf为等效时钟频漂所对应的速度误差。Where: X G (t) = [δl δl f ] T , δl is the distance error corresponding to the clock offset, and δl f is the speed error corresponding to the equivalent clock frequency drift.

以上(2)和(3)两式合并为：The above equations (2) and (3) are combined into:

Figure GDA0003972715100000041
Figure GDA0003972715100000041

离散化后，得：After discretization, we get:

X(k)＝Φ(k,k-1)X(k-1)+Γ(k-1)U(k-1)+W(k-1) (5)。X(k)=Φ(k,k-1)X(k-1)+Γ(k-1)U(k-1)+W(k-1) (5).

三、建立北斗导航的观测模型，建立北斗导航动态滤波的常规系统模型3. Establish the observation model of Beidou navigation and the conventional system model of Beidou navigation dynamic filtering

北斗卫星i测得的伪距ρi及伪距率

Figure GDA0003972715100000042
经过线性化并取其线性部分，如对ρi有Pseudorange ρ i and pseudorange rate measured by BeiDou satellite i
Figure GDA0003972715100000042
After linearization and taking the linear part, for example, for ρ i

δρi＝Hi·δX+vi (6)δρ i =H i ·δX+v i (6)

其中：Hi＝[-ei1 0 0 -ei2 0 0 -ei3 0 0 1 0]，

Figure GDA0003972715100000043
Figure GDA0003972715100000044
Rsi＝[(x-xsi)2+(y-ysi)2+(z-zsi)2]1/2。Among them: H i =[-e i1 0 0 -e i2 0 0 -e i3 0 0 1 0],
Figure GDA0003972715100000043
Figure GDA0003972715100000044
R si =[(xx si ) 2 +(yy si ) 2 +(zz si ) 2 ] 1/2 .

得如下系统方程和量测方程：The following system equations and measurement equations are obtained:

Figure GDA0003972715100000045
Figure GDA0003972715100000045

建立离散的北斗导航动态滤波常规滤波模型如下：The conventional filter model of discrete Beidou navigation dynamic filtering is established as follows:

Figure GDA0003972715100000046
Figure GDA0003972715100000046

其中：in:

Figure GDA0003972715100000047
Figure GDA0003972715100000047

Figure GDA0003972715100000048
Figure GDA0003972715100000048

四、考虑到前后两时刻系统状态模型的相关性及北斗导航定位接收机伪距、伪距率观测的独立性，建立地球坐标系下北斗高精度导航的系统状态方程与量测方程4. Considering the correlation of the system state model between the previous and the next moments and the independence of the pseudorange and pseudorange rate observations of the Beidou navigation and positioning receiver, the system state equation and measurement equation of Beidou high-precision navigation in the earth coordinate system are established.

取：Xm(k)＝[XT(k-1) XT(k)]T、Xm(k-1)＝[XT(k-3) XT(k-2)]T、Zm(k)＝[ZT(k-1) ZT(k)]T，Xm(k)、Xm(k-1)和Zm(k)相互间的关系为：Assume: Xm (k)=[ XT (k-1) XT (k)] T , Xm (k-1)=[ XT (k-3 ) XT(k-2)] T , Zm (k)=[ ZT (k-1) ZT (k)] T , the relationship between Xm (k), Xm (k-1) and Zm (k) is:

Xm(k)＝Φm(k,k-1)Xm(k-1)+Γm(k-1)Um(k-1)+Bm(k-1)Wm(k-1) (9)X m (k)＝Φ m (k,k-1)X m (k-1)+Γ m (k-1)U m (k-1)+B m (k-1)W m (k- 1) (9)

Zm(k)＝Hm(k)Xm(k)+Vm(k) (10)Z m (k)=H m (k)X m (k)+V m (k) (10)

其中：in:

Figure GDA0003972715100000051
Figure GDA0003972715100000051

Figure GDA0003972715100000052
Figure GDA0003972715100000052

Figure GDA0003972715100000053
Figure GDA0003972715100000053

Figure GDA0003972715100000054
Figure GDA0003972715100000054

五、对前后两时刻系统状态模型中相同变量及伪距、伪距率观测量中相同变量进行正交变换，设计并完成了北斗高精度导航的系统最优滤波算法5. Perform orthogonal transformation on the same variables in the system state model and the same variables in the pseudorange and pseudorange rate observations at the previous and next moments, and design and complete the optimal filtering algorithm for Beidou high-precision navigation system

