CN115616637A - A Navigation and Positioning Method for Urban Complex Environment Based on 3D Grid Multipath Modeling - Google Patents

A Navigation and Positioning Method for Urban Complex Environment Based on 3D Grid Multipath Modeling Download PDF

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CN115616637A
CN115616637A CN202211612232.3A CN202211612232A CN115616637A CN 115616637 A CN115616637 A CN 115616637A CN 202211612232 A CN202211612232 A CN 202211612232A CN 115616637 A CN115616637 A CN 115616637A
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grid
multipath
model
value
multipath error
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CN115616637B (en
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孙蕊
盛琪
魏华波
吉天翊
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • 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
    • G01S19/22—Multipath-related issues
    • 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

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Abstract

The invention provides a navigation and positioning method for an urban complex environment based on three-dimensional grid multipath modeling, which comprises the following steps: step 1, constructing a three-dimensional grid model of a region, comprising: constructing a GNSS training data set; constructing a regional three-dimensional grid layout; carrying out multi-path error modeling based on random forests one by one grid layer; step 2, calling the regional three-dimensional grid model, comprising: constructing and traversing a GNSS test data set; matching the prior positions of the test samples to a corresponding grid layer, calling a multipath error model and judging the usability of the multipath error model; and obtaining a corrected positioning result. The invention fully considers the reflection environments at different elevations, and improves the positioning performance in rugged road sections, complex interchange environments and unmanned aerial vehicle application scenes; multipath errors caused by NLOS and MI are modeled and predicted as a whole, so that the problem of neglecting some NLOS or MI does not exist.

Description

一种基于三维格网多径建模的城市复杂环境导航定位方法A Navigation and Positioning Method for Urban Complex Environment Based on 3D Grid Multipath Modeling

技术领域technical field

本发明涉及一种城市复杂环境导航定位方法，特别是一种基于三维格网多径建模的城市复杂环境导航定位方法。The invention relates to a navigation and positioning method for a complex urban environment, in particular to a navigation and positioning method for a complex urban environment based on three-dimensional grid multipath modeling.

背景技术Background technique

在城市复杂环境中，GNSS（全球导航卫星系统，Global Navigation SatelliteSystem，GNSS）信号易被高大建筑物遮挡、反射产生MI（多路径干扰，MultipathInterference，MI）和NLOS（非视距接收，Non-Light-of-Sight，NLOS），无法通过差分消除。GNSS数据质量严重影响其定位结果，而在日常生活、生产对导航系统的应用场景中，典型城市复杂环境又占据着相当大的比例。因此，有必要在城市复杂环境这种特殊区域下，修正GNSS的观测数据的多径误差，从而提高其性能。目前对城市复杂环境下的多径干扰问题有三种解决思路：通过信号处理检测干扰分量、通过天线设计抑制反射信号和基于观测值建模的方法。In the complex urban environment, GNSS (Global Navigation Satellite System, Global Navigation Satellite System, GNSS) signals are easily blocked by tall buildings and reflected to produce MI (Multipath Interference, MI) and NLOS (Non-Line-of-Sight Reception, Non-Light -of-Sight, NLOS), which cannot be eliminated by differential. The quality of GNSS data seriously affects its positioning results, and in the application scenarios of daily life and production to navigation systems, typical urban complex environments occupy a considerable proportion. Therefore, it is necessary to correct the multipath error of GNSS observation data in the special area of urban complex environment, so as to improve its performance. At present, there are three solutions to the problem of multipath interference in complex urban environments: detecting interference components through signal processing, suppressing reflected signals through antenna design, and modeling based on observations.

信号处理主要包含硬件层面的相关器设计方法，以及基于软硬件结合的信号参数估计方法，但是必须同时接收到直射与反射信号才能发挥应用，无法处理仅含NLOS的情况。天线设计方法包括使用扼流圈天线、右旋极化天线、双极化天线以及多天线阵列等。但基于天线设计的方法成本高昂且天线体积庞大，不适用于城市复杂环境下移动载体的定位导航且无法排除来自城市中高楼等障碍物反射的高仰角反射信号。Signal processing mainly includes the correlator design method at the hardware level, and the signal parameter estimation method based on the combination of software and hardware, but the direct and reflected signals must be received at the same time to be able to be applied, and it cannot handle the case of only NLOS. Antenna design methods include the use of choke coil antennas, right-hand polarized antennas, dual-polarized antennas, and multi-antenna arrays. However, the method based on antenna design is expensive and the antenna is bulky, which is not suitable for positioning and navigation of mobile carriers in complex urban environments and cannot exclude high-elevation angle reflection signals reflected from obstacles such as tall buildings in the city.

基于观测值建模方法的思路有借助城市3D地图辅助、借助机器学习挖掘观测值与多径误差的联系从而进行信号分类等。著名的阴影匹配方法使用3D城市模型辅助模拟各卫星在各个候选位置处的可见性，从而匹配最佳候选位置。将利用3D地图来考虑城市建筑物布置的不确定性模型用于城市峡谷导航，能够将北向最大误差从13m降低到2m。蒋荣设计制作了一种简易高效的3D数字地图，并基于此地图设计了一种卫星选星算法，来剔除明显的非视距传播的卫星信号，通过提高观测数据的质量来提高伪距观测量的精度，但卫星数量减少导致了位置精度因子（Position Dilution of Precision，PDOP）下降，且城市环境中可用卫星数量本就不足，选星算法将导致缺星现象更加严重。这种利用城市3D地图辅助的方法虽然缓解了NLOS的影响，但接收信号的判定极度依赖城市3D模型的精度，而高精度的3D模型又会导致解算的时间成本上升，无法做到实时定位，且无法应对动态障碍物引起的多径效应。机器学习能够对所接收的卫星信号进行分类，通过支持向量机（Support VectorMachines，SVM）学习城市峡谷内GNSS原始观测量的特征与卫星信号接收类型的联系，以利用前者对后者进行预测，准确率可达75%左右；将输入特征选取为卫星仰角以及双极化天线两信道间的信号强度差，利用决策树来训练GNSS信号分类器，分类准确率可达99%。基于机器学习的信号分类方法通常将预测的NLOS信号剔除，这将导致城市复杂环境本就存在的缺星现象更加严重。The ideas based on the observation value modeling method include the assistance of urban 3D maps, and the use of machine learning to mine the relationship between observation values and multipath errors to perform signal classification. The well-known shadow matching method uses a 3D city model to aid in simulating the visibility of each satellite at each candidate location to match the best candidate. Using 3D maps to consider the uncertainty model of urban building layout is used for urban canyon navigation, which can reduce the maximum error in the north direction from 13m to 2m. Jiang Rong designed and produced a simple and efficient 3D digital map, and based on this map, designed a satellite selection algorithm to eliminate the obvious non-line-of-sight satellite signals, and improve the pseudo-range observation by improving the quality of observation data. However, the decrease in the number of satellites leads to a decrease in the Position Dilution of Precision (PDOP), and the number of available satellites in urban environments is insufficient. The star selection algorithm will lead to a more serious lack of stars. Although this method of using urban 3D map assistance alleviates the impact of NLOS, the judgment of the received signal is extremely dependent on the accuracy of the urban 3D model, and the high-precision 3D model will lead to an increase in the time cost of the solution, making it impossible to achieve real-time positioning. , and cannot cope with the multipath effect caused by dynamic obstacles. Machine learning can classify the received satellite signals, and learn the relationship between the characteristics of GNSS raw observations in urban canyons and the type of satellite signal reception through Support Vector Machines (SVM), so as to use the former to predict the latter, accurately The rate can reach about 75%; the input feature is selected as the satellite elevation angle and the signal strength difference between the two channels of the dual-polarized antenna, and the decision tree is used to train the GNSS signal classifier, and the classification accuracy can reach 99%. The signal classification method based on machine learning usually removes the predicted NLOS signal, which will lead to a more serious lack of stars that already exists in the complex urban environment.

综上所述，GNSS能够为用户提供定位、导航、授时（Positioning, Navigation andTiming, PNT）信息，其精度至关重要。然而在城市峡谷环境下，密集高大建筑物对GNSS信号的遮挡和反射造成了严重的多径干扰（MI）和非视距接收（NLOS），GNSS信号质量下降导致定位精度大幅降低。现有技术具有如下缺陷：To sum up, GNSS can provide users with positioning, navigation and timing (Positioning, Navigation and Timing, PNT) information, and its accuracy is very important. However, in the urban canyon environment, the occlusion and reflection of GNSS signals by dense tall buildings cause serious multipath interference (MI) and non-line-of-sight reception (NLOS), and the degradation of GNSS signal quality leads to a significant decrease in positioning accuracy. Prior art has following defective:

a)现有的GNSS观测数据平面建模方法无法对不同高程的用户进行精确修正。由于在崎岖不平路段以及复杂立交环境下，同一地点的不同高程上具有不同的反射环境。现有的对GNSS信号进行区域平面格网划分建模的导航定位方法将同一地点不同高程的所有用户投影到二维平面，用同一个多径预测模型进行多径误差修正，无法对不同高程的行人、车辆进行精确定位，也无法应对无人机应用场景下的精确定位情况。a) Existing planar modeling methods for GNSS observation data cannot accurately correct users at different elevations. Due to the uneven road section and complex interchange environment, the same site has different reflection environments at different elevations. The existing navigation and positioning method for regional plane grid division and modeling of GNSS signals projects all users at the same location and different elevations onto a two-dimensional plane, and uses the same multipath prediction model for multipath error correction, which cannot be used for different elevations. The precise positioning of pedestrians and vehicles cannot cope with the precise positioning of UAV application scenarios.

b)现有的信号处理方法必须同时接收到直射与反射信号才能使用，无法应对仅含NLOS信号的情况；基于天线设计的方法无法排除城市中高楼等障碍物反射的高仰角NLOS/MI。b) Existing signal processing methods must receive direct and reflected signals at the same time, and cannot cope with the situation that only contains NLOS signals; the method based on antenna design cannot exclude high-elevation NLOS/MI reflected by obstacles such as tall buildings in cities.

发明内容Contents of the invention

发明目的：本发明所要解决的技术问题是针对现有技术的不足，提供一种基于三维格网多径建模的城市复杂环境导航定位方法。Purpose of the invention: The technical problem to be solved by the present invention is to provide a navigation and positioning method for urban complex environments based on three-dimensional grid multipath modeling for the deficiencies of the prior art.

为了解决上述技术问题，本发明公开了一种基于三维格网多径建模的城市复杂环境导航定位方法，包括以下步骤：In order to solve the above-mentioned technical problems, the present invention discloses a method for navigation and positioning of urban complex environments based on three-dimensional grid multipath modeling, which includes the following steps:

步骤1，构建区域三维格网模型，包括：Step 1, build a regional 3D grid model, including:

步骤1-1，构建GNSS训练数据集；Step 1-1, construct GNSS training data set;

步骤1-2，构建区域三维格网布局；Step 1-2, constructing the regional three-dimensional grid layout;

步骤1-3，逐个格网层进行基于随机森林的多径误差建模；Steps 1-3, perform multipath error modeling based on random forest layer by grid layer;

步骤2，调用区域三维格网模型，包括：Step 2, calling the regional 3D grid model, including:

步骤2-1，GNSS测试数据集构建与遍历；Step 2-1, GNSS test data set construction and traversal;

步骤2-2，根据各测试样本的先验位置匹配到相应格网层，调用多径误差模型并判定其可用性；Step 2-2, match the corresponding grid layer according to the prior position of each test sample, call the multipath error model and determine its availability;

步骤2-3，得到修正后的定位结果，完成基于三维格网多径建模的城市复杂环境导航定位。In steps 2-3, the corrected positioning result is obtained, and the navigation and positioning of the urban complex environment based on the three-dimensional grid multipath modeling is completed.

有益效果：Beneficial effect:

a) 针对现有二维建模辅助技术无法对不同高程的用户提供精准定位这一问题，本发明进一步做立体延伸，选定高度间隔来划分格网层，以格网层为单位对GNSS信号建模，充分考虑到不同高程上的反射环境，提升在崎岖路段、复杂立交环境以及无人机应用场景下的定位性能。a) Aiming at the problem that the existing two-dimensional modeling auxiliary technology cannot provide accurate positioning for users at different elevations, the present invention further makes a three-dimensional extension, selects height intervals to divide the grid layer, and uses the grid layer as a unit to analyze the GNSS signal Modeling fully takes into account the reflection environment at different elevations, and improves the positioning performance in rugged road sections, complex interchange environments, and UAV application scenarios.

b) 针对信号处理方法无法应对仅含NLOS信号的情况、天线设计方法无法应对高仰角NLOS/MI的问题，本发明将由NLOS和MI引起的多径误差作为一个整体进行建模和预测，故而不存在忽略某类NLOS或MI的问题。b) Aiming at the problem that the signal processing method cannot deal with the situation containing only NLOS signals, and the antenna design method cannot deal with high elevation angle NLOS/MI, the present invention models and predicts the multipath error caused by NLOS and MI as a whole, so it does not There is a problem with ignoring certain classes of NLOS or MI.

附图说明Description of drawings

下面结合附图和具体实施方式对本发明做更进一步的具体说明，本发明的上述和/或其他方面的优点将会变得更加清楚。The advantages of the above and/or other aspects of the present invention will become clearer as the present invention will be further described in detail in conjunction with the accompanying drawings and specific embodiments.

图1为本发明流程示意图。Fig. 1 is a schematic flow chart of the present invention.

图2为六边形格网中心点生成方式示意图。Fig. 2 is a schematic diagram of the generation method of the center point of the hexagonal grid.

图3为六边形格网柱平面投影示意图。Fig. 3 is a schematic diagram of a planar projection of a hexagonal grid column.

图4为回归模型算法示意图。Figure 4 is a schematic diagram of the regression model algorithm.

