CN105241474B - A kind of tilting configuration inertial navigation system scaling method - Google Patents

A kind of tilting configuration inertial navigation system scaling method Download PDF

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CN105241474B
CN105241474B CN201410326080.XA CN201410326080A CN105241474B CN 105241474 B CN105241474 B CN 105241474B CN 201410326080 A CN201410326080 A CN 201410326080A CN 105241474 B CN105241474 B CN 105241474B
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王迪
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Beijing Automation Control Equipment Institute BACEI
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Abstract

本发明属于导航技术领域，涉及一种敏感轴斜置的惯导系统的标定方法。本发明技术方案通过采用归一正交化的方法，把斜置的陀螺、加速度计敏感轴通过方向余弦矩阵转换到弹体轴上，使得虚拟的陀螺坐标系、加速度计坐标系与真实的弹体系重合，从而法解决了敏感轴斜置的惯导系统的参数辨识问题。The invention belongs to the technical field of navigation and relates to a calibration method of an inertial navigation system with a sensitive axis tilted. The technical solution of the present invention adopts the normalized orthogonalization method to convert the inclined gyroscope and accelerometer sensitive axis to the body axis through the direction cosine matrix, so that the virtual gyroscope coordinate system and the accelerometer coordinate system are consistent with the real elastic body axis. The system coincides, so the method solves the parameter identification problem of the inertial navigation system with the sensitive axis tilted.

Description

一种斜置构型惯导系统标定方法A Calibration Method for Inertial Navigation System in Inclined Configuration

技术领域technical field

本发明属于导航技术领域，涉及一种敏感轴斜置的惯导系统的标定方法。The invention belongs to the technical field of navigation and relates to a calibration method of an inertial navigation system with a sensitive axis tilted.

背景技术Background technique

捷联惯导系统通常采用余度技术提高系统的可靠性和精度,惯性敏感器件多采用倾斜配置。而对于非冗余的惯性导航系统,其敏感器件也可以采用斜置,其优点在于可以扩大载体三个轴方向的角速度和加速度测量范围,节省惯性器件的安装空间。但是这种安装方式给惯测装置的标定带来了困难。常规的标定方法要求惯性器件沿正交的载体坐标系安装，通过转台上的位置试验、速率试验,辨识惯性器件的各项参数。Strapdown inertial navigation systems usually use redundancy technology to improve system reliability and accuracy, and inertial sensitive devices are mostly configured with tilt. For the non-redundant inertial navigation system, the sensitive components can also be placed obliquely, which has the advantage of expanding the angular velocity and acceleration measurement range of the three axes of the carrier and saving the installation space of the inertial components. However, this installation method brings difficulties to the calibration of the inertial measurement device. The conventional calibration method requires the inertial device to be installed along the orthogonal carrier coordinate system, and the parameters of the inertial device are identified through the position test and speed test on the turntable.

因此，亟需研制一种斜置构型惯导系统标定方法，既可以在捷联惯导系统或非冗余的惯性导航系统中倾斜配置惯性敏感器件，又可以准确、快速辨识敏感轴斜置的惯导系统的各项参数，方便对惯导系统进行标定。Therefore, there is an urgent need to develop a calibration method for oblique configuration inertial navigation systems, which can not only configure the inertial sensitive devices obliquely in the strapdown inertial navigation system or non-redundant inertial navigation system, but also accurately and quickly identify the oblique position of the sensitive axis. The parameters of the inertial navigation system are convenient for calibrating the inertial navigation system.

发明内容Contents of the invention

本发明的目的在于提供一种斜置构型惯导系统标定方法，从而准确、快速辨识敏感轴斜置的惯导系统的各项参数。The purpose of the present invention is to provide a calibration method for an inertial navigation system with an oblique configuration, so as to accurately and quickly identify various parameters of an inertial navigation system with an oblique sensitive axis.

