WO2018028711A1 - 一种对无人机的噪声协方差进行估算的方法 - Google Patents

一种对无人机的噪声协方差进行估算的方法 Download PDF

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WO2018028711A1
WO2018028711A1 PCT/CN2017/097384 CN2017097384W WO2018028711A1 WO 2018028711 A1 WO2018028711 A1 WO 2018028711A1 CN 2017097384 W CN2017097384 W CN 2017097384W WO 2018028711 A1 WO2018028711 A1 WO 2018028711A1
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drone
covariance
axis
coordinate system
noise
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French (fr)
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刘国良
邬静云
黄涛
张瑞
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贵州火星探索科技有限公司
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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  • the present invention relates to the field of unmanned aerial vehicles, and more particularly to a method for estimating the noise covariance of a drone.
  • the unmanned aircraft referred to as the "unmanned aerial vehicle” is a non-manned aircraft operated by radio remote control equipment and its own program control device. It is widely used in military and civilian fields, such as airborne warning, agriculture, geology. , weather, electricity, disaster relief, video shooting and other industries.
  • a drone operated by a self-contained program control device it has strong coupling, nonlinearity, high control difficulty, and the dynamic modeling is complicated.
  • the disturbances faced by the control and operation of the drone include: external disturbance torque such as gravity, and system noise in the drone dynamics model and observation noise in the measurement equation, etc. Interference needs to be estimated by high-precision models and algorithms to achieve high-precision control.
  • a filtering algorithm for processing process noise and measurement noise of a drone such as a Kalman filter
  • a filtering algorithm for processing process noise and measurement noise of a drone such as a Kalman filter
  • the covariance of the process noise in the UAV dynamics model and the covariance of the observed noise in the measurement equation need to be debugged to achieve the best effect. Therefore, the prior art has the following drawbacks: the covariance matrix of the noise needs to pass the empirical value or The method of debugging can be obtained, and the more experienced operators are required.
  • the self-covariance least squares theory proposed by Odelson in 2003 can effectively estimate the covariance matrix of noise and save debugging time.
  • the auto-covariance least squares theory algorithm is currently used for noise estimation in the chemical industry and has not been used in the field of drones.
  • Rajamani et al. proposed a linear time-varying auto-covariance least squares method for nonlinear systems in 2011.
  • the invention combines the above method with the UAV dynamic model to estimate the process noise and observed noise of the UAV.
  • the technical problem of the present invention is to overcome the existing filtering algorithm for processing UAV process noise and measurement noise.
  • the noise characteristics are unknown, it is necessary to obtain the covariance matrix value of the noise by using the empirical value or by debugging.
  • an estimation method that can automatically estimate the process noise and the covariance matrix value caused by the observation is designed.
  • the technical solution adopted by the present invention to solve the technical problem thereof is to provide a method for estimating the noise covariance of a drone, which is characterized in that the self-covariance least squares theory method is used in the dynamic model of the drone
  • the process noise and the characteristics of the observed noise in the measurement equation are estimated, including the following steps:
  • the covariance of the process noise and the covariance of the measurement noise are obtained through a semi-definite programming algorithm.
  • step S1 further includes the following steps:
  • m is the mass of the drone and X is the position vector of the drone.
  • T is the thrust generated by the rotor
  • M is the torque generated by the rotor
  • J is the moment of inertia of the drone
  • ⁇ is the angular velocity of the drone.
  • G is the gravity received by the drone
  • F is the air resistance received by the drone.
  • L is the distance from the center of the rotor to the X-axis or the Y-axis
  • ⁇ 1 , ⁇ 2 , ⁇ 3 , and ⁇ 4 are the rotational speeds of the four blades, respectively
  • b and d are the tensile and torque coefficients of the blade, respectively;
  • the angle between the body axis X and the horizontal plane is defined as the pitch angle ⁇ , and the head is positive; the angle between the projection of the body axis X on the horizontal plane and the X E axis is defined as the yaw angle.
  • the right angle of the nose is positive; the angle between the body axis Z and the vertical plane passing through the X axis of the body is defined as the roll angle ⁇ , and the drone is rightly turned to be positive, and the three angles are Euler angles;
  • F fx , F fy , and F fz are the components of F on the three axes of the body coordinate system
  • [ ⁇ x , ⁇ y , ⁇ z ] are the components of ⁇ on the three axes of the body coordinate system
  • ⁇ z ] and Euler angle is as follows
  • step S2 further includes the following steps:
  • L k is the Kalman filter gain
  • a k , B k , G k , C k are all the coefficient matrix
  • step S3 further includes the following steps:
  • the expected value of the used interest constitutes an autocovariance matrix.
  • the Euler angle and the rotational speed of the four blades are used as the control amount.
