WO2016169227A1 - Gnss单点定位的方法及装置 - Google Patents

Gnss单点定位的方法及装置 Download PDF

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WO2016169227A1
WO2016169227A1 PCT/CN2015/091867 CN2015091867W WO2016169227A1 WO 2016169227 A1 WO2016169227 A1 WO 2016169227A1 CN 2015091867 W CN2015091867 W CN 2015091867W WO 2016169227 A1 WO2016169227 A1 WO 2016169227A1
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matrix
state value
predicted state
variance matrix
variance
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PCT/CN2015/091867
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English (en)
French (fr)
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陈孔哲
高庆余
胡刚
李涛
张思静
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和芯星通科技(北京)有限公司
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Priority to EP15889713.2A priority Critical patent/EP3287811A4/en
Publication of WO2016169227A1 publication Critical patent/WO2016169227A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/40—Correcting position, velocity or attitude

Definitions

  • GNSS global satellite navigation and positioning system
  • the Global Navigation Satellite Positioning System consists of the United States' Global Positioning System (GPS), Russia's GLONASS navigation system (GLONASS), China's Beidou navigation system (BeiDou) and the European Union's Galileo satellite navigation system. .
  • the GPS and GLONASS systems have all been completed and have global positioning capabilities.
  • China's BeiDou has launched 16 satellites, including 5 Medium Earth Orbit (MEO) satellites, 5 Incidated Geosynchronous Satellite Orbit (IGSO) satellites and 6 geostationary orbits (GEO). , Geostatation Earth Orbit) satellite, which achieves positioning in the Asia Pacific region.
  • MEO Medium Earth Orbit
  • IGSO Incidated Geosynchronous Satellite Orbit
  • GEO geostationary orbits
  • Geostatation Earth Orbit Geostatation Earth Orbit
  • the traditional GNSS single-point positioning method uses the least squares estimation, from the observation of a single epoch, through the established observation model and stochastic model, based on the principle of the smallest sum of squared weight residuals, estimates the coordinate increase relative to the initial coordinates. Quantity, thus obtaining the final coordinates and other parameters estimated together, such as the clock difference.
  • the established observation model is shown in formula (1):
  • z k is the observed value of the receiver at time k (the observed measurement in GNSS single point positioning minus the calculated known value).
  • x k represents the state value of the receiver at time k
  • ⁇ k represents the random error of the observed model
  • R represents the observed error variance matrix
  • H represents the design matrix
  • N(0, R) represents the random error obeying the 0 expectation and the R variance.
  • the estimated coordinate values are indeed the optimal values based on the existing observations.
  • the positioning result obtained by least squares can be basically stabilized at the meter level, which satisfies most applications.
  • the observation measurement is limited and the observation quality is relatively poor.
  • the positioning results generally have large deviations, which seriously reduces the usability of the positioning results.
  • GNSS global satellite navigation and positioning system
  • a method for GNSS single point positioning comprising:
  • a dynamic model of Kalman filtering is established according to the dynamic error variance matrix and the state transition matrix, and an observation model of Kalman filtering is established according to the observed error variance matrix and the design matrix;
  • the smoothing speed is obtained, and a variance matrix of the state value and the state value at the next moment is calculated based on the obtained smoothing speed and the second predicted state value and the variance matrix of the second predicted state value.
  • the dynamic model is established according to the following formula:
  • x k ⁇ x k-1 +w k-1 ;
  • the observation model is established according to the following formula:
  • x k-1 and x k represent the state values of the receiver at (k-1) and k, respectively, ⁇ represents the state transition matrix, H is the design matrix, and z k is the observed value of the receiver at time k; w k-1 and ⁇ k represent the random error of the dynamic model and the random error of the observed model, respectively, and obey the following distributions:
  • Q and R represent the dynamic error variance matrix and the observation error variance matrix, respectively.
  • the first predicted state value is obtained according to the following formula:
  • Q represents a dynamic error variance matrix and ⁇ represents a state transition matrix, Indicates the state value of the receiver at time (k-1), and P k-1 represents the variance matrix of the state value of the receiver at time (k-1).
  • the gain matrix is calculated according to the following formula:
  • a variance matrix representing the first predicted state value of the receiver at time k R represents the observed error variance matrix
  • H is the design matrix.
  • the state value of the second prediction is obtained according to the following formula:
  • I represents the identity matrix
  • a variance matrix representing the first predicted state value of the receiver at time k
  • Kk represents the gain matrix
  • the state value of the next moment is calculated according to the following formula:
  • the acquiring the smoothing speed includes: acquiring the current time and the speeds of the two moments before the current moment;
  • the smoothing speed is calculated based on each of the obtained speeds and the assigned weight values.