为了实现这一目的，本发明采取的技术方案如下：In order to realize this object, the technical scheme that the present invention takes is as follows:

一种斜置构型惯导系统标定方法，具体包括以下步骤：A method for calibrating an inertial navigation system in an oblique configuration, specifically comprising the following steps:

一、对惯导系统陀螺仪、加速度计进行配置1. Configure the gyroscope and accelerometer of the inertial navigation system

设置惯导系统三个非正交的陀螺仪分别为G1、G2、G3，三个正交的弹体轴分别为OXb、OYb、OZb；陀螺仪的三个输入轴OG1、OG2、OG3均匀分布在以+OYb为中心，与+OYb轴的夹角为α的圆锥面上，相邻的陀螺仪的两个输入轴在OXbZb平面内的投影夹角为120°，其中，OG1在OXbZb平面内的投影与+OXb重合；Set the three non-orthogonal gyroscopes of the inertial navigation system as G 1 , G 2 , and G 3 , and the three orthogonal projectile axes as OX b , OY b , and OZ b ; the three input axes of the gyroscope OG 1. OG 2 and OG 3 are evenly distributed on the conical surface with +OY b as the center and the angle between the +OY b axis and the +OY b axis is α. The two input axes of the adjacent gyroscopes are in the OX b Z b plane The included angle of projection is 120°, wherein, the projection of OG 1 in the OX b Z b plane coincides with +OX b ;

三个非正交的加速度计分别为A1、A2、A3，加速度计的三个输入轴OA1、OA2、OA3均匀分布在以+OYb为中心，与+OYb轴夹角为β的圆锥面上，相邻的加速度计的两个输入轴在OXbZb平面内的投影夹角为120°，其中，OA1在OXbZb平面内的投影与+OXb重合；The three non-orthogonal accelerometers are A 1 , A 2 , and A 3 , and the three input axes OA 1 , OA 2 , and OA 3 of the accelerometer are evenly distributed in the center of +OY b , and are clamped with +OY b axis. On the conical surface with angle β, the projection angle between the two input axes of adjacent accelerometers in the OX b Z b plane is 120°, where the projection of OA 1 in the OX b Z b plane is the same as +OX b coincide;

其中，α+β＝90°；在本具体实施例中：α为54.73°，β为35.27°。Wherein, α+β=90°; in this specific embodiment: α is 54.73°, and β is 35.27°.

二、分别对陀螺仪、加速度计输出归一化2. Normalize the output of the gyroscope and accelerometer respectively

设定陀螺仪G1、G2、G3，加速度计A1、A2、A3输出的量纲均为LSB/s；Set the output dimensions of gyroscopes G 1 , G 2 , G 3 , and accelerometers A 1 , A 2 , and A 3 to be LSB/s;

在标定之前,将陀螺仪的输出量纲转化为°/s,加速度计的输出量纲转化g；Before calibration, the output dimension of the gyroscope is converted into °/s, and the output dimension of the accelerometer is converted into g;

陀螺仪、加速度计的输出归一化公式如下：The output normalization formula of gyroscope and accelerometer is as follows:

式中：In the formula:

——陀螺仪G1、G2、G3原始输出脉冲数，单位：LSB/s； ——the number of original output pulses of gyroscopes G 1 , G 2 , and G 3 , unit: LSB/s;

——陀螺仪G1、G2、G3零位，单位：LSB/s； ——Gyroscope G 1 , G 2 , G 3 zero position, unit: LSB/s;

——陀螺仪G1、G2、G3标度因数，单位：(LSB/s)/(°/s)； —— Gyroscope G 1 , G 2 , G 3 scale factor, unit: (LSB/s)/(°/s);

Ngx1、Ng2、Ng3——陀螺仪G1、G2、G3归一化后输出，单位：°/s；N gx1 , N g2 , N g3 ——the normalized output of gyroscopes G 1 , G 2 , G 3 , unit: °/s;

——加速度计A1、A2、A3原始输出脉冲数，单位：LSB/s； ——Number of original output pulses of accelerometers A 1 , A 2 , A 3 , unit: LSB/s;