  • the rotational speeds of the four blades are taken as the control amount.
  • the self-covariance least squares theory method can estimate the process noise and process modeling of the drone, and reduce the covariance matrix value of the debugging process noise and observation noise in the prior art, and the requirements for the empirical value and the operator. It can provide operators with a more accurate valuation interval, saving debugging time and ensuring the accuracy of system noise and observation noise.
  • FIG. 1 is a schematic diagram of a method for estimating noise covariance of a drone according to the present invention
  • FIG. 2 is a schematic view of a ground coordinate system and a body coordinate system in the present invention
  • Figure 3 is a position curve of the X E- axis direction in the ground coordinate system of the present invention.
  • Figure 4 is a velocity curve in the X E- axis direction of the ground coordinate system of the present invention.
  • Figure 5 is a positional curve of the Y E- axis direction in the ground coordinate system of the present invention.
  • Figure 6 is a velocity curve in the Y E- axis direction of the ground coordinate system of the present invention.
  • Figure 7 is a positional curve of the Z E- axis direction in the ground coordinate system of the present invention.
  • Figure 8 is a velocity curve in the Z E- axis direction of the ground coordinate system of the present invention.
  • Figure 9 is a graph showing the variation of the roll angle ⁇ of the present invention.
  • Figure 10 is the rate of change of roll angle of the present invention Change curve
  • Figure 11 is a graph showing the variation of the pitch angle ⁇ of the present invention.
  • Figure 12 is a graph showing the rate of change of the pitch angle of the present invention. Change curve
  • Figure 13 is a yaw angle of the present invention Change curve
  • Figure 14 is a yaw angle change rate of the present invention Change curve
  • FIG. 1 is a schematic diagram of a method for estimating noise covariance of a drone of the present invention.
  • the present invention includes: step S1, establishing a drone dynamics model, and step S2, using an extended Kalman filter.
  • the control quantity u and the observation value h(x) obtained by the sensor linearize the drone dynamics model; in step S3, the linearized coefficient matrix A, B, C, G, the Kalman gain L and the new interest y are substituted
  • the expected value of the obtained new interest constitutes the estimated value of the autocovariance matrix [R(N)] s and the self-covariance matrix composed of the expected value of the innovation.
  • Step S4 the expected value of the obtained new interest constitutes an estimate of the autocovariance matrix [R(N)] s and the self-covariance matrix formed by the expected value of the innovation.
  • the process noise covariance Q and the measurement noise covariance R are obtained.
  • Step S1 includes, as shown in FIG. 2, for the "X"-shaped quadrotor UAV, the ground coordinate system and the body coordinate system are established as shown in FIG. 2.
  • Body coordinate system B-XYZ The origin is taken at the centroid of the drone, and the coordinate system is fixed to the body.
  • the X axis is parallel to the longitudinal axis of the fuselage design and is in the symmetry plane of the drone, pointing to the front; the Y axis is perpendicular to the symmetry plane of the drone pointing to the right; the Z axis is in the symmetry plane of the drone, and perpendicular to The X axis points down.
  • the entire coordinate system conforms to the right-hand rule of the Euler coordinate system.
  • Ground coordinate system EX E Y E Z E The northeast ground coordinate system is adopted, the X E axis points to the north side, the Y E axis points to the east side, and the Z E axis points vertically downward.
  • S1 further includes step S11, and the dynamic model of the drone is established as follows.
  • the line motion equations are established in the ground coordinate system and the rotation equations are established in the body coordinate system as follows:
  • m is the mass of the drone and X is the position vector of the drone.
  • M is the torque generated by the rotor
  • J is the moment of inertia of the drone
  • ⁇ is the angular velocity of the drone.
  • L is the distance from the center of the rotor to the X-axis or the Y-axis
  • ⁇ 1 , ⁇ 2 , ⁇ 3 , and ⁇ 4 are the rotational speeds of the four blades, respectively
  • b and d are the tensile and torque coefficients of the blade, respectively.
  • S1 further includes step S12, defining an angle between the body axis X and the horizontal plane as a pitch angle ⁇ , and the head is positive; defining an angle between the projection of the body axis X on the horizontal plane and the X E axis as a yaw angle
  • the right side of the nose is positive; the angle between the body axis Z and the vertical plane passing through the X-axis of the body is defined as the roll angle ⁇ , and the drone is right-turned to be positive.
