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CN113984042B - Series combined navigation method applicable to high-dynamic aircraft - Google Patents

Series combined navigation method applicable to high-dynamic aircraft Download PDF

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CN113984042B
CN113984042B CN202111012824.7A CN202111012824A CN113984042B CN 113984042 B CN113984042 B CN 113984042B CN 202111012824 A CN202111012824 A CN 202111012824A CN 113984042 B CN113984042 B CN 113984042B
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CN113984042A (en
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龙达峰
孙俊丽
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Huizhou University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/04Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means
    • G01C21/08Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means involving use of the magnetic field of the earth
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20Instruments for performing navigational calculations
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining 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
    • G01S19/42Determining position
    • G01S19/45Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining 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
    • G01S19/42Determining position
    • G01S19/45Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
    • G01S19/47Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial
    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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Abstract

本发明提供一种适用高动态飞行器串联组合导航方法,采用“快速获取”与“高精度组合滤波”两种工作模式的串联组合,其中,在飞行器飞行的初始阶段,在外弹道约束下的无控飞行,通过初始姿态快速估计器分别根据三轴地磁传感器的测量值,角速率滤波器输出的三轴向角速率,以及卫星导航系统输出的导航坐标系下载体速度三个输入值,进行载体初始参数的空中快速获取,输出当前载体的飞行初始参数;在飞行器进入受控飞行阶段,通过飞行姿态高精度滤波器,采用离散EKF滤波算法实时完成飞行姿态高精度滤波估计。

The present invention provides a serial combination navigation method suitable for highly dynamic aircraft, which adopts a series combination of two working modes: "quick acquisition" and "high-precision combined filtering". In the initial stage of aircraft flight, the uncontrolled navigation under external ballistic constraints During flight, the initial attitude rapid estimator performs carrier initialization based on three input values: the measurement value of the three-axis geomagnetic sensor, the three-axis angular rate output by the angular rate filter, and the body speed in the navigation coordinate system output by the satellite navigation system. The parameters are quickly acquired in the air and the initial flight parameters of the current carrier are output; when the aircraft enters the controlled flight stage, the flight attitude high-precision filter is used to complete the high-precision filter estimation of the flight attitude in real time using the discrete EKF filtering algorithm.

Description

一种适用高动态飞行器串联组合导航方法A tandem integrated navigation method suitable for highly dynamic aircraft

技术领域Technical Field

本发明涉及常规弹药、高速旋转弹药、高动态飞行器等飞行姿态测量技术领域,尤其是涉及一种适用高动态飞行器串联组合导航方法。The invention relates to the technical field of flight attitude measurement of conventional ammunition, high-speed rotating ammunition, high-dynamic aircraft, etc., and in particular to a tandem combined navigation method suitable for high-dynamic aircraft.

背景技术Background Art

常规弹药发射后,在外弹道约束下弹丸全程依靠惯性力飞行,具有大初始 速度,高过载和高速度旋转等“高动态”特性。在常规弹药智能化导航改造中, 弹轴向高达14000°/s的滚转角速率,使得现有陀螺的量程与精度很难同时满足弹载测试的要求,另外高达10000g的发射大过载,极易造成机载传感器出现 测量大误差、短时失效、甚至损坏等。大初速、高过载、高自旋等这些恶劣应 用环境使得现有成熟的机载组合导航系统很难直接移植应用于常规弹药这类高 动态飞行器的智能化改造中,存在参数测试不全、测量精度较低或系统可靠性 差等问题。因此,寻求一种适用于具有高过载、高自旋和高动态运动特征的飞行器的导航系统,是常规弹药智能化改造亟需解决的关键技术之一。After conventional ammunition is fired, the projectile flies by inertia force throughout the whole process under the constraint of external ballistics, and has "high dynamic" characteristics such as high initial velocity, high overload and high-speed rotation. In the intelligent navigation transformation of conventional ammunition, the axial roll angular rate of the projectile is as high as 14000°/s, which makes it difficult for the existing gyroscope to simultaneously meet the requirements of the missile-borne test. In addition, the large overload of the launch is as high as 10000g, which is very likely to cause large measurement errors, short-term failure, or even damage to the airborne sensor. The harsh application environment such as high initial velocity, high overload, and high spin makes it difficult for the existing mature airborne combined navigation system to be directly transplanted and applied to the intelligent transformation of high-dynamic aircraft such as conventional ammunition, and there are problems such as incomplete parameter testing, low measurement accuracy or poor system reliability. Therefore, seeking a navigation system suitable for aircraft with high overload, high spin and high dynamic motion characteristics is one of the key technologies that need to be solved in the intelligent transformation of conventional ammunition.

发明内容Summary of the invention

针对上述问题,本专利提出了一种适用高动态飞行器串联组合导航方法, 针对上述问题,本发明根据高动态飞行器运动特点,采用“快速获取”与“高 精度组合滤波”两种工作模式的串联组合方案,具体为在飞行器飞行初始阶段, 完成载体初始参数的空中快速获取;然后导航系统切换到高精度组合滤波模式, 进入受控飞行阶段,最终实现高动态飞行器受控飞行参数高精度估计。In response to the above problems, this patent proposes a serial combined navigation method suitable for high-dynamic aircraft. In response to the above problems, the present invention adopts a serial combination scheme of two working modes, "fast acquisition" and "high-precision combined filtering", according to the movement characteristics of high-dynamic aircraft. Specifically, in the initial stage of aircraft flight, the initial parameters of the carrier are quickly acquired in the air; then the navigation system switches to the high-precision combined filtering mode and enters the controlled flight stage, finally achieving high-precision estimation of the controlled flight parameters of the high-dynamic aircraft.

具体的,所述适用高动态飞行器串联组合导航方法,包括:Specifically, the method for tandem combined navigation of highly dynamic aircraft includes:

在飞行器飞行的初始阶段,在外弹道约束下的无控飞行,通过初始姿态快 速估计器分别根据三轴地磁传感器的测量值角速率滤波器 输出的三轴向角速率以及卫星导航系统输出的导航坐标系下载体速 度三个输入值,进行载体初始参数的空中快速获取,输出当前载体的 飞行初始参数 In the initial stage of the flight, the aircraft is in uncontrolled flight under the constraint of external ballistics. The initial attitude fast estimator is used to calculate the measured values of the three-axis geomagnetic sensor. The three-axis angular rate output of the angular rate filter And the carrier speed in the navigation coordinate system output by the satellite navigation system Three input values are used to quickly obtain the initial parameters of the carrier in the air and output the initial flight parameters of the current carrier.