  • An apparatus for GNSS single point positioning comprising: a modeling module, a first obtaining module, a first calculating module, a second acquiring module, and a second calculating module;
  • the modeling module is configured to: establish a dynamic model of the Kalman filter according to the dynamic error variance matrix and the state transition matrix, and establish an observation model of the Kalman filter according to the observed error variance matrix and the design matrix;
  • the first obtaining module is configured to: obtain a variance matrix of the first predicted state value and the first predicted state value according to the established Kalman filter dynamic model and the observation model;
  • a first calculating module configured to: calculate a gain matrix according to the obtained variance matrix of the first predicted state value, the design matrix, and the observed error variance matrix;
  • a second acquiring module configured to: calculate a second predicted state value according to the obtained first predicted state value and the design matrix, the observation value, and the gain matrix; and obtain a variance matrix, a gain matrix, and a first predicted state value according to the obtained Designing a matrix to calculate a variance matrix of the second predicted state value;
  • the second calculating module is configured to: obtain a smoothing speed, and calculate a variance matrix of the state value and the state value at the next moment according to the obtained smoothing speed and the second predicted state value and the variance matrix of the second predicted state value.
  • the foregoing second calculating module is configured to: acquire a speed of two moments before the current time and the current time;
  • the smoothing speed is calculated based on each of the obtained speeds and the assigned weight values.
  • a computer readable storage medium storing computer executable instructions for performing the method of any of the above.
  • the technical schemes of this paper include: establishing a dynamic model of Kalman filter based on dynamic error variance matrix and state transition matrix, and establishing an observation model of Kalman filter based on the observed error variance matrix and design matrix; based on the established Kalman filter dynamic model and observation model Obtaining a variance matrix of the first predicted state value and the first predicted state value respectively; calculating a gain matrix according to the obtained variance matrix of the first predicted state value, the design matrix, and the observed error variance matrix; Predicting the state value and the design matrix, the observation value, and the gain matrix to calculate a second predicted state value; calculating a variance matrix of the second predicted state value according to the obtained variance matrix, gain matrix, and design matrix of the first predicted state value And obtaining a smoothing speed, and calculating a variance matrix of the state value and the state value at the next moment according to the obtained smoothing speed and the second predicted state value and the variance matrix of the second predicted state value.
  • the technical solution in this paper improves the accuracy and usability of the positioning results.
  • FIG. 1 is a flowchart of a method for GNSS single point positioning based on Kalman filtering according to an embodiment of the present invention
  • FIG. 2 is a schematic structural diagram of an apparatus for GNSS single point positioning based on Kalman filtering according to an embodiment of the present invention.
  • FIG. 1 is a flowchart of a method for GNSS single point positioning based on Kalman filtering according to an embodiment of the present invention. As shown in FIG. 1 , the method includes:
  • Step 101 Establish a dynamic model of the Kalman filter according to the dynamic error variance matrix and the state transition matrix, and establish an observation model of the Kalman filter according to the observed error variance matrix and the design matrix.
  • x k-1 and x k represent the state values of the receiver at (k-1) and k, respectively, ⁇ represents the state transition matrix, H is the design matrix, and z k is the observed value of the receiver at time k; w k-1 and ⁇ k represent the random error of the dynamic model and the random error of the observed model, respectively, and obey the following distributions:
  • Q and R represent the dynamic error variance matrix and the observation error variance matrix.
  • ⁇ is obtained according to the real-time dynamic condition of the receiver
  • H is obtained by linearizing the geometric distance between the satellite and the receiver given the initial value of the receiver position x.
  • x k-1 and x k can be derived according to equation (1.1).
  • z k is the observed value, which can be obtained by subtracting the calculated known value from the observation in the GNSS single point positioning, wherein the observation of the GNSS can be obtained from the receiver, and the calculated known value is obtained by the receiver.
  • the initial distance x is used to determine the geometric distance from the satellite to the receiver.
  • Step 102 Acquire a variance matrix of the first predicted state value and the first predicted state value according to the established Kalman filter dynamic model and the observation model.
  • the variance matrix of the first predicted state value and the first predicted state value is obtained according to formula (1.3) and formula (1.4), respectively:
  • Q represents a dynamic error variance matrix and ⁇ represents a state transition matrix, Indicates the state value of the receiver at time (k-1), and P k-1 represents the variance matrix of the state value of the receiver at time (k-1).
  • Step 103 Calculate a gain matrix according to the obtained variance matrix of the first predicted state value, the design matrix, and the observed error variance matrix.
  • the gain matrix is calculated according to formula (1.5):
  • a variance matrix representing the first predicted state value of the receiver at time k R represents the observed error variance matrix
  • H is the design matrix.
  • Step 104 Calculate a second predicted state value according to the obtained first predicted state value and the design matrix, the observation value, and the gain matrix; and calculate the variance matrix, the gain matrix, and the design matrix according to the obtained first predicted state value.
  • the variance matrix of the predicted state values is
  • the variance matrix of the second predicted state value and the second predicted state value are obtained according to formulas (1.6) and (1.7), respectively:
  • I represents the identity matrix
  • a variance matrix representing the first predicted state value of the receiver at time k
  • Kk represents the gain matrix
  • Step 105 Acquire a smoothing speed, and calculate a variance value matrix of the state value and the state value at the next moment according to the obtained smoothing speed and the second predicted state value and the variance matrix of the second predicted state value.
  • the obtaining smoothing speed in this step includes: acquiring the current time and the speeds of the two moments before the current time;
  • the smoothing speed is calculated based on each of the obtained speeds and the assigned weight values.
  • weight values to each speed can be allocated according to actual needs, for example, all can be 1/3; in addition, those skilled in the art can also determine the speed of selecting several consecutive moments according to actual application conditions. Smooth the speed.
