WO2019144480A1 - 基于速度约束的低成本接收机平滑rtd算法 - Google Patents

基于速度约束的低成本接收机平滑rtd算法 Download PDF

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WO2019144480A1
WO2019144480A1 PCT/CN2018/079118 CN2018079118W WO2019144480A1 WO 2019144480 A1 WO2019144480 A1 WO 2019144480A1 CN 2018079118 W CN2018079118 W CN 2018079118W WO 2019144480 A1 WO2019144480 A1 WO 2019144480A1
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observation
satellite
receiver
pseudo
speed
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PCT/CN2018/079118
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English (en)
French (fr)
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潘树国
张建
闫志跃
喻国荣
刘国良
张瑞成
王彦恒
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东南大学
南京康帕斯导航科技有限公司
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Publication of WO2019144480A1 publication Critical patent/WO2019144480A1/zh

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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
    • G01S19/42—Determining position
    • G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
    • 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
    • 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
    • G01S19/52—Determining velocity

Definitions

  • the invention relates to a low-cost receiver smoothing RTD technology based on speed constraint, and belongs to the technical field of GNSS positioning and navigation.
  • GNSS Global Navigation Satellite System
  • RTK Real-time kinematic positioning of low-cost receivers.
  • the variance of the pseudo-range and carrier phase of the low-cost receiver is determined by the method of variance estimation. And covariance can guarantee the positioning accuracy of RTK centimeter level; other researchers based on GPS + BDS (GPS: Global Positioning System, BDS: BeiDou Navigation Satellite System) dual system, using a low-cost single-frequency helical antenna to obtain centimeter-level positioning; Greatly meet the needs of industries such as drones, precision agriculture and robot guidance. It is worth pointing out that the above research results were obtained in an open environment.
  • the present invention provides the user with reliable positioning of the sub-meter level and the meter level on the premise of ensuring the positioning continuity and the environmental adaptability.
  • the present invention considers that the carrier phase observation value has certain problems in a complicated environment, and therefore adopts an RTD (Real Time Differential real-time dynamic code differential) positioning mode to ensure continuity of positioning.
  • RTD Real Time Differential real-time dynamic code differential
  • the present invention adopts a phase smoothing pseudorange method to improve the accuracy of the pseudorange observation value while ensuring reliable carrier phase quality, and
  • the anti-difference M-LS filtering is used to eliminate the influence of the gross error of the observation on the filtering solution to ensure the reliability of the positioning.
  • a low-cost receiver smoothing RTD algorithm based on speed constraints including the following steps:
  • Step 1) Doppler speed measurement
  • the Doppler shift observation characterizes the magnitude of the Doppler effect caused by the relative motion of the satellite and the GPS receiver antenna, that is, the instantaneous observation of the carrier phase change rate.
  • the GPS pseudorange observation equation is as follows:
  • ⁇ refers to the wavelength
  • the three-dimensional position of the station can be solved by pseudo-point single-point positioning, assuming that the receiver position error is 10 m, and the influence on the speed measurement accuracy is about 2 mm; the three-dimensional speed of the satellite can use the value based on the navigation satellite position sequence.
  • the difference method is solved; the satellite clock drift can be obtained by the satellite clock rate change rate in a certain period of time; the present invention ignores the influence of the atmospheric delay change rate.
  • Step 2 a smooth RTD algorithm based on speed constraints
  • the j-th satellite pseudo-range differential observation equation can be expressed as follows:
  • It is a double-difference operator
  • P is the pseudo-range observation value after carrier phase smoothing
  • superscripts i and j are reference stars and non-reference stars respectively
  • subscripts m and n are reference stations and rover respectively
  • ⁇ is satellite Geometric distance to the receiver
  • T is the tropospheric delay
  • I is the ionospheric delay
  • ⁇ is the residual error such as observation noise and multipath
  • the single epoch GPS+BDS observation equation can be expressed as follows:
  • V BX-L (6)
  • G stands for GPS system
  • C stands for Beidou system
  • i stands for reference star
  • j and k represent non-reference stars
  • V refers to observed residuals, the last three are observed residuals of velocity items, and the rest are pseudo-range observation residuals.
  • ;l, m, n refer to the Taylor series first-order expansion term of the geometric distance between the satellite and the receiver
  • X is the parameter vector to be estimated, wherein the first three terms are position correction numbers, and the last three items are speed correction numbers; Observed value vector;
  • the present invention uses the velocity pseudo observation to constrain the parameter to be estimated, and the velocity pseudo observation value equation is as follows:
  • the representative pseudo-observation value is a prior value that can be obtained by the Doppler velocimetry equation in step 1).