——加速度计A1、A2、A3零位，单位：LSB/s； —— zero position of accelerometers A 1 , A 2 , A 3 , unit: LSB/s;

——加速度计A1、A2、A3标度因数，单位：(LSB/s)/g； ——accelerometer A 1 , A 2 , A 3 scale factor, unit: (LSB/s)/g;

Na1、Na2、Na3——加速度计A1、A2、A3归一化后输出，单位：g；N a1 , N a2 , N a3 —— output of accelerometers A 1 , A 2 , A 3 after normalization, unit: g;

归一化处理之后，陀螺仪G1、G2、G3加速度计A1、A2、A3输出仍然是非正交的；After the normalization process, the outputs of the gyroscopes G 1 , G 2 , G 3 accelerometers A 1 , A 2 , A 3 are still non-orthogonal;

三、陀螺仪、加速度计输出正交化3. Orthogonalization of gyroscope and accelerometer output

(3.1)对陀螺仪输出正交化(3.1) Orthogonalization of gyroscope output

确定O-XbYbZb与O-G1G2G3之间的转换矩阵：Determine the transformation matrix between OX b Y b Z b and OG 1 G 2 G 3 :

式中：In the formula:

O-Ng1Ng2Ng3——步骤二中得到的陀螺仪G1、G2、G3归一化后输出；ON g1 N g2 N g3 ——the output of the gyroscopes G 1 , G 2 , and G 3 obtained in step 2 after normalization;

O-NgxNgyNgz——与弹体系O-XbYbZb重合的、虚拟陀螺坐标系；ON gx N gy N gz ——virtual gyroscope coordinate system coincident with missile system OX b Y b Z b ;

经过如上公式，非正交的陀螺坐标系O-G1G2G3通过转换矩阵Tg转化到成正交的虚拟陀螺坐标系O-NgxNgyNgz；After the above formula, the non-orthogonal gyro coordinate system OG 1 G 2 G 3 is transformed into an orthogonal virtual gyro coordinate system ON gx N gy N gz through the transformation matrix T g ;

(3.2)对加速度计输出正交化(3.2) Orthogonalize the accelerometer output

确定O-XbYbZb与O-A1A2A3之间的转换矩阵：Determine the transformation matrix between OX b Y b Z b and OA 1 A 2 A 3 :

式中：In the formula:

O-Na1Na2Na3——步骤二中得到的加速度计A1、A2、A3归一化后输出；ON a1 N a2 N a3 ——The accelerometers A 1 , A 2 , and A 3 obtained in step 2 are output after normalization;

O-NaxNayNaz——与弹体系O-XbYbZb重合的、虚拟的加速度计坐标系；ON ax N ay N az ——virtual accelerometer coordinate system coincident with missile system OX b Y b Z b ;

经过如上公式，非正交的加速度计坐标系O-A1A2A3通过转换矩阵Ta转化到成正交的虚拟加速度计坐标系O-NaxNayNaz；After the above formula, the non-orthogonal accelerometer coordinate system OA 1 A 2 A 3 is transformed into an orthogonal virtual accelerometer coordinate system ON ax N ay N az through the transformation matrix Ta;

四、确定惯导系统数学模型4. Determine the mathematical model of the inertial navigation system

归一正交化后，惯导系统数学模型如下：After normalization and orthogonalization, the mathematical model of the inertial navigation system is as follows:

式中：In the formula:

Ngx,Ngy,Ngz——陀螺通道在虚拟陀螺坐标系中各坐标轴上的输出；N gx , N gy , N gz ——the output of the gyro channel on each coordinate axis in the virtual gyro coordinate system;

Dfx,Dfy,Dfz——陀螺通道在虚拟陀螺坐标系中各坐标轴上的常值漂移；D fx , D fy , D fz ——the constant value drift of the gyro channel on each coordinate axis in the virtual gyro coordinate system;