定义如下变换：Define the following transformation:

Figure GDA0003972715100000055
Figure GDA0003972715100000055

其中：T＝LT·Ti·L，L为将Xm(k)变换成相同变量相邻的线性算子，Ti是对相同变量进行正交变换的块矩阵，且满足Ti TTi＝I及TTT＝I。Wherein: T＝ LT · Ti ·L, L is a linear operator that transforms Xm (k) into adjacent linear operators of the same variable, Ti is a block matrix that performs orthogonal transformation on the same variable, and satisfies TiTTi ＝ I and TTT ＝I.

将式(9)、(10)、(11)结合，并考虑到Ti TTi＝I、TTT＝I。则有Combining equations (9), (10), and (11), and considering that T i T T i = I, T T T = I, we have

Figure GDA0003972715100000056
Figure GDA0003972715100000056

Figure GDA0003972715100000057
Figure GDA0003972715100000057

其中：

Figure GDA0003972715100000058
Figure GDA0003972715100000059
in:
Figure GDA0003972715100000058
Figure GDA0003972715100000059

利用系统模型(12)和观测模型(13)进行卡尔曼最优滤波Kalman optimal filtering is performed using the system model (12) and the observation model (13)

Figure GDA00039727151000000510
Figure GDA00039727151000000510

其中：in:

Figure GDA0003972715100000061
Figure GDA0003972715100000061

Figure GDA0003972715100000062
Figure GDA0003972715100000062

Figure GDA0003972715100000063
Figure GDA0003972715100000063

Figure GDA0003972715100000064
Figure GDA0003972715100000064

六、对上述滤波结果

Figure GDA0003972715100000065
进行反正交变换，有：6. The above filtering results
Figure GDA0003972715100000065
Performing inverse orthogonal transformation, we have:

Figure GDA0003972715100000066
Figure GDA0003972715100000066

利用式(15)，

Figure GDA0003972715100000067
中当前时刻的系统状态估计值
Figure GDA0003972715100000068
能够精确表达载体在地球坐标系三个轴上的位置、速度、加速度分量以及北斗接收机时钟偏差及等效时钟漂移估计值；利用载体在地球坐标系三个轴上的位置、速度分量还能够以计算载体的经度、纬度、高度及该三个方向速度信息；同时利用
Figure GDA0003972715100000069
还能够以对北斗接收机时钟偏差及等效时钟频漂进行校正。Using formula (15),
Figure GDA0003972715100000067
The estimated value of the system state at the current time
Figure GDA0003972715100000068
It can accurately express the position, velocity, acceleration components of the carrier on the three axes of the earth coordinate system, as well as the Beidou receiver clock deviation and equivalent clock drift estimation value; the position and velocity components of the carrier on the three axes of the earth coordinate system can also be used to calculate the longitude, latitude, altitude and speed information of the carrier in these three directions; at the same time,
Figure GDA0003972715100000069
It can also correct the Beidou receiver clock deviation and equivalent clock frequency drift.

以某次在机动环境下的北斗导航定位实验为例，以说明本发明方法在提高导航定位参数的优越性。图2、图5为利用伪距、伪距率方程进行泰勒级数展开而解算的位置与速度误差，而图3、图6、图8为利用常规滤波方法对北斗导航定位系统进行直接估计的位置、速度、加速度误差，而图4、图7、图9为利用本发明方法对北斗导航定位系统进行直接估计的位置、速度、加速度误差。由图能够看出本发明方法不仅能够高精度地给出北斗导航定位系统的位置、速度，并且能够高精度地估计载体的加速度，而这是普通算法无法完成的。Take a Beidou navigation and positioning experiment in a maneuvering environment as an example to illustrate the superiority of the method of the present invention in improving navigation and positioning parameters. Figures 2 and 5 are the position and velocity errors solved by Taylor series expansion using pseudorange and pseudorange rate equations, while Figures 3, 6, and 8 are the position, velocity, and acceleration errors directly estimated for the Beidou navigation and positioning system using conventional filtering methods, and Figures 4, 7, and 9 are the position, velocity, and acceleration errors directly estimated for the Beidou navigation and positioning system using the method of the present invention. It can be seen from the figure that the method of the present invention can not only give the position and velocity of the Beidou navigation and positioning system with high precision, but also estimate the acceleration of the carrier with high precision, which is impossible for ordinary algorithms to accomplish.