  • the speed can be given by the INS and is not affected by the observation environment.
  • the Kalman filter can achieve reliable positioning. It can be extended to use acceleration to predict the speed and then predict the coordinates.
  • the instantaneous velocity is generally estimated from the Doppler observations or from the phase observation difference between the epochs.
  • the accuracy of the estimated value of the speed also deteriorates, resulting in a decrease in the accuracy of the state prediction value of the Kalman filter. Therefore, it is necessary to properly smooth the estimated speed in a complex scene (which can be judged based on the number of satellites or the DOP value).
  • the smoothing method is shown in equations (2.0) and (2.1):
  • the amount of change in speed that is, the value of acceleration
  • the simple GNSS system cannot obtain the acceleration value, so it can be obtained by the speed change of two consecutive epochs.
  • there is a limit to the amount of change in this speed For example, in an in-vehicle application, the amount of change in speed will generally be within a range of gravitational acceleration. Therefore, it is possible to limit the amount of change in speed (taking car navigation as an example):
  • g is the acceleration of gravity.
  • the Kalman filter (formula 1.1-1.7) is used to predict the position of the next epoch and its variance (formula 1.8-1.9), and then the result of the positioning estimation and its variance are updated by GNSS observation. Therefore, the positioning results between each epoch are linked by speed, which increases the reliability and accuracy of the positioning.
  • the method in the embodiment of the present invention smoothes the speed in the complex scene (formula 2.0-2.1), improves the reliability of the speed, and then uses the position prediction to improve the positioning. result.
  • FIG. 2 is a schematic structural diagram of an apparatus for GNSS single-point positioning based on Kalman filtering according to an embodiment of the present invention. As shown in FIG. 2, the method includes: a modeling module 21, a first obtaining module 22, a first calculating module 23, and a second acquiring. Module 24 and second computing module 25; wherein
  • the modeling module 21 is configured to: respectively establish a dynamic model and an observation model of the Kalman filter according to the dynamic error variance matrix and the state transition matrix, and the observation error variance matrix and the design matrix.
  • the modeling module 21 is configured to: establish a dynamic model and an observation model according to formulas (1.1) and (1.2), respectively.
  • the first obtaining module 22 is configured to respectively acquire a variance matrix of the first predicted state value and the first predicted state value according to the established Kalman filter dynamic model and the observation model.
  • the first obtaining module 22 is configured to obtain a variance matrix of the first predicted state value and the first predicted state value according to the formula (1.3) and the formula (1.4), respectively.
  • the first calculating module 23 is configured to: calculate a gain matrix according to the obtained variance matrix of the first predicted state value, the design matrix, and the observed error variance matrix.
  • the first calculation module 23 is configured to calculate the gain matrix according to formula (1.5).
  • the second obtaining module 24 is configured to: calculate a second predicted state value according to the obtained first predicted state value and the design matrix, the observation value, and the gain matrix; and a variance matrix and a gain matrix according to the obtained first predicted state value And design a matrix to calculate a variance matrix of the second predicted state value.
  • the second obtaining module 24 is configured to obtain a variance matrix of the second predicted state value and the second predicted state value according to the formulas (1.6) and (1.7), respectively.
  • the second calculating module 25 is configured to: obtain a smoothing speed, according to the obtained smoothing speed and the second The predicted state value and the variance matrix of the second predicted state value calculate the state value of the next time and the variance matrix of the state value.
  • the second calculation module 25 is configured to calculate the state value and the variance matrix of the next time according to the formulas (1.8) and (1.9), respectively.
  • the second calculating module 25 acquires the smoothing speed, including: acquiring the current time and the speeds of the two moments before the current time;
  • the smoothing speed is calculated based on each of the obtained speeds and the assigned weight values.
  • all or part of the steps of the above embodiments may also be implemented by using an integrated circuit. These steps may be separately fabricated into individual integrated circuit modules, or multiple modules or steps may be fabricated into a single integrated circuit module. achieve.
  • the devices/function modules/functional units in the above embodiments may be implemented by a general-purpose computing device, which may be centralized on a single computing device or distributed over a network of multiple computing devices.
  • the device/function module/functional unit in the above embodiment When the device/function module/functional unit in the above embodiment is implemented in the form of a software function module and sold or used as a stand-alone product, it can be stored in a computer readable storage medium.
  • the above mentioned computer readable storage medium may be a read only memory, a magnetic disk or an optical disk or the like.
  • the velocity is used to predict the position of the next epoch and its variance, and then the result of the positioning estimation and its variance are updated by GNSS observation, so that each The positioning results between the epochs are linked by speed, which increases the reliability and accuracy of the positioning.
  • the embodiment of the present invention smoothes the speed in the complex scene, improves the reliability of the speed, and then uses the position prediction to improve the positioning result.