  • F fx , F fy , and F fz are the components of F on the three axes of the body coordinate system
  • [ ⁇ x , ⁇ y , ⁇ z ] are the components of ⁇ on the three axes of the body coordinate system
  • ⁇ z ] and Euler angle is as follows
  • Step S2 further includes S21 writing the state equation and the measurement equation of the system into the following general form:
  • Step S2 further includes S22, and the equation (5) is Linearized
  • a k , B k , G k , C k are all the coefficient matrix
  • Step S2 further includes S23, and the linearized state estimation equation is
  • Step S3 further includes S31, and constructing an autocovariance matrix with the expected value of the innovation
  • Step S3 further includes S31 to And an estimate of the autocovariance matrix formed by the expected value of the innovation
  • the square of the difference between the two norms is the optimization goal
  • the state equation in the linear motion is the linear motion equation of the drone dynamics model, ie
  • the initial value of the state quantity And set the measurement equation as follows
  • the fixed step size generates 10 seconds of observation data.
  • the coefficient matrix and the Kalman gain are obtained by using the extended Kalman filter algorithm combined with the state equation, the control amount and the observation data. Then, the theory of the self-covariance least squares algorithm is applied to give the self-covariance matrix composed of the expected value of the interest rate and the estimated value of the auto-covariance matrix composed of the expected value of the interest. Finally, the semi-definite programming method is used to solve the optimal problem in equation (14), and the obtained process noise covariance Q and measurement noise covariance R are obtained.
  • the equation of state in angular motion is the angular motion equation of the dynamic model of the drone, ie
  • the sampling time is set to 0.1 second
  • the initial estimate of Q is set to 8 ⁇ 10 -3
  • the initial estimate of R is set to 3 ⁇ 10 -3 I 6 ⁇ 6 with the smallest covariance.
  • the sampling time is set to 0.1 second
  • the initial estimation value of Q is set to 3 ⁇ 10 -3
  • the initial estimation value of R is set to 3 ⁇ 10 -3 I 6 ⁇ 6 .
  • the estimated noise characteristics in the line motion and angular motion models are substituted into the extended Kalman filter for filtering.
  • the comparison between the filtered variable curves and the real and observed values of each variable is shown in Figure 3-14.