在飞行器进入受控飞行阶段,飞行姿态高精度滤波器分别根据所述飞行初 始参数所述三轴地磁传感器的测量值Hb,所述三轴向角速率以 及所述载体速度四个输入值,采用离散EKF滤波算法实时完成飞行姿 态高精度滤波估计 When the aircraft enters the controlled flight phase, the flight attitude high-precision filter is respectively based on the initial flight parameters The measured value H b of the three-axis geomagnetic sensor, the three-axis angular rate and the carrier speed Four input values, using discrete EKF filtering algorithm to complete high-precision filtering estimation of flight attitude in real time

其中,所述角速率滤波器的输入数据为MEMS陀螺实测值以及三轴 地磁传感器的测量值Hb;所述MEMS陀螺包括分别安装于所述载体坐标系 O-XbYbZb的X轴上的单轴陀螺Gx和Z轴上的单轴陀螺Gz;所述三轴地磁传感器 各轴敏感方向均与载体坐标系完全重合,用于测量载体坐标系下地磁场矢量信 息;所述卫星导航系统的接收机天线安装于飞行器壳体表面。The input data of the angular rate filter is the actual measured value of the MEMS gyroscope. and and the measurement value Hb of the three-axis geomagnetic sensor; the MEMS gyroscope includes a single-axis gyroscope Gx and a single-axis gyroscope Gz installed on the X-axis and the Z-axis of the carrier coordinate system OXb , Yb, and Zb respectively; the sensitive directions of each axis of the three-axis geomagnetic sensor completely coincide with the carrier coordinate system, and is used to measure the geomagnetic field vector information in the carrier coordinate system; the receiver antenna of the satellite navigation system is installed on the surface of the aircraft shell.

进一步的,通过所述初始姿态快速估计器计算飞行初始参数还包括以下计算过程:Furthermore, the initial flight parameters are calculated by the initial attitude fast estimator The following calculations are also included:

通过速度信息进行估算载体的初始俯仰角θ0,俯仰角解算公式为:The initial pitch angle θ 0 of the carrier is estimated by the velocity information. The pitch angle calculation formula is:

式中,分别表示为导航坐标系下的飞行器初始速度分量,由 卫星导航系统测量所得;In the formula, and They are respectively represented as the initial velocity components of the aircraft in the navigation coordinate system, measured by the satellite navigation system;

由磁测信息解算载体的偏航角和滚转角γ0初始姿态信息,公式为:Calculate the carrier's yaw angle from magnetic information And the roll angle γ 0 initial attitude information, the formula is:

式中,分别表示为三轴地磁传感器X、Y和Z轴向地磁传感 器测量输出值 为导航系下的地磁场北向地磁分量。In the formula, and Represented as the measurement output values of the three-axis geomagnetic sensor X, Y and Z axis geomagnetic sensor It is the northward geomagnetic component of the geomagnetic field under the navigation system.

进一步的,所述三轴向角速率的角速率滤波方程由状态方程式和 观测方程式共同组成,并采用卡尔曼滤波算法完成状态变量X(k)最优滤波估计为飞行姿态高精度滤波器提供精确的飞行器载体角速率信息 Furthermore, the three-axis angular velocity The angular rate filter equation is composed of the state equation and the observation equation, and the Kalman filter algorithm is used to complete the optimal filter estimation of the state variable X(k). Provide accurate aircraft carrier angular rate information for high-precision flight attitude filters

进一步的,所述状态方程式,还包括:Furthermore, the state equation also includes:

选取角速率作为系统的状态变量X(k)=[ωxyz]T,则系统的状态方程可 以表示为:Selecting the angular velocity as the state variable of the system X(k) = [ω x , ω y , ω z ] T , the state equation of the system can be expressed as:

X(k)=Φk,k-1X(k-1)+w(k);X(k)=Φ k,k-1 X(k-1)+w(k);

式中,状态转移矩阵量测噪声w(k)=[nx,ny,nz]T,满 足均值为E[w(k)]=0,方差为E[w(k),wT(j)]=Q(k),Q(k)为系统噪声序列方差 阵。In the formula, the state transfer matrix The measurement noise w(k) = [ nx , ny , nz ] T , satisfies the mean E[w(k)] = 0, and the variance E[w(k), wT (j)] = Q(k), where Q(k) is the variance matrix of the system noise sequence.

进一步的,所述观测方程式,还包括:Furthermore, the observation equation also includes:

选取为各轴向角速率测量值作为滤波系统的观测量则角速率滤波器的观测方程可表示为:Select The angular velocity measurements of each axis are used as the observations of the filtering system. Then the observation equation of the angular rate filter can be expressed as:

Z(k)=H(k)X(k)+v(k);Z(k)=H(k)X(k)+v(k);

式中,量测阵v(k)为系统的量测噪声,满足均值为 E[v(k)]=0,方差为E[v(k),vT(j)]=R(k),R(k)为量测噪声序列方差阵。In the formula, the measurement array v(k) is the measurement noise of the system, satisfying the mean E[v(k)]=0 and the variance E[v(k),v T (j)]=R(k), where R(k) is the variance matrix of the measurement noise sequence.

其中,所述角速率滤波器的角速率滤波方程,还包括如下两个更新过程:The angular rate filter equation of the angular rate filter further includes the following two updating processes:

时间更新过程:Time update process:

和量测更新过程:And measurement update process:

式中,为状态一步预测;P(k,k-1)为一步预测均方误差;Kk表示滤 波增益;R(k)为量测噪声阵;Q(k-1)为k-1时刻系统噪声方差阵;I为单位矩 阵;Pk为估计均方误差;为状态估计。In the formula, is the state one-step prediction; P (k, k-1) is the one-step prediction mean square error; K k represents the filter gain; R (k) is the measurement noise matrix; Q (k-1) is the system noise variance matrix at time k-1; I is the unit matrix; P k is the estimated mean square error; For state estimation.