具体实施方式detailed description

本发明核心内容为一种区域三维格网多径建模辅助的用于城市复杂环境导航定位方法。流程如图1所示。其中，选择的传感器为GNSS接收机（可接收北斗和GNSS信号）和IMU（惯性测量单元，Inertial Measurement Unit，IMU）。一种基于三维格网多径建模的城市复杂环境导航定位方法，包括以下步骤：The core content of the present invention is a regional three-dimensional grid multi-path modeling aided method for navigation and positioning in urban complex environments. The process is shown in Figure 1. Among them, the selected sensors are GNSS receiver (which can receive Beidou and GNSS signals) and IMU (inertial measurement unit, Inertial Measurement Unit, IMU). A method for navigation and positioning in complex urban environments based on three-dimensional grid multipath modeling, comprising the following steps:

步骤1，构建区域三维格网模型，包括：Step 1, build a regional 3D grid model, including:

步骤1-1，构建GNSS训练数据集，具体方法包括：Step 1-1, construct the GNSS training data set, the specific methods include:

在所述城市复杂环境中重复行驶，采集GNSS接收机输出的原始观测量，并从中提取输入特征作为样本；所述输入特征包括：伪距残差

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、载噪比
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、卫星高度角
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和卫星方位角
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，所述样本为：
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；Repeated driving in the complex environment of the city, collecting the original observations output by the GNSS receiver, and extracting input features therefrom as samples; the input features include: pseudorange residuals
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, carrier-to-noise ratio
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, satellite elevation angle
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and satellite azimuth
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, the sample is:
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;

采用多径误差值对样本进行标定，伪距误差值

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表达式为：The sample is calibrated by using the multipath error value, and the pseudorange error value
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The expression is:

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其中，c为真空中的光速，

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和
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为卫星和接收机钟差，
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和
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分别为电离层和对流层延迟中未修正的残差，
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为多路径效应造成的误差；
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对伪距误差影响占极大比例，故将上式视为多径误差；where c is the speed of light in vacuum,
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and
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is the satellite and receiver clock difference,
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and
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are the uncorrected residuals in ionospheric and tropospheric delays, respectively,
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errors due to multipath effects;
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The influence on pseudorange error accounts for a large proportion, so the above formula is regarded as multipath error;

标定完成后，将GNSS接收机解算的先验位置

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纳入训练数据集并与相应历元的样本以及多径误差值对应，构建得到所述训练数据集，其中训练样本表示为：
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。After the calibration is completed, the a priori position calculated by the GNSS receiver
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Incorporate the training data set and correspond to the samples of the corresponding epoch and the multipath error value, and construct the described training data set, wherein the training samples are expressed as:
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.

步骤1-2，构建区域三维格网布局，具体方法包括：Step 1-2, constructing the regional three-dimensional grid layout, the specific methods include:

根据地理信息系统提供的城市区域的地理信息，将所述训练数据集中的位置数据匹配到城市地图中的相应区域，取所述相应区域的最小外包正方形

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为建模区域；所述正方形的一边与ENU坐标系下的
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轴平行，边长为
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米；在所述建模区域上进行平面六边形格网划分；根据建模区域大小以及定位精度，综合设定六边形格网边长
Figure 237660DEST_PATH_IMAGE018
；其中，所述六边形格网边长的下限值
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确定原则为：保证80%以上格网内训练样本数据总量不少于2000个；边长上限值
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确定原则为：保证
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；若所述边长的上下限值相互矛盾，则提高采样率，在城市复杂环境下重新采集GNSS数据；沿正方形的南北向边从端点开始以
Figure 377599DEST_PATH_IMAGE022
的间隔取点作为六边形的中心点，记为
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，其中
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为此边上的取点数量，
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；再从
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出发沿东西向边的方向以
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的长度取点，将所有点记为：
Figure 391394DEST_PATH_IMAGE027
，其中
Figure 322441DEST_PATH_IMAGE028
为正方形一条东西向边上的取点数量，
Figure 171711DEST_PATH_IMAGE029
；According to the geographical information of the urban area provided by the geographic information system, match the location data in the training data set to the corresponding area in the city map, and take the smallest outsourcing square of the corresponding area
Figure 280571DEST_PATH_IMAGE015
is the modeling area; one side of the square and the ENU coordinate system
Figure 74346DEST_PATH_IMAGE016
Axis parallel, side length is
Figure 492689DEST_PATH_IMAGE017
Meters; carry out planar hexagonal grid division on the modeling area; according to the size of the modeling area and positioning accuracy, comprehensively set the side length of the hexagonal grid
Figure 237660DEST_PATH_IMAGE018
; Wherein, the lower limit value of the side length of the hexagonal grid
Figure 766861DEST_PATH_IMAGE019
The determination principle is: ensure that the total number of training sample data in more than 80% of the grid is not less than 2000; the upper limit of the side length
Figure 290508DEST_PATH_IMAGE020
The principle of determination is: guarantee
Figure 660179DEST_PATH_IMAGE021
; If the upper and lower limits of the length of the side are contradictory, then increase the sampling rate, re-gather the GNSS data in the complex environment of the city; start from the end point to
Figure 377599DEST_PATH_IMAGE022
Take the point at the interval as the center point of the hexagon, denoted as
Figure 744381DEST_PATH_IMAGE023
,in
Figure 496437DEST_PATH_IMAGE024
For the number of points on this edge,
Figure 912374DEST_PATH_IMAGE025
; then from
Figure 867823DEST_PATH_IMAGE023
Depart in the direction of the east-west edge to
Figure 269986DEST_PATH_IMAGE026
Take points for the length of , and record all points as:
Figure 391394DEST_PATH_IMAGE027
,in
Figure 322441DEST_PATH_IMAGE028
is the number of points on an east-west side of the square,
Figure 171711DEST_PATH_IMAGE029
;

以

Figure 95673DEST_PATH_IMAGE027
为坐标原点，ENU坐标系下的
Figure 822321DEST_PATH_IMAGE016
轴与
Figure 206160DEST_PATH_IMAGE030
轴为
Figure 651048DEST_PATH_IMAGE031
轴与
Figure 113122DEST_PATH_IMAGE032
轴，将坐标原点作为六边形的中心，并按照选取的六边形边长
Figure 694276DEST_PATH_IMAGE018
，将一个顶点固定在
Figure 852944DEST_PATH_IMAGE032
轴上以此方式在每个坐标系中生成六边形，在整个建模区域上进行密集排布；by
Figure 95673DEST_PATH_IMAGE027
is the coordinate origin, in the ENU coordinate system
Figure 822321DEST_PATH_IMAGE016
axis with
Figure 206160DEST_PATH_IMAGE030
Axis is
Figure 651048DEST_PATH_IMAGE031
axis with
Figure 113122DEST_PATH_IMAGE032
Axis, take the coordinate origin as the center of the hexagon, and follow the selected hexagon side length
Figure 694276DEST_PATH_IMAGE018
, fix a vertex at
Figure 852944DEST_PATH_IMAGE032
In this way, hexagons are generated in each coordinate system on the axis, densely arranged over the entire modeling area;

将上述所得密集排布的

Figure 768816DEST_PATH_IMAGE033
个二维格网在高度方向延伸形成
Figure 50893DEST_PATH_IMAGE033
个格网柱，其中
Figure 502865DEST_PATH_IMAGE034
，每个格网柱高度
Figure 212195DEST_PATH_IMAGE035
的值初始设为100米，在后续步骤中根据实际情况自动更新；以
Figure 349784DEST_PATH_IMAGE036
为间隔，将每个格网柱分为
Figure 435552DEST_PATH_IMAGE037
层，以每个三维格网层为单位进行GNSS信号建模；
Figure 476452DEST_PATH_IMAGE036
的最小值
Figure 356683DEST_PATH_IMAGE038
确定原则为：保证80%以上格网层内训练样本数据总量不少于500个；
Figure 122514DEST_PATH_IMAGE036
的最大值
Figure 231546DEST_PATH_IMAGE039
确定原则为：保证
Figure 641799DEST_PATH_IMAGE040
；若间隔
Figure 207778DEST_PATH_IMAGE036
的最大值和最小值相互矛盾，则提高采样率，在城市环境下重新采集GNSS数据。The above-mentioned densely arranged
Figure 768816DEST_PATH_IMAGE033
A two-dimensional grid is extended in the height direction to form
Figure 50893DEST_PATH_IMAGE033
grid columns, where
Figure 502865DEST_PATH_IMAGE034
, each grid column height
Figure 212195DEST_PATH_IMAGE035
The value of is initially set to 100 meters, and will be automatically updated according to the actual situation in subsequent steps;
Figure 349784DEST_PATH_IMAGE036
As the interval, each grid column is divided into
Figure 435552DEST_PATH_IMAGE037
layer, GNSS signal modeling is carried out in units of each 3D grid layer;
Figure 476452DEST_PATH_IMAGE036
minimum value of
Figure 356683DEST_PATH_IMAGE038
The determination principle is: ensure that the total number of training sample data in more than 80% of the grid layer is not less than 500;
Figure 122514DEST_PATH_IMAGE036
the maximum value of
Figure 231546DEST_PATH_IMAGE039
The principle of determination is: guarantee
Figure 641799DEST_PATH_IMAGE040
; if interval
Figure 207778DEST_PATH_IMAGE036
If the maximum and minimum values are contradictory, increase the sampling rate and re-collect GNSS data in an urban environment.

步骤1-3，逐个格网层进行基于随机森林的多径误差建模，具体方法包括：Steps 1-3, conduct multipath error modeling based on random forest layer by grid layer, the specific methods include:

步骤1-3-1，按照步骤1-2构建的三维格网布局，确定每个训练样本的所属格网层，具体方法包括：Step 1-3-1, according to the three-dimensional grid layout constructed in step 1-2, determine the grid layer to which each training sample belongs, and the specific methods include:

设六边形格网柱平面投影的中心点为

Figure DEST_PATH_IMAGE041
，ENU坐标系下的
Figure 18827DEST_PATH_IMAGE016
轴与
Figure 180819DEST_PATH_IMAGE030
轴分别对应
Figure 694845DEST_PATH_IMAGE031
轴与
Figure 808557DEST_PATH_IMAGE032
轴，取某训练样本的位置为
Figure 158767DEST_PATH_IMAGE042
，判定其是否属于该六边形：Let the center point of the plane projection of the hexagonal grid column be
Figure DEST_PATH_IMAGE041
, in the ENU coordinate system
Figure 18827DEST_PATH_IMAGE016
axis with
Figure 180819DEST_PATH_IMAGE030
Axis corresponds to
Figure 694845DEST_PATH_IMAGE031
axis with
Figure 808557DEST_PATH_IMAGE032
axis, take the position of a training sample as
Figure 158767DEST_PATH_IMAGE042
, to determine whether it belongs to the hexagon:

Figure 639296DEST_PATH_IMAGE043
Figure 639296DEST_PATH_IMAGE043

仅当上述两式都满足时，判定

Figure 24141DEST_PATH_IMAGE042
在格网柱内；对训练数据集的每个训练样本执行此判断，得到各个格网柱的训练数据集，更新每个格网柱高度
Figure 167808DEST_PATH_IMAGE044
，其中
Figure DEST_PATH_IMAGE045
为此格网柱内训练数据集中训练样本的高程最大值，并同时更新格网层数
Figure 192265DEST_PATH_IMAGE046
；再根据训练数据集中各个训练样本的高度数据，将训练样本划分到所属格网层。Only when the above two formulas are satisfied, the judgment
Figure 24141DEST_PATH_IMAGE042
In the grid column; execute this judgment on each training sample of the training data set, get the training data set of each grid column, and update the height of each grid column
Figure 167808DEST_PATH_IMAGE044
,in
Figure DEST_PATH_IMAGE045
For this purpose, the maximum elevation of the training samples in the training data set in the grid column, and update the number of grid layers at the same time
Figure 192265DEST_PATH_IMAGE046
; Then according to the height data of each training sample in the training data set, the training samples are divided into the grid layer to which they belong.