通过前述还能够以看出本发明方法在估计载体在地球坐标系三个坐标轴方向的位置、速度及加速度时，是相互解耦的，这样能够大幅降低计算量进而保证系统的实时性。为此，本发明计算量适中，在保证系统实时性的同时能够显著提高北斗导航系统导航定位精度高，减小导航定位误差，并能够高精度地估计载体的加速度。It can also be seen from the above that the method of the present invention is mutually decoupled when estimating the position, velocity and acceleration of the carrier in the three coordinate axis directions of the earth coordinate system, which can greatly reduce the amount of calculation and thus ensure the real-time performance of the system. To this end, the present invention has a moderate amount of calculation, and can significantly improve the navigation and positioning accuracy of the Beidou navigation system while ensuring the real-time performance of the system, reduce the navigation and positioning error, and can estimate the acceleration of the carrier with high accuracy.

Claims (6)

1. A high-precision Beidou navigation and positioning system navigation and positioning parameter calculation method is characterized by comprising the following steps:
(1) Calculating initial positions and velocity components of a carrier on three coordinate axes of an earth coordinate system according to pseudo ranges and pseudo range rates measured by a Beidou receiver, establishing a carrier motion model in the earth coordinate system according to the kinematics principle of the carrier, establishing an error model of Beidou navigation, and combining the two models to form a conventional system model of dynamic filtering;
(2) Establishing an observation model of the Beidou navigation, discretizing the system by combining the step (1), and establishing a conventional system model of the Beidou navigation dynamic filtering;
(3) Based on the conventional system model of the Beidou navigation dynamic filtering established in the step (2), considering the correlation of the conventional system model at the front moment and the rear moment and the independence of pseudo range and pseudo range rate observation of the Beidou navigation positioning receiver, establishing a system state equation and a measurement equation of the Beidou high-precision navigation in a global coordinate system;
(4) Orthogonal transformation is carried out on the same variable and the same variable in pseudo range and pseudo range rate observed quantity in a conventional system model at the front moment and the rear moment, and a system optimal filtering algorithm for Beidou high-precision navigation is designed and completed;
(5) And performing inverse orthogonal transformation to obtain a conventional system model of the current moment in a filtering result, wherein the filtering result can express the position and the velocity component of the carrier on three axes of a terrestrial coordinate system with high precision, can also perform high-precision calculation on the longitude, the latitude and the height of the carrier and the velocity in the three directions, and simultaneously performs feedback correction on the Beidou receiver to reduce the influence of clock deviation and equivalent clock drift on navigation positioning precision.
2. The method for calculating the navigation and positioning parameters of the high-precision Beidou navigation and positioning system according to claim 1 is characterized in that a carrier motion model and an error model of Beidou navigation are established in the global coordinate system in step (1) according to the kinematics principle of a carrier, and the two models are combined to form a conventional system model of dynamic filtering, and the method comprises the following specific steps:
establishing a carrier motion model in a global coordinate system according to the kinematics principle of a carrier, wherein the motion state of the carrier is as follows:
Figure FDA0003961564840000011
wherein the state variable is
Figure FDA0003961564840000012
Respectively representing the position, the speed and the acceleration component of the carrier on three coordinate axes of x, y and z under the terrestrial coordinate system, thereby establishing a motion model of the system:
Figure FDA0003961564840000013
the error of the Beidou navigation positioning receiver is as follows:
Figure FDA0003961564840000014
wherein: x G (t)＝[δl δl f ] T Where δ l is the distance error corresponding to the clock offset, δ l f The speed error corresponding to the equivalent clock frequency drift;
the two formulas (2) and (3) are combined into:
Figure FDA0003961564840000021
discretizing the formula (4) to obtain:
X(k)＝Φ(k,k-1)X(k-1)+Γ(k-1)U(k-1)+W(k-1) (5)。
3. the method for calculating the navigation and positioning parameters of the high-precision Beidou navigation and positioning system according to claim 2 is characterized in that the Beidou navigation observation model is established in the step (2), and the system is discretized by combining the step (1) to establish a conventional Beidou navigation dynamic filtering system model, which specifically comprises the following steps:
pseudo range rho measured by Beidou satellite i i After linearization and taking the linear part of it, there are
δρ i ＝H i ·δX+v i (6)
The following system equation and measurement equation are obtained:
Figure FDA0003961564840000022
a discrete Beidou navigation dynamic filtering conventional filtering model is established as follows:
Figure FDA0003961564840000023
4. the method for calculating the navigation and positioning parameters of the Beidou navigation and positioning system with high precision according to claim 3 is characterized in that based on the conventional system model based on the Beidou navigation dynamic filtering established in the step (2) in the step (3), a system state equation and a measurement equation of the Beidou navigation with high precision under a terrestrial coordinate system are established in consideration of the correlation of the conventional system model at the front moment and the rear moment and the independence of pseudo range and pseudo range rate observation of the Beidou navigation and positioning receiver, and the method specifically comprises the following steps:
taking: x m (k)＝[X T (k-1) X T (k)] T 、X m (k-1)＝[X T (k-3) X T (k-2)] T 、Z m (k)＝[Z T (k-1) Z T (k)] T ，X m (k)、X m (k-1) and Z m (k) The relationship between each other is:
X m (k)＝Φ m (k,k-1)X m (k-1)+Γ m (k-1)U m (k-1)+B m (k-1)W m (k-1) (9)
Z m (k)＝H m (k)X m (k)+V m (k) (10)
wherein:
Figure FDA0003961564840000024
Figure FDA0003961564840000031
Figure FDA0003961564840000032
Figure FDA0003961564840000033
5. the method for calculating the navigation and positioning parameters of the Beidou navigation and positioning system with high precision according to claim 4, wherein the step (4) is implemented by performing orthogonal transformation on the same variable and the same variable in the pseudo range and the pseudo range rate observed quantity in the conventional system model at the front and rear moments, and designing and completing the optimal filtering algorithm of the Beidou navigation and positioning system with high precision, which is specifically as follows:
Figure FDA0003961564840000034
wherein: t = T i L, L is X m (k) Conversion into linear operators, T, of the same variable neighbourhood i Is a block matrix orthogonally transformed on the same variable and satisfies T i T T i = I and T T T＝I；
Combining formulae (9), (10), (11) with consideration of T i T T i ＝I、T T T = I; then there is
Figure FDA0003961564840000035
Figure FDA0003961564840000036
Wherein:
Figure FDA0003961564840000037
Figure FDA0003961564840000038
kalman optimal filtering using a system model (12) and an observation model (13)
Figure FDA0003961564840000039
Wherein:
Figure FDA00039615648400000310
Figure FDA00039615648400000311
Figure FDA00039615648400000312
Figure FDA00039615648400000313
6. the method for calculating the navigation and positioning parameters of the high-precision Beidou navigation and positioning system according to claim 1, wherein the step (5) of performing inverse orthogonal transformation to obtain the conventional system model of the current time in the filtering result, the filtering result can express the position and the velocity component of the carrier on three axes of a terrestrial coordinate system with high precision, and can also perform high-precision calculation on the longitude, the latitude, the altitude and the three directional velocities of the carrier, and the filtering result simultaneously performs feedback correction on the Beidou receiver to reduce the influence of clock deviation and equivalent clock drift on the navigation and positioning precision, specifically as follows:
the filtering result according to equation (14)
Figure FDA0003961564840000041
The inverse orthogonal transformation is carried out, and the method comprises the following steps:
Figure FDA0003961564840000042
by using the formula (15),
Figure FDA0003961564840000043
system state estimation value of current time
Figure FDA0003961564840000044
The position, the speed and the acceleration component of the vector on three axes of a terrestrial coordinate system, and the clock deviation and the equivalent clock drift estimated value of the Beidou receiver can be accurately expressed; the longitude, latitude, height and the three direction speed information of the carrier can be calculated by utilizing the position and the speed components of the carrier on the three axes of the terrestrial coordinate system; at the same time utilize
Figure FDA0003961564840000045
And the clock deviation of the Beidou receiver and the equivalent clock frequency drift can be corrected.
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