Abstract

一种GNSS单点定位的方法及装置，包括：分别建立卡尔曼滤波的动态模型和观测模型；根据建立的动态模型和观测模型，分别获取第一预测的状态值和第一预测的状态值的方差矩阵；根据获得的第一预测的状态值的方差矩阵、设计矩阵和观测误差方差阵，计算增益矩阵；根据获得的第一预测的状态值和设计矩阵、观测值以及增益矩阵计算第二预测的状态值；根据获得的第一预测的状态值的方差矩阵、增益矩阵和设计矩阵，计算第二预测的状态值的方差矩阵；获取平滑速度，根据获得的平滑速度和第二预测的状态值以及第二预测的状态值的方差矩阵计算下一时刻的状态值及状态值的方差矩阵。

Description

GNSS单点定位的方法及装置 技术领域
本文涉及卫星导航领域，尤指一种全球卫星导航定位系统(GNSS)单点定位的方法及装置。
背景技术
目前，全球卫星导航定位系统(GNSS)由美国的全球卫星定位系统(GPS)，俄罗斯的格洛纳斯卫星导航系统(GLONASS)，中国的北斗导航系统(BeiDou)以及欧盟的Galileo卫星导航系统组成。其中GPS和GLONASS系统已经全部建设完成，具备全球定位的功能。中国的BeiDou目前已经发射了16颗卫星，其中包括5颗中地球轨道(MEO，Medium Earth Orbit)卫星，5颗倾斜地球同步轨道(IGSO，Inclined Geosynchronous Satellite Orbit)卫星和6颗地球静止轨道(GEO，Geostationary Earth Orbit)卫星，实现了亚太地区的定位功能。欧盟的Galileo系统则有四颗卫星可用。日本和印度也在研制自己的区域卫星导航定位系统。不难看出，GNSS行业目前发展势头迅猛，已经形成了产业化，因而可靠的导航定位算法及结果则显得尤为重要。
传统的GNSS单点定位方法采用最小二乘估计，由单个历元的观测量，通过所建立的观测模型和随机模型，根据加权残差平方和最小的原则，估计出相对于初始坐标的坐标增量，从而得到最终的坐标及其他一起估计的参数，如钟差等。其中，建立的观测模型如公式(1)所示：
zk＝Hxk+εk         (1)
建立的随机模型如公式(2)所示：
p(εk)～N(0,R)        (2)
其中，zk为接收机在k时刻的观测值(GNSS单点定位中的观测量减去可计算出来的已知值)。xk表示接收机在k时刻的状态值，εk表示观测模型的随机误差，R表示观测误差方差阵，H表示设计矩阵，N(0,R)表示随机误差服从0期望和R方差。
从理论上来讲，所估计的坐标值的确是根据已有的观测信息得出的最优值。在观测量可靠的情况下，由最小二乘所得到的定位结果基本可以稳定在米级，满足大多数的应用。然而，在一些复杂场景下，如信号重捕，高楼遮挡,过桥等，观测量有限且观测质量比较差，此时的定位结果一般都存在较大的偏差，严重降低了定位结果的可用性。
发明内容
本文提供了一种全球卫星导航定位系统(GNSS)单点定位的方法及装置，能够提高定位结果的精度和可用性。
一种GNSS单点定位的方法，包括：
根据动态误差方差阵和状态转移矩阵建立卡尔曼滤波的动态模型以及根据观测误差方差阵和设计矩阵建立卡尔曼滤波的观测模型；
根据建立的卡尔曼滤波的动态模型和观测模型，分别获取第一预测的状态值和第一预测的状态值的方差矩阵；
根据获得的第一预测的状态值的方差矩阵、设计矩阵和观测误差方差阵，计算增益矩阵；
根据获得的第一预测的状态值和设计矩阵、观测值以及增益矩阵计算第二预测的状态值；根据获得的第一预测的状态值的方差矩阵、增益矩阵和设计矩阵，计算第二预测的状态值的方差矩阵；
获取平滑速度，根据获得的平滑速度和第二预测的状态值以及第二预测的状态值的方差矩阵计算下一时刻的状态值及状态值的方差矩阵。
可选地，按照下式建立所述动态模型：
xk＝Φxk-1+wk-1；
按照下式建立所述观测模型：
zk＝Hxk+εk；
其中，xk-1和xk分别表示接收机在(k-1)时刻和k时刻的状态值，Φ表示状态转移矩阵，H为设计矩阵，zk为接收机在k时刻的观测值；wk-1和εk分别表 示动态模型的随机误差和观测模型的随机误差，并且分别服从下列分布：
p(wk-1)～N(0,Q)
p(εk)～N(0,R)
Q和R分别表示动态误差方差阵和观测误差方差阵。
可选地，按照下式获取第一预测的状态值：
Figure PCTCN2015091867-appb-000001
按照下式获取第一预测的状态值的方差矩阵；
Figure PCTCN2015091867-appb-000002
其中，Q表示动态误差方差阵，Φ表示状态转移矩阵，
Figure PCTCN2015091867-appb-000003
表示接收机在(k-1)时刻的状态值，Pk-1表示接收机在(k-1)时刻的状态值的方差矩阵。
可选地，按照下式计算所述增益矩阵：
Figure PCTCN2015091867-appb-000004
其中，
Figure PCTCN2015091867-appb-000005
表示接收机在k时刻的第一预测的状态值的方差矩阵，R表示观测误差方差阵，H为设计矩阵。
可选地，按照下式获取所述第二预测的状态值：
Figure PCTCN2015091867-appb-000006