  • the continuity and reliability of the positioning can be ensured, and the problem that the positioning cannot be located in a complicated environment such as an urban canyon is avoided.
  • the navigation device used by the invention greatly reduces the cost of the user and is convenient for the user to carry, and has great practical value.
  • the invention can ensure the fast and reliable positioning of the low-cost receiver, and basically achieves the sub-meter positioning accuracy in an open environment, and can ensure reliable positioning within 2 meters; in a complex environment, the positioning accuracy within 5 m can be basically guaranteed.
  • 1 is a relative position diagram of a receiver of the present invention and a Ublox M8T module antenna;
  • Figure 3 is a signal to noise ratio in an open environment static condition of the present invention
  • Figure 4 is a road trajectory diagram of the open environment dynamic condition of the present invention.
  • Figure 5 is a diagram showing the positioning accuracy of the N and E directions under the open environment dynamic condition of the present invention.
  • Figure 6 is a signal to noise ratio of the open environment dynamic condition of the present invention.
  • Figure 7 is a road trajectory diagram of the complex environment under dynamic conditions of the present invention.
  • Figure 8 is a diagram showing the positioning accuracy of the N and E directions under dynamic conditions of the complex environment of the present invention.
  • Figure 9 is a signal to noise ratio in a complex environment dynamic condition of the present invention
  • Figure 10 is a road trajectory diagram of the actual road dynamic condition of the present invention.
  • Figure 11 is a signal to noise ratio under actual road dynamic conditions of the present invention.
  • Figure 12 is a diagram showing changes in the number of GPS+BDS satellites according to the present invention.
  • Figure 13 is a view of the satellite in the actual road dynamic condition of the present invention.
  • Figure 14 is a diagram showing the positioning accuracy of the N and E directions under actual road dynamic conditions of the present invention.
  • 15 is a flow chart of a low-cost receiver smoothing RTD algorithm based on speed constraint according to the present invention.
  • a low-cost receiver smoothing RTD algorithm based on velocity constraint firstly using the Doppler observation to solve the velocity component; then using the obtained velocity component as the pseudo-observation value combined with the pseudorange observation to establish the constrained filtering position solution of the anti-difference Kalman filter . Including the following specific steps:
  • Step 1) the Doppler observations are used to solve the velocity component.
  • the formula is derived as follows:
  • the Doppler shift observation characterizes the magnitude of the Doppler effect caused by the relative motion of the satellite and the GPS receiver antenna, that is, the instantaneous observation of the carrier phase change rate.
  • the GPS pseudorange observation equation is as follows:
  • the tropospheric delay and the ionospheric delay are combined into one, and the station distance ⁇ in (1) is linearized and fully differentiated:
  • the three-dimensional position of the station can be solved by pseudo-point single-point positioning, assuming that the receiver position error is 10 m, and the influence on the speed measurement accuracy is about 2 mm; the three-dimensional speed of the satellite can use the value based on the navigation satellite position sequence.
  • the difference method is solved; the satellite clock drift can be obtained by the satellite clock rate change rate in a certain period of time; the present invention ignores the influence of the atmospheric delay change rate.
  • the above derivation of the velocity measurement equation is mainly used to solve the speed of the receiver, and provides a pseudo-observation of the velocity for the pseudorange difference to constrain the position solution.
  • Step 2 a smooth RTD algorithm based on velocity constraints
  • the j-th satellite pseudo-range differential observation equation can be expressed as follows:
  • It is a double-difference operator
  • P is the pseudo-range observation value after carrier phase smoothing
  • superscripts i and j are reference stars and non-reference stars respectively
  • subscripts m and n are reference stations and rover respectively
  • ⁇ is satellite Geometric distance to the receiver
  • T is the tropospheric delay
  • I is the ionospheric delay
  • ⁇ is the residual error such as observation noise and multipath
  • the single epoch GPS+BDS observation equation can be expressed as follows:
  • V BX-L (6)
  • G stands for GPS system
  • C stands for Beidou system
  • i stands for reference star
  • j and k represent non-reference stars
  • V refers to observed residuals, the last three are observed residuals of velocity items, and the rest are pseudo-range observation residuals.
  • ;l, m, n refer to the Taylor series first-order expansion term of the geometric distance between the satellite and the receiver
  • X is the parameter vector to be estimated, wherein the first three terms are position correction numbers, and the last three items are speed correction numbers
  • the present invention uses the velocity pseudo observation to constrain the parameter to be estimated, and the velocity pseudo observation value equation is as follows:
  • the representative pseudo-observation value is a prior value that can be obtained by the Doppler velocimetry equation in step 1).