其中,所述飞行姿态高精度滤波器,还包括:Wherein, the flight attitude high-precision filter also includes:

滤波器状态方程:选取飞行器三维姿态角作为系统状态变量以及根据惯性导航原理推导出飞行器在东北天导航坐标系下 的欧拉角微分方程作为系统的状态方程,公式为:Filter state equation: Select the three-dimensional attitude angle of the aircraft As system state variables And according to the inertial navigation principle, the Euler angle differential equation of the aircraft in the northeast sky navigation coordinate system is derived as the state equation of the system, and the formula is:

其中,f[X(t),t]是关于X(t)的非线性方程组:where f[X(t),t] is a set of nonlinear equations about X(t):

式中,w(t)是系统过程噪声,并满足均值为E[w(t)]=0,方差 E[w(t),wT(τ)]=Q(t).为滤波后的飞行器载体角速率信息;Where w(t) is the system process noise, and its mean is E[w(t)] = 0, and its variance is E[w(t), w T (τ)] = Q(t). is the filtered aircraft carrier angular rate information;

以及滤波器观测方程:选取地磁传感器测量输出以及通过卫星 导航系统测量所得的速度信息计算俯仰角(θv)作为系统的观测量系统的观测方程,公式为:And the filter observation equation: Select the geomagnetic sensor measurement output The velocity information obtained by the satellite navigation system is used to calculate the pitch angle (θ v ) as the observation quantity of the system. The observation equation of the system is:

Z(t)=h[X(t),t]+v(k);Z(t)=h[X(t),t]+v(k);

其中,h[X(t),t]是关于X(t)的非线性方程组:where h[X(t),t] is a set of nonlinear equations about X(t):

式中,v(t)是量测噪声,并满足均值为E[v(t)]=0,方差E[v(t),vT(τ)]=Q(t)。Where v(t) is the measurement noise, and satisfies the mean E[v(t)] = 0 and the variance E[v(t),v T (τ)] = Q(t).

进一步的,所述采用离散EKF滤波算法实时完成飞行姿态高精度滤波估计还包括:Furthermore, the discrete EKF filtering algorithm is used to complete the high-precision filtering estimation of the flight attitude in real time. Also includes:

构建飞行器姿态滤波模型:Constructing the aircraft attitude filter model:

并进行进行离散化可得:And discretize it to get:

其中,状态转移矩阵Φk,k-1按如下公式计算:Among them, the state transfer matrix Φ k,k-1 is calculated according to the following formula:

式中,Φk,k-1为雅可比矩阵,表示为方程组f[X(t),t]对各状态变量的一阶偏导数;为状态一步预测;Where Φ k,k-1 is the Jacobian matrix, It is expressed as the equation system f[X(t),t] for each state variable The first partial derivative of ; One-step prediction for the state;

其中,观测矩阵H(k)为雅可比阵:Among them, the observation matrix H(k) is the Jacobian matrix:

式中,表示为方程组h[X(t),t]对各状态变量的一阶偏导数;为状态一步预测;v(k)为量测噪。 In the formula, It is expressed as the system of equations h[X(t),t] for each state variable The first partial derivative of ; is the one-step prediction of the state; v(k) is the measurement noise.

此外,所述离散EKF滤波算法还包括如下两个滤波过程:In addition, the discrete EKF filtering algorithm also includes the following two filtering processes:

时间更新过程:Time update process:

Pk,k-1=Φk,k-1Pk-1k,k-1)T+Qk-1P k,k-1k,k-1 P k-1k,k-1 ) T +Q k-1 ;

和测量更新过程:And the measurement update process:

Kk=P(k,k-1)(H(k))T[H(k)Pk,k-1(H(k))T+R(k)]-1 K k =P (k,k-1) (H(k)) T [H(k)P k,k-1 (H(k)) T +R(k)] -1

Pk=(I-KkH(k))Pk,k-1(I-KkH(k))T+KkR(K)(Kk)TP k =(IK k H(k))P k, k-1 (IK k H(k)) T +K k R(K)(K k ) T ;

式中,Kk为滤波增益;Φk,k-1为状态转移阵;H(k)为量测矩阵;R(k)为量 测噪声阵;Q(k-1)为k-1时刻系统噪声方差阵;Pk-1为前一时刻系统估计方差 阵;Pk,k-1为一步预测均方误差;Pk为估计均方误差;为状态估计。Where K k is the filter gain; Φ k, k-1 is the state transition matrix; H(k) is the measurement matrix; R(k) is the measurement noise matrix; Q(k-1) is the system noise variance matrix at time k-1; P k-1 is the system estimated variance matrix at the previous moment; P k, k-1 is the one-step prediction mean square error; P k is the estimated mean square error; For state estimation.

综上所述,本发明提供一种适用高动态飞行器串联组合导航方法,采用“快 速获取”与“高精度组合滤波”两种工作模式的串联组合,其中,在飞行器飞 行的初始阶段,在外弹道约束下的无控飞行,通过初始姿态快速估计器分别根 据三轴地磁传感器的测量值,角速率滤波器输出的三轴向角速率,以及卫星导 航系统输出的导航坐标系下载体速度三个输入值,进行载体初始参数的空中快速获取,输出当前载体的飞行初始参数;在飞行器进入受控飞行阶段,通过飞 行姿态高精度滤波器,采用离散EKF滤波算法实时完成飞行姿态高精度滤波估 计。In summary, the present invention provides a method for serial combined navigation of high-dynamic aircraft, which adopts a serial combination of two working modes, namely, "fast acquisition" and "high-precision combined filtering". In the initial stage of the aircraft flight, in uncontrolled flight under the constraint of external ballistics, the initial parameters of the carrier are quickly acquired in the air by an initial attitude fast estimator according to the three input values of the measurement value of the three-axis geomagnetic sensor, the three-axis angular velocity output by the angular velocity filter, and the carrier velocity in the navigation coordinate system output by the satellite navigation system, and the initial flight parameters of the current carrier are output; when the aircraft enters the controlled flight stage, the high-precision flight attitude filter is used to complete the high-precision filtering estimation of the flight attitude in real time by adopting the discrete EKF filtering algorithm.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为飞行姿态串联组合滤波器结构示意图。Figure 1 is a schematic diagram of the flight attitude series combination filter structure.