步骤1-3-2，对每个格网层进行基于随机森林的多径误差模型训练，具体方法包括：Step 1-3-2, conduct random forest-based multipath error model training for each grid layer, the specific methods include:

将每个格网层所属的训练样本的集合划分为

Figure 587737DEST_PATH_IMAGE030
个子样本集，先令
Figure 100002_DEST_PATH_IMAGE047
，得到
Figure 545197DEST_PATH_IMAGE048
个子样本集，训练得到
Figure 843454DEST_PATH_IMAGE048
颗回归树，计算回归树输出值均值和平均绝对误差MAE；若MAE<0.05，则取此时的
Figure 178709DEST_PATH_IMAGE030
值，否则
Figure 486193DEST_PATH_IMAGE049
重复迭代；其中回归算法将每个子样本集划分为
Figure 704685DEST_PATH_IMAGE050
个不重叠的区域，再对区域内的每个训练样本求出一个预测结果，找到使残差平方和RSS最小的划分方法，RSS计算方法为：The set of training samples to which each grid layer belongs is divided into
Figure 587737DEST_PATH_IMAGE030
subsample sets, shilling
Figure 100002_DEST_PATH_IMAGE047
,get
Figure 545197DEST_PATH_IMAGE048
sub-sample set, trained to get
Figure 843454DEST_PATH_IMAGE048
A regression tree, calculate the mean value of the regression tree output value and the mean absolute error MAE; if MAE<0.05, take the current
Figure 178709DEST_PATH_IMAGE030
value, otherwise
Figure 486193DEST_PATH_IMAGE049
Repeat iterations; where the regression algorithm divides each subsample set into
Figure 704685DEST_PATH_IMAGE050
A non-overlapping area, and then calculate a prediction result for each training sample in the area, and find the division method that minimizes the residual square sum RSS. The RSS calculation method is:

Figure 455735DEST_PATH_IMAGE051
Figure 455735DEST_PATH_IMAGE051

其中，

Figure 267833DEST_PATH_IMAGE052
为划分出的不重叠的区域，
Figure 628276DEST_PATH_IMAGE053
为第j个区域，区域数量为J，
Figure 842220DEST_PATH_IMAGE054
为第
Figure 498591DEST_PATH_IMAGE055
个训练样本的标签值，
Figure 922619DEST_PATH_IMAGE056
表示第j个区域的预测值；内层求和是将该区域内所有训练样本真实值和预测值的差值平方进行加和，外层求和是遍历所有划分的区域；最小化RSS的过程采用递归二分方法：在划分区域时，根据下式进行特征选择和节点分裂，直至无法分裂：in,
Figure 267833DEST_PATH_IMAGE052
For the non-overlapping regions divided,
Figure 628276DEST_PATH_IMAGE053
is the jth region, the number of regions is J,
Figure 842220DEST_PATH_IMAGE054
for the first
Figure 498591DEST_PATH_IMAGE055
label values of training samples,
Figure 922619DEST_PATH_IMAGE056
Indicates the predicted value of the jth area; the inner summation is to sum the square of the difference between the true value and the predicted value of all training samples in the area, and the outer summation is to traverse all divided areas; the process of minimizing RSS Using the recursive binary method: when dividing the area, perform feature selection and node splitting according to the following formula until it cannot be split:

Figure 837486DEST_PATH_IMAGE057
Figure 837486DEST_PATH_IMAGE057

其中，

Figure 391089DEST_PATH_IMAGE058
表示切分的维度即输入数据的值，s表示切分点；
Figure 733209DEST_PATH_IMAGE059
和
Figure 503587DEST_PATH_IMAGE060
表示以
Figure 956565DEST_PATH_IMAGE058
为切分维度，以s为切分点划分出的两个区域；in,
Figure 391089DEST_PATH_IMAGE058
Indicates the dimension of segmentation, that is, the value of the input data, and s indicates the segmentation point;
Figure 733209DEST_PATH_IMAGE059
and
Figure 503587DEST_PATH_IMAGE060
expressed by
Figure 956565DEST_PATH_IMAGE058
is the segmentation dimension, two areas divided by s as the segmentation point;

Figure 788778DEST_PATH_IMAGE030
个子样本集以上述方式进行分支，得到回归树模型预测规则，预测结果由下式表示：
Figure 788778DEST_PATH_IMAGE030
The sub-sample sets are branched in the above way, and the prediction rules of the regression tree model are obtained, and the prediction results are expressed by the following formula:

Figure 551067DEST_PATH_IMAGE061
Figure 551067DEST_PATH_IMAGE061

式中，

Figure 559474DEST_PATH_IMAGE062
为回归树模型预测输出，
Figure 566875DEST_PATH_IMAGE063
为输入特征，
Figure 609918DEST_PATH_IMAGE064
；
Figure 277528DEST_PATH_IMAGE065
为回归树模型预测函数，将
Figure 507652DEST_PATH_IMAGE030
个回归树的预测输出取平均值，即作为随机森林输出的多径误差预测值
Figure 194111DEST_PATH_IMAGE066
；
Figure 340927DEST_PATH_IMAGE067
为随机森林训练的多径误差模型的预测函数，则多径误差预测规则为：In the formula,
Figure 559474DEST_PATH_IMAGE062
Predict the output for the regression tree model,
Figure 566875DEST_PATH_IMAGE063
is the input feature,
Figure 609918DEST_PATH_IMAGE064
;
Figure 277528DEST_PATH_IMAGE065
For the prediction function of the regression tree model, the
Figure 507652DEST_PATH_IMAGE030
The predicted output of the regression trees is averaged, which is the multipath error predicted value output by the random forest
Figure 194111DEST_PATH_IMAGE066
;
Figure 340927DEST_PATH_IMAGE067
is the prediction function of the multipath error model trained by random forest, then the multipath error prediction rule is:

Figure 195751DEST_PATH_IMAGE068
Figure 195751DEST_PATH_IMAGE068

由所有格网柱划分而得的格网层总数用

Figure 100002_DEST_PATH_IMAGE069
表示，对每个格网层的训练数据进行建模，得到
Figure 522958DEST_PATH_IMAGE069
个多径误差模型；多径误差模型精度用均方根误差RMSE衡量：The total number of grid layers divided by all grid columns is given by
Figure 100002_DEST_PATH_IMAGE069
Indicates that the training data of each grid layer is modeled to obtain
Figure 522958DEST_PATH_IMAGE069
multipath error model; the accuracy of the multipath error model is measured by the root mean square error RMSE:

Figure 855850DEST_PATH_IMAGE070
Figure 855850DEST_PATH_IMAGE070

其中，

Figure 352779DEST_PATH_IMAGE071
为第
Figure 378504DEST_PATH_IMAGE072
个多径误差模型的均方根误差，
Figure 98067DEST_PATH_IMAGE073
为第
Figure 500229DEST_PATH_IMAGE055
个训练样本的多径误差真实值，
Figure 326365DEST_PATH_IMAGE074
为第
Figure 788571DEST_PATH_IMAGE055
个训练样本的多径误差模型预测值，
Figure 870796DEST_PATH_IMAGE075
为训练样本数量；in,
Figure 352779DEST_PATH_IMAGE071
for the first
Figure 378504DEST_PATH_IMAGE072
The root mean square error of the multipath error model,
Figure 98067DEST_PATH_IMAGE073
for the first
Figure 500229DEST_PATH_IMAGE055
The true value of the multipath error of training samples,
Figure 326365DEST_PATH_IMAGE074
for the first
Figure 788571DEST_PATH_IMAGE055
The multipath error model prediction value of training samples,
Figure 870796DEST_PATH_IMAGE075
is the number of training samples;

精度参数包括：所有格网模型均方根误差的平均值

Figure 561803DEST_PATH_IMAGE076
和标准差
Figure 100002_DEST_PATH_IMAGE077
、第
Figure 475401DEST_PATH_IMAGE072
个格网均方根误差值的标准化处理结果
Figure 108508DEST_PATH_IMAGE078
和比重
Figure 772969DEST_PATH_IMAGE079
，计算方法分别如下所列：Accuracy parameters include: the average of the root mean square errors of all grid models
Figure 561803DEST_PATH_IMAGE076
and standard deviation
Figure 100002_DEST_PATH_IMAGE077
, No.
Figure 475401DEST_PATH_IMAGE072
Standardized processing results of grid root mean square error values
Figure 108508DEST_PATH_IMAGE078
and specific gravity
Figure 772969DEST_PATH_IMAGE079
, the calculation methods are as follows:

Figure 641568DEST_PATH_IMAGE080
Figure 641568DEST_PATH_IMAGE080

Figure 488301DEST_PATH_IMAGE081
Figure 488301DEST_PATH_IMAGE081

Figure 506024DEST_PATH_IMAGE082
Figure 506024DEST_PATH_IMAGE082

Figure 438208DEST_PATH_IMAGE083
Figure 438208DEST_PATH_IMAGE083

其中，

Figure 969552DEST_PATH_IMAGE084
为第
Figure 296891DEST_PATH_IMAGE072
个多径误差模型的均方根误差，
Figure 6221DEST_PATH_IMAGE085
为所有多径误差模型均方根误差的最小值，
Figure 674968DEST_PATH_IMAGE086
为所有多径误差模型均方根误差的最大值。in,
Figure 969552DEST_PATH_IMAGE084
for the first
Figure 296891DEST_PATH_IMAGE072
The root mean square error of the multipath error model,
Figure 6221DEST_PATH_IMAGE085
is the minimum value of the root mean square error of all multipath error models,
Figure 674968DEST_PATH_IMAGE086
is the maximum value of the root mean square error of all multipath error models.

步骤1-3-3，完成区域三维格网模型构建，包括：Step 1-3-3, complete the construction of the regional 3D grid model, including:

计算得到区域三维格网布局、各个格网层的多径误差模型、所述多径误差模型的多径误差预测规则以及各个多径误差模型的精度参数。The regional three-dimensional grid layout, the multipath error models of each grid layer, the multipath error prediction rules of the multipath error models, and the precision parameters of each multipath error model are obtained through calculation.

步骤2，调用区域三维格网模型，包括：Step 2, calling the regional 3D grid model, including:

步骤2-1，GNSS测试数据集构建与遍历，具体方法包括：Step 2-1, GNSS test data set construction and traversal, specific methods include:

从用户GNSS接收机输出的原始观测量中提取测试数据的先验位置

Figure 495157DEST_PATH_IMAGE013
、位置精度因子PDOP、伪距残差、载噪比、卫星高度角和卫星方位角组成测试样本构建测试数据集
Figure 801635DEST_PATH_IMAGE087
；Extract the prior location of the test data from the raw observations output by the user's GNSS receiver
Figure 495157DEST_PATH_IMAGE013
, position precision factor PDOP, pseudorange residual, carrier-to-noise ratio, satellite elevation angle and satellite azimuth angle to form a test sample to construct a test data set
Figure 801635DEST_PATH_IMAGE087
;

测试数据集构建完成后进行遍历，计算以下参数：所有测试样本的位置精度因子PDOP的均值

Figure 72080DEST_PATH_IMAGE088
和标准差
Figure 713277DEST_PATH_IMAGE089
、第
Figure 87888DEST_PATH_IMAGE090
个测试样本PDOP的标准化处理结果
Figure 100002_DEST_PATH_IMAGE091
和比重
Figure 950671DEST_PATH_IMAGE092
，计算方法分别如下所列：After the test data set is constructed, traverse and calculate the following parameters: the mean value of the position factor of precision PDOP of all test samples
Figure 72080DEST_PATH_IMAGE088
and standard deviation
Figure 713277DEST_PATH_IMAGE089
, No.
Figure 87888DEST_PATH_IMAGE090
The normalized processing results of PDOP of test samples
Figure 100002_DEST_PATH_IMAGE091
and specific gravity
Figure 950671DEST_PATH_IMAGE092
, the calculation methods are as follows:

Figure 100002_DEST_PATH_IMAGE093
Figure 100002_DEST_PATH_IMAGE093

Figure 825305DEST_PATH_IMAGE094
Figure 825305DEST_PATH_IMAGE094

Figure 100002_DEST_PATH_IMAGE095
Figure 100002_DEST_PATH_IMAGE095

Figure 140749DEST_PATH_IMAGE096
Figure 140749DEST_PATH_IMAGE096

其中，

Figure 100002_DEST_PATH_IMAGE097
为测试数据样本数量，
Figure 256735DEST_PATH_IMAGE098
为第
Figure 770762DEST_PATH_IMAGE090
个测试样本对应的PDOP，
Figure 992796DEST_PATH_IMAGE099
为所有测试样本PDOP的最小值，
Figure 234683DEST_PATH_IMAGE100
为所有测试样本PDOP的最大值。in,
Figure 100002_DEST_PATH_IMAGE097
is the number of test data samples,
Figure 256735DEST_PATH_IMAGE098
for the first
Figure 770762DEST_PATH_IMAGE090
PDOP corresponding to test samples,
Figure 992796DEST_PATH_IMAGE099
is the minimum value of PDOP for all test samples,
Figure 234683DEST_PATH_IMAGE100
is the maximum value of PDOP of all test samples.

步骤2-2，根据各测试样本的先验位置匹配到相应格网层，调用多径误差模型并判定其可用性，具体方法包括：Step 2-2, match the corresponding grid layer according to the prior position of each test sample, call the multipath error model and determine its availability, the specific methods include:

利用已有的三维格网布局，将测试数据逐个匹配到各自的所属格网层，并调用相应格网层的多径误差模型，随后根据格网层模型精度与测试数据质量，基于平均值和比重进行模型可用性判断；对于某一历元的数据，作如下判定：Using the existing three-dimensional grid layout, match the test data to their respective grid layers one by one, and call the multipath error model of the corresponding grid layer, and then according to the accuracy of the grid layer model and the quality of the test data, based on the average value and The specific gravity is used to judge the usability of the model; for the data of a certain epoch, the following judgment is made:

Figure 449633DEST_PATH_IMAGE101
Figure 834478DEST_PATH_IMAGE102
Figure 449633DEST_PATH_IMAGE101
Figure 834478DEST_PATH_IMAGE102

其中，

Figure 243725DEST_PATH_IMAGE103
为第
Figure 81231DEST_PATH_IMAGE090
个测试数据所属格网对应的多径误差模型的均方根误差值，
Figure 975237DEST_PATH_IMAGE076
为所有多径误差模型均方根误差的平均值，
Figure 982899DEST_PATH_IMAGE098
为第
Figure 546736DEST_PATH_IMAGE090
个测试数据对应历元的PDOP，
Figure 386385DEST_PATH_IMAGE088
为测试数据集中所有样本历元PDOP的平均值；若某一历元数据同时满足两式，则判定其对应的多径误差模型可用，用所述多径误差模型预测多径误差并进行后续修正和最终定位解算，否则进行基于比重的判定如下：in,
Figure 243725DEST_PATH_IMAGE103
for the first
Figure 81231DEST_PATH_IMAGE090
The root mean square error value of the multipath error model corresponding to the grid to which the test data belongs,
Figure 975237DEST_PATH_IMAGE076
is the mean value of the root mean square error of all multipath error models,
Figure 982899DEST_PATH_IMAGE098
for the first
Figure 546736DEST_PATH_IMAGE090
test data corresponding to the PDOP of the epoch,
Figure 386385DEST_PATH_IMAGE088
is the average value of the PDOP of all sample epochs in the test data set; if a certain epoch data satisfies the two formulas at the same time, it is determined that its corresponding multipath error model is available, and the multipath error model is used to predict the multipath error and perform subsequent corrections and the final positioning solution, otherwise the judgment based on the specific gravity is as follows:

Figure 693869DEST_PATH_IMAGE104
Figure 679405DEST_PATH_IMAGE105
Figure 693869DEST_PATH_IMAGE104
Figure 679405DEST_PATH_IMAGE105

其中，

Figure 928990DEST_PATH_IMAGE106
为第
Figure 475509DEST_PATH_IMAGE090
个测试数据的比重，
Figure 602996DEST_PATH_IMAGE107
为预设的比重门限值，若该历元测试样本满足上述不等式，则判定多径误差模型可用从而进行多径预测和修正，否则判定不可用，不进行建模修正。in,
Figure 928990DEST_PATH_IMAGE106
for the first
Figure 475509DEST_PATH_IMAGE090
The proportion of test data,
Figure 602996DEST_PATH_IMAGE107
is the preset proportion threshold value, if the epoch test sample satisfies the above inequality, it is determined that the multipath error model is available for multipath prediction and correction, otherwise it is determined that it is not available, and no modeling correction is performed.