Sgx,Sgy,Sgz——陀螺通道在虚拟陀螺坐标系中各坐标轴上的标度因数；S gx , S gy , S gz ——the scale factor of the gyro channel on each coordinate axis in the virtual gyro coordinate system;

Kgij——i轴方向对j陀螺仪的安装误差系数；K gij ——the installation error coefficient of the i-axis direction to the j gyroscope;

Dix——X轴向线运动对X轴上陀螺输出的影响；D ix ——the influence of the X-axis linear motion on the gyro output on the X-axis;

Diy——X轴向线运动对Y轴上陀螺输出的影响；D iy ——the influence of the X-axis linear motion on the gyro output on the Y-axis;

Diz——X轴向线运动对Z轴上陀螺输出的影响；D iz ——the influence of X-axis linear motion on Z-axis gyro output;

Dox——Y轴向线运动对X轴上陀螺输出的影响；D ox ——the influence of the Y-axis linear motion on the gyro output on the X-axis;

Doy——Y轴向线运动对Y轴上陀螺输出的影响；D oy ——the influence of the Y-axis linear motion on the gyro output on the Y-axis;

Doz——Y轴向线运动对Z轴上陀螺输出的影响；D oz ——the influence of Y-axis linear motion on Z-axis gyro output;

Dsx——Z轴向线运动对X轴上陀螺输出的影响；D sx ——the influence of the Z-axis linear motion on the gyro output on the X-axis;

Dsy——Z轴向线运动对Y轴上陀螺输出的影响；D sy ——the influence of Z-axis linear motion on Y-axis gyro output;

Dsz——Z轴向线运动对Z轴上陀螺输出的影响；D sz ——the influence of Z-axis linear motion on Z-axis gyro output;

式中：In the formula:

Nax,Nay,Naz——加速度计通道在虚拟的加速度计坐标系各坐标轴上的脉冲输出；N ax ,N ay ,N az ——the pulse output of the accelerometer channel on each coordinate axis of the virtual accelerometer coordinate system;

Kax0,Kay0,Kaz0——加速度计通道在虚拟的加速度计坐标系各坐标轴上的偏值；K ax0 ,K ay0 ,K az0 ——the offset value of the accelerometer channel on each coordinate axis of the virtual accelerometer coordinate system;

Kaij——i轴对j加速度计通道的安装误差系数；K aij ——the installation error coefficient of the i-axis to the j accelerometer channel;

Ka1x,Ka1y,Ka1z——加速度计通道在虚拟的加速度计坐标系各坐标轴上的标度因数。K a1x ,K a1y ,K a1z ——scale factors of the accelerometer channel on each coordinate axis of the virtual accelerometer coordinate system.

进一步的，如上所述的一种斜置构型惯导系统标定方法，其中：α为54.73°，β为35.27°。Further, a calibration method for an oblique configuration inertial navigation system as described above, wherein: α is 54.73°, and β is 35.27°.

本发明技术方案的有益效果在于，通过采用归一正交化的方法，把斜置的陀螺、加速度计敏感轴通过方向余弦矩阵转换到弹体轴上，使得虚拟的陀螺坐标系、加速度计坐标系与真实的弹体系重合，从而法解决了敏感轴斜置的惯导系统的参数辨识问题。The beneficial effect of the technical solution of the present invention is that, by adopting the normalized orthogonalization method, the inclined gyroscope and the accelerometer sensitive axis are converted to the projectile body axis through the direction cosine matrix, so that the virtual gyroscope coordinate system and the accelerometer coordinate system The system coincides with the real missile system, thus solving the parameter identification problem of the inertial navigation system with the sensitive axis tilted.

具体实施方式Detailed ways

下面结合具体实施例对本发明技术方案进行详细说明。The technical solutions of the present invention will be described in detail below in conjunction with specific embodiments.