  • the observations, true values, and values filtered using the extended Kalman filter are plotted in -14.
  • the gray scattered points in the figure are the observed values of the variables, and the black solid lines are the true values. It can be seen that there is an error in the observed values due to the presence of process noise and observed noise.
  • the process noise covariance Q and the measurement noise covariance R identified by the covariance least squares theoretical method algorithm are substituted into the extended Kalman filter algorithm for filtering, and the filtered values indicated by the black dotted lines in the figure are obtained. Although the filtered value still has an error, it is very close to the true value, indicating the covariance least squares
  • the covariance estimated by the method algorithm is more accurate.
  • the estimation accuracy of the process noise covariance Q and the measurement noise covariance R is high by the method for estimating the noise covariance of the drone in the present invention.
  • the estimation method provides a numerical reference for the operator, so the general operator is more convenient and quicker in debugging the process noise covariance Q and measuring the noise covariance R.

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Abstract

一种对无人机的噪声协方差进行估算的方法，利用扩展卡尔曼滤波器结合控制量和观测值将无人机动力学模型线性化得到线性化后的状态估计方程；将所述线性化后的状态估计方程得到的系数矩阵、卡尔曼增益以及新息代入到自协方差最小二乘算法中得到用新息的期望值构成的协方差矩阵和新息期望值构成的自协方差矩阵的估计值，后经过半定规划算法，得到过程噪声的协方差和量测噪声的协方差。通过该方法，对过程噪声协方差Q和量测噪声协方差R的估算精确度高。同时，该估算方法为操作人员提供了数值参考，故此一般操作人员在调试过程噪声协方差Q和量测噪声协方差R时较为方便快捷。

Description

一种对无人机的噪声协方差进行估算的方法 技术领域
本发明涉及无人机技术领域，更具体地说，涉及一种对无人机的噪声协方差进行估算的方法。
背景技术
无人驾驶飞机简称“无人机”，是利用无线电遥控设备和自备的程序控制装置操纵的不载人飞机，其用途广泛，被广泛应用在军用和民用领域，例如空中预警，农业、地质、气象、电力、抢险救灾、视频拍摄等行业。作为利用自备程序控制装置操纵的无人机，其具有强耦合、非线性、控制难度高等特性，动力学建模较为复杂。无人机的控制和操纵面临的干扰包括：重力等外部干扰力矩，以及无人机动力学模型中的***造声以及量测方程中的观测噪声等来自无人机自身内部的干扰，以上多源干扰需要通过高精度模型和算法进行估算，从而达到高精度控制。
然而，现有技术中，处理无人机过程噪声和量测噪声的滤波算法，例如卡尔曼滤波，在噪声特性未知时，一般使用经验值或通过调试的方法得到噪声的协方差矩阵值，即，现有技术中，对无人机动力学模型中的过程噪声的协方差以及量测方程中的观测噪声的协方差均需要通过调试方能达到最佳效果。因此，现有技术中存下如下缺陷：噪声的协方差矩阵需要通过经验值或 者调试的方法方可获得，需要较有经验的操作人员，对操作人员的要求较高，且若调试所给的噪声协方差偏差过大，会直接导致滤波值在递推的某一过程中，甚至整个过程中越来越偏离实际值，导致滤波发散，造成无人机的飞行偏离目标结果。
Odelson于2003年提出的自协方差最小二乘理论方法可以有效地估计出噪声的协方差矩阵，节省调试的时间。自协方差最小二乘理论算法目前常用于化工行业的噪声估计，尚未用于无人机领域。Rajamani等人于2011年提出了针对非线性***的线性时变自协方差最小二乘方法。本发明将以上方法结合无人机动力学模型对无人机的过程噪声和观测噪声进行了估算。
发明内容
本发明的技术解决问题是：克服了现有的处理无人机过程噪声和量测噪声的滤波算法中，在噪声特性未知时，需要使用经验值或通过调试的方法得到噪声的协方差矩阵值，对操作人员要求较高，且易造成偏差的问题，设计一种能够自动对过程噪声和观测造成的协方差矩阵值进行估值的估算方法。