按照下式获取所述第二预测的状态值的方差矩阵：
Figure PCTCN2015091867-appb-000007
其中，I表示单位矩阵，
Figure PCTCN2015091867-appb-000008
表示接收机在k时刻的第一预测的状态值，
Figure PCTCN2015091867-appb-000009
表示接收机在k时刻的第一预测的状态值的方差矩阵，Kk表示增益矩阵。
可选地，按照下式计算下一时刻的状态值：
Figure PCTCN2015091867-appb-000010
按照下式计算下一时刻的状态值的方差矩阵：
Figure PCTCN2015091867-appb-000011
其中，
Figure PCTCN2015091867-appb-000012
表示在k时刻获得的接收机的平滑速度，t表示k时刻到(k+1)时刻之间的时间间隔，
Figure PCTCN2015091867-appb-000013
表示在k时刻获得的接收机的平滑速度的方差矩 阵，
Figure PCTCN2015091867-appb-000014
表示接收机在k时刻的第二预测的状态值。
可选地，所述获取平滑速度包括：获取当前时刻和当前时刻之前的两个时刻的速度；
为获得的每个速度分配权重值，其中分配的权重值之和为1；
根据获得的每个速度和分配的权重值，计算平滑速度。
一种GNSS单点定位的装置，包括：建模模块、第一获取模块、第一计算模块、第二获取模块和第二计算模块；其中，
建模模块，设置为：根据动态误差方差阵和状态转移矩阵建立卡尔曼滤波的动态模型以及根据观测误差方差阵和设计矩阵建立卡尔曼滤波的观测模型；
第一获取模块，设置为：根据建立的卡尔曼滤波的动态模型和观测模型，分别获得第一预测的状态值和第一预测的状态值的方差矩阵；
第一计算模块，设置为：根据获得的第一预测的状态值的方差矩阵、设计矩阵和观测误差方差阵，计算增益矩阵；
第二获取模块，设置为：根据获得的第一预测的状态值和设计矩阵、观测值以及增益矩阵计算第二预测的状态值；根据获得的第一预测的状态值的方差矩阵、增益矩阵和设计矩阵，计算第二预测的状态值的方差矩阵；
第二计算模块，设置为：获取平滑速度，根据获得的平滑速度和第二预测的状态值以及第二预测的状态值的方差矩阵计算下一时刻的状态值及状态值的方差矩阵。
可选地，上述第二计算模块是设置为：获取当前时刻和当前时刻之前的两个时刻的速度；
为获得的每个速度分配权重值，其中分配的权重值之和为1；
根据获得的每个速度和分配的权重值，计算平滑速度。
一种计算机可读存储介质，存储有计算机可执行指令，所述计算机可执行指令用于执行上述任一项的方法。
本文技术方案包括：根据动态误差方差阵和状态转移矩阵建立卡尔曼滤波的动态模型以及根据观测误差方差阵和设计矩阵建立卡尔曼滤波的观测模型；根据建立的卡尔曼滤波的动态模型和观测模型，分别获取第一预测的状态值和第一预测的状态值的方差矩阵；根据获得的第一预测的状态值的方差矩阵、设计矩阵和观测误差方差阵，计算增益矩阵；根据获得的第一预测的状态值和设计矩阵、观测值以及增益矩阵计算第二预测的状态值；根据获得的第一预测的状态值的方差矩阵、增益矩阵和设计矩阵，计算第二预测的状态值的方差矩阵；获取平滑速度，根据获得的平滑速度和第二预测的状态值以及第二预测的状态值的方差矩阵计算下一时刻的状态值及状态值的方差矩阵。本文技术方案提高了定位结果的精度和可用性。
附图概述
图1为本发明实施例的基于卡尔曼滤波的GNSS单点定位的方法的流程图；
图2为本发明实施例的基于卡尔曼滤波的GNSS单点定位的装置的结构示意图。
本发明的实施方式
下文中将结合附图对本发明的实施方式进行详细说明。需要说明的是，在不冲突的情况下，本文中的实施例及实施例中的特征可以相互任意组合。
图1为本发明实施例基于卡尔曼滤波的GNSS单点定位的方法的流程图，如图1所示，包括：
步骤101：根据动态误差方差阵和状态转移矩阵建立卡尔曼滤波的动态模型以及根据观测误差方差阵和设计矩阵建立卡尔曼滤波的观测模型。
其中，分别按照公式(1.1)和(1.2)建立动态模型和观测模型：
xk＝Φxk-1+wk-1          (1.1)
zk＝Hxk+εk           (1.2)
其中，xk-1和xk分别表示接收机在(k-1)时刻和k时刻的状态值，Φ表示状 态转移矩阵，H为设计矩阵，zk为接收机在k时刻的观测值；wk-1和εk分别表示动态模型的随机误差和观测模型的随机误差，并且分别服从下列分布：
p(wk-1)～N(0,Q)
p(εk)～N(0,R)
Q和R表示动态误差方差阵和观测误差方差阵。
需要说明的是，Φ是根据接收机实时的动态情况获取的，H则是在给定接收机位置x初值的情况下，对卫星到接收机间的几何距离进行线性化得到的。在给定接收机位置x初值的情况下，xk-1和xk可以根据公式(1.1)进行推导。关于如何获取以及计算Φ和H以及计算Q和R，属于本领域技术人员所熟知的惯用技术手段，在此不再赘述。zk为观测值，可以由GNSS单点定位中的观测量减去可计算出来的已知值获得，其中，GNSS的观测量可以从接收机中获得，计算出来的已知值是由接收机位置初值x来求得的卫星至接收机间的几何距离。