  • a common ceramic patch antenna is used, and the module has a U-blox M8T data sampling rate of 1 s and a cutoff height angle of 12°.
  • the RTK data was collected synchronously by the Haida H32 receiver.
  • Figure 1 the placement relationship between the U-blox M8T module and the Zhonghaida H32 receiver is shown in Figure 1.
  • the experiment compares and analyzes the GPS+BDS data of 4 different time periods in October 2017 (static, pedestrian dynamics in an open environment, pedestrian dynamics in a complex environment, and vehicle dynamics under actual road conditions)
  • Figure 2 and Figure 3 show the plane positioning accuracy and signal-to-noise ratio of the open environment under static conditions.
  • the static coordinate reference value takes the RTK fixed solution of the Haida H32 receiver. It can be seen from Fig. 3 that the signal-to-noise ratio of the satellite in the open environment is better than 30, and the signal quality is good, which also ensures the plane positioning accuracy from the side.
  • Table 1 provides a statistical analysis of the results of planar positioning in an open environment.
  • RMS root meam square root square error
  • Table 1 provides a statistical analysis of the results of planar positioning in an open environment.
  • RMS root meam square root square error
  • Table 1 provides a statistical analysis of the results of planar positioning in an open environment.
  • RMS root meam square root square error
  • Table 1 provides a statistical analysis of the results of planar positioning in an open environment.
  • RMS root meam square root square error
  • Figure 4 is a route trajectory diagram in an open environment collected at the top of the southeast university center building.
  • White is the fixed solution of RTK, which is the coordinate reference value.
  • Black is the coordinate solution calculated by the present invention.
  • Figure 5 and Figure 6 respectively show Plane positioning accuracy and signal-to-noise ratio under open environmental dynamic conditions. Table 2 provides statistical analysis of planar results under dynamic conditions.
  • the number of epochs in Fig. 6 is inconsistent with the number of plane points in Fig. 5, which is caused by the loss of the signal (Fig. 4) caused by the receiver passing through a house in the measured environment, that is, the above plane positioning accuracy is RTK fixed phasing comparison results.
  • the signal quality received by the low-cost receiver is inferior to the static condition, which is also confirmed by the positioning results of the plane, but it can be seen from Table 2 that it is better than 0.5 under dynamic conditions.
  • the plane accuracy of m is better than the static condition, which may be related to the length of the data acquisition. It can be seen from Table 2 that under dynamic conditions, the RMS is second only to the static condition, which is 0.77 m, and the plane can ensure reliable positioning within 2 m.
  • Figure 7 is a route trajectory diagram of the complex environment dynamic conditions collected on the playground of Southeast University on October 18, 2017. The playground is surrounded by lush trees and high-rise buildings.
  • the white is the RTK fixed solution, which is the coordinate reference value.
  • the coordinate solution calculated by the present invention, FIG. 8 and FIG. 9 respectively show the plane positioning accuracy and the signal-to-noise ratio under complex environmental dynamic conditions.
  • the number of epochs in Fig. 9 is inconsistent with the number of plane points in Fig. 8 as well due to signal loss of lock.
  • the low-cost receiver signal quality is worse in a complex environment.
  • Table 3 summarizes the plane positioning accuracy under complex environmental dynamic conditions.
  • the RMS in the plane direction is 1.48, and the plane positioning accuracy is 33.6% better than 1 m, but the positioning accuracy within 3 meters can be guaranteed.
  • Figure 10 is a dynamic trajectory diagram of the vehicle under actual road conditions on October 23, 2017. Black is the coordinate solution calculated by the present invention, and white is the coordinate reference value.
  • the coordinate reference value is the GNSS data collected under the actual road conditions collected by the Beidou terminal dynamic detection system (referred to as the detection vehicle) of the GNSS/INS fusion of the Nanjing Metrology Supervision and Inspection Institute, and the after-effect solution of the dynamic detection system is obtained. 1cm) obtained.
  • the data signal received by the low-cost receiver passes through the measurement antenna of the dynamic detection system, and the data signal quality is good. However, as can be seen from the satellite signal-to-noise ratio diagram shown in Figure 11, the satellite signal quality is still poor in many epochs.