一种斜置构型惯导系统标定方法，具体包括以下步骤：A method for calibrating an inertial navigation system in an oblique configuration, specifically comprising the following steps:

一、对惯导系统陀螺仪、加速度计进行配置1. Configure the gyroscope and accelerometer of the inertial navigation system

设置惯导系统三个非正交的陀螺仪分别为G1、G2、G3，三个正交的弹体轴分别为OXb、OYb、OZb；陀螺仪的三个输入轴OG1、OG2、OG3均匀分布在以+OYb为中心，与+OYb轴的夹角为α的圆锥面上，相邻的陀螺仪的两个输入轴在OXbZb平面内的投影夹角为120°，其中，OG1在OXbZb平面内的投影与+OXb重合；Set the three non-orthogonal gyroscopes of the inertial navigation system as G 1 , G 2 , and G 3 , and the three orthogonal projectile axes as OX b , OY b , and OZ b ; the three input axes of the gyroscope OG 1. OG 2 and OG 3 are evenly distributed on the conical surface with +OY b as the center and the angle between the +OY b axis and the +OY b axis is α. The two input axes of the adjacent gyroscopes are in the OX b Z b plane The included angle of projection is 120°, wherein, the projection of OG 1 in the OX b Z b plane coincides with +OX b ;

三个非正交的加速度计分别为A1、A2、A3，加速度计的三个输入轴OA1、OA2、OA3均匀分布在以+OYb为中心，与+OYb轴夹角为β的圆锥面上，相邻的加速度计的两个输入轴在OXbZb平面内的投影夹角为120°，其中，OA1在OXbZb平面内的投影与+OXb重合；The three non-orthogonal accelerometers are A 1 , A 2 , and A 3 , and the three input axes OA 1 , OA 2 , and OA 3 of the accelerometer are evenly distributed in the center of +OY b , and are clamped with +OY b axis. On the conical surface with angle β, the projection angle between the two input axes of adjacent accelerometers in the OX b Z b plane is 120°, where the projection of OA 1 in the OX b Z b plane is the same as +OX b coincide;

其中，α+β＝90°；Among them, α+β=90°;

二、分别对陀螺仪、加速度计输出归一化2. Normalize the output of the gyroscope and accelerometer respectively

设定陀螺仪G1、G2、G3，加速度计A1、A2、A3输出的量纲均为LSB/s；Set the output dimensions of gyroscopes G 1 , G 2 , G 3 , and accelerometers A 1 , A 2 , and A 3 to be LSB/s;

在标定之前,将陀螺仪的输出量纲转化为°/s,加速度计的输出量纲转化g；Before calibration, the output dimension of the gyroscope is converted into °/s, and the output dimension of the accelerometer is converted into g;

陀螺仪、加速度计的输出归一化公式如下：The output normalization formula of gyroscope and accelerometer is as follows:

式中：In the formula:

——陀螺仪G1、G2、G3原始输出脉冲数，单位：LSB/s； ——the number of original output pulses of gyroscopes G 1 , G 2 , and G 3 , unit: LSB/s;

——陀螺仪G1、G2、G3零位，单位：LSB/s； ——Gyroscope G 1 , G 2 , G 3 zero position, unit: LSB/s;

——陀螺仪G1、G2、G3标度因数，单位：(LSB/s)/(°/s)； —— Gyroscope G 1 , G 2 , G 3 scale factor, unit: (LSB/s)/(°/s);

Ngx1、Ng2、Ng3——陀螺仪G1、G2、G3归一化后输出，单位：°/s；N gx1 , N g2 , N g3 ——the normalized output of gyroscopes G 1 , G 2 , G 3 , unit: °/s;

——加速度计A1、A2、A3原始输出脉冲数，单位：LSB/s； ——Number of original output pulses of accelerometers A 1 , A 2 , A 3 , unit: LSB/s;

——加速度计A1、A2、A3零位，单位：LSB/s； —— zero position of accelerometers A 1 , A 2 , A 3 , unit: LSB/s;