图2为导航传感器安装示意图。Figure 2 is a schematic diagram of the navigation sensor installation.

具体实施方式DETAILED DESCRIPTION

为了使本技术领域的人员更好地理解本发明方案,下面将结合本发明实施 例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所 描述的实施例仅仅是本发明一部分实施例,而不是全部的实施例。基于本发明 中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有 其他实施例,都属于本发明保护的范围。In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

如图1所示,为本发明提出了一种适用高动态飞行器串联组合导航方法, 具体过程为:As shown in FIG1 , the present invention proposes a method for tandem integrated navigation of highly dynamic aircraft, and the specific process is as follows:

在飞行器飞行的初始阶段,在外弹道约束下的无控飞行,通过初始姿态快 速估计器分别根据三轴地磁传感器的测量值角速率滤波器 输出的三轴向角速率以及卫星导航系统输出的导航坐标系下载体速 度三个输入值,进行载体初始参数的空中快速获取,输出当前载体的 飞行初始参数 In the initial stage of the flight, the aircraft is in uncontrolled flight under the constraint of external ballistics. The initial attitude fast estimator is used to calculate the measured values of the three-axis geomagnetic sensor. The three-axis angular rate output of the angular rate filter And the carrier speed in the navigation coordinate system output by the satellite navigation system Three input values are used to quickly obtain the initial parameters of the carrier in the air and output the initial flight parameters of the current carrier.

在飞行器进入受控飞行阶段,飞行姿态高精度滤波器分别根据所述飞行初 始参数所述三轴地磁传感器的测量值Hb,所述三轴向角速率以 及所述载体速度四个输入值,采用离散EKF滤波算法实时完成飞行姿 态高精度滤波估计 When the aircraft enters the controlled flight phase, the flight attitude high-precision filter is respectively based on the initial flight parameters The measured value H b of the three-axis geomagnetic sensor, the three-axis angular rate and the carrier speed Four input values, using discrete EKF filtering algorithm to complete high-precision filtering estimation of flight attitude in real time

本发明所述高动态飞行器机载捷联导航传感器主要有三轴地磁传感器、陀 螺和卫星导航接收机组成,各传感器测量安装方式如图2所示。The strapdown navigation sensor onboard the high-dynamic aircraft of the present invention mainly comprises a three-axis geomagnetic sensor, a gyroscope and a satellite navigation receiver. The measurement installation method of each sensor is shown in FIG2 .

其中,所述角速率滤波器的输入数据为MEMS陀螺实测值以及三轴 地磁传感器的测量值Hb;所述MEMS陀螺包括分别安装于所述载体坐标系 O-XbYbZb的X轴上的单轴陀螺Gx和Z轴上的单轴陀螺Gz;所述三轴地磁传感 器各轴敏感方向均与载体坐标系完全重合,用于测量载体坐标系下地磁场矢量 信息;所述卫星导航系统的接收机天线安装于飞行器壳体表面。The input data of the angular rate filter is the actual measured value of the MEMS gyroscope. and and the measurement value H b of the three-axis geomagnetic sensor; the MEMS gyroscope includes a single-axis gyroscope Gx and a single-axis gyroscope Gz respectively installed on the X-axis and the Z-axis of the carrier coordinate system O-XbYbZb; the sensitive directions of each axis of the three-axis geomagnetic sensor completely coincide with the carrier coordinate system, and are used to measure the geomagnetic field vector information in the carrier coordinate system; the receiver antenna of the satellite navigation system is installed on the surface of the aircraft shell.

本发明采用的飞行姿态串联组合滤波器主要由角速率滤波器、初始姿态快 速估计器和飞行姿态高精度滤波器三个完全不同模块组成。具体为:The flight attitude series combined filter used in the present invention is mainly composed of three completely different modules: angular rate filter, initial attitude fast estimator and flight attitude high-precision filter. Specifically:

初始姿态快速估计器Fast initial pose estimator

本发明选取东北天坐标系(ENU)为导航坐标系(n系),高动态飞行器发 射后,机载卫星接收机正常工作时,可测量得到飞行器的实时速度信息。考虑 到飞行器在无控飞行时其攻角很小,载体的初始俯仰角θ0可通过速度信息进行 估算,俯仰角解算公式为:The present invention selects the Northeastern celestial coordinate system (ENU) as the navigation coordinate system (n system). After the high-dynamic aircraft is launched, when the onboard satellite receiver works normally, the real-time velocity information of the aircraft can be measured. Considering that the angle of attack of the aircraft is very small during uncontrolled flight, the initial pitch angle θ 0 of the carrier can be estimated through the velocity information, and the pitch angle solution formula is:

公式1:Formula 1:

上式(1)中,分别表示为导航坐标系下的飞行器初始速度分 量,由卫星导航系统测量所得,其由卫星导航系统测量所得。In the above formula (1), and They are respectively represented as the initial velocity components of the aircraft in the navigation coordinate system, which are measured by the satellite navigation system, and they are respectively represented as the initial velocity components of the aircraft in the navigation coordinate system, which are measured by the satellite navigation system.

由公式(1)可计算出飞行器初始俯仰角,因此,在公式(1)计算得到俯 仰角θ0情况下,再由磁测信息解算载体的偏航角和滚转角γ0初始姿态信息, 其磁测姿态解算公式为:The initial pitch angle of the aircraft can be calculated by formula (1). Therefore, when the pitch angle θ 0 is calculated by formula (1), the yaw angle of the carrier can be calculated by the magnetic measurement information. and the initial attitude information of the rolling angle γ 0 , the magnetic attitude solution formula is:

公式2:Formula 2:

公式3:Formula 3:

上式(2)、(3)中,分别表示为三轴地磁传感器X、Y和 Z轴向地磁传感器测量输出值 为导航系下的地磁场 北向地磁分量。In the above formulas (2) and (3), and Represented as the measurement output values of the three-axis geomagnetic sensor X, Y and Z axis geomagnetic sensor It is the northward geomagnetic component of the geomagnetic field under the navigation system.