步骤2-3，得到修正后的定位结果，完成基于三维格网多径建模的城市复杂环境导航定位。In steps 2-3, the corrected positioning result is obtained, and the navigation and positioning of the urban complex environment based on the three-dimensional grid multipath modeling is completed.

所述的得到修正后的定位结果，包括：The corrected positioning results include:

假设第

Figure 816940DEST_PATH_IMAGE090
个历元观测伪距为
Figure 112792DEST_PATH_IMAGE108
，所述多径误差模型预测的多径误差值为
Figure 162918DEST_PATH_IMAGE109
，则修正后的伪距为
Figure 812206DEST_PATH_IMAGE110
，依据伪距定位原理利用
Figure 129923DEST_PATH_IMAGE111
代替
Figure 472043DEST_PATH_IMAGE108
，解算修正后的定位解。Assuming the first
Figure 816940DEST_PATH_IMAGE090
The epoch observed pseudorange is
Figure 112792DEST_PATH_IMAGE108
, the multipath error predicted by the multipath error model is
Figure 162918DEST_PATH_IMAGE109
, then the corrected pseudorange is
Figure 812206DEST_PATH_IMAGE110
, according to the principle of pseudo-range positioning using
Figure 129923DEST_PATH_IMAGE111
replace
Figure 472043DEST_PATH_IMAGE108
, solve the corrected positioning solution.

实施例：Example:

如图1所示，本发明分为区域三维格网构建和三维格网模型调用两个部分。利用卫星-城市这一整体环境的时空重复性，用户可调用构建完成的三维格网模型来预测多径误差，从而修正伪距。具体步骤如下：As shown in Fig. 1, the present invention is divided into two parts: regional 3D grid construction and 3D grid model calling. Using the spatio-temporal repeatability of the satellite-city environment as a whole, users can use the completed 3D grid model to predict multipath errors and correct pseudoranges. Specific steps are as follows:

1） 构建区域三维格网模型1) Construct the regional 3D grid model

Figure 878973DEST_PATH_IMAGE112
Figure 878973DEST_PATH_IMAGE112

c为真空中的光速，

Figure 581218DEST_PATH_IMAGE113
和
Figure 504175DEST_PATH_IMAGE114
为卫星和接收机钟差，
Figure 767928DEST_PATH_IMAGE115
和
Figure 41915DEST_PATH_IMAGE116
分别为电离层和对流层延迟中未能修正的残差，
Figure 423218DEST_PATH_IMAGE012
为多路径效应造成的误差。上式中，
Figure 216992DEST_PATH_IMAGE012
对伪距误差影响占极大比例，故将上式视为多径误差，对样本进行标定。 c is the speed of light in vacuum,
Figure 581218DEST_PATH_IMAGE113
and
Figure 504175DEST_PATH_IMAGE114
is the satellite and receiver clock difference,
Figure 767928DEST_PATH_IMAGE115
and
Figure 41915DEST_PATH_IMAGE116
are the uncorrected residuals in ionospheric and tropospheric delays, respectively,
Figure 423218DEST_PATH_IMAGE012
Errors due to multipath effects. In the above formula,
Figure 216992DEST_PATH_IMAGE012
The influence on the pseudorange error accounts for a large proportion, so the above formula is regarded as multipath error, and the sample is calibrated.

标定完成后，对上述步骤构建的GNSS初始训练数据集进行预处理，GNSS接收机解算的先验位置

Figure 635335DEST_PATH_IMAGE013
纳入训练集并与相应历元的样本、多径误差一一对应，构建GNSS训练数据集，其中训练样本为：
Figure 380306DEST_PATH_IMAGE117
。After the calibration is completed, preprocess the GNSS initial training data set constructed in the above steps, and the prior position of the GNSS receiver solution
Figure 635335DEST_PATH_IMAGE013
Include the training set and correspond one-to-one with the samples and multipath errors of the corresponding epoch to construct the GNSS training data set, where the training samples are:
Figure 380306DEST_PATH_IMAGE117
.

第二步，构建区域三维格网布局。地理信息系统（Geographic InformationSystem, GIS）可提供城市区域的地理信息，将GNSS训练数据集中的位置数据匹配到城市地图中的相应区域，取能够将该定位区域包含的最小正方形

Figure 440666DEST_PATH_IMAGE015
为建模区域。该正方形的一边与ENU坐标系下的
Figure 964314DEST_PATH_IMAGE016
轴平行，边长为
Figure 802826DEST_PATH_IMAGE017
米。在此正方形区域上进行平面六边形格网划分。根据建模区域大小以及所需定位精度，综合决定六边形格网边长
Figure 51404DEST_PATH_IMAGE018
。实际应用中，
Figure 394749DEST_PATH_IMAGE018
的值需要进行人为设定。六边形格网边长的下限值
Figure 146804DEST_PATH_IMAGE019
确定原则为：保证80%以上格网内训练样本数据总量不少于2000个；边长上限值
Figure 562742DEST_PATH_IMAGE020
确定原则为：保证
Figure 518191DEST_PATH_IMAGE021
。若上下限值相互矛盾，则需要提高采样率，在城市环境下重新采集GNSS数据进行训练。若人为设定的
Figure 654774DEST_PATH_IMAGE018
值不满足上述要求，则提示错误，需要重新进行设定。选定合适的六边形格网边长
Figure 41762DEST_PATH_IMAGE018
，由于正方形
Figure 238388DEST_PATH_IMAGE015
的一边与ENU坐标系下的
Figure 556499DEST_PATH_IMAGE016
轴平行，如图2所示，沿正方形的南北向边（①边）从端点开始以
Figure 11620DEST_PATH_IMAGE022
的间隔取点作为六边形的中心点，记为
Figure 738268DEST_PATH_IMAGE023
，其中
Figure 856528DEST_PATH_IMAGE024
为此边上的取点数量，
Figure 426049DEST_PATH_IMAGE025
；再从
Figure 904435DEST_PATH_IMAGE023
出发沿正方形的东西向边（②边）的方向以
Figure 496041DEST_PATH_IMAGE026
的长度取点，将所有点记为：The second step is to construct the regional three-dimensional grid layout. Geographic Information System (GIS) can provide geographical information of urban areas, match the location data in the GNSS training data set to the corresponding area in the city map, and take the smallest square that can contain the positioning area
Figure 440666DEST_PATH_IMAGE015
for the modeling area. One side of the square and the ENU coordinate system
Figure 964314DEST_PATH_IMAGE016
Axis parallel, side length is
Figure 802826DEST_PATH_IMAGE017
rice. A planar hexagonal grid is performed on this square area. According to the size of the modeling area and the required positioning accuracy, comprehensively determine the side length of the hexagonal grid
Figure 51404DEST_PATH_IMAGE018
. Practical applications,
Figure 394749DEST_PATH_IMAGE018
The value of needs to be manually set. The lower limit of the side length of the hexagonal grid
Figure 146804DEST_PATH_IMAGE019
The determination principle is: ensure that the total number of training sample data in more than 80% of the grid is not less than 2000; the upper limit of the side length
Figure 562742DEST_PATH_IMAGE020
The principle of determination is: guarantee
Figure 518191DEST_PATH_IMAGE021
. If the upper and lower limits are contradictory, it is necessary to increase the sampling rate and re-collect GNSS data for training in an urban environment. artificially set
Figure 654774DEST_PATH_IMAGE018
If the value does not meet the above requirements, an error will be displayed and it needs to be reset. Choose a suitable hexagonal grid side length
Figure 41762DEST_PATH_IMAGE018
, due to the square
Figure 238388DEST_PATH_IMAGE015
One side and the ENU coordinate system
Figure 556499DEST_PATH_IMAGE016
axes parallel to each other, as shown in Figure 2, along the north-south side (① side) of the square from the end point to
Figure 11620DEST_PATH_IMAGE022
Take the point at the interval as the center point of the hexagon, denoted as
Figure 738268DEST_PATH_IMAGE023
,in
Figure 856528DEST_PATH_IMAGE024
For the number of points on this edge,
Figure 426049DEST_PATH_IMAGE025
; then from
Figure 904435DEST_PATH_IMAGE023
Start along the direction of the east-west side (② side) of the square to
Figure 496041DEST_PATH_IMAGE026
Take points for the length of , and record all points as:

Figure 34470DEST_PATH_IMAGE027
，
Figure 950342DEST_PATH_IMAGE029
Figure 34470DEST_PATH_IMAGE027
,
Figure 950342DEST_PATH_IMAGE029

其中

Figure 124097DEST_PATH_IMAGE028
为正方形一条东西向边上的取点数量。以
Figure 559758DEST_PATH_IMAGE027
为坐标原点，ENU坐标系（东-北-天坐标系ENU， local Cartesian coordinates coordinate system）下的轴与
Figure 518355DEST_PATH_IMAGE030
轴为
Figure 937835DEST_PATH_IMAGE031
轴与
Figure 774335DEST_PATH_IMAGE032
轴，将坐标原点作为六边形的中心，并按照选取的六边形边长
Figure 454715DEST_PATH_IMAGE018
，将一个顶点固定在
Figure 69368DEST_PATH_IMAGE032
轴上，如图3所示。以此方式在每个坐标系中生成六边形，在整个建模区域上进行密集排布。in
Figure 124097DEST_PATH_IMAGE028
Take the number of points on an east-west side of the square. by
Figure 559758DEST_PATH_IMAGE027
is the origin of the coordinates, the axes in the ENU coordinate system (East-North-day coordinate system ENU, local Cartesian coordinates coordinate system) and
Figure 518355DEST_PATH_IMAGE030
Axis is
Figure 937835DEST_PATH_IMAGE031
axis with
Figure 774335DEST_PATH_IMAGE032
Axis, take the coordinate origin as the center of the hexagon, and follow the selected hexagon side length
Figure 454715DEST_PATH_IMAGE018
, fix a vertex at
Figure 69368DEST_PATH_IMAGE032
axis, as shown in Figure 3. In this way hexagons are generated in each coordinate system, densely packed over the entire modeling area.

将上述所得密集排布的

Figure 461297DEST_PATH_IMAGE069
个二维格网在高度方向延伸形成
Figure 350755DEST_PATH_IMAGE069
个格网柱，其中
Figure 744697DEST_PATH_IMAGE118
，并进行分层。每个格网柱高度
Figure 61408DEST_PATH_IMAGE119
的值初始设为100米，在后续步骤中根据实际情况进行自动更新，以
Figure 833578DEST_PATH_IMAGE036
为间隔，将每个格网柱分为
Figure 510416DEST_PATH_IMAGE037
层，以每个三维格网层为单位进行GNSS信号建模。实际应用中，
Figure 40754DEST_PATH_IMAGE036
的值需要根据实际情况和所需精度进行人为设定。
Figure 420045DEST_PATH_IMAGE036
的最小值
Figure 285102DEST_PATH_IMAGE120
确定原则为：保证80%以上格网层内训练样本数据总量不少于500个；最大值
Figure 516363DEST_PATH_IMAGE039
确定原则为：保证
Figure 386362DEST_PATH_IMAGE121
。若上下限值相互矛盾，则需要提高采样率，在城市环境下重新采集GNSS数据进行训练。若人为设定的
Figure 169510DEST_PATH_IMAGE122
值不满足上述要求，则提示错误，需要重新进行设定。The above-mentioned densely arranged
Figure 461297DEST_PATH_IMAGE069
A two-dimensional grid is extended in the height direction to form
Figure 350755DEST_PATH_IMAGE069
grid columns, where
Figure 744697DEST_PATH_IMAGE118
, and layered. height of each grid column
Figure 61408DEST_PATH_IMAGE119
The value of is initially set to 100 meters, and will be automatically updated according to the actual situation in subsequent steps to
Figure 833578DEST_PATH_IMAGE036
As the interval, each grid column is divided into
Figure 510416DEST_PATH_IMAGE037
Layer, GNSS signal modeling is carried out in units of each 3D grid layer. Practical applications,
Figure 40754DEST_PATH_IMAGE036
The value of needs to be manually set according to the actual situation and the required accuracy.
Figure 420045DEST_PATH_IMAGE036
minimum value of
Figure 285102DEST_PATH_IMAGE120
The determination principle is: ensure that the total number of training sample data in more than 80% of the grid layer is not less than 500; the maximum
Figure 516363DEST_PATH_IMAGE039
The principle of determination is: guarantee
Figure 386362DEST_PATH_IMAGE121
. If the upper and lower limits are contradictory, it is necessary to increase the sampling rate and re-collect GNSS data for training in an urban environment. artificially set
Figure 169510DEST_PATH_IMAGE122
If the value does not meet the above requirements, an error will be displayed and it needs to be reset.

第三步，逐个格网层进行基于随机森林的多径误差建模。In the third step, multipath error modeling based on random forest is carried out grid layer by grid layer.

按照步骤二构建的三维格网布局，确定每个训练样本的所属格网层。According to the 3D grid layout constructed in step 2, determine the grid layer to which each training sample belongs.