——加速度计A1、A2、A3标度因数，单位：(LSB/s)/g； ——accelerometer A 1 , A 2 , A 3 scale factor, unit: (LSB/s)/g;

Na1、Na2、Na3——加速度计A1、A2、A3归一化后输出，单位：g；N a1 , N a2 , N a3 —— output of accelerometers A 1 , A 2 , A 3 after normalization, unit: g;

归一化处理之后，陀螺仪G1、G2、G3加速度计A1、A2、A3输出仍然是非正交的；After the normalization process, the outputs of the gyroscopes G 1 , G 2 , G 3 accelerometers A 1 , A 2 , A 3 are still non-orthogonal;

三、陀螺仪、加速度计输出正交化3. Orthogonalization of gyroscope and accelerometer output

(3.1)对陀螺仪输出正交化(3.1) Orthogonalization of gyroscope output

确定O-XbYbZb与O-G1G2G3之间的转换矩阵：Determine the transformation matrix between OX b Y b Z b and OG 1 G 2 G 3 :

式中：In the formula:

O-Ng1Ng2Ng3——步骤二中得到的陀螺仪G1、G2、G3归一化后输出；ON g1 N g2 N g3 ——the output of the gyroscopes G 1 , G 2 , and G 3 obtained in step 2 after normalization;

O-NgxNgyNgz——与弹体系O-XbYbZb重合的、虚拟陀螺坐标系；ON gx N gy N gz ——virtual gyroscope coordinate system coincident with missile system OX b Y b Z b ;

经过如上公式，非正交的陀螺坐标系O-G1G2G3通过转换矩阵Tg转化到成正交的虚拟陀螺坐标系O-NgxNgyNgz；After the above formula, the non-orthogonal gyro coordinate system OG 1 G 2 G 3 is transformed into an orthogonal virtual gyro coordinate system ON gx N gy N gz through the transformation matrix T g ;

(3.2)对加速度计输出正交化(3.2) Orthogonalize the accelerometer output

确定O-XbYbZb与O-A1A2A3之间的转换矩阵：Determine the transformation matrix between OX b Y b Z b and OA 1 A 2 A 3 :

式中：In the formula:

O-Na1Na2Na3——步骤二中得到的加速度计A1、A2、A3归一化后输出；ON a1 N a2 N a3 ——The accelerometers A 1 , A 2 , and A 3 obtained in step 2 are output after normalization;

O-NaxNayNaz——与弹体系O-XbYbZb重合的、虚拟的加速度计坐标系；ON ax N ay N az ——virtual accelerometer coordinate system coincident with missile system OX b Y b Z b ;

经过如上公式，非正交的加速度计坐标系O-A1A2A3通过转换矩阵Ta转化到成正交的虚拟加速度计坐标系O-NaxNayNaz；After the above formula, the non-orthogonal accelerometer coordinate system OA 1 A 2 A 3 is transformed into an orthogonal virtual accelerometer coordinate system ON ax N ay N az through the transformation matrix Ta;

四、确定惯导系统数学模型4. Determine the mathematical model of the inertial navigation system

归一正交化后，惯导系统数学模型如下：After normalization and orthogonalization, the mathematical model of the inertial navigation system is as follows:

式中：In the formula:

Ngx,Ngy,Ngz——陀螺通道在虚拟陀螺坐标系中各坐标轴上的输出；N gx , N gy , N gz ——the output of the gyro channel on each coordinate axis in the virtual gyro coordinate system;

Dfx,Dfy,Dfz——陀螺通道在虚拟陀螺坐标系中各坐标轴上的常值漂移；D fx , D fy , D fz ——the constant value drift of the gyro channel on each coordinate axis in the virtual gyro coordinate system;

Sgx,Sgy,Sgz——陀螺通道在虚拟陀螺坐标系中各坐标轴上的标度因数；S gx , S gy , S gz ——the scale factor of the gyro channel on each coordinate axis in the virtual gyro coordinate system;