因此,联合上述公式(1)-(3),可以快速计算得到飞行器在无控飞行时 三维初始姿态参数:偏航角俯仰角θ0和滚转角γ0,为串联二级飞行姿态高 精度滤波器提供较为准确的滤波初始参数。Therefore, by combining the above formulas (1)-(3), the three-dimensional initial attitude parameters of the aircraft during uncontrolled flight can be quickly calculated: yaw angle The pitch angle θ 0 and the roll angle γ 0 provide relatively accurate initial filtering parameters for the series-connected two-stage flight attitude high-precision filter.

角速率滤波器Angular Rate Filter

由于机载陀螺仪测量输出()及通过磁测信息计算得到滚转速率均存在测量误差,其误差模型可表示为:Since the onboard gyroscope measures the output ( and ) and the roll rate calculated from magnetic information There are measurement errors, and the error model can be expressed as:

公式4:Formula 4:

上式(4)中,为各轴向角速率测量值,ωxyz为各轴向理 想角速率,nx,ny,nz为各轴向角速率的测量噪声。In the above formula (4), are the measured values of the angular velocity of each axis, ω x , ω y , ω z are the ideal angular velocity of each axis, and n x , ny , nz are the measurement noise of the angular velocity of each axis.

本发明选取角速率作为系统的状态变量X(k)=[ωxyz]T,则系统的状态 方程可以表示为:The present invention selects angular velocity as the state variable of the system X(k)=[ω xyz ] T , then the state equation of the system can be expressed as:

公式5:Formula 5:

X(k)=Φk,k-1X(k-1)+w(k);X(k)=Φ k,k-1 X(k-1)+w(k);

上式(5)中,状态转移矩阵量测噪声w(k)=[nx,ny,nz]T, 满足均值为E[w(k)]=0,方差为E[w(k),wT(j)]=Q(k),Q(k)为系统噪声序列方 差阵。In the above formula (5), the state transfer matrix The measurement noise w(k) = [ nx , ny , nz ] T , satisfies the mean E[w(k)] = 0 and the variance E[w(k), wT (j)] = Q(k), where Q(k) is the variance matrix of the system noise sequence.

选取为各轴向角速率测量值作为滤波系统的观测量则角速率滤波器的观测方程可表示为:Select The angular velocity measurements of each axis are used as the observations of the filtering system. Then the observation equation of the angular rate filter can be expressed as:

公式6:Formula 6:

Z(k)=H(k)X(k)+v(k);Z(k)=H(k)X(k)+v(k);

上式(6)中,量测阵v(k)为系统的量测噪声,满足均 值为E[v(k)]=0,方差为E[v(k),vT(j)]=R(k),R(k)为量测噪声序列方差阵。In the above formula (6), the measurement array v(k) is the measurement noise of the system, satisfying the mean E[v(k)]=0 and the variance E[v(k),v T (j)]=R(k), where R(k) is the variance matrix of the measurement noise sequence.

因此,本发明由状态方程式(5)和观测方程式(6)共同组成角速率滤波 方程,并采用卡尔曼滤波算法完成状态变量X(k)最优滤波估计为飞行 姿态高精度滤波器提供精确的飞行器载体角速率信息 Therefore, the present invention uses the state equation (5) and the observation equation (6) to form an angular rate filter equation, and uses the Kalman filter algorithm to complete the optimal filtering estimation of the state variable X(k): Provide accurate aircraft carrier angular rate information for high-precision flight attitude filters

本发明所述角速率滤波器的滤波算法包括如下两个更新过程:The filtering algorithm of the angular rate filter of the present invention includes the following two updating processes:

(1)时间更新过程,公式7:(1) Time update process, formula 7:

(2)量测更新过程,公式8:(2) Measurement update process, formula 8:

上式(7)、(8)中,为状态一步预测;P(k,k-1)为一步预测均方 误差;Kk表示滤波增益;R(k)为量测噪声阵;Q(k-1)为k-1时刻系统噪声方 差阵;I为单位矩阵;Pk为估计均方误差;为状态估计。In the above formulas (7) and (8), is the state one-step prediction; P (k, k-1) is the one-step prediction mean square error; K k represents the filter gain; R (k) is the measurement noise matrix; Q (k-1) is the system noise variance matrix at time k-1; I is the unit matrix; P k is the estimated mean square error; For state estimation.

飞行姿态高精度滤波器Flight attitude high precision filter

1.滤波器状态方程1. Filter state equation

根据惯性导航原理,可推导出飞行器在东北天导航坐标系下的欧拉角微分 方程为公式9:According to the inertial navigation principle, the Euler angle differential equation of the aircraft in the northeast sky navigation coordinate system can be derived as formula 9:

上式(9)中,为载体姿态变化率,为滤波后的飞行器载 体角速率信息。In the above formula (9), is the carrier attitude change rate, is the filtered aircraft carrier angular rate information.

选取飞行器三维姿态角作为系统状态变量并选取上式(9)作为系统的状态方程,则其可简写为一般形式公式10:Select the 3D attitude angle of the aircraft As system state variables If the above formula (9) is selected as the state equation of the system, it can be simplified into the general form formula 10:

上式(10),f[X(t),t]是关于X(t)的非线性方程组,In the above formula (10), f[X(t),t] is a nonlinear equation system about X(t).

w(t)是系统过程噪声,并满足均值为E[w(t)]=0,方差E[w(t),wT(τ)]=Q(t)。 w(t) is the system process noise, and satisfies the mean E[w(t)] = 0 and the variance E[w(t), w T (τ)] = Q(t).

2、滤波器观测方程2. Filter observation equation

根据磁测原理,地磁传感器的测量输出可表示为公式11:According to the principle of magnetic measurement, the measurement output of the geomagnetic sensor can be expressed as formula 11:

上式(11)中,是东北天导航坐标系下的地磁场矢量;为姿 态变换矩阵。In the above formula (11), is the geomagnetic field vector in the northeast sky navigation coordinate system; is the posture transformation matrix.

如前所述,可通过卫星导航系统测量所得的速度信息计算俯仰角,公式12:As mentioned above, the pitch angle can be calculated using the velocity information measured by the satellite navigation system, formula 12:

上式中,为导航坐标系下载体的速度。In the above formula, is the velocity of the carrier in the navigation coordinate system.