如图3所示，设六边形格网柱平面投影的中心点为

Figure 272595DEST_PATH_IMAGE041
，ENU坐标系下的
Figure 527121DEST_PATH_IMAGE016
轴与
Figure 766473DEST_PATH_IMAGE030
轴分别对应
Figure 579577DEST_PATH_IMAGE031
轴与
Figure 904379DEST_PATH_IMAGE032
轴，取某训练样本的位置为
Figure 956736DEST_PATH_IMAGE042
，判定其是否属于该六边形：As shown in Figure 3, let the center point of the plane projection of the hexagonal grid column be
Figure 272595DEST_PATH_IMAGE041
, in the ENU coordinate system
Figure 527121DEST_PATH_IMAGE016
axis with
Figure 766473DEST_PATH_IMAGE030
Axis corresponds to
Figure 579577DEST_PATH_IMAGE031
axis with
Figure 904379DEST_PATH_IMAGE032
axis, take the position of a training sample as
Figure 956736DEST_PATH_IMAGE042
, to determine whether it belongs to the hexagon:

Figure 440807DEST_PATH_IMAGE123
Figure 440807DEST_PATH_IMAGE123

仅当两式都满足时，判定

Figure 175545DEST_PATH_IMAGE042
在格网柱内。对训练集的每个样本执行此判断，在得到各个格网柱的训练数据集后，更新每个格网柱高度
Figure 738376DEST_PATH_IMAGE124
，其中
Figure 849551DEST_PATH_IMAGE045
为此格网柱内训练数据高程最大值，并同时更新格网层数
Figure DEST_PATH_IMAGE125
。再根据训练集各个样本的高度数据，将其划分到所属格网层。Only when the two formulas are satisfied, the judgment
Figure 175545DEST_PATH_IMAGE042
Inside the grid column. Perform this judgment for each sample in the training set, and update the height of each grid column after obtaining the training data set for each grid column
Figure 738376DEST_PATH_IMAGE124
,in
Figure 849551DEST_PATH_IMAGE045
For this purpose, the maximum elevation of the training data in the grid column, and update the number of grid layers at the same time
Figure DEST_PATH_IMAGE125
. Then according to the height data of each sample in the training set, it is divided into the grid layer to which it belongs.

如图4所示，对逐个格网层进行基于随机森林的多径误差模型训练。As shown in Figure 4, the random forest-based multipath error model training is performed on each grid layer.

模型训练第一步是将样本集划分为

Figure 250446DEST_PATH_IMAGE030
个子样本集，先令
Figure 47763DEST_PATH_IMAGE047
，得到
Figure 330845DEST_PATH_IMAGE048
个子样本集，训练得到
Figure 245712DEST_PATH_IMAGE048
颗回归树，计算回归树输出值均值和平均绝对误差（Mean Absolute Error,MAE）。若MAE<0.05，则取此时的
Figure 330473DEST_PATH_IMAGE030
值，否则
Figure 672593DEST_PATH_IMAGE049
重复迭代。其中回归算法将每个子样本集划分为多个不重叠的区域，找到使残差平方和RSS最小的划分方法，RSS计算方法为：The first step in model training is to divide the sample set into
Figure 250446DEST_PATH_IMAGE030
subsample sets, shilling
Figure 47763DEST_PATH_IMAGE047
,get
Figure 330845DEST_PATH_IMAGE048
sub-sample set, trained to get
Figure 245712DEST_PATH_IMAGE048
A regression tree is used to calculate the mean value and mean absolute error (Mean Absolute Error, MAE) of the regression tree output value. If MAE<0.05, take the current
Figure 330473DEST_PATH_IMAGE030
value, otherwise
Figure 672593DEST_PATH_IMAGE049
Repeat iterations. The regression algorithm divides each sub-sample set into multiple non-overlapping areas, and finds the division method that minimizes the residual square sum RSS. The RSS calculation method is:

Figure 177393DEST_PATH_IMAGE126
Figure 177393DEST_PATH_IMAGE126

Figure DEST_PATH_IMAGE127
为划分出的多个不重叠的区域，
Figure 719451DEST_PATH_IMAGE128
为第个区域，区域总数为J，
Figure 157255DEST_PATH_IMAGE054
为第
Figure 670276DEST_PATH_IMAGE055
个训练样本的标签值，
Figure 163836DEST_PATH_IMAGE056
表示第j个区域的预测值。内层求和是将该区域内所有训练样本真实值和预测值的差值平方进行加和，外层求和是遍历所有划分的区域。最小化RSS的过程采用递归二分方法：在划分区域时，根据下式进行特征选择和节点分裂，直至无法分裂：
Figure DEST_PATH_IMAGE127
For the divided multiple non-overlapping regions,
Figure 719451DEST_PATH_IMAGE128
is the th region, the total number of regions is J,
Figure 157255DEST_PATH_IMAGE054
for the first
Figure 670276DEST_PATH_IMAGE055
label values of training samples,
Figure 163836DEST_PATH_IMAGE056
Indicates the predicted value of the jth region. The inner summation is to sum the square of the difference between the true value and the predicted value of all training samples in the area, and the outer summation is to traverse all divided areas. The process of minimizing RSS adopts the recursive binary method: when dividing the area, perform feature selection and node splitting according to the following formula until it cannot be split:

Figure 545139DEST_PATH_IMAGE129
Figure 545139DEST_PATH_IMAGE129

其中，

Figure 588181DEST_PATH_IMAGE130
表示切分的维度即输入数据的值，s表示切分点；
Figure 22836DEST_PATH_IMAGE059
和
Figure 518539DEST_PATH_IMAGE060
表示以
Figure 562588DEST_PATH_IMAGE130
为切分维度、s为切分点划分出的两个区域；in,
Figure 588181DEST_PATH_IMAGE130
Indicates the dimension of segmentation, that is, the value of the input data, and s indicates the segmentation point;
Figure 22836DEST_PATH_IMAGE059
and
Figure 518539DEST_PATH_IMAGE060
expressed by
Figure 562588DEST_PATH_IMAGE130
is the segmentation dimension, and s is the two areas divided by the segmentation point;

N个子样本集以上述方式进行分支，得回归树模型预测规则，预测结果可表示为：The N sub-sample sets are branched in the above way to obtain the prediction rules of the regression tree model, and the prediction results can be expressed as:

Figure 351814DEST_PATH_IMAGE131
Figure 351814DEST_PATH_IMAGE131

式中，

Figure 941059DEST_PATH_IMAGE062
为模型预测输出，
Figure 907747DEST_PATH_IMAGE063
为输入特征，
Figure 506218DEST_PATH_IMAGE064
；
Figure 268726DEST_PATH_IMAGE065
为回归树模型预测函数。每个回归树都有一个预测输出，将
Figure 294451DEST_PATH_IMAGE030
个回归树的预测输出取平均值，即作为随机森林输出的多径误差预测值
Figure 748435DEST_PATH_IMAGE066
。
Figure 776696DEST_PATH_IMAGE067
为随机森林训练的多径误差模型预测函数，则多径误差预测规则可表述为：In the formula,
Figure 941059DEST_PATH_IMAGE062
For the model prediction output,
Figure 907747DEST_PATH_IMAGE063
is the input feature,
Figure 506218DEST_PATH_IMAGE064
;
Figure 268726DEST_PATH_IMAGE065
Predict function for regression tree model. Each regression tree has a predicted output, the
Figure 294451DEST_PATH_IMAGE030
The predicted output of the regression trees is averaged, which is the multipath error predicted value output by the random forest
Figure 748435DEST_PATH_IMAGE066
.
Figure 776696DEST_PATH_IMAGE067
is the multipath error model prediction function trained by random forest, then the multipath error prediction rule can be expressed as:

Figure 383258DEST_PATH_IMAGE132
Figure 383258DEST_PATH_IMAGE132

格网层总数用

Figure 563572DEST_PATH_IMAGE069
表示，对每个格网层的数据集进行建模，得到
Figure 255585DEST_PATH_IMAGE069
个多径误差模型。多径误差模型精度用均方根误差RMSE衡量：The total number of grid layers used
Figure 563572DEST_PATH_IMAGE069
Indicates that the data set of each grid layer is modeled to obtain
Figure 255585DEST_PATH_IMAGE069
A multipath error model. The accuracy of the multipath error model is measured by the root mean square error RMSE:

Figure 212170DEST_PATH_IMAGE133
Figure 212170DEST_PATH_IMAGE133

其中

Figure 938818DEST_PATH_IMAGE071
为第
Figure 555613DEST_PATH_IMAGE050
个模型的均方根误差，
Figure 734922DEST_PATH_IMAGE073
为第
Figure 104985DEST_PATH_IMAGE055
个训练样本的多径误差真实值，
Figure 669828DEST_PATH_IMAGE074
为第
Figure 473836DEST_PATH_IMAGE055
个训练样本的多径误差模型预测值，
Figure 643172DEST_PATH_IMAGE075
为训练样本数量。为进行后续格网可用性判定，计算如下精度参数：所有格网层多径误差模型均方根误差的平均值
Figure 190828DEST_PATH_IMAGE134
和标准差
Figure 875756DEST_PATH_IMAGE077
、第
Figure 585086DEST_PATH_IMAGE050
个格网均方根误差值的标准化处理结果
Figure 100002_DEST_PATH_IMAGE135
和比重
Figure 552036DEST_PATH_IMAGE136
，计算方法分别如下所列：in
Figure 938818DEST_PATH_IMAGE071
for the first
Figure 555613DEST_PATH_IMAGE050
The root mean square error of the model,
Figure 734922DEST_PATH_IMAGE073
for the first
Figure 104985DEST_PATH_IMAGE055
The true value of the multipath error of training samples,
Figure 669828DEST_PATH_IMAGE074
for the first
Figure 473836DEST_PATH_IMAGE055
The multipath error model prediction value of training samples,
Figure 643172DEST_PATH_IMAGE075
is the number of training samples. In order to determine the availability of subsequent grids, the following precision parameters are calculated: the average root mean square error of all grid layer multipath error models
Figure 190828DEST_PATH_IMAGE134
and standard deviation
Figure 875756DEST_PATH_IMAGE077
, No.
Figure 585086DEST_PATH_IMAGE050
Standardized processing results of grid root mean square error values
Figure 100002_DEST_PATH_IMAGE135
and specific gravity
Figure 552036DEST_PATH_IMAGE136
, the calculation methods are as follows:

Figure 637804DEST_PATH_IMAGE137
Figure 637804DEST_PATH_IMAGE137

Figure 944282DEST_PATH_IMAGE138
Figure 944282DEST_PATH_IMAGE138

Figure 90093DEST_PATH_IMAGE139
Figure 90093DEST_PATH_IMAGE139

Figure 855923DEST_PATH_IMAGE140
Figure 855923DEST_PATH_IMAGE140

其中，

Figure 496114DEST_PATH_IMAGE084
为第
Figure 906367DEST_PATH_IMAGE072
个多径误差模型的均方根误差，
Figure 206767DEST_PATH_IMAGE085
为所有多径误差模型均方根误差的最小值，
Figure 69681DEST_PATH_IMAGE086
为所有多径误差模型均方根误差的最大值。in,
Figure 496114DEST_PATH_IMAGE084
for the first
Figure 906367DEST_PATH_IMAGE072
The root mean square error of the multipath error model,
Figure 206767DEST_PATH_IMAGE085
is the minimum value of the root mean square error of all multipath error models,
Figure 69681DEST_PATH_IMAGE086
is the maximum value of the root mean square error of all multipath error models.

至此完成区域三维格网构建，得到区域三维格网布局、各个格网层的多径误差预测模型、模型的多径误差预测规则以及各个模型的精度参数。So far, the regional three-dimensional grid construction has been completed, and the regional three-dimensional grid layout, the multipath error prediction model of each grid layer, the multipath error prediction rules of the model, and the accuracy parameters of each model have been obtained.

2） 三维格网模型调用2) 3D grid model call

第一步，GNSS测试数据集构建与遍历。从用户GNSS接收机输出的原始观测量中提取测试数据的先验位置

Figure 242125DEST_PATH_IMAGE013
、位置精度因子（Position Dilution of Precision, PDOP）、伪距残差、载噪比、卫星高度角和卫星方位角作为测试样本构建GNSS测试数据集
Figure 506884DEST_PATH_IMAGE087
。其中先验位置
Figure 712606DEST_PATH_IMAGE013
用于格网层匹配，PDOP用于格网可用性判断，其余数据输入模型预测多径误差。为进行后续格网可用性判定，数据集构建完成后进行遍历，计算以下参数：所有历元PDOP的均值
Figure 954494DEST_PATH_IMAGE088
和标准差
Figure 920176DEST_PATH_IMAGE089
、第
Figure 554288DEST_PATH_IMAGE090
个历元PDOP的标准化处理结果
Figure 212803DEST_PATH_IMAGE091
和比重
Figure 535462DEST_PATH_IMAGE092
，计算方法分别如下所列：The first step is to construct and traverse the GNSS test data set. Extract the prior location of the test data from the raw observations output by the user's GNSS receiver
Figure 242125DEST_PATH_IMAGE013
, Position Dilution of Precision (PDOP), pseudorange residual, carrier-to-noise ratio, satellite elevation and satellite azimuth as test samples to build a GNSS test data set
Figure 506884DEST_PATH_IMAGE087
. where the prior position
Figure 712606DEST_PATH_IMAGE013
It is used for grid layer matching, PDOP is used for grid availability judgment, and the rest of the data is input into the model to predict multipath errors. In order to determine the availability of the subsequent grid, the data set is traversed after the construction is completed, and the following parameters are calculated: the mean value of PDOP of all epochs
Figure 954494DEST_PATH_IMAGE088
and standard deviation
Figure 920176DEST_PATH_IMAGE089
, No.
Figure 554288DEST_PATH_IMAGE090
The normalized processing result of PDOP for each epoch
Figure 212803DEST_PATH_IMAGE091
and specific gravity
Figure 535462DEST_PATH_IMAGE092
, the calculation methods are as follows:

Figure 304835DEST_PATH_IMAGE141
Figure 304835DEST_PATH_IMAGE141

Figure 934399DEST_PATH_IMAGE142
Figure 934399DEST_PATH_IMAGE142

Figure 248968DEST_PATH_IMAGE143
Figure 248968DEST_PATH_IMAGE143

Figure 308191DEST_PATH_IMAGE144
Figure 308191DEST_PATH_IMAGE144

其中

Figure 130522DEST_PATH_IMAGE097
为测试数据样本数量，
Figure 489960DEST_PATH_IMAGE098
为第
Figure 235150DEST_PATH_IMAGE090
个测试样本对应历元的PDOP，
Figure 781669DEST_PATH_IMAGE099
为所有测试样本PDOP的最小值，
Figure 17478DEST_PATH_IMAGE100
为所有测试样本PDOP的最大值。in
Figure 130522DEST_PATH_IMAGE097
is the number of test data samples,
Figure 489960DEST_PATH_IMAGE098
for the first
Figure 235150DEST_PATH_IMAGE090
PDOP of test samples corresponding to epochs,
Figure 781669DEST_PATH_IMAGE099
is the minimum value of PDOP for all test samples,
Figure 17478DEST_PATH_IMAGE100
is the maximum value of PDOP of all test samples.