Kgij——i轴方向对j陀螺仪的安装误差系数；K gij ——the installation error coefficient of the i-axis direction to the j gyroscope;

Dix——X轴向线运动对X轴上陀螺输出的影响；D ix ——the influence of the X-axis linear motion on the gyro output on the X-axis;

Diy——X轴向线运动对Y轴上陀螺输出的影响；D iy ——the influence of the X-axis linear motion on the gyro output on the Y-axis;

Diz——X轴向线运动对Z轴上陀螺输出的影响；D iz ——the influence of X-axis linear motion on Z-axis gyro output;

Dox——Y轴向线运动对X轴上陀螺输出的影响；D ox ——the influence of the Y-axis linear motion on the gyro output on the X-axis;

Doy——Y轴向线运动对Y轴上陀螺输出的影响；D oy ——the influence of the Y-axis linear motion on the gyro output on the Y-axis;

Doz——Y轴向线运动对Z轴上陀螺输出的影响；D oz ——the influence of Y-axis linear motion on Z-axis gyro output;

Dsx——Z轴向线运动对X轴上陀螺输出的影响；D sx ——the influence of the Z-axis linear motion on the gyro output on the X-axis;

Dsy——Z轴向线运动对Y轴上陀螺输出的影响；D sy ——the influence of Z-axis linear motion on Y-axis gyro output;

Dsz——Z轴向线运动对Z轴上陀螺输出的影响；D sz ——the influence of Z-axis linear motion on Z-axis gyro output;

式中：In the formula:

Nax,Nay,Naz——加速度计通道在虚拟的加速度计坐标系各坐标轴上的脉冲输出；N ax ,N ay ,N az ——the pulse output of the accelerometer channel on each coordinate axis of the virtual accelerometer coordinate system;

Kax0,Kay0,Kaz0——加速度计通道在虚拟的加速度计坐标系各坐标轴上的偏值；K ax0 ,K ay0 ,K az0 ——the offset value of the accelerometer channel on each coordinate axis of the virtual accelerometer coordinate system;

Kaij——i轴对j加速度计通道的安装误差系数；K aij ——the installation error coefficient of the i-axis to the j accelerometer channel;

Ka1x,Ka1y,Ka1z——加速度计通道在虚拟的加速度计坐标系各坐标轴上的标度因数。K a1x ,K a1y ,K a1z ——scale factors of the accelerometer channel on each coordinate axis of the virtual accelerometer coordinate system.

Claims (2)