选取地磁传感器测量输出以及通过卫星导航系统测量所得的速 度信息计算俯仰角(θv)作为系统的观测量并选取磁 测公式(11)和俯仰角计算公式(12)作为系统的观测方程,其可简写为一般 形式为公式13:Select the geomagnetic sensor measurement output The velocity information obtained by the satellite navigation system is used to calculate the pitch angle (θ v ) as the observation quantity of the system. The magnetic measurement formula (11) and the pitch angle calculation formula (12) are selected as the observation equations of the system, which can be simplified into the general form of formula 13:

Z(t)=h[X(t),t]+v(t);Z(t)=h[X(t),t]+v(t);

上式(13),v(t)是量测噪声,并满足均值为E[v(t)]=0,方差 E[v(t),vT(τ)]=Q(t)。h[X(t),t]是关于X(t)的非线性方程组:In equation (13), v(t) is the measurement noise, and satisfies the mean E[v(t)] = 0 and the variance E[v(t), v T (τ)] = Q(t). h[X(t), t] is a set of nonlinear equations about X(t):

3、EKF滤波算法3. EKF filtering algorithm

综合滤波器状态方程(10)和滤波器观测方程(13)组成飞行器姿态滤波 模型,为非线性连续系统,可简写一般形式,为公式14:The combined filter state equation (10) and filter observation equation (13) form the aircraft attitude filter model, which is a nonlinear continuous system and can be simplified in general form as formula 14:

采用离散EKF算法进行状态估计,EKF是基于Taylor级数展开的线性化处 理的滤波方法,首先对滤波模型进行线性化处理,然后再对式(15)进行离散 化可得公式15:The discrete EKF algorithm is used for state estimation. EKF is a filtering method based on the linearization of Taylor series expansion. First, the filter model is linearized, and then the formula (15) is discretized to obtain formula 15:

上式(15)中,状态转移矩阵Φk,k-1按如下公式16计算:In the above formula (15), the state transfer matrix Φ k,k-1 is calculated according to the following formula 16:

Φk,k-1为雅可比矩阵,表示为方程组f[X(t),t]对各状态变量的一阶偏导数; Φ k,k-1 is the Jacobian matrix, It is expressed as the equation system f[X(t),t] for each state variable The first partial derivative of ;

为状态一步预测。 One-step prediction for the state.

上式(15)中,观测矩阵H(k)为雅可比阵, In the above formula (15), the observation matrix H(k) is the Jacobian matrix,

表示为方程组h[X(t),t]对各状态变量的一阶偏导数, It is expressed as the system of equations h[X(t),t] for each state variable The first-order partial derivative of

为状态一步预测;v(k)为量测噪声。 is the one-step prediction of the state; v(k) is the measurement noise.

因此,基于离散EKF的滤波算法包括如下两个滤波过程:Therefore, the filtering algorithm based on discrete EKF includes the following two filtering processes:

(1)时间更新过程,采用公式17:(1) Time update process, using formula 17:

Pk,k-1=Φk,k-1Pk-1k,k-1)T+Qk-1P k,k-1k,k-1 P k-1k,k-1 ) T +Q k-1 ;

(2)测量更新过程,采用公式18:(2) Measurement update process, using formula 18:

Kk=P(k,k-1)(H(k))T[H(k)Pk,k-1(H(k))T+R(k)]-1K k =P (k,k-1) (H(k)) T [H(k)P k,k-1 (H(k)) T +R(k)] -1 ;

Pk=(I-KkH(k))Pk,k-1(I-KkH(k))T+KkR(k)(Kk)TP k =(IK k H(k))P k,k-1 (IK k H(k)) T +K k R(k)(K k ) T ;

上述滤波方程(17)-(18)中,Kk为滤波增益;Φk,k-1为状态转移阵;H(k) 为量测矩阵;R(k)为量测噪声阵;Q(k-1)为k-1时刻系统噪声方差阵;Pk-1为 前一时刻系统估计方差阵;Pk,k-1为一步预测均方误差;Pk为估计均方误差;为状态估计。In the above filter equations (17)-(18), K k is the filter gain; Φ k,k-1 is the state transition matrix; H(k) is the measurement matrix; R(k) is the measurement noise matrix; Q(k-1) is the system noise variance matrix at time k-1; P k-1 is the system estimated variance matrix at the previous time; P k,k-1 is the one-step prediction mean square error; P k is the estimated mean square error; For state estimation.

可见在初始姿态快速估计器提供的初始姿态参数通过上述 离本发明所述串联组合方案中,机载导航系统在不同阶段所面临的问题及算法 要求不同。在初始参数未知的无控飞行阶段,对导航算法的要求是快速估计出 初始参数、估计精度其次;而其后的受控飞行阶段,初始参数已知(精度低),但机载导航系统体现出强非线性、存在大的解算误差等,此阶段对导航算法的 要求是提高滤波估计的精度、并兼顾实时性问题。It can be seen that the initial attitude parameters provided by the initial attitude fast estimator Through the above-mentioned series combination scheme of the present invention, the problems and algorithm requirements faced by the airborne navigation system at different stages are different. In the uncontrolled flight stage when the initial parameters are unknown, the requirement for the navigation algorithm is to quickly estimate the initial parameters, and the estimation accuracy is second; while in the subsequent controlled flight stage, the initial parameters are known (with low accuracy), but the airborne navigation system shows strong nonlinearity and has large solution errors. The requirement for the navigation algorithm at this stage is to improve the accuracy of the filter estimation and take into account the real-time problem.

以上所述实施例仅表达了本发明的几种实施方式,其描述较为具体和详细, 但并不能因此而理解为对本发明专利范围的限制。应当指出的是,对于本领域 的普通技术人员来说,在不脱离本发明构思的前提下,还可以做出若干变形和 改进,这些都属于本发明的保护范围。因此,本发明专利的保护范围应以所附 权利要求为准。The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present invention. It should be pointed out that, for a person skilled in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims (7)