第二步，根据各测试样本的先验位置匹配到相应格网层，调用模型并判定其可用性。利用已有的三维格网布局，将测试数据逐个匹配到各自的所属格网层，并调用相应格网层的多径误差预测模型，随后根据格网层模型精度与GNSS测试数据质量，基于平均值和比重进行模型可用性判断。对于某一历元的数据，作如下判定：The second step is to match the prior location of each test sample to the corresponding grid layer, call the model and determine its availability. Using the existing three-dimensional grid layout, match the test data to their respective grid layers one by one, and call the multipath error prediction model of the corresponding grid layer, and then according to the accuracy of the grid layer model and the quality of GNSS test data, based on the average Value and proportion to judge the usability of the model. For the data of a certain epoch, the following judgments are made:

Figure DEST_PATH_IMAGE145
Figure 919837DEST_PATH_IMAGE146
Figure DEST_PATH_IMAGE145
Figure 919837DEST_PATH_IMAGE146

Figure 340323DEST_PATH_IMAGE103
为第
Figure 374138DEST_PATH_IMAGE090
个测试数据所属格网对应的GNSS多径误差模型的均方根误差值，
Figure 39737DEST_PATH_IMAGE134
为所有模型均方根误差的平均值，
Figure 232821DEST_PATH_IMAGE098
为第
Figure 309361DEST_PATH_IMAGE090
个测试数据对应历元的PDOP，
Figure 846784DEST_PATH_IMAGE088
为测试数据集中所有样本历元PDOP的平均值。若某一历元数据同时满足两式，则判定其对应的模型可用，可用其预测多径误差并进行后续修正和最终定位解算，否则进行下一步基于比重的判定：
Figure 340323DEST_PATH_IMAGE103
for the first
Figure 374138DEST_PATH_IMAGE090
The root mean square error value of the GNSS multipath error model corresponding to the grid to which the test data belongs,
Figure 39737DEST_PATH_IMAGE134
is the average of the root mean square errors of all models,
Figure 232821DEST_PATH_IMAGE098
for the first
Figure 309361DEST_PATH_IMAGE090
test data corresponding to the PDOP of the epoch,
Figure 846784DEST_PATH_IMAGE088
is the mean value of PDOP over all sample epochs in the test dataset. If a certain epoch data satisfies the two formulas at the same time, it is judged that the corresponding model is available, and it can be used to predict the multipath error and perform subsequent correction and final positioning calculation, otherwise, proceed to the next step based on the proportion of judgment:

Figure 565341DEST_PATH_IMAGE147
Figure 471986DEST_PATH_IMAGE148
Figure 565341DEST_PATH_IMAGE147
Figure 471986DEST_PATH_IMAGE148

其中，

Figure 985007DEST_PATH_IMAGE149
为第
Figure 738288DEST_PATH_IMAGE090
个测试数据的比重，
Figure 119591DEST_PATH_IMAGE150
为预设的比重门限值，根据定位所需精度要求以及具体数据质量对
Figure 162633DEST_PATH_IMAGE150
的大小进行适当调节。若该历元测试样本满足不等式，则判定模型可用从而进行多径预测和修正，否则判定不可用，不进行建模修正。in,
Figure 985007DEST_PATH_IMAGE149
for the first
Figure 738288DEST_PATH_IMAGE090
The proportion of test data,
Figure 119591DEST_PATH_IMAGE150
is the preset specific gravity threshold, according to the positioning accuracy requirements and the specific data quality
Figure 162633DEST_PATH_IMAGE150
Adjust the size appropriately. If the epoch test sample satisfies the inequality, it is determined that the model is available for multipath prediction and correction, otherwise it is determined that it is not available and no modeling correction is performed.

第三步，得到修正后的定位结果。假设第

Figure 331708DEST_PATH_IMAGE090
个历元观测伪距为
Figure 92991DEST_PATH_IMAGE108
，模型预测的多径误差值为
Figure 137039DEST_PATH_IMAGE151
，则修正后的伪距为
Figure 769009DEST_PATH_IMAGE110
，依据伪距定位原理利用
Figure 374565DEST_PATH_IMAGE111
代替
Figure 91985DEST_PATH_IMAGE108
，解算修正后的定位解。The third step is to obtain the corrected positioning result. Assuming the first
Figure 331708DEST_PATH_IMAGE090
The epoch observed pseudorange is
Figure 92991DEST_PATH_IMAGE108
, the multipath error value predicted by the model is
Figure 137039DEST_PATH_IMAGE151
, then the corrected pseudorange is
Figure 769009DEST_PATH_IMAGE110
, according to the principle of pseudo-range positioning using
Figure 374565DEST_PATH_IMAGE111
replace
Figure 91985DEST_PATH_IMAGE108
, solve the corrected positioning solution.

具体实现中，本申请提供计算机存储介质以及对应的数据处理单元，其中，该计算机存储介质能够存储计算机程序，所述计算机程序通过数据处理单元执行时可运行本发明提供的一种基于三维格网多径建模的城市复杂环境导航定位方法的发明内容以及各实施例中的部分或全部步骤。所述的存储介质可为磁碟、光盘、只读存储记忆体（read-onlymemory，ROM）或随机存储记忆体（random access memory，RAM）等。In a specific implementation, the present application provides a computer storage medium and a corresponding data processing unit, wherein the computer storage medium can store a computer program, and when the computer program is executed by the data processing unit, it can run a three-dimensional grid-based Summary of the invention of the method for navigation and positioning in a complex urban environment based on multipath modeling and some or all of the steps in each embodiment. The storage medium may be a magnetic disk, an optical disk, a read-only memory (read-only memory, ROM) or a random access memory (random access memory, RAM), and the like.

本领域的技术人员可以清楚地了解到本发明实施例中的技术方案可借助计算机程序以及其对应的通用硬件平台的方式来实现。基于这样的理解，本发明实施例中的技术方案本质上或者说对现有技术做出贡献的部分可以以计算机程序即软件产品的形式体现出来，该计算机程序软件产品可以存储在存储介质中，包括若干指令用以使得一台包含数据处理单元的设备（可以是个人计算机，服务器，单片机，MUU或者网络设备等）执行本发明各个实施例或者实施例的某些部分所述的方法。Those skilled in the art can clearly understand that the technical solutions in the embodiments of the present invention can be implemented by means of computer programs and their corresponding general-purpose hardware platforms. Based on this understanding, the essence of the technical solutions in the embodiments of the present invention or the part that contributes to the prior art can be embodied in the form of a computer program, that is, a software product, and the computer program software product can be stored in a storage medium. Including several instructions to make a device including a data processing unit (which may be a personal computer, server, single-chip microcomputer, MUU or network device, etc.) execute the methods described in various embodiments or some parts of the embodiments of the present invention.

本发明提供了一种基于三维格网多径建模的城市复杂环境导航定位方法的思路及方法，具体实现该技术方案的方法和途径很多，以上所述仅是本发明的优选实施方式，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。本实施例中未明确的各组成部分均可用现有技术加以实现。The present invention provides an idea and method of a navigation and positioning method in a complex urban environment based on three-dimensional grid multipath modeling. There are many methods and approaches for realizing the technical solution. It is pointed out that those skilled in the art can make some improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention. All components that are not specified in this embodiment can be realized by existing technologies.

Claims (10)