步骤102：根据建立的卡尔曼滤波的动态模型和观测模型，分别获取第一预测的状态值和第一预测的状态值的方差矩阵。
其中，分别按照公式(1.3)和公式(1.4)获取第一预测的状态值和第一预测的状态值的方差矩阵：
Figure PCTCN2015091867-appb-000015
Figure PCTCN2015091867-appb-000016
其中，Q表示动态误差方差阵，Φ表示状态转移矩阵，
Figure PCTCN2015091867-appb-000017
表示接收机在(k-1)时刻的状态值，Pk-1表示接收机在(k-1)时刻的状态值的方差矩阵。
步骤103：根据获得的第一预测的状态值的方差矩阵、设计矩阵和观测误差方差阵，计算增益矩阵。
其中，按照公式(1.5)计算增益矩阵：
Figure PCTCN2015091867-appb-000018
其中，
Figure PCTCN2015091867-appb-000019
表示接收机在k时刻的第一预测的状态值的方差矩阵，R表示观测误差方差阵，H为设计矩阵。
步骤104：根据获得的第一预测的状态值和设计矩阵、观测值以及增益矩阵计算第二预测的状态值；根据获得的第一预测的状态值的方差矩阵、增益矩阵和设计矩阵，计算第二预测的状态值的方差矩阵。
其中，分别按照公式(1.6)和(1.7)获取所述第二预测的状态值和第二预测的状态值的方差矩阵：
Figure PCTCN2015091867-appb-000020
Figure PCTCN2015091867-appb-000021
其中，I表示单位矩阵，
Figure PCTCN2015091867-appb-000022
表示接收机在k时刻的第一预测的状态值，
Figure PCTCN2015091867-appb-000023
表示接收机在k时刻的第一预测的状态值的方差矩阵，Kk表示增益矩阵。
步骤105：获取平滑速度，根据获得的平滑速度和第二预测的状态值以及第二预测的状态值的方差矩阵计算下一时刻的状态值及状态值的方差矩阵。
其中，分别按照公式(1.8)和(1.9)计算下一时刻的状态值及方差矩阵：
Figure PCTCN2015091867-appb-000024
Figure PCTCN2015091867-appb-000025
其中，
Figure PCTCN2015091867-appb-000026
表示在k时刻获得的接收机的平滑速度，t表示k时刻到(k+1)时刻之间的时间间隔，
Figure PCTCN2015091867-appb-000027
表示在k时刻获得的接收机的平滑速度的方差矩阵，
Figure PCTCN2015091867-appb-000028
表示接收机在k时刻的第二预测的状态值。
本步骤中的获取平滑速度包括：获取当前时刻和当前时刻之前的两个时刻的速度；
为获得的每个速度分配权重值，其中分配的权重值之和为1；
根据获得的每个速度和分配的权重值，计算平滑速度。
需要说明的是，关于如何为每个速度分配权重值可以根据实际需要进行分配，例如可以都为1/3；另外，本领域技术人员也可以根据实际的应用情况确定选择几个连续时刻的速度进行速度平滑。
举例说明，对于有惯性导航系统(INS)集成的GNSS系统，速度可以由INS给出，不受观测环境的影响，该卡尔曼滤波则可以实现可靠的定位，甚 至可以扩展到运用加速度来进行速度的预测，然后再对坐标进行预测。而对于单纯的GNSS系统，瞬时速度一般由多普勒观测值可以估计求得，或者是由历元间的相位观测值差分进行估计。在较差的观测环境下，速度的估计值精度也变差，从而导致卡尔曼滤波的状态预测值精度下降。因此，需要适当的对复杂场景下(可根据卫星数或者DOP值进行判断)估计的速度进行平滑。平滑的方法如公式(2.0)和(2.1)所示：
Figure PCTCN2015091867-appb-000029
Figure PCTCN2015091867-appb-000030
其中，
Figure PCTCN2015091867-appb-000031
表示平滑后的速度，
Figure PCTCN2015091867-appb-000032
表示接收机在k时刻的速度，
Figure PCTCN2015091867-appb-000033
表示接收机在(k-1)时刻的速度，
Figure PCTCN2015091867-appb-000034
接收机在(k-2)时刻的速度，a，b和c表示用当前和之前两个历元速度的权重，并且符合a+b+c＝1。鉴于较早的历史速度对当前速度的作用影响很小，只有最近的几个历元的速度参考价值较大，用户可以自己设置a，b和c的大小，例如可以取a＝b＝c＝1/3；例如也可以取a＝0，b＝c＝0.5；a＝1，b＝c＝0；用户也可以根据自己的情况来选择用多少个历元(不限于本发明实施例中所提到的3个历元)来进行速度平滑。
然而在实际应用中，速度的变化量，即加速度值，也需要进行考虑。单纯的GNSS系统无法获得加速度值，因此可以通过连续两个历元的速度变化量来求得。除非在高动态情况下(一般这种情况下观测环境受遮挡较小)，该速度的变化量也有一定的限值。比如说在车载应用中，一般情况下速度的变化量都会在一个重力加速度范围以内。因此可以对速度的变化量加以限制(以车载导航为例)：