  • RMS root meam square
  • N the north direction coordinate error
  • E the east direction coordinate deviation

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
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  • Physics & Mathematics (AREA)
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Abstract

一种基于速度约束的低成本接收机平滑RTD方法，首先利用多普勒观测值求解速度分量；然后利用已获得的速度分量作为伪观测值联合伪距观测值建立抗差卡尔曼滤波器约束滤波位置解；采用相位平滑伪距的方法来提高伪距观测值的精度，并利用多普勒观测值对接收机的速度和方向进行了约束，联合伪距和速度伪观测值建立抗差卡尔曼滤波器进行实时动态解算。结果表明：该方法可以保证低成本接收机的快速、可靠定位，开阔环境下基本达到了亚米级的定位精度，可以保证2米以内的可靠定位；复杂环境下，也基本可以保证5m以内的定位精度。

Description

基于速度约束的低成本接收机平滑RTD算法 技术领域
本发明涉及一种基于速度约束的低成本接收机平滑RTD技术，属于GNSS定位与导航技术领域。
背景技术
我国当前城镇化水平已达到60％，经济发展与城市规模的扩大使得大众导航已成为GNSS(Global Navigation Satellite System全球导航卫星系统)应用的主要增长点。对于传统测绘行业而言，测量型接收机价格昂贵且体积偏大，限制了其在大部分民用领域的发展。因此，成本低、体积小的GNSS导航设备成为了大众导航发展的关键所在。
国内外很多学者都对低成本接收机的RTK(Real-time kinematic，载波相位差分技术)定位做了分析，有实验表明，采用方差分量估计的方法确定低成本接收机伪距和载波相位的方差和协方差，可以保证RTK厘米级的定位精度；也有其他学者基于GPS+BDS(GPS：Global Positioning System，BDS：BeiDou Navigation Satellite System)双系统，利用低成本单频螺旋天线获得厘米级定位；这极大地满足了无人机、精密农业及机器人制导等行业的需求。值得指出的是，以上研究成果均在开阔环境下获得的。在城镇复杂环境下，由于观测卫星遮挡严重，可见卫星数不多且卫星可视并不连续，导致载波相位频繁出现周跳或缺失等问题，厘米级RTK定位困难，定位的连续性无法得到保证。而事实上，对于一些民用领域而言，用户可能不需要厘米级甚至毫米级的定位精度，如位置服务(LBS，Location Based Service)等，而是更加关注GNSS定位的连续性、可靠性以及对环境的适应性。因此，本发明在保证定位连续性和环境适应性的前提下，提供给用户亚米级、米级可靠定位。
发明内容
因此，本发明从实用价值方面出发，考虑到载波相位观测值在复杂环境下存在一定的问题，因而采用RTD(Real Time Differential实时动态码差分)定位模式，以保证定位的连续性。但是鉴于伪距的观测噪声较大,且易受多路径效应等误差的影响，因此本发明在保证载波相位质量可靠的情况下，采用相位平滑伪距的方法来提高伪距观测值精度，并采用抗差M-LS滤波消除观测值粗差对滤波解的影响，以保证定位的可靠性。该发明的技术方案如下：
基于速度约束的低成本接收机平滑RTD算法，包括如下步骤：
步骤1)，多普勒测速；
多普勒频移观测量表征卫星与GPS接收机天线相对运动所造成的多普勒效应的大小，亦即载波相位变化率的瞬时观测值。
GPS伪距观测方程如下：
Figure PCTCN2018079118-appb-000001
其中：
Figure PCTCN2018079118-appb-000002
表示伪距观测值，下标m表示接收机，上标s表示卫星，ρ表示卫星与接收机之间的几何距离，
Figure PCTCN2018079118-appb-000003
表示接收机钟差等效距离，
Figure PCTCN2018079118-appb-000004
表示卫星钟差等效距离，I表示电离层延迟，T表示对流层延迟，ε表示其他未顾及的误差项；
将对流层延迟和电离层延迟合并为一项，对(1)式中站心距ρ进行线性化并取全微分：
Figure PCTCN2018079118-appb-000005
其中：
Figure PCTCN2018079118-appb-000006
指的是伪距的全微分，(X m,Y m,Z m)为测站坐标，(δX m,δY m,δZ m)为测站坐标的全微分，(X s,Y s,Z s)为卫星空间坐标，(δX s,δY s,δZ s)为卫星空间坐标的全微分，
Figure PCTCN2018079118-appb-000007