本发明解决其技术问题所采用的技术方案是：提供一种对无人机的噪声协方差进行估算的方法，其特征在于，利用自协方差最小二乘理论方法对无人机动力学模型中的过程噪声以及量测方程中的观测噪声的特性进行估算，包括以下步骤：
S1、建立无人机动力学模型；
S2、利用扩展卡尔曼滤波器结合控制量和观测值将无人机动力学模型线性化得到线性化后的状态估计方程；并根据所述线性化后的状态估计方程得 到的系数矩阵、卡尔曼增益以及新息；
S3、将所述系数矩阵、所述卡尔曼增益以及所述新息代入到自协方差最小二乘算法中得到用新息的期望值构成的协方差矩阵和所述用新息期望值构成的自协方差矩阵的估计值；
S4、利用所述新息的期望值构成的协方差矩阵和所述用新息期望值构成的自协方差矩阵的估计值，经过半定规划算法，得到过程噪声的协方差和量测噪声的协方差。
进一步地，所述步骤S1进一步包括如下步骤：
S11、所述无人机动力学模型在地面坐标系中建立的线运动方程和在机体坐标系中建立的转动方程为：
Figure PCTCN2017097384-appb-000001
其中，m为无人机的质量，X为无人机的位置矢量，
Figure PCTCN2017097384-appb-000002
为无人机的加速度矢量，T为旋翼产生的推力，M为旋翼产生的转矩，J为无人机的转动惯量，ω为无人机转动的角速度，
Figure PCTCN2017097384-appb-000003
为无人机转动的角加速度，G为无人机受到的重力，F为无人机受到的空气阻力，
Figure PCTCN2017097384-appb-000004
Figure PCTCN2017097384-appb-000005
其中，L为旋翼中心到X轴或Y轴的距离，Ω1、Ω2、Ω3、Ω4分别为四个桨叶的转速，b、d分别为桨叶的拉力系数和扭矩系数；
S12、将机体轴X与水平面之间的夹角定义为俯仰角θ，抬头为正；将机 体轴X在水平面上的投影与XE轴之间的夹角定义为偏航角
Figure PCTCN2017097384-appb-000006
机头右偏为正；将机体轴Z与通过机体X轴的铅垂面间的夹角定义为滚转角φ，无人机右滚转为正，这三个角即为欧拉角；
令
Figure PCTCN2017097384-appb-000007
则从机体坐标系到地面坐标系的坐标转换矩阵为
Figure PCTCN2017097384-appb-000008
则无人机的动力学模型写为
Figure PCTCN2017097384-appb-000009
其中，
Figure PCTCN2017097384-appb-000010
分别为无人机在地面坐标系XE,YE,ZE轴方向上的加速度；
Figure PCTCN2017097384-appb-000011
Figure PCTCN2017097384-appb-000012
分别为无人机在机体坐标系X,Y,Z轴方向上的角加速度；Ixx、Iyy、Izz分别为无人机绕机体坐标系X轴、Y轴、Z轴的转动惯量，Ffx、Ffy、Ffz分别为F在机体坐标系三轴上的分量，[ωx,ωy,ωz]为ω在机体坐标系三轴上的分量，[ωx,ωy,ωz]与欧拉角的关系如下
Figure PCTCN2017097384-appb-000013
进一步地，所述步骤S2进一步包括如下步骤：
S21、将***的状态方程和量测方程写成如下的一般形式：
Figure PCTCN2017097384-appb-000014
其中，xk为状态量，yk为所述观测量，所述观测量从传感器中获取，uk为所述控制量，所述控制量由人为设定，wk为所述过程噪声，vk为所述量测噪声；wk～N(0,Q)与vk～N(0,R)不相关，通过方程式(5)对其状态进行估计，得到
Figure PCTCN2017097384-appb-000015
其中，Lk为所述卡尔曼滤波增益，所述新息为
Figure PCTCN2017097384-appb-000016
S22、将所述方程式(5)在
Figure PCTCN2017097384-appb-000017
处线性化得
Figure PCTCN2017097384-appb-000018
其中，Ak，Bk，Gk，Ck均为所述系数矩阵，
Figure PCTCN2017097384-appb-000019
Figure PCTCN2017097384-appb-000020
S23、所述线性化后的状态估计方程为：
Figure PCTCN2017097384-appb-000021
进一步地，所述步骤S3进一步包括如下步骤：
S31、所述用新息的期望值构成自协方差矩阵，
Figure PCTCN2017097384-appb-000022
S32、以[R(N)]s和所述用新息期望值构成的自协方差矩阵的估计值
Figure PCTCN2017097384-appb-000023
之差的二范数的平方最小为优化目标,
Figure PCTCN2017097384-appb-000024
s.t. Q,R≥0,Q＝Q',R＝R'
其中，
Figure PCTCN2017097384-appb-000025
进一步地，当对线运动的噪声协方差进行估算时，将所述欧拉角和所述四个桨叶的转速作为所述控制量。
进一步地，当对角运动的噪声协方差进行估算时，将所述四个桨叶的转速作为所述控制量。
本发明提供的一个或多个技术方案，至少具有如下技术效果或优点：
通过自协方差最小二乘理论方法能够对无人机的过程噪声和过程造型进行估算，降低了现有技术中，调试过程噪声和观测噪声的协方差矩阵值了对经验值和操作人员的要求，能够给操作人员提供较为准确的估值区间，节省调试的时间，同时确保了***造成和观测噪声的精确度。
附图说明
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的实施例，对于本领域普通技术人员来讲，在不 付出创造性劳动的前提下，还可以根据提供的附图获得其他的附图。