Figure PCTCN2015091867-appb-000035
其中，g为重力加速度。当速度的变化量在一个g的范围之内时，表示速度的估计值比较可靠，不需要进行速度平滑，即相当于上述的a＝1，b＝c＝0的取值情况；当速度的变化量超出一个g的范围时，当前的速度估计值不可靠，需要用式(2.0)和(2.1)来进行速度平滑以求得当前历元的速度值，同时当前时刻的速度权重值需要设置为0，之前两个历元的权重值也相应的需要进行调整，如均设置为0.5，即相当于上述的a＝0，b＝c＝0.5的取值情况。 这样，相对可靠的速度加上所建立的卡尔曼滤波模型就可以提高我们在观测环境条件较差环境下的定位精度和可靠性。
本发明实施例通过采用卡尔曼滤波(公式1.1-1.7)，运用速度来预测下个历元的位置及其方差(公式1.8-1.9)，然后通过GNSS观测量来更新定位估计的结果及其方差，从而使每个历元间的定位结果通过速度联系起来，增加了定位的可靠性及其精度。此外，由于复杂场景下的速度估计也存在偏差，本发明实施例方法对复杂场景下的速度进行平滑(公式2.0-2.1)，提高了速度的可靠性，然后再用于位置预测，从而改善定位结果。
图2为本发明实施例基于卡尔曼滤波的GNSS单点定位的装置的结构示意图，如图2所示，包括：建模模块21、第一获取模块22、第一计算模块23、第二获取模块24和第二计算模块25；其中，
建模模块21，设置为：根据动态误差方差阵和状态转移矩阵以及观测误差方差阵和设计矩阵分别建立卡尔曼滤波的动态模型和观测模型。
其中，建模模块21，是设置为：分别按照公式(1.1)和(1.2)建立动态模型和观测模型。
第一获取模块22，设置为：根据建立的卡尔曼滤波的动态模型和观测模型，分别获取第一预测的状态值和第一预测的状态值的方差矩阵。
其中，第一获取模块22，是设置为：分别按照公式(1.3)和公式(1.4)获取第一预测的状态值和第一预测的状态值的方差矩阵。
第一计算模块23，设置为：根据获得的第一预测的状态值的方差矩阵、设计矩阵和观测误差方差阵，计算增益矩阵。
其中，第一计算模块23，是设置为：按照公式(1.5)计算所述增益矩阵。
第二获取模块24，设置为：根据获得的第一预测的状态值和设计矩阵、观测值以及增益矩阵计算第二预测的状态值；根据获得的第一预测的状态值的方差矩阵、增益矩阵和设计矩阵，计算第二预测的状态值的方差矩阵。
其中，第二获取模块24是设置为：分别按照公式(1.6)和(1.7)获取第二预测的状态值和第二预测的状态值的方差矩阵。
第二计算模块25，设置为：获取平滑速度，根据获得的平滑速度和第二 预测的状态值以及第二预测的状态值的方差矩阵计算下一时刻的状态值及状态值的方差矩阵。
其中，第二计算模块25，是设置为：分别按照公式(1.8)和(1.9)计算下一时刻的状态值及方差矩阵。
另外，第二计算模块25获取平滑速度，包括：获取当前时刻和当前时刻之前的两个时刻的速度；
为获得的每个速度分配权重值，其中分配的权重值之和为1；
根据获得的每个速度和分配的权重值，计算平滑速度。
本领域普通技术人员可以理解上述实施例的全部或部分步骤可以使用计算机程序流程来实现，所述计算机程序可以存储于一计算机可读存储介质中，所述计算机程序在相应的硬件平台上(如系统、设备、装置、器件等)执行，在执行时，包括方法实施例的步骤之一或其组合。
可选地，上述实施例的全部或部分步骤也可以使用集成电路来实现，这些步骤可以被分别制作成一个个集成电路模块，或者将它们中的多个模块或步骤制作成单个集成电路模块来实现。
上述实施例中的装置/功能模块/功能单元可以采用通用的计算装置来实现，它们可以集中在单个的计算装置上，也可以分布在多个计算装置所组成的网络上。
上述实施例中的装置/功能模块/功能单元以软件功能模块的形式实现并作为独立的产品销售或使用时，可以存储在一个计算机可读取存储介质中。上述提到的计算机可读取存储介质可以是只读存储器，磁盘或光盘等。
工业实用性
本发明实施例通过采用卡尔曼滤波，运用速度来预测下个历元的位置及其方差，然后通过GNSS观测量来更新定位估计的结果及其方差，从而使每 个历元间的定位结果通过速度联系起来，增加了定位的可靠性及其精度。此外，由于复杂场景下的速度估计也存在偏差，本发明实施例对复杂场景下的速度进行平滑，提高了速度的可靠性，然后再用于位置预测，从而改善定位结果。

Claims (10)

  1. 一种GNSS单点定位的方法，包括：
    根据动态误差方差阵和状态转移矩阵建立卡尔曼滤波的动态模型以及根据观测误差方差阵和设计矩阵建立卡尔曼滤波的观测模型；
    根据建立的卡尔曼滤波的动态模型和观测模型，分别获取第一预测的状态值和第一预测的状态值的方差矩阵；
    根据获得的第一预测的状态值的方差矩阵、设计矩阵和观测误差方差阵，计算增益矩阵；
    根据获得的第一预测的状态值和设计矩阵、观测值以及增益矩阵计算第二预测的状态值；根据获得的第一预测的状态值的方差矩阵、增益矩阵和设计矩阵，计算第二预测的状态值的方差矩阵；