为接收机钟差的全微分，
Figure PCTCN2018079118-appb-000008
为卫星钟差的全微分，δΔ为大气延迟项全微分；
对(2)式两边除以时间并取零极限：
Figure PCTCN2018079118-appb-000009
其中：
Figure PCTCN2018079118-appb-000010
为伪距变化率；
Figure PCTCN2018079118-appb-000011
为测站的三维速度；
Figure PCTCN2018079118-appb-000012
为卫星的三维速度；
Figure PCTCN2018079118-appb-000013
为接收机钟漂；
Figure PCTCN2018079118-appb-000014
为卫星钟漂；
Figure PCTCN2018079118-appb-000015
为大气延迟变化率；
Figure PCTCN2018079118-appb-000016
为其他误差项；
上述推导了伪距率的测速方程，伪距率
Figure PCTCN2018079118-appb-000017
与多普勒观测值D有如下关系：
Figure PCTCN2018079118-appb-000018
其中：λ指的是波长。
对于(3)式，测站的三维位置可以通过伪距单点定位求解，假定接收机位置误差为10m，对于测速精度的影响约为2mm；卫星的三维速度可利用基于导航卫星位置序列的数值差分法 求解；卫星钟漂可以通过某一段时间内的卫星钟差变化率获得；本发明忽略了大气延迟变化率的影响。
步骤2)，基于速度约束的平滑RTD算法；
第j颗卫星伪距差分观测方程可表示如下：
Figure PCTCN2018079118-appb-000019
其中：
Figure PCTCN2018079118-appb-000020
为双差算子；P为是经载波相位平滑后的伪距观测值；上标i、j分别为参考星和非参考星；下标m、n分别为基准站和流动站；ρ为卫星至接收机间几何距离；T为对流层延迟；I为电离层延迟；ε为观测噪声及多路径等残留误差；
单历元GPS+BDS观测方程可表示如下：
V＝BX-L     (6)
其中：
Figure PCTCN2018079118-appb-000021
Figure PCTCN2018079118-appb-000022
Figure PCTCN2018079118-appb-000023
Figure PCTCN2018079118-appb-000024
G代表GPS系统，C代表北斗系统，i表示参考星，j、k表示非参考星；V指的是观测残差，其中后三项为速度项的观测残差，其余为伪距观测残差；l、m、n指的是卫星至接收机间几何距离的泰勒级数一阶展开项；X为待估参数向量，其中前三项为位置改正数，后三项为速度改正数；L为观测值向量；
在上述模型中，本发明采用速度伪观测值来约束待估参数，速度伪观测值方程如下：
Figure PCTCN2018079118-appb-000025
其中：Y、Z方向速度约束方程同上，
Figure PCTCN2018079118-appb-000026
为待估参数，
Figure PCTCN2018079118-appb-000027
代表速度伪观测值，是一个先验值，可以通过步骤1)中多普勒测速方程获得。
有益效果：采用本发明所提出的技术手段，可以保证定位的连续性和可靠性，避免了在 城市峡谷等复杂环境下无法定位的难题。同时，本发明所采用的导航设备极大的降低了用户的成本，方便用户携带，具有很大的实用价值。本发明可以保证低成本接收机的快速、可靠定位，开阔环境下基本达到了亚米级的定位精度，可以保证2米以内的可靠定位；复杂环境下，也基本可以保证5m以内的定位精度。
附图说明
图1为本发明接收机与Ublox M8T模块天线相对位置图；
图2本发明开阔环境静态条件下N、E方向的定位精度图；
图3本发明开阔环境静态条件下信噪比；
图4本发明开阔环境动态条件下路线轨迹图；
图5本发明开阔环境动态条件下N、E方向的定位精度图；
图6本发明开阔环境动态条件下信噪比；
图7本发明复杂环境动态条件下路线轨迹图；
图8本发明复杂环境动态条件下N、E方向的定位精度图；
图9本发明复杂环境动态条件下信噪比
图10本发明实际道路动态条件下路线轨迹图；
图11本发明实际道路动态条件下信噪比；
图12本发明GPS+BDS卫星数随历元变化图；
图13本发明实际道路动态条件下卫星可视图；
图14本发明实际道路动态条件下N、E方向的定位精度图；
图15为本发明基于速度约束的低成本接收机平滑RTD算法流程图。
具体实施方式
下面结合附图对本发明作更进一步的说明。
基于速度约束的低成本接收机平滑RTD算法，首先利用多普勒观测值求解速度分量；然后利用已获得的速度分量作为伪观测值联合伪距观测值建立抗差卡尔曼滤波器约束滤波位置解。包括入下具体步骤：
步骤1)，多普勒观测值求解速度分量，公式推导如下：