1.一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，包括以下步骤：1. A navigation and positioning method for urban complex environments based on three-dimensional grid multipath modeling, characterized in that it comprises the following steps: 步骤1，构建区域三维格网模型，包括：Step 1, build a regional 3D grid model, including: 步骤1-1，构建GNSS训练数据集；Step 1-1, construct GNSS training data set; 步骤1-2，构建区域三维格网布局；Step 1-2, constructing the regional three-dimensional grid layout; 步骤1-3，逐个格网层进行基于随机森林的多径误差建模；Steps 1-3, perform multipath error modeling based on random forest layer by grid layer; 步骤2，调用区域三维格网模型，包括：Step 2, calling the regional 3D grid model, including: 步骤2-1，GNSS测试数据集构建与遍历；Step 2-1, GNSS test data set construction and traversal; 步骤2-2，根据各测试样本的先验位置匹配到相应格网层，调用多径误差模型并判定其可用性；Step 2-2, match the corresponding grid layer according to the prior position of each test sample, call the multipath error model and determine its availability; 步骤2-3，得到修正后的定位结果，完成基于三维格网多径建模的城市复杂环境导航定位。In steps 2-3, the corrected positioning result is obtained, and the navigation and positioning of the urban complex environment based on the three-dimensional grid multipath modeling is completed. 2.根据权利要求1所述的一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，步骤1-1中所述的构建GNSS训练数据集，具体方法包括：2. a kind of urban complex environment navigation positioning method based on three-dimensional grid multipath modeling according to claim 1, is characterized in that, the construction GNSS training data set described in step 1-1, concrete method comprises: 在所述城市复杂环境中重复行驶，采集GNSS接收机输出的原始观测量，并从中提取输入特征作为样本；所述输入特征包括：伪距残差
Figure DEST_PATH_IMAGE001
、载噪比
Figure 328087DEST_PATH_IMAGE002
、卫星高度角
Figure 165593DEST_PATH_IMAGE004
和卫星方位角
Figure DEST_PATH_IMAGE005
，所述样本为：
Figure DEST_PATH_IMAGE007
；Repeated driving in the complex environment of the city, collecting the original observations output by the GNSS receiver, and extracting input features therefrom as samples; the input features include: pseudorange residuals
Figure DEST_PATH_IMAGE001
, carrier-to-noise ratio
Figure 328087DEST_PATH_IMAGE002
, satellite elevation angle
Figure 165593DEST_PATH_IMAGE004
and satellite azimuth
Figure DEST_PATH_IMAGE005
, the sample is:
Figure DEST_PATH_IMAGE007
; 采用多径误差值对样本进行标定，伪距误差值
Figure 187163DEST_PATH_IMAGE008
表达式为：The sample is calibrated by using the multipath error value, and the pseudorange error value
Figure 187163DEST_PATH_IMAGE008
The expression is:
Figure 472520DEST_PATH_IMAGE010
Figure 472520DEST_PATH_IMAGE010
 其中，c为真空中的光速，
Figure DEST_PATH_IMAGE011
和
Figure 364252DEST_PATH_IMAGE012
为卫星和接收机钟差，
Figure DEST_PATH_IMAGE013
和
Figure 404234DEST_PATH_IMAGE014
分别为电离层和对流层延迟中未修正的残差，
Figure DEST_PATH_IMAGE015
为多路径效应造成的误差；where c is the speed of light in vacuum,
Figure DEST_PATH_IMAGE011
and
Figure 364252DEST_PATH_IMAGE012
is the satellite and receiver clock difference,
Figure DEST_PATH_IMAGE013
and
Figure 404234DEST_PATH_IMAGE014
are the uncorrected residuals in ionospheric and tropospheric delays, respectively,
Figure DEST_PATH_IMAGE015
errors due to multipath effects; 标定完成后，将GNSS接收机解算的先验位置
Figure 554461DEST_PATH_IMAGE016
纳入训练数据集并与相应历元的样本以及多径误差值对应，构建得到所述训练数据集，其中训练样本表示为：
Figure 913898DEST_PATH_IMAGE018
。After the calibration is completed, the a priori position calculated by the GNSS receiver
Figure 554461DEST_PATH_IMAGE016
Incorporate the training data set and correspond to the samples of the corresponding epoch and the multipath error value, and construct the described training data set, wherein the training samples are expressed as:
Figure 913898DEST_PATH_IMAGE018
. 3.根据权利要求2所述的一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，步骤1-2中所述的构建区域三维格网布局，具体方法包括：3. a kind of urban complex environment navigation positioning method based on three-dimensional grid multi-path modeling according to claim 2, it is characterized in that, the construction area three-dimensional grid layout described in step 1-2, concrete method comprises: 根据地理信息系统提供的城市区域的地理信息，将所述训练数据集中的位置数据匹配到城市地图中的相应区域，取所述相应区域的最小外包正方形
Figure DEST_PATH_IMAGE019
为建模区域；所述正方形的一边与ENU坐标系下的
Figure 570008DEST_PATH_IMAGE020
轴平行，边长为
Figure DEST_PATH_IMAGE021
米；在所述建模区域上进行平面六边形格网划分；根据建模区域大小以及定位精度，综合设定六边形格网边长
Figure 962199DEST_PATH_IMAGE022
；其中，所述六边形格网边长的下限值
Figure DEST_PATH_IMAGE023
确定原则为：保证80%以上格网内训练样本数据总量不少于2000个；边长上限值
Figure 57063DEST_PATH_IMAGE024
确定原则为：保证
Figure DEST_PATH_IMAGE025
；若所述六边形格网边长的上下限值相互矛盾，则提高采样率，在城市复杂环境下重新采集GNSS数据；沿正方形的南北向边从端点开始以
Figure 926799DEST_PATH_IMAGE026
的间隔取点作为六边形的中心点，记为
Figure DEST_PATH_IMAGE027
，其中
Figure 688563DEST_PATH_IMAGE028
为此边上的取点数量，
Figure DEST_PATH_IMAGE029
；再从
Figure 643750DEST_PATH_IMAGE027
出发沿东西向边的方向以
Figure 542304DEST_PATH_IMAGE030
的长度取点，将所有点记为：
Figure DEST_PATH_IMAGE031
，其中
Figure 63284DEST_PATH_IMAGE032
为正方形一条东西向边上的取点数量，
Figure DEST_PATH_IMAGE033
；According to the geographical information of the urban area provided by the geographic information system, match the location data in the training data set to the corresponding area in the city map, and take the smallest outsourcing square of the corresponding area
Figure DEST_PATH_IMAGE019
is the modeling area; one side of the square and the ENU coordinate system
Figure 570008DEST_PATH_IMAGE020
Axis parallel, side length is
Figure DEST_PATH_IMAGE021
Meters; carry out planar hexagonal grid division on the modeling area; according to the size of the modeling area and positioning accuracy, comprehensively set the side length of the hexagonal grid
Figure 962199DEST_PATH_IMAGE022
; Wherein, the lower limit value of the side length of the hexagonal grid
Figure DEST_PATH_IMAGE023
The determination principle is: ensure that the total number of training sample data in more than 80% of the grid is not less than 2000; the upper limit of the side length
Figure 57063DEST_PATH_IMAGE024
The principle of determination is: guarantee
Figure DEST_PATH_IMAGE025
; If the upper and lower limits of the hexagonal grid side length contradict each other, then increase the sampling rate, re-gather the GNSS data in the complex environment of the city; start from the endpoint along the north-south side of the square
Figure 926799DEST_PATH_IMAGE026
Take the point at the interval as the center point of the hexagon, denoted as
Figure DEST_PATH_IMAGE027
,in
Figure 688563DEST_PATH_IMAGE028
For the number of points on this edge,
Figure DEST_PATH_IMAGE029
; then from
Figure 643750DEST_PATH_IMAGE027
Depart in the direction of the east-west edge to
Figure 542304DEST_PATH_IMAGE030
Take points for the length of , and record all points as:
Figure DEST_PATH_IMAGE031
,in
Figure 63284DEST_PATH_IMAGE032
is the number of points on an east-west side of the square,
Figure DEST_PATH_IMAGE033
; 以
Figure 1809DEST_PATH_IMAGE031
为坐标原点，ENU坐标系下的
Figure 506609DEST_PATH_IMAGE020
轴与
Figure 490745DEST_PATH_IMAGE034
轴为
Figure DEST_PATH_IMAGE035
轴与
Figure 335073DEST_PATH_IMAGE036
轴，将坐标原点作为六边形的中心，并按照选取的六边形边长
Figure 503886DEST_PATH_IMAGE022
，将一个顶点固定在
Figure 493052DEST_PATH_IMAGE036
轴上以此方式在每个坐标系中生成六边形，在整个建模区域上进行密集排布；by
Figure 1809DEST_PATH_IMAGE031
is the coordinate origin, in the ENU coordinate system
Figure 506609DEST_PATH_IMAGE020
axis with
Figure 490745DEST_PATH_IMAGE034
Axis is
Figure DEST_PATH_IMAGE035
axis with
Figure 335073DEST_PATH_IMAGE036
Axis, take the coordinate origin as the center of the hexagon, and follow the selected hexagon side length
Figure 503886DEST_PATH_IMAGE022
, fix a vertex at
Figure 493052DEST_PATH_IMAGE036
In this way, hexagons are generated in each coordinate system on the axis, densely arranged over the entire modeling area; 将上述所得密集排布的
Figure DEST_PATH_IMAGE037
个二维格网在高度方向延伸形成
Figure 467830DEST_PATH_IMAGE037
个格网柱，其中
Figure 979714DEST_PATH_IMAGE038
，每个格网柱高度
Figure DEST_PATH_IMAGE039
的值初始设为100米，在后续步骤中根据实际情况自动更新；以
Figure 240800DEST_PATH_IMAGE040
为间隔，将每个格网柱分为
Figure 267662DEST_PATH_IMAGE042
层；
Figure 49061DEST_PATH_IMAGE040
的最小值
Figure DEST_PATH_IMAGE043
确定原则为：保证80%以上格网层内训练样本数据总量不少于500个；
Figure 274506DEST_PATH_IMAGE040
的最大值
Figure 113018DEST_PATH_IMAGE044
确定原则为：保证
Figure 892755DEST_PATH_IMAGE046
；若间隔
Figure 474915DEST_PATH_IMAGE040
的最大值和最小值相互矛盾，则提高采样率，在城市环境下重新采集GNSS数据。The above-mentioned densely arranged
Figure DEST_PATH_IMAGE037
A two-dimensional grid is extended in the height direction to form
Figure 467830DEST_PATH_IMAGE037
grid columns, where
Figure 979714DEST_PATH_IMAGE038
, each grid column height
Figure DEST_PATH_IMAGE039
The value of is initially set to 100 meters, and will be automatically updated according to the actual situation in subsequent steps;
Figure 240800DEST_PATH_IMAGE040
As the interval, each grid column is divided into
Figure 267662DEST_PATH_IMAGE042
layer;
Figure 49061DEST_PATH_IMAGE040
minimum value of
Figure DEST_PATH_IMAGE043
The determination principle is: ensure that the total number of training sample data in more than 80% of the grid layer is not less than 500;
Figure 274506DEST_PATH_IMAGE040
the maximum value of
Figure 113018DEST_PATH_IMAGE044
The principle of determination is: guarantee
Figure 892755DEST_PATH_IMAGE046
; if interval
Figure 474915DEST_PATH_IMAGE040
If the maximum and minimum values are contradictory, increase the sampling rate and re-collect GNSS data in an urban environment. 4.根据权利要求3所述的一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，步骤1-3中所述的逐个格网层进行基于随机森林的多径误差建模，具体方法包括：4. a kind of urban complex environment navigation and positioning method based on three-dimensional grid multipath modeling according to claim 3, is characterized in that, described in step 1-3 carries out the multipath based on random forest one by one grid layer Error modeling, specific methods include: 步骤1-3-1，按照步骤1-2构建的三维格网布局，确定每个训练样本的所属格网层；Step 1-3-1, according to the three-dimensional grid layout constructed in step 1-2, determine the grid layer to which each training sample belongs; 步骤1-3-2，对每个格网层进行基于随机森林的多径误差模型训练；Step 1-3-2, carry out multipath error model training based on random forest for each grid layer; 步骤1-3-3，完成区域三维格网模型构建。Step 1-3-3, complete the construction of the regional 3D grid model. 5.根据权利要求4所述的一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，步骤1-3-1所述的确定每个训练样本的所属格网层，具体方法包括：5. A kind of method for navigation and positioning of urban complex environment based on three-dimensional grid multipath modeling according to claim 4, characterized in that, the grid layer to which each training sample belongs is determined in step 1-3-1 , the specific methods include: 设六边形格网柱平面投影的中心点为
Figure DEST_PATH_IMAGE047
，ENU坐标系下的
Figure 903270DEST_PATH_IMAGE020
轴与
Figure 850366DEST_PATH_IMAGE034
轴分别对应
Figure 789504DEST_PATH_IMAGE035
轴与
Figure 972092DEST_PATH_IMAGE036
轴，取某训练样本的位置为
Figure 47496DEST_PATH_IMAGE048
，判定其是否属于该六边形：Let the center point of the plane projection of the hexagonal grid column be
Figure DEST_PATH_IMAGE047
, in the ENU coordinate system
Figure 903270DEST_PATH_IMAGE020
axis with
Figure 850366DEST_PATH_IMAGE034
Axis corresponds to
Figure 789504DEST_PATH_IMAGE035
axis with
Figure 972092DEST_PATH_IMAGE036
axis, take the position of a training sample as
Figure 47496DEST_PATH_IMAGE048
, to determine whether it belongs to the hexagon:
Figure 165493DEST_PATH_IMAGE050
Figure 165493DEST_PATH_IMAGE050
 仅当上述两式都满足时，判定
Figure 109703DEST_PATH_IMAGE048
在格网柱内；对训练数据集的每个训练样本执行此判断，得到各个格网柱的训练数据集，更新每个格网柱高度
Figure 518819DEST_PATH_IMAGE052
，其中
Figure DEST_PATH_IMAGE053
为此格网柱内训练数据集中样本的高程最大值，并同时更新格网层数
Figure 697996DEST_PATH_IMAGE042
；再根据训练数据集中各个样本的高度数据，将训练样本划分到所属格网层。Only when the above two formulas are satisfied, the judgment
Figure 109703DEST_PATH_IMAGE048
In the grid column; execute this judgment on each training sample of the training data set, get the training data set of each grid column, and update the height of each grid column
Figure 518819DEST_PATH_IMAGE052
,in
Figure DEST_PATH_IMAGE053
The maximum elevation of the sample in the training data set in the grid column, and update the number of grid layers at the same time
Figure 697996DEST_PATH_IMAGE042
; Then according to the height data of each sample in the training data set, the training samples are divided into the grid layer to which they belong. 6.根据权利要求5所述的一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，步骤1-3-2所述的对每个格网层进行基于随机森林的多径误差模型训练，具体方法包括：6. A kind of urban complex environment navigation positioning method based on three-dimensional grid multipath modeling according to claim 5, it is characterized in that, each grid layer described in step 1-3-2 is based on random forest The multipath error model training, the specific methods include: 将每个格网层所属的训练样本的集合划分为
Figure 314791DEST_PATH_IMAGE034
个子样本集，先令
Figure 149892DEST_PATH_IMAGE054
，得到
Figure DEST_PATH_IMAGE055
个子样本集，训练得到
Figure 546720DEST_PATH_IMAGE055
颗回归树，计算回归树输出值均值和平均绝对误差MAE；若MAE<0.05，则取此时的
Figure 127874DEST_PATH_IMAGE034
值，否则
Figure 181149DEST_PATH_IMAGE056
重复迭代；其中回归算法将每个子样本集划分为j个不重叠的区域，再对区域内的每个训练样本求出一个预测结果，找到使残差平方和RSS最小的划分方法，RSS计算方法为：The set of training samples to which each grid layer belongs is divided into
Figure 314791DEST_PATH_IMAGE034
subsample sets, shilling
Figure 149892DEST_PATH_IMAGE054
,get
Figure DEST_PATH_IMAGE055
sub-sample set, trained to get
Figure 546720DEST_PATH_IMAGE055
A regression tree, calculate the mean value of the regression tree output value and the mean absolute error MAE; if MAE<0.05, take the current
Figure 127874DEST_PATH_IMAGE034
value, otherwise