图1是本发明中无人机的噪声协方差进行估算的方法原理图；
图2是本发明中地面坐标系和机体坐标系的示意图；
图3是本发明地面坐标系中XE轴方向的位置曲线；
图4是本发明地面坐标系中XE轴方向的速度曲线；
图5是本发明地面坐标系中YE轴方向的位置曲线；
图6是本发明地面坐标系中YE轴方向的速度曲线；
图7是本发明地面坐标系中ZE轴方向的位置曲线；
图8是本发明地面坐标系中ZE轴方向的速度曲线；
图9是本发明滚转角φ的变化曲线；
图10是本发明滚转角变化率
Figure PCTCN2017097384-appb-000026
的变化曲线；
图11是本发明俯仰角θ的变化曲线；
图12是本发明俯仰角变化率
Figure PCTCN2017097384-appb-000027
的变化曲线；
图13是本发明偏航角
Figure PCTCN2017097384-appb-000028
的变化曲线；
图14是本发明偏航角变化率
Figure PCTCN2017097384-appb-000029
的变化曲线；
具体实施方式
如图1所示，为本发明的无人机的噪声协方差进行估算的方法原理图，首先，本发明包括：步骤S1，建立无人机动力学模型，步骤S2，利用扩展卡尔曼滤波器结合控制量u和通过传感器获得的观测值h(x)将无人机动力学模型线性化；步骤S3，将线性化得到的系数矩阵A,B,C,G,卡尔曼增益L以及新息y代入自线性时变-自协方差最小二乘算法中，获得新息的期望值构成自协方差矩阵[R(N)]s和用新息期望值构成的自协方差矩阵的估计值
Figure PCTCN2017097384-appb-000030
步骤S4， 将获得新息的期望值构成自协方差矩阵[R(N)]s和所述用新息期望值构成的自协方差矩阵的估计值
Figure PCTCN2017097384-appb-000031
代入半正定规划算法中，求得过程噪声协方差Q和量测噪声协方差R。
步骤S1包括，如图2所示，针对“X”形的四旋翼无人机，建立地面坐标系和机体坐标系如图2所示。机体坐标系B-XYZ：原点取在无人机的质心，坐标系与机体固连。X轴与机身设计的纵轴平行，且处于无人机的对称平面内，指向前方；Y轴垂直于无人机对称平面指向右方；Z轴在无人机对称平面内，且垂直于X轴指向下方。整个坐标系符合欧拉坐标系右手定则。地面坐标系E-XEYEZE：采用北东地坐标系，XE轴指向北面，YE轴指向东面，而ZE轴垂直向下。
在只考虑无人机重力G、旋翼产生的拉力T和无人机受到的空气阻力F的情况下，S1进一步包括步骤S11，建立无人机的动力学模型如下。分别在地面坐标系中建立线运动方程和在机体坐标系中建立转动方程如下：
Figure PCTCN2017097384-appb-000032
其中，m为无人机的质量，X为无人机的位置矢量，
Figure PCTCN2017097384-appb-000033
为无人机的加速度矢量，M为旋翼产生的转矩，J为无人机的转动惯量，ω为无人机转动的角速度，
Figure PCTCN2017097384-appb-000034
为无人机转动的角加速度，
Figure PCTCN2017097384-appb-000035
Figure PCTCN2017097384-appb-000036
其中，L为旋翼中心到X轴或Y轴的距离，Ω1、Ω2、Ω3、Ω4分别为四个桨叶 的转速，b、d分别为桨叶的拉力系数和扭矩系数。
S1进一步包括步骤S12，将机体轴X与水平面之间的夹角定义为俯仰角θ，抬头为正；将机体轴X在水平面上的投影与XE轴之间的夹角定义为偏航角
Figure PCTCN2017097384-appb-000037
机头右偏为正；将机体轴Z与通过机体X轴的铅垂面间的夹角定义为滚转角φ，无人机右滚转为正。这三个角即为欧拉角。
令
Figure PCTCN2017097384-appb-000038
则从机体坐标系到地面坐标系的坐标转换矩阵为
Figure PCTCN2017097384-appb-000039
则无人机的动力学模型写为
Figure PCTCN2017097384-appb-000040
其中，
Figure PCTCN2017097384-appb-000041
分别为无人机在地面坐标系XE,YE,ZE轴方向上的加速度；
Figure PCTCN2017097384-appb-000042
Figure PCTCN2017097384-appb-000043
分别为无人机在机体坐标系X,Y,Z轴方向上的角加速度；Ixx、Iyy、Izz分别为无人机绕机体坐标系X轴、Y轴、Z轴的转动惯量，Ffx、Ffy、Ffz分别为F在机体坐标系三轴上的分量，[ωx,ωy,ωz]为ω在机体坐标系三轴上的分量， [ωx,ωy,ωz]与欧拉角的关系如下
Figure PCTCN2017097384-appb-000044
步骤S2进一步包括S21将***的状态方程和量测方程写成如下的一般形式：
Figure PCTCN2017097384-appb-000045
对其状态进行估计，其中，xk为状态量，yk为所述观测量，所述观测量从传感器中获取，uk为所述控制量，所述控制量由人为设定，wk为所述过程噪声，vk为所述量测噪声；wk～N(0,Q)与vk～N(0,R)不相关，通过方程式(1)对其状态进行估计，得到
Figure PCTCN2017097384-appb-000046
其中，Lk为卡尔曼滤波增益，新息
Figure PCTCN2017097384-appb-000047
步骤S2进一步包括S22，将所述方程式(5)在
Figure PCTCN2017097384-appb-000048
处线性化得
Figure PCTCN2017097384-appb-000049
其中，Ak，Bk，Gk，Ck均为所述系数矩阵，