多普勒频移观测量表征卫星与GPS接收机天线相对运动所造成的多普勒效应的大小，亦即载波相位变化率的瞬时观测值。
GPS伪距观测方程如下：
Figure PCTCN2018079118-appb-000028
其中：
Figure PCTCN2018079118-appb-000029
表示伪距观测值，下标m表示接收机，上标s表示卫星，ρ表示卫星与接收机之间的几何距离，
Figure PCTCN2018079118-appb-000030
表示接收机钟差等效距离，
Figure PCTCN2018079118-appb-000031
表示卫星钟差等效距离，I表示电离层延迟，T表示对流层延迟，ε表示其他未顾及的误差项。
为讨论方便，将对流层延迟和电离层延迟合并为一项，对(1)式中站心距ρ进行线性化并取全微分：
Figure PCTCN2018079118-appb-000032
其中：
Figure PCTCN2018079118-appb-000033
指的是伪距的全微分，(X m,Y m,Z m)为测站坐标，(δX m,δY m,δZ m)为测站坐标的全微分，(X s,Y s,Z s)为卫星空间坐标，(δX s,δY s,δZ s)为卫星空间坐标的全微分，
Figure PCTCN2018079118-appb-000034
为接收机钟差的全微分，
Figure PCTCN2018079118-appb-000035
为卫星钟差的全微分，δΔ为大气延迟项全微分。
对(2)式两边除以时间并取零极限：
Figure PCTCN2018079118-appb-000036
其中：
Figure PCTCN2018079118-appb-000037
为伪距变化率；
Figure PCTCN2018079118-appb-000038
为测站的三维速度；
Figure PCTCN2018079118-appb-000039
为卫星的三维速度；
Figure PCTCN2018079118-appb-000040
为接收机钟漂；
Figure PCTCN2018079118-appb-000041
为卫星钟漂；
Figure PCTCN2018079118-appb-000042
为大气延迟变化率；
Figure PCTCN2018079118-appb-000043
为其他误差项。
上述推导了伪距率的测速方程，伪距率
Figure PCTCN2018079118-appb-000044
与多普勒观测值D有如下关系：
Figure PCTCN2018079118-appb-000045
对于(3)式，测站的三维位置可以通过伪距单点定位求解，假定接收机位置误差为10m，对于测速精度的影响约为2mm；卫星的三维速度可利用基于导航卫星位置序列的数值差分法求解；卫星钟漂可以通过某一段时间内的卫星钟差变化率获得；本发明忽略了大气延迟变化率的影响。
以上测速方程的推导主要是用于求解接收机的速度，为伪距差分提供速度伪观测值以约束位置解。
步骤2)，基于速度约束的平滑RTD算法
第j颗卫星伪距差分观测方程可表示如下：
Figure PCTCN2018079118-appb-000046
其中：
Figure PCTCN2018079118-appb-000047
为双差算子；P为是经载波相位平滑后的伪距观测值；上标i、j分别为参考星和非参考星；下标m、n分别为基准站和流动站；ρ为卫星至接收机间几何距离；T为对流层延迟；I为电离层延迟；ε为观测噪声及多路径等残留误差；
单历元GPS+BDS观测方程可表示如下：
V＝BX-L     (6)
其中：
Figure PCTCN2018079118-appb-000048
Figure PCTCN2018079118-appb-000049
Figure PCTCN2018079118-appb-000050
Figure PCTCN2018079118-appb-000051
G代表GPS系统，C代表北斗系统，i表示参考星，j、k表示非参考星；V指的是观测残差，其中后三项为速度项的观测残差，其余为伪距观测残差；l、m、n指的是卫星至接收机间几何距离的泰勒级数一阶展开项；X为待估参数向量，其中前三项为位置改正数，后三项为速度改正数；L为观测值向量。
在上述模型中，本发明采用速度伪观测值来约束待估参数，速度伪观测值方程如下：
Figure PCTCN2018079118-appb-000052
其中：Y、Z方向速度约束方程同上，
Figure PCTCN2018079118-appb-000053
为待估参数，
Figure PCTCN2018079118-appb-000054
代表速度伪观测值，是一个先验值，可以通过步骤1)中多普勒测速方程获得。
本实施例中，采用普通陶瓷贴片天线，模块为U-blox M8T数据采样率为1s，截止高度角为12°。以中海达H32接收机同步采集了RTK数据，作为检验参考值，U-blox M8T模块与中海达H32接收机放置关系如图1如所示。实验对比分析了2017年10月4个不同时段的GPS+BDS数据(开阔环境下的静态、行人动态，复杂环境下的行人动态以及实际道路条件下的车载动态)