1.一种适用高动态飞行器串联组合导航方法,其特征在于,包括:1. A method for tandem integrated navigation of highly dynamic aircraft, characterized by comprising: 在飞行器飞行的初始阶段,在外弹道约束下的无控飞行,通过初始姿态快速估计器分别根据三轴地磁传感器的测量值角速率滤波器输出的三轴向角速率以及卫星导航系统输出的导航坐标系下载体速度三个输入值,进行载体初始参数的空中快速获取,输出当前载体的飞行初始参数 In the initial stage of the flight, the aircraft is in uncontrolled flight under the constraint of external ballistics. The initial attitude fast estimator is used to calculate the measured values of the three-axis geomagnetic sensor. The three-axis angular rate output of the angular rate filter And the carrier speed in the navigation coordinate system output by the satellite navigation system Three input values are used to quickly obtain the initial parameters of the carrier in the air and output the initial flight parameters of the current carrier. 在飞行器进入受控飞行阶段,飞行姿态高精度滤波器分别根据所述飞行初始参数所述三轴地磁传感器的测量值Hb,所述三轴向角速率以及所述载体速度四个输入值,采用离散EKF滤波算法实时完成飞行姿态高精度滤波估计 When the aircraft enters the controlled flight phase, the flight attitude high-precision filter is respectively based on the initial flight parameters The measured value H b of the three-axis geomagnetic sensor, the three-axis angular rate and the carrier speed Four input values, using discrete EKF filtering algorithm to complete high-precision filtering estimation of flight attitude in real time 所述角速率滤波器的输入数据为MEMS陀螺实测值以及三轴地磁传感器的测量值Hb;所述MEMS陀螺包括分别安装于所述载体坐标系O-XbYbZb的X轴上的单轴陀螺Gx和Z轴上的单轴陀螺Gz;所述三轴地磁传感器各轴敏感方向均与载体坐标系完全重合,用于测量载体坐标系下地磁场矢量信息;所述卫星导航系统的接收机天线安装于飞行器壳体表面;The input data of the angular rate filter is the actual measured value of the MEMS gyroscope and and the measured value H b of the three-axis geomagnetic sensor; the MEMS gyroscope includes a single-axis gyroscope Gx and a single-axis gyroscope Gz respectively installed on the X-axis and the Z-axis of the carrier coordinate system OX b Y b Z b ; the sensitive directions of each axis of the three-axis geomagnetic sensor completely coincide with the carrier coordinate system, and are used to measure the geomagnetic field vector information in the carrier coordinate system; the receiver antenna of the satellite navigation system is installed on the surface of the aircraft shell; 通过所述初始姿态快速估计器计算飞行初始参数还包括以下计算过程:The initial flight parameters are calculated by the initial attitude fast estimator The following calculations are also included: 通过速度信息进行估算载体的初始俯仰角θ0和偏航角俯仰角解算公式为:The initial pitch angle θ0 and yaw angle of the carrier are estimated using velocity information The pitch angle calculation formula is: 式中,分别表示为导航坐标系下的飞行器初始速度分量,由卫星导航系统测量所得;In the formula, and They are respectively represented as the initial velocity components of the aircraft in the navigation coordinate system, measured by the satellite navigation system; 由磁测信息解算载体的滚转角γ0初始姿态信息,公式为:The initial attitude information of the carrier's roll angle γ 0 is calculated from the magnetic measurement information. The formula is: 式中,分别表示为三轴地磁传感器X、Y和Z轴向地磁传感器测量输出值;为导航系下的地磁场分量;In the formula, and They are respectively represented as the measurement output values of the three-axis geomagnetic sensor X, Y and Z axes; is the geomagnetic field component under the navigation system; 所述飞行姿态高精度滤波器,还包括:The flight attitude high-precision filter also includes: 滤波器状态方程:选取飞行器三维姿态角作为系统状态变量以及根据惯性导航原理推导出飞行器在东北天导航坐标系下的欧拉角微分方程作为系统的状态方程,公式为:Filter state equation: Select the three-dimensional attitude angle of the aircraft As system state variables And according to the inertial navigation principle, the Euler angle differential equation of the aircraft in the northeast sky navigation coordinate system is derived as the state equation of the system, and the formula is: 其中,f[X(t),t]是关于X(t)的非线性方程组:where f[X(t),t] is a set of nonlinear equations about X(t): 式中,w(t)是系统过程噪声,并满足均值为E[w(t)]=0,方差E[w(t),wT(τ)]=Q(t);为滤波后的飞行器载体角速率信息;Where w(t) is the system process noise, and satisfies the mean E[w(t)] = 0 and the variance E[w(t), w T (τ)] = Q(t); is the filtered aircraft carrier angular rate information; 以及滤波器观测方程:选取地磁传感器测量输出以及通过卫星导航系统测量所得的速度信息计算俯仰角(θv)作为系统的观测量系统的观测方程,公式为:And the filter observation equation: Select the geomagnetic sensor measurement output The velocity information obtained by the satellite navigation system is used to calculate the pitch angle (θ v ) as the observation quantity of the system. The observation equation of the system is: Z(t)=h[X(t),t]+v(t);Z(t)=h[X(t),t]+v(t); 其中,h[X(t),t]是关于X(t)的非线性方程组:where h[X(t), t] is a set of nonlinear equations about X(t): 式中,v(t)是量测噪声,并满足均值为E[v(t)]=0,方差E[v(t),vT(τ)]=Q(t);为三轴地磁传感器各轴测量输出值。Where v(t) is the measurement noise, and satisfies the mean E[v(t)] = 0 and the variance E[v(t),v T (τ)] = Q(t); It is the output value measured by each axis of the three-axis geomagnetic sensor. 2.根据权利要求1所述的一种适用高动态飞行器串联组合导航方法,其特征在于,所述三轴向角速率的角速率滤波方程由状态方程式和观测方程式共同组成,并采用卡尔曼滤波算法完成状态变量X(k)最优滤波估计为飞行姿态高精度滤波器提供精确的飞行器载体角速率信息 2. A method for tandem integrated navigation of a highly dynamic aircraft according to claim 1, characterized in that the three-axis angular velocity The angular rate filter equation is composed of the state equation and the observation equation, and the Kalman filter algorithm is used to complete the optimal filter estimation of the state variable X(k). Provide accurate aircraft carrier angular rate information for high-precision flight attitude filters 3.