    获取平滑速度，根据获得的平滑速度和第二预测的状态值以及第二预测的状态值的方差矩阵计算下一时刻的状态值及状态值的方差矩阵。
  2. 根据权利要求1所述的方法，其中，按照下式建立所述动态模型：
    xk＝Φxk-1+wk-1；
    按照下式建立所述观测模型：
    zk＝Hxk+εk；
    其中，xk-1和xk分别表示接收机在(k-1)时刻和k时刻的状态值，Φ表示状态转移矩阵，H为设计矩阵，zk为接收机在k时刻的观测值；wk-1和εk分别表示动态模型的随机误差和观测模型的随机误差，并且分别服从下列分布：
    p(wk-1)～N(0,Q)
    p(εk)～N(0,R)
    Q和R分别表示动态误差方差阵和观测误差方差阵。
  3. 根据权利要求1或2所述的方法，其中，按照下式获取第一预测的状态值：
    Figure PCTCN2015091867-appb-100001
    按照下式获取第一预测的状态值的方差矩阵；
    Figure PCTCN2015091867-appb-100002
    其中，Q表示动态误差方差阵，Φ表示状态转移矩阵，
    Figure PCTCN2015091867-appb-100003
    表示接收机在(k-1)时刻的状态值，Pk-1表示接收机在(k-1)时刻的状态值的方差矩阵。
  4. 根据权利要求3所述的方法，其中，按照下式计算所述增益矩阵：
    Figure PCTCN2015091867-appb-100004
    其中，
    Figure PCTCN2015091867-appb-100005
    表示接收机在k时刻的第一预测的状态值的方差矩阵，R表示观测误差方差阵，H为设计矩阵。
  5. 根据权利要求4所述的方法，其中，按照下式获取所述第二预测的状态值：
    Figure PCTCN2015091867-appb-100006
    按照下式获取所述第二预测的状态值的方差矩阵：
    Figure PCTCN2015091867-appb-100007
    其中，I表示单位矩阵，
    Figure PCTCN2015091867-appb-100008
    表示接收机在k时刻的第一预测的状态值，
    Figure PCTCN2015091867-appb-100009
    表示接收机在k时刻的第一预测的状态值的方差矩阵，Kk表示增益矩阵。
  6. 根据权利要求5所述的方法，其中，按照下式计算下一时刻的状态值：
    Figure PCTCN2015091867-appb-100010
    按照下式计算下一时刻的状态值的方差矩阵：
    Figure PCTCN2015091867-appb-100011
    其中，
    Figure PCTCN2015091867-appb-100012
    表示在k时刻获得的接收机的平滑速度，t表示k时刻到(k+1)时刻之间的时间间隔，
    Figure PCTCN2015091867-appb-100013
    表示在k时刻获得的接收机的平滑速度的方差矩阵，
    Figure PCTCN2015091867-appb-100014
    表示接收机在k时刻的第二预测的状态值。
  7. 根据权利要求1所述的方法，其中，所述获取平滑速度包括：获取当前时刻和当前时刻之前的两个时刻的速度；
    为获得的每个速度分配权重值，其中分配的权重值之和为1；
    根据获得的每个速度和分配的权重值，计算平滑速度。
  8. 一种GNSS单点定位的装置，包括：建模模块、第一获取模块、第一计算模块、第二获取模块和第二计算模块；其中，
    建模模块，设置为：根据动态误差方差阵和状态转移矩阵建立卡尔曼滤波的动态模型以及根据观测误差方差阵和设计矩阵建立卡尔曼滤波的观测模型；
    第一获取模块，设置为：根据建立的卡尔曼滤波的动态模型和观测模型，分别获得第一预测的状态值和第一预测的状态值的方差矩阵；
    第一计算模块，设置为：根据获得的第一预测的状态值的方差矩阵、设计矩阵和观测误差方差阵，计算增益矩阵；
    第二获取模块，设置为：根据获得的第一预测的状态值和设计矩阵、观测值以及增益矩阵计算第二预测的状态值；根据获得的第一预测的状态值的方差矩阵、增益矩阵和设计矩阵，计算第二预测的状态值的方差矩阵；
    第二计算模块，设置为：获取平滑速度，根据获得的平滑速度和第二预测的状态值以及第二预测的状态值的方差矩阵计算下一时刻的状态值及状态值的方差矩阵。
  9. 根据权利要求8所述的装置，其中，所述第二计算模块是设置为：获取当前时刻和当前时刻之前的两个时刻的速度；
    为获得的每个速度分配权重值，其中分配的权重值之和为1；
    根据获得的每个速度和分配的权重值，计算平滑速度。
  10. 一种计算机可读存储介质，存储有计算机可执行指令，所述计算机可执行指令用于执行权利要求1-7任一项的方法。
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