1. a kind of tilting configuration inertial navigation system scaling method, which is characterized in that specifically include following steps：
(1) inertial navigation system gyroscope, accelerometer are configured
It is respectively G to set three non-orthogonal gyroscopes of inertial navigation system1、G2、G3, three orthogonal body axis are respectively OXb、OYb、 OZb；Three input shaft OG of gyroscope1、OG2、OG3It is evenly distributed on+OYbCentered on, with+OYbThe circular cone that the angle of axis is α On face, two input shafts of adjacent gyroscope are in OXbZbProjection angle in plane is 120 °, wherein, OG1In OXbZbPlane Interior projection and+OXbIt overlaps；
Three non-orthogonal accelerometers are respectively A1、A2、A3, three input shaft OA of accelerometer1、OA2、OA3It is uniformly distributed With+OYbCentered on, with+OYbAxle clamp angle is on the circular conical surface of β, and two input shafts of adjacent accelerometer are in OXbZbPlane Interior projection angle is 120 °, wherein, OA1In OXbZbProjection and+OX in planebIt overlaps；
Wherein, alpha+beta=90 °；
(2) respectively to gyroscope, accelerometer output normalization
Set gyroscope G1、G2、G3, accelerometer A1、A2、A3The dimension of output is LSB/s；
Before calibration, the output dimension of gyroscope is converted into °/s, the output dimension of accelerometer is converted into g；
Gyroscope, the output normalization formula of accelerometer are as follows：
In formula：
--- gyroscope G1、G2、G3Original output umber of pulse, unit：LSB/s；
--- gyroscope G1、G2、G3Zero-bit, unit：LSB/s；
--- gyroscope G1、G2、G3Constant multiplier, unit：(LSB/s)/(°/s)；
Ngx1、Ng2、Ng3--- gyroscope G1、G2、G3It is exported after normalization, unit：°/s；
--- accelerometer A1、A2、A3Original output umber of pulse, unit：LSB/s；
--- accelerometer A1、A2、A3Zero-bit, unit：LSB/s；
--- accelerometer A1、A2、A3Constant multiplier, unit：(LSB/s)/g；
Na1、Na2、Na3--- accelerometer A1、A2、A3It is exported after normalization, unit：g；
After normalized, gyroscope G1、G2、G3Accelerometer A1、A2、A3Output is still non-orthogonal；
(3) gyroscope, accelerometer output orthogonalization
(3.1) orthogonalization is exported to gyroscope
Determine O-XbYbZbWith O-G1G2G3Between transition matrix：
In formula：
Ng1Ng2Ng3--- the gyroscope G obtained in step (2)1、G2、G3It is exported after normalization；
O-NgxNgyNgz--- with body system O-XbYbZbGyro coordinate system overlap, virtual；
By as above formula, non-orthogonal gyro coordinate system O-G1G2G3Pass through transition matrix TgIt is transformed into the virtual gyro being orthogonal Coordinate system O-NgxNgyNgz；
(3.2) orthogonalization is exported to accelerometer
Determine O-XbYbZbWith O-A1A2A3Between transition matrix：
In formula：
Na1Na2Na3--- the accelerometer A obtained in step (2)1、A2、A3It is exported after normalization；
O-NaxNayNaz--- with body system O-XbYbZbAccelerometer coordinate system overlap, virtual；
By as above formula, non-orthogonal accelerometer coordinate system O-A1A2A3Pass through transition matrix TaBe transformed into be orthogonal it is virtual Accelerometer coordinate system O-NaxNayNaz；
(4) inertial navigation system mathematical model is determined
After orthonormalization, inertial navigation system mathematical model is as follows：
In formula：
Ngx,Ngy,Ngz--- output of the gyro channel in virtual gyro coordinate system in each reference axis；
Dfx,Dfy,Dfz--- constant value drift of the gyro channel in virtual gyro coordinate system in each reference axis；
Sgx,Sgy,Sgz--- constant multiplier of the gyro channel in virtual gyro coordinate system in each reference axis；
Kgij--- i axis directions are to the installation error coefficient of j gyroscopes；
Dix--- the influence that the movement of X axis line exports gyro in X-axis；
Diy--- the influence that the movement of X axis line exports gyro in Y-axis；
Diz--- the influence that the movement of X axis line exports gyro on Z axis；
Dox--- the influence that the movement of Y-axis line exports gyro in X-axis；
Doy--- the influence that the movement of Y-axis line exports gyro in Y-axis；
Doz--- the influence that the movement of Y-axis line exports gyro on Z axis；
Dsx--- Z axis moves the influence exported to gyro in X-axis to line；
Dsy--- Z axis moves the influence exported to gyro in Y-axis to line；
Dsz--- Z axis moves the influence exported to gyro on Z axis to line；
In formula：
Nax,Nay,Naz--- pulse output of the accelerometer channel in virtual each reference axis of accelerometer coordinate system；
Kaox,Kaoy,Kaoz--- bias of the accelerometer channel in virtual each reference axis of accelerometer coordinate system；
Kaij--- i axis is to the installation error coefficient of j accelerometer channels；
Ka1x,Ka1y,Ka1z--- constant multiplier of the accelerometer channel in virtual each reference axis of accelerometer coordinate system.
2. a kind of tilting configuration inertial navigation system scaling method as described in claim 1, which is characterized in that in step (1)：α is 54.73 °, β is 35.27 °.
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