1)、开阔环境下静态测试
图2和图3分别展示了开阔环境静态条件下的平面定位精度和信噪比，静态坐标参考值取中海达H32接收机RTK固定解。从图3中可以看出，开阔环境下卫星的信噪比均优于30，信号质量较好，这也从侧面保证了平面定位精度。
表1对开阔环境下的平面定位结果进行了统计分析，RMS(root meam square均方根误差)对一组测量中的特大或特小误差反映非常敏感，可以很好反映测量的精密度。从表1中可以看出，平面方向RMS仅为0.69m，平面精度95.4％优于1m，可以保证2m以内的定位精度。
2)、开阔环境下的动态测试
图4是在东南大学中心楼楼顶采集的开阔环境下的路线轨迹图，白色为RTK固定解，为坐标参考值，黑色为本发明计算得到的坐标解,图5和图6分别给出了开阔环境动态条件下平面定位精度以及信噪比，表2对动态条件下平面结果进行了统计分析。
图6中的历元数目和图5的平面点位个数不一致，这是由于在实测环境下接收机经过一栋房屋导致信号失锁(图4)造成的，即上述平面定位精度都是与RTK固定解相比较的结果。
从图6中可以看出动态条件下，低成本接收机接收的信号质量要次于静态条件，这也与平面的定位结果相互印证，但从表2中可以看到，动态条件下优于0.5m的平面精度相比静态条件要更好，这可能是与数据采集的长度有关。从表2可以看出，动态条件下RMS仅次于静态条件，为0.77m，平面可以保证2m以内的可靠定位。
3)、复杂环境下动态测试
图7是2017年10月18日在东南大学操场采集的复杂环境动态条件下的路线轨迹图，操场外围有枝叶繁茂的树木和高楼的遮挡，白色为RTK固定解，为坐标参考值，黑色为本发明计算得到的坐标解，图8和图9分别给出了复杂环境动态条件下平面定位精度以及信噪比。图9中历元数目与图8中平面点位个数不一致同样也是由于信号失锁导致。相比于图6，复杂环境下低成本接收机信号质量更差。
表3统计了复杂环境动态条件下的平面定位精度，平面方向RMS为1.48，平面定位精度33.6％优于1m，但可以保证3米以内的定位精度。
4)、实际道路条件下车载动态测试
图10为2017年10月23日在实际道路条件下车载动态轨迹图，黑色为本发明计算得到的坐标解，白色为坐标参考值。坐标参考值是利用南京市计量监督检测院GNSS/INS融合的北斗终端动态检测系统(简称检测车)采集的实际道路条件下GNSS数据，通过动态检测系统的事后解(事后解算精度平面优于1cm)获得。值得注意的是，利用低成本接收机接收的 数据信号经过了动态检测系统的测量型天线，数据信号质量较好。但从图11显示的卫星信噪比图中可以看出，在很多历元，卫星信号质量仍然不佳，结合图12所示的卫星数目的频繁变化可知，这是由于在城市峡谷等复杂环境下，道路两旁树木茂密，高楼林立，导致卫星信号遮挡严重，多路径效应明显增强。尤其是在第1900历元左右，检测车由于行驶至东南大学校园，道路两旁树木茂密，出现了如图13中所示的卫星可视图，卫星结构较差，导致最终的平面定位结果也有较大偏移。结合图14所示的实际道路条件下的N、E方向的定位精度图可以发现，在某些遮挡严重、卫星结构差的历元，平面会出现7米左右的定位偏差，大部分历元还是可以5米以内的可靠定位。
从表4中的统计结果可以明显看出，平面方向RMS为2.47m，这是由于部分历元观测环境差，定位误差偏大导致的，平面方向仍可以保证93.0％优于5m的定位精度。
表1
Figure PCTCN2018079118-appb-000055
表2
Figure PCTCN2018079118-appb-000056
表3
Figure PCTCN2018079118-appb-000057
表4
Figure PCTCN2018079118-appb-000058
其中：RMS(root meam square)指的是均方根值；N指的是北方向坐标误差；E指的是东方向的坐标偏差。
以上所述仅是本发明所包含的测速和速度约束两个主要方面，抗差滤波由于目前较为成 熟，不属于本发明的重点描述的方向。应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。

Claims (2)

  1. 基于速度约束的低成本接收机平滑RTD算法，其特征在于：首先利用多普勒观测值求解速度分量；然后利用已获得的速度分量作为伪观测值联合伪距观测值建立抗差卡尔曼滤波器约束滤波位置解。
  2. 根据权利要求1所述的基于速度约束的低成本接收机平滑RTD算法，其特征为：包括如下步骤：
    步骤1)，多普勒测速；
    多普勒频移观测量表征卫星与GPS接收机天线相对运动所造成的多普勒效应的大小，亦即载波相位变化率的瞬时观测值。
    GPS伪距观测方程如下：
    Figure PCTCN2018079118-appb-100001
    其中：