Figure PCTCN2017097384-appb-000050
Figure PCTCN2017097384-appb-000051
步骤S2进一步包括S23，线性化后的状态估计方程为
Figure PCTCN2017097384-appb-000052
状态估计误差表示为
Figure PCTCN2017097384-appb-000053
且
Figure PCTCN2017097384-appb-000054
则
Figure PCTCN2017097384-appb-000055
步骤S3进一步包括S31，用新息的期望值构成自协方差矩阵
Figure PCTCN2017097384-appb-000056
步骤S3进一步包括S31，以
Figure PCTCN2017097384-appb-000057
和所述用新息期望值构成的自协方差矩阵的估计值
Figure PCTCN2017097384-appb-000058
之差的二范数的平方最小为优化目标
Figure PCTCN2017097384-appb-000059
s.t. Q,R≥0,Q＝Q',R＝R'
其中，
Figure PCTCN2017097384-appb-000060
实施例一
由于无人机动力学模型为一个12维的方程组，使用协方差最小二乘理论方法算法估计模型中的噪声协方差时，为缩短程序运行时间，分别对线运动与角运动中的噪声协方差进行估计。仿真时使用的模型中各参数值如表1所 示。
表1 参数值
参数名 参数值 参数名 参数值
无人机质量m 1.5kg 重力加速度g 9.79m/s2
x轴转动惯量Ixx 0.024kg·m2 y轴转动惯量Iyy 0.024kg·m2
z轴转动惯量Izz 0.112kg·m2 L 0.232m
桨叶拉力系数b 1.0643×10-5 桨叶扭矩系数d 2.3528×10-7
空气阻力系数k -0.2334   
①线运动
线运动中状态方程即为无人机动力学模型的线运动方程，即
Figure PCTCN2017097384-appb-000061
其中，状态变量为X＝[x,y,z,u,v,w]T。将欧拉角和四个电机的转速作为控制量，[φ,θ,φ]＝[0,0,0]，[Ω1,Ω2,Ω3,Ω4]＝[588.9737,588.9737,588.9737,588.9737]。状态量初值为
Figure PCTCN2017097384-appb-000062
并设定量测方程如下
Figure PCTCN2017097384-appb-000063
在线运动模型中加入协方差为Q＝2.5×10-5的零均值高斯白噪声，在观测方程 中加入协方差为R＝10-3I6×6的高斯白噪声，利用ODE45函数以0.001秒的定步长生成10秒的观测数据。
首先，利用扩展卡尔曼滤波算法结合状态方程、控制量和观测数据求出系数矩阵和卡尔曼增益。然后，应用自协方差最小二乘算法的理论给出新息期望值构成的自协方差矩阵以及新息期望值构成的自协方差矩阵的估计值。最后，使用半正定规划方法求解式(14)中的最优问题，得到所求的过程噪声协方差Q和量测噪声协方差R。
②角运动
角运动中状态方程即为无人机动力学模型的角运动方程，即
Figure PCTCN2017097384-appb-000064
其中，状态变量为
Figure PCTCN2017097384-appb-000065
角运动中控制量为四个电机的转速，[Ω1,Ω2,Ω3,Ω4]＝[481.5,481.5,481.5,481.5]。
状态量初值为
Figure PCTCN2017097384-appb-000066
设定量测方程如下
Figure PCTCN2017097384-appb-000067
在线运动模型中加入协方差为Q＝2.5×10-5的零均值高斯白噪声，在观测方程中加入协方差为R＝10-3I6×6的高斯白噪声，利用ODE45函数以0.001秒的定步长生成10秒的观测数据。协方差估计的过程与线运动中相同。
实施例一的仿真结果如下：
①线运动
利用协方差最小二乘理论方法算法时采样时间设为0.1秒，Q的初始估计值设为8×10-3，R的初始估计值设为3×10-3I6×6，协方差最小二乘理论方法程序辨识得到的结果为
Figure PCTCN2017097384-appb-000068
Figure PCTCN2017097384-appb-000069
Figure PCTCN2017097384-appb-000070
②角运动
利用协方差最小二乘理论方法算法仿真时采样时间设为0.1秒，Q的初始估计值均设为3×10-3，R的初始估计值均设为3×10-3I6×6，辨识得到的结果为
Figure PCTCN2017097384-appb-000071
Figure PCTCN2017097384-appb-000072
Figure PCTCN2017097384-appb-000073
将线运动和角运动模型中估计到的噪声特性代入扩展卡尔曼滤波中进行滤波，得到滤波后的各变量曲线与各变量真实值、观测值的对比图如图3-14所示，图3-14中画出了各状态变量的观测值、真实值和使用扩展卡尔曼滤波滤波后的值。图中灰色分散的点为各变量的观测值，黑色的实线为真实值。可以看出，由于存在过程噪声和观测噪声，观测值存在误差。将协方差最小二乘理论方法算法辨识得到的过程噪声协方差Q和量测噪声协方差R代入扩展卡尔曼滤波算法中进行滤波，得到了图中黑色虚线表示的滤波后的值。虽然滤波后的值仍存在误差，但已十分接近真实值，说明了协方差最小二乘理 论方法算法估计得到的协方差较准确。
综上所述，通过本发明中的对无人机的噪声协方差进行估算的方法，对过程噪声协方差Q和量测噪声协方差R的估算精确度高。同时，该估算方法为操作人员提供了数值参考，故此一般操作人员在调试过程噪声协方差Q和量测噪声协方差R时较为方便快捷。

Claims (6)

  1. 一种对无人机的噪声协方差进行估算的方法，其特征在于，包括以下步骤：