根据权利要求2所述的一种适用高动态飞行器串联组合导航方法,其特征在于,所述状态方程式,还包括:3. The method for tandem integrated navigation of a highly dynamic aircraft according to claim 2, wherein the state equation further comprises: 选取角速率作为系统的状态变量X(k)=[ωxyz]T,则系统的状态方程表示为:Selecting the angular rate as the state variable of the system X(k) = [ω x , ω y , ω z ] T , the state equation of the system is expressed as: X(k)=Φk,k-1X(k-1)+w(k);X(k)=Φ k,k-1 X(k-1)+w(k); 式中,状态转移矩阵量测噪声w(k)=[nx,ny,nz]T,满足均值为E[w(k)]=0,方差为E[w(k),wT(j)]=Q(k),Q(k)为系统噪声序列方差阵。In the formula, the state transfer matrix The measurement noise w(k) = [ nx , ny , nz ] T , satisfies the mean E[w(k)] = 0, and the variance E[w(k), wT (j)] = Q(k), where Q(k) is the variance matrix of the system noise sequence. 4.根据权利要求2所述的一种适用高动态飞行器串联组合导航方法,其特征在于,所述观测方程式,还包括:4. The method for tandem integrated navigation of a highly dynamic aircraft according to claim 2, wherein the observation equation further comprises: 选取为各轴向角速率测量值作为滤波系统的观测量则角速率滤波器的观测方程可表示为:Select The angular velocity measurements of each axis are used as the observations of the filtering system. Then the observation equation of the angular rate filter can be expressed as: Z(k)=H(k)X(k)+v(k);Z(k)=H(k)X(k)+v(k); 式中,量测阵v(k)为系统的量测噪声,满足均值为E[v(k)]=0,方差为E[v(k),vT(j)]=R(k),R(k)为量测噪声序列方差阵。In the formula, the measurement array v(k) is the measurement noise of the system, satisfying the mean E[v(k)]=0 and the variance E[v(k),v T (j)]=R(k), where R(k) is the variance matrix of the measurement noise sequence. 5.根据权利要求2所述的一种适用高动态飞行器串联组合导航方法,其特征在于,所述角速率滤波器的角速率滤波方程,还包括如下两个更新过程:5. The method for tandem integrated navigation of a highly dynamic aircraft according to claim 2, wherein the angular velocity filter equation of the angular velocity filter further comprises the following two updating processes: 时间更新过程:Time update process: 和量测更新过程:And measurement update process: 式中,为状态一步预测;P(k,k-1)为一步预测均方误差;Kk表示滤波增益;R(k)为量测噪声阵;Q(k-1)为k-1时刻系统噪声方差阵;I为单位矩阵;Pk为估计均方误差;为状态估计;Φk,k-1为状态转移矩阵;Z(k)为系统的观测量;H(k)为系统的观测矩阵;Pk-1为预测均方误差。In the formula, is the state one-step prediction; P (k, k-1) is the one-step prediction mean square error; K k represents the filter gain; R (k) is the measurement noise matrix; Q (k-1) is the system noise variance matrix at time k-1; I is the unit matrix; P k is the estimated mean square error; is the state estimation; Φ k,k-1 is the state transfer matrix; Z(k) is the observation quantity of the system; H(k) is the observation matrix of the system; P k-1 is the prediction mean square error. 6.根据权利要求1所述的一种适用高动态飞行器串联组合导航方法,其特征在于,所述采用离散EKF滤波算法实时完成飞行姿态高精度滤波估计还包括:6. The method for tandem integrated navigation of a highly dynamic aircraft according to claim 1, characterized in that the discrete EKF filtering algorithm is used to perform high-precision filtering estimation of flight attitude in real time. Also includes: 构建飞行器姿态滤波模型:Constructing the aircraft attitude filter model: 并进行离散化可得:And discretize it to get: 式中,Z(k)为系统观测量;H(k)为观测矩阵;V(k)为量测噪声;Where Z(k) is the system observation; H(k) is the observation matrix; V(k) is the measurement noise; 其中,状态转移矩阵Φk,k-1按如下公式计算:Among them, the state transfer matrix Φ k,k-1 is calculated according to the following formula: 式中,Φk,k-1为雅可比矩阵,表示为方程组f[X(t),t]对各状态变量的一阶偏导数;为状态一步预测;Where Φ k,k-1 is the Jacobian matrix, It is expressed as the equation system f[X(t),t] for each state variable The first partial derivative of ; One-step prediction for the state; 其中,观测矩阵H(k)为雅可比阵:Among them, the observation matrix H(k) is the Jacobian matrix: 式中,表示为方程组h[X(t),t]对各状态变量的一阶偏导数;为状态一步预测;v(k)为量测噪声。In the formula, It is expressed as the system of equations h[X(t),t] for each state variable The first partial derivative of ; is the one-step prediction of the state; v(k) is the measurement noise. 7.根据权利要求6所述的一种适用高动态飞行器串联组合导航方法,其特征在于,所述离散EKF滤波算法还包括如下两个滤波过程:7. The method for tandem integrated navigation of a highly dynamic aircraft according to claim 6, wherein the discrete EKF filtering algorithm further comprises the following two filtering processes: 时间更新过程:Time update process: Pk,k-1=Φk,k-1Pk-1k,k-1)T+Qk-1P k, k-1 = Φ k, k-1 P k-1k, k-1 ) T +Q k-1 ; 和测量更新过程:And the measurement update process: Kk=Pk,k-1(H(k))T[H(k)Pk,k-1(H(k))T+R(k)]-1K k =P k,k-1 (H(k)) T [H(k)P k,k-1 (H(k)) T +R(k)] -1 ; Pk=(I-KkH(k))Pk,k-1(I-KkH(k))T+KkR(k)(Kk)TP k =(IK k H(k))P k, k-1 (IK k H(k)) T +K k R(k)(K k ) T ; 式中,Kk为滤波增益;Φk,k-1为状态转移阵;H(k)为量测矩阵;R(k)为量测噪声阵;Q(k-1)为k-1时刻系统噪声方差阵;Pk-1为前一时刻系统估计方差阵;Pk,k-1为一步预测均方误差;Pk为估计均方误差;为状态估计;为状态一步预测;I为单位矩阵。Where K k is the filter gain; Φ k, k-1 is the state transition matrix; H(k) is the measurement matrix; R(k) is the measurement noise matrix; Q(k-1) is the system noise variance matrix at time k-1; P k-1 is the system estimated variance matrix at the previous moment; P k, k-1 is the one-step prediction mean square error; P k is the estimated mean square error; is the state estimation; is the one-step prediction of the state; I is the identity matrix.
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