    Figure PCTCN2018079118-appb-100002
    表示伪距观测值，下标m表示接收机，上标s表示卫星，ρ表示卫星与接收机之间的几何距离，
    Figure PCTCN2018079118-appb-100003
    表示接收机钟差等效距离，
    Figure PCTCN2018079118-appb-100004
    表示卫星钟差等效距离，I表示电离层延迟，T表示对流层延迟，ε表示其他未顾及的误差项；
    将对流层延迟和电离层延迟合并为一项，对(1)式中站心距ρ进行线性化并取全微分：
    Figure PCTCN2018079118-appb-100005
    其中：
    Figure PCTCN2018079118-appb-100006
    指的是伪距的全微分，(X m,Y m,Z m)为测站坐标，(δX m,δY m,δZ m)为测站坐标的全微分，(X s,Y s,Z s)为卫星空间坐标，(δX s,δY s,δZ s)为卫星空间坐标的全微分，
    Figure PCTCN2018079118-appb-100007
    为接收机钟差的全微分，
    Figure PCTCN2018079118-appb-100008
    为卫星钟差的全微分，δΔ为大气延迟项全微分；
    对(2)式两边除以时间并取零极限：
    Figure PCTCN2018079118-appb-100009
    其中：
    Figure PCTCN2018079118-appb-100010
    为伪距变化率；
    Figure PCTCN2018079118-appb-100011
    为测站的三维速度；
    Figure PCTCN2018079118-appb-100012
    为卫星的三维速度；
    Figure PCTCN2018079118-appb-100013
    为接收机钟漂；
    Figure PCTCN2018079118-appb-100014
    为卫星钟漂；
    Figure PCTCN2018079118-appb-100015
    为大气延迟变化率；
    Figure PCTCN2018079118-appb-100016
    为其他误差项；
    上述推导了伪距率的测速方程，伪距率
    Figure PCTCN2018079118-appb-100017
    与多普勒观测值D有如下关系：
    Figure PCTCN2018079118-appb-100018
    对于(3)式，测站的三维位置可以通过伪距单点定位求解，假定接收机位置误差为10m，对于测速精度的影响约为2mm；卫星的三维速度可利用基于导航卫星位置序列的数值差分法求解；卫星钟漂可以通过某一段时间内的卫星钟差变化率获得；忽略了大气延迟变化率的影响；
    步骤2)，基于速度约束的平滑RTD算法；
    第j颗卫星伪距差分观测方程可表示如下：
    Figure PCTCN2018079118-appb-100019
    其中：
    Figure PCTCN2018079118-appb-100020
    为双差算子；P为是经载波相位平滑后的伪距观测值；上标i、j分别为参考星和非参考星；下标m、n分别为基准站和流动站；ρ为卫星至接收机间几何距离；T为对流层延迟；I为电离层延迟；ε为观测噪声及多路径等残留误差；
    单历元GPS+BDS观测方程可表示如下：
    V＝BX-L  (6)
    其中：
    Figure PCTCN2018079118-appb-100021
    Figure PCTCN2018079118-appb-100022
    Figure PCTCN2018079118-appb-100023
    Figure PCTCN2018079118-appb-100024
    G代表GPS系统，C代表北斗系统，i表示参考星，j、k表示非参考星；V指的是观测残差，其中后三项为速度项的观测残差，其余为伪距观测残差；l、m、n指的是卫星至接收机间几何距离的泰勒级数一阶展开项；X为待估参数向量，其中前三项为位置改正数，后三项为速度改正数；L为观测值向量；
    在上述模型中，本发明采用速度伪观测值来约束待估参数，速度伪观测值方程如下：
    Figure PCTCN2018079118-appb-100025
    其中：Y、Z方向速度约束方程同上，
    Figure PCTCN2018079118-appb-100026
    为待估参数，
    Figure PCTCN2018079118-appb-100027
    代表速度伪观测值，是一个先验值，可以通过步骤1)中多普勒测速方程获得。
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