    S1、建立无人机动力学模型；
    S2、利用扩展卡尔曼滤波器结合控制量和观测值将所述无人机动力学模型线性化得到线性化后的状态估计方程；并根据所述线性化后的状态估计方程得到的系数矩阵、卡尔曼增益以及新息；
    S3、将所述系数矩阵、所述卡尔曼增益以及所述新息代入到自协方差最小二乘算法中得到用新息的期望值构成的协方差矩阵和所述用新息期望值构成的自协方差矩阵的估计值；
    S4、利用所述新息的期望值构成的协方差矩阵和所述用新息期望值构成的自协方差矩阵的估计值，经过半定规划算法，得到过程噪声的协方差和量测噪声的协方差。
  2. 根据权利要求1中的估算方法，其特征在于，所述步骤S1进一步包括如下步骤：
    S11、所述无人机动力学模型在地面坐标系中建立的线运动方程和在机体坐标系中建立的转动方程为：
    Figure PCTCN2017097384-appb-100001
    其中，m为无人机的质量，X为无人机的位置矢量，
    Figure PCTCN2017097384-appb-100002
    为无人机的加速度矢量，T为旋翼产生的推力，M为旋翼产生的转矩，J为无人机的转动惯量，ω为无人机转动的角速度，
    Figure PCTCN2017097384-appb-100003
    为无人机转动的角加速度，G为无人机受到的重 力，F为无人机受到的空气阻力，
    Figure PCTCN2017097384-appb-100004
    Figure PCTCN2017097384-appb-100005
    其中，L为旋翼中心到X轴或Y轴的距离，Ω1、Ω2、Ω3、Ω4分别为四个桨叶的转速，b、d分别为桨叶的拉力系数和扭矩系数；
    S12、将机体轴X与水平面之间的夹角定义为俯仰角θ，抬头为正；将机体轴X在水平面上的投影与XE轴之间的夹角定义为偏航角
    Figure PCTCN2017097384-appb-100006
    机头右偏为正；将机体轴Z与通过机体X轴的铅垂面间的夹角定义为滚转角φ，无人机右滚转为正，这三个角即为欧拉角；
    令
    Figure PCTCN2017097384-appb-100007
    则从机体坐标系到地面坐标系的坐标转换矩阵为
    Figure PCTCN2017097384-appb-100008
    则无人机的动力学模型写为
    Figure PCTCN2017097384-appb-100009
    其中，
    Figure PCTCN2017097384-appb-100010
    分别为无人机在地面坐标系XE,YE,ZE轴方向上的加速度；
    Figure PCTCN2017097384-appb-100011
    Figure PCTCN2017097384-appb-100012
    分别为无人机在机体坐标系X,Y,Z轴方向上的角加速度；Ixx、Iyy、Izz分别为无人机绕机体坐标系X轴、Y轴、Z轴的转动惯量，Ffx、Ffy、Ffz分别为F在机体坐标系三轴上的分量，[ωx,ωy,ωz]为ω在机体坐标系三轴上的分量，所述[ωx,ωy,ωz]与欧拉角的关系如下
    Figure PCTCN2017097384-appb-100013
  3. 根据权利要求1中的估算方法，其特征在于，所述步骤S2进一步包括如下步骤：
    S21、根据卡尔曼滤波理论，将***的状态方程和量测方程写成如下的一般形式：
    Figure PCTCN2017097384-appb-100014
    其中，xk为状态量，yk为所述观测量，所述观测量从传感器中获取，uk为所述控制量，所述控制量由人为设定，wk为所述过程噪声，vk为所述量测噪声；wk～N(0,Q)与vk～N(0,R)不相关，通过方程式(5)对其状态进行估计，得到
    Figure PCTCN2017097384-appb-100015
    其中，Lk为所述卡尔曼滤波增益，所述新息为
    Figure PCTCN2017097384-appb-100016
    S22、将所述方程式(5)在
    Figure PCTCN2017097384-appb-100017
    处线性化得
    Figure PCTCN2017097384-appb-100018
    其中，Ak，Bk，Gk，Ck均为所述系数矩阵，
    Figure PCTCN2017097384-appb-100019
    Figure PCTCN2017097384-appb-100020
    S23、所述线性化后的状态估计方程为：
    Figure PCTCN2017097384-appb-100021
  4. 根据权利要求1中的估算方法，其特征在于，所述步骤S3进一步包括如下步骤：
    S31、所述用新息的期望值构成自协方差矩阵，
    Figure PCTCN2017097384-appb-100022
    S32、以[R(N)]s和所述用新息的期望值构成自协方差矩阵的估计值
    Figure PCTCN2017097384-appb-100023
    之差的二范数的平方最小为优化目标,
    Figure PCTCN2017097384-appb-100024
    其中，
    Figure PCTCN2017097384-appb-100025
  5. 根据权利要求2中的估算方法，其特征在于，当对线运动的噪声协方差进行估算时，将所述欧拉角和所述四个桨叶的转速作为所述控制量。
  6. 根据权利要求2中的估算方法，其特征在于，当对角运动的噪声协方差进行估算时，将所述四个桨叶的转速作为所述控制量。
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