Figure 181149DEST_PATH_IMAGE056
Repeat iterations; the regression algorithm divides each sub-sample set into j non-overlapping areas, and then calculates a prediction result for each training sample in the area, and finds the division method that minimizes the residual square sum RSS, RSS calculation method for:
Figure 847754DEST_PATH_IMAGE058
Figure 847754DEST_PATH_IMAGE058
 其中，
Figure 785623DEST_PATH_IMAGE060
为划分出的不重叠的区域，
Figure 204972DEST_PATH_IMAGE062
为第j个区域，区域数量为J，
Figure DEST_PATH_IMAGE063
为第
Figure 369761DEST_PATH_IMAGE064
个训练样本的标签值，
Figure DEST_PATH_IMAGE065
表示第j个区域的预测值；内层求和是将该区域内所有训练样本真实值和预测值的差值平方进行加和，外层求和是遍历所有划分的区域；最小化RSS的过程采用递归二分方法：在划分区域时，根据下式进行特征选择和节点分裂，直至无法分裂：in,
Figure 785623DEST_PATH_IMAGE060
For the non-overlapping regions divided,
Figure 204972DEST_PATH_IMAGE062
is the jth region, the number of regions is J,
Figure DEST_PATH_IMAGE063
for the first
Figure 369761DEST_PATH_IMAGE064
label values of training samples,
Figure DEST_PATH_IMAGE065
Indicates the predicted value of the jth area; the inner summation is to sum the square of the difference between the true value and the predicted value of all training samples in the area, and the outer summation is to traverse all divided areas; the process of minimizing RSS Using the recursive binary method: when dividing the area, perform feature selection and node splitting according to the following formula until it cannot be split:
Figure DEST_PATH_IMAGE067
Figure DEST_PATH_IMAGE067
 其中，
Figure DEST_PATH_IMAGE068A
表示切分的维度即输入数据的值，s表示切分点；
Figure DEST_PATH_IMAGE069
和
Figure 897564DEST_PATH_IMAGE070
表示以
Figure DEST_PATH_IMAGE068AA
为切分维度，以s为切分点划分出的两个区域；in,
Figure DEST_PATH_IMAGE068A
Indicates the dimension of segmentation, that is, the value of the input data, and s indicates the segmentation point;
Figure DEST_PATH_IMAGE069
and
Figure 897564DEST_PATH_IMAGE070
expressed by
Figure DEST_PATH_IMAGE068AA
is the segmentation dimension, two areas divided by s as the segmentation point;
Figure 760828DEST_PATH_IMAGE034
个子样本集以上述方式进行分支，得到回归树模型预测规则，预测结果由下式表示：
Figure 760828DEST_PATH_IMAGE034
The sub-sample sets are branched in the above way, and the prediction rules of the regression tree model are obtained, and the prediction results are expressed by the following formula:
Figure 300262DEST_PATH_IMAGE072
Figure 300262DEST_PATH_IMAGE072
 式中，
Figure DEST_PATH_IMAGE073
为回归树模型预测输出，
Figure 898603DEST_PATH_IMAGE074
为输入特征，
Figure 8641DEST_PATH_IMAGE076
；
Figure DEST_PATH_IMAGE077
为回归树模型预测函数，将
Figure 478193DEST_PATH_IMAGE034
个回归树的预测输出取平均值，即作为随机森林输出的多径误差预测值
Figure 622867DEST_PATH_IMAGE078
；
Figure DEST_PATH_IMAGE079
为随机森林训练的多径误差模型的预测函数，则多径误差预测规则为：In the formula,
Figure DEST_PATH_IMAGE073
Predict the output for the regression tree model,
Figure 898603DEST_PATH_IMAGE074
is the input feature,
Figure 8641DEST_PATH_IMAGE076
;
Figure DEST_PATH_IMAGE077
For the prediction function of the regression tree model, the
Figure 478193DEST_PATH_IMAGE034
The predicted output of the regression trees is averaged, which is the multipath error predicted value output by the random forest
Figure 622867DEST_PATH_IMAGE078
;
Figure DEST_PATH_IMAGE079
is the prediction function of the multipath error model trained by random forest, then the multipath error prediction rule is:
Figure DEST_PATH_IMAGE081
Figure DEST_PATH_IMAGE081
 由所有格网柱划分而得的格网层总数用
Figure 313480DEST_PATH_IMAGE082
表示，对每个格网层的训练数据进行建模，得到
Figure 94835DEST_PATH_IMAGE082
个多径误差模型；多径误差模型精度用均方根误差RMSE衡量：The total number of grid layers divided by all grid columns is given by
Figure 313480DEST_PATH_IMAGE082
Indicates that the training data of each grid layer is modeled to obtain
Figure 94835DEST_PATH_IMAGE082
multipath error model; the accuracy of the multipath error model is measured by the root mean square error RMSE:
Figure 991247DEST_PATH_IMAGE084
Figure 991247DEST_PATH_IMAGE084
 其中，
Figure DEST_PATH_IMAGE085
为第
Figure 239695DEST_PATH_IMAGE086
个多径误差模型的均方根误差，
Figure DEST_PATH_IMAGE087
为第
Figure 304472DEST_PATH_IMAGE064
个训练样本的多径误差真实值，
Figure 654682DEST_PATH_IMAGE088
为第
Figure 606982DEST_PATH_IMAGE064
个训练样本的多径误差模型预测值，
Figure DEST_PATH_IMAGE089
为训练样本数量；in,
Figure DEST_PATH_IMAGE085
for the first
Figure 239695DEST_PATH_IMAGE086
The root mean square error of the multipath error model,
Figure DEST_PATH_IMAGE087
for the first
Figure 304472DEST_PATH_IMAGE064
The true value of the multipath error of training samples,
Figure 654682DEST_PATH_IMAGE088
for the first
Figure 606982DEST_PATH_IMAGE064
The multipath error model prediction value of training samples,
Figure DEST_PATH_IMAGE089
is the number of training samples; 精度参数包括：所有格网模型均方根误差的平均值
Figure 647619DEST_PATH_IMAGE090
和标准差
Figure DEST_PATH_IMAGE091
、第
Figure 758663DEST_PATH_IMAGE086
个格网均方根误差值的标准化处理结果
Figure 517541DEST_PATH_IMAGE092
和比重
Figure DEST_PATH_IMAGE093
，计算方法分别如下所列：Accuracy parameters include: the average of the root mean square errors of all grid models
Figure 647619DEST_PATH_IMAGE090
and standard deviation
Figure DEST_PATH_IMAGE091
, No.
Figure 758663DEST_PATH_IMAGE086
Standardized processing results of grid root mean square error values
Figure 517541DEST_PATH_IMAGE092
and specific gravity
Figure DEST_PATH_IMAGE093
, the calculation methods are as follows:
Figure DEST_PATH_IMAGE095
Figure DEST_PATH_IMAGE095
Figure DEST_PATH_IMAGE097
Figure DEST_PATH_IMAGE097
Figure DEST_PATH_IMAGE099
Figure DEST_PATH_IMAGE099
Figure DEST_PATH_IMAGE101
Figure DEST_PATH_IMAGE101
 其中，
Figure 415743DEST_PATH_IMAGE102
为第
Figure 373204DEST_PATH_IMAGE086
个多径误差模型的均方根误差，
Figure DEST_PATH_IMAGE103
为所有多径误差模型均方根误差的最小值，
Figure 658079DEST_PATH_IMAGE104
为所有多径误差模型均方根误差的最大值。in,
Figure 415743DEST_PATH_IMAGE102
for the first
Figure 373204DEST_PATH_IMAGE086
The root mean square error of the multipath error model,
Figure DEST_PATH_IMAGE103
is the minimum value of the root mean square error of all multipath error models,
Figure 658079DEST_PATH_IMAGE104
is the maximum value of the root mean square error of all multipath error models. 7.根据权利要求6所述的一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，步骤1-3-3所述的完成区域三维格网模型构建，包括：7. A kind of urban complex environment navigation and positioning method based on three-dimensional grid multi-path modeling according to claim 6, it is characterized in that, the construction of regional three-dimensional grid model described in step 1-3-3 includes: 计算得到区域三维格网布局、各个格网层的多径误差模型、所述多径误差模型的多径误差预测规则以及各个多径误差模型的精度参数。The regional three-dimensional grid layout, the multipath error models of each grid layer, the multipath error prediction rules of the multipath error models, and the precision parameters of each multipath error model are obtained through calculation. 8.根据权利要求7所述的一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，步骤2-1所述的GNSS测试数据集构建与遍历，具体方法包括：8. A kind of urban complex environment navigation and positioning method based on three-dimensional grid multipath modeling according to claim 7, it is characterized in that, the GNSS test data set described in step 2-1 is constructed and traversed, and specific methods include: 从用户GNSS接收机输出的原始观测量中提取测试数据的先验位置
Figure 982881DEST_PATH_IMAGE016
、位置精度因子PDOP、伪距残差、载噪比、卫星高度角和卫星方位角组成测试样本构建GNSS测试数据集
Figure 680579DEST_PATH_IMAGE106
；Extract the prior location of the test data from the raw observations output by the user's GNSS receiver
Figure 982881DEST_PATH_IMAGE016
, position precision factor PDOP, pseudorange residual, carrier-to-noise ratio, satellite elevation angle, and satellite azimuth angle to form a test sample to construct a GNSS test data set
Figure 680579DEST_PATH_IMAGE106
; GNSS测试数据集构建完成后进行遍历，计算以下参数：所有测试样本的位置精度因子PDOP的均值
Figure DEST_PATH_IMAGE107
和标准差
Figure 758125DEST_PATH_IMAGE108
、第
Figure DEST_PATH_IMAGE109
个测试样本PDOP的标准化处理结果
Figure 414235DEST_PATH_IMAGE110
和比重
Figure 879195DEST_PATH_IMAGE112
，计算方法分别如下所列：After the GNSS test data set is constructed, traverse and calculate the following parameters: the mean value of the position factor of precision PDOP of all test samples
Figure DEST_PATH_IMAGE107
and standard deviation
Figure 758125DEST_PATH_IMAGE108
, No.
Figure DEST_PATH_IMAGE109
The normalized processing results of PDOP of test samples
Figure 414235DEST_PATH_IMAGE110
and specific gravity
Figure 879195DEST_PATH_IMAGE112
, the calculation methods are as follows:
Figure 239638DEST_PATH_IMAGE114
Figure 239638DEST_PATH_IMAGE114
Figure 719161DEST_PATH_IMAGE116
Figure 719161DEST_PATH_IMAGE116
Figure 874068DEST_PATH_IMAGE118
Figure 874068DEST_PATH_IMAGE118
Figure 642304DEST_PATH_IMAGE120
Figure 642304DEST_PATH_IMAGE120
 其中，
Figure DEST_PATH_IMAGE121
为测试样本数量，
Figure 871684DEST_PATH_IMAGE122
为第
Figure 736872DEST_PATH_IMAGE109
个测试样本对应的PDOP，
Figure DEST_PATH_IMAGE123
为所有测试样本PDOP的最小值，
Figure 734784DEST_PATH_IMAGE124
为所有测试样本PDOP的最大值。in,
Figure DEST_PATH_IMAGE121
is the number of test samples,
Figure 871684DEST_PATH_IMAGE122
for the first
Figure 736872DEST_PATH_IMAGE109
PDOP corresponding to test samples,
Figure DEST_PATH_IMAGE123
is the minimum value of PDOP for all test samples,
Figure 734784DEST_PATH_IMAGE124
is the maximum value of PDOP of all test samples. 9.根据权利要求8所述的一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，步骤2-2所述的根据各测试样本的先验位置匹配到相应格网层，调用模型并判定其可用性，具体方法包括：9. A kind of urban complex environment navigation and positioning method based on three-dimensional grid multi-path modeling according to claim 8, it is characterized in that, according to the prior position of each test sample described in step 2-2, match to the corresponding grid The network layer calls the model and determines its availability. The specific methods include: 利用已有的三维格网布局，将测试数据逐个匹配到各自的所属格网层，并调用相应格网层的多径误差模型，随后根据格网层模型精度与测试数据质量，基于平均值和比重进行模型可用性判断；对于某一历元的数据，作如下判定：Using the existing three-dimensional grid layout, match the test data to their respective grid layers one by one, and call the multipath error model of the corresponding grid layer, and then according to the accuracy of the grid layer model and the quality of the test data, based on the average value and The specific gravity is used to judge the usability of the model; for the data of a certain epoch, the following judgment is made:
Figure 177267DEST_PATH_IMAGE126
Figure 145092DEST_PATH_IMAGE128
Figure 177267DEST_PATH_IMAGE126
Figure 145092DEST_PATH_IMAGE128
 其中，
Figure DEST_PATH_IMAGE129
为第
Figure 986490DEST_PATH_IMAGE109
个测试数据所属格网对应的多径误差模型的均方根误差值，
Figure 155303DEST_PATH_IMAGE090
为所有多径误差模型均方根误差的平均值，
Figure 163710DEST_PATH_IMAGE122
为第
Figure 138489DEST_PATH_IMAGE109
个测试数据对应历元的PDOP，
Figure 447110DEST_PATH_IMAGE107
为测试数据集中所有样本历元PDOP的平均值；若某一历元数据同时满足两式，则判定其对应的多径误差模型可用，用所述多径误差模型预测多径误差并进行后续修正和最终定位解算，否则进行基于比重的判定如下：in,
Figure DEST_PATH_IMAGE129
for the first
Figure 986490DEST_PATH_IMAGE109
The root mean square error value of the multipath error model corresponding to the grid to which the test data belongs,
Figure 155303DEST_PATH_IMAGE090
is the mean value of the root mean square error of all multipath error models,
Figure 163710DEST_PATH_IMAGE122
for the first
Figure 138489DEST_PATH_IMAGE109
test data corresponding to the PDOP of the epoch,
Figure 447110DEST_PATH_IMAGE107
is the average value of the PDOP of all sample epochs in the test data set; if a certain epoch data satisfies the two formulas at the same time, it is determined that its corresponding multipath error model is available, and the multipath error model is used to predict the multipath error and perform subsequent corrections and the final positioning solution, otherwise the judgment based on the specific gravity is as follows:
Figure DEST_PATH_IMAGE131
Figure DEST_PATH_IMAGE133
Figure DEST_PATH_IMAGE131
Figure DEST_PATH_IMAGE133
 其中，
Figure 914388DEST_PATH_IMAGE134
为第
Figure 128201DEST_PATH_IMAGE109
个测试数据的比重，
Figure DEST_PATH_IMAGE135
为预设的比重门限值，若该历元测试样本满足上述不等式，则判定多径误差模型可用从而进行多径误差预测和修正，否则判定不可用，不进行建模修正。in,
Figure 914388DEST_PATH_IMAGE134
for the first
Figure 128201DEST_PATH_IMAGE109
The proportion of test data,
Figure DEST_PATH_IMAGE135
is the preset proportion threshold value, if the epoch test sample satisfies the above inequality, it is determined that the multipath error model is available to perform multipath error prediction and correction, otherwise it is determined that it is not available, and no modeling correction is performed. 10.根据权利要求9所述的一种基于三维格网多径建模的城市复杂环境导航定位方法，其特征在于，步骤2-3所述的得到修正后的定位结果，包括：10. A kind of method for navigation and positioning of urban complex environment based on three-dimensional grid multipath modeling according to claim 9, characterized in that, obtaining the corrected positioning results described in step 2-3 comprises: 假设第
Figure 313194DEST_PATH_IMAGE109
个历元观测伪距为
Figure 194431DEST_PATH_IMAGE136
，所述多径误差模型预测的多径误差值为
Figure DEST_PATH_IMAGE137
，则修正后的伪距为
Figure 498855DEST_PATH_IMAGE138
，依据伪距定位原理利用
Figure DEST_PATH_IMAGE139
代替
Figure 403226DEST_PATH_IMAGE136
，解算修正后的定位解。Assuming the first
Figure 313194DEST_PATH_IMAGE109
The epoch observed pseudorange is
Figure 194431DEST_PATH_IMAGE136
, the multipath error predicted by the multipath error model is
Figure DEST_PATH_IMAGE137
, then the corrected pseudorange is
Figure 498855DEST_PATH_IMAGE138
, according to the principle of pseudo-range positioning using
Figure DEST_PATH_IMAGE139
replace
Figure 403226DEST_PATH_IMAGE136
, solve the corrected positioning solution.
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