CN102768043B

CN102768043B - Integrated attitude determination method without external observed quantity for modulated strapdown system

Info

Publication number: CN102768043B
Application number: CN201210194586.0A
Authority: CN
Inventors: 孙伟; 徐爱功; 车莉娜
Original assignee: Liaoning Technical University
Current assignee: Liaoning Technical University
Priority date: 2012-06-14
Filing date: 2012-06-14
Publication date: 2015-03-04
Anticipated expiration: 2032-06-14
Also published as: CN102768043A

Abstract

The invention provides a method for determining the combined posture of a modulation type strapdown system without appearance measurement. Use the Global Positioning System (GPS) to determine the initial position parameters of the carrier and bind them to the navigation computer; collect and process the data output by the fiber optic gyroscope and quartz accelerometer; set the inertial measurement unit (IMU) single-axis four-position rotation stop scheme; Convert the output of the accelerometer to the semi-fixed coordinate system of the carrier; design an infinite impact response (IIR) digital high-pass filter to filter the carrier velocity calculated under the navigation system; combine the filtered velocity with the velocity calculated by the modulated strapdown system The difference is taken as the system observation, and the attitude information of the modulated SINS is estimated by using the Kalman filter technique. The invention does not require external auxiliary equipment to provide observation information, can effectively solve the problem of mismatch between the information frequency provided by the auxiliary equipment and the frequency calculated by the modulation type strapdown system, and realize the combined attitude determination of the modulation type strapdown inertial navigation system.

Description

A Combination Attitude Determination Method for Modulated Strapdown System Without Appearance Measurement

(一)技术领域 (1) Technical field

本发明涉及的是一种测量方法，尤其涉及的是一种无外观测量的调制型捷联系统组合姿态确定方法。The invention relates to a measurement method, in particular to a method for determining the combined posture of a modulated strapdown system without appearance measurement.

(二)背景技术 (2) Background technology

在捷联惯性导航系统中，所有的惯性测量元件直接安装在载体上，惯性元件输出的就是载体相对于惯性空间的角速度和加速度，由计算机将载体坐标系下测得的加速度数据转换到导航坐标系再进行导航解算，相当于利用陀螺仪输出数据在计算机内构建一个数学平台作为导航计算的参考。由于捷联系统没有平台框架及相连的伺服机构，因而简化了硬件，与平台惯导相比具有体积小、重量轻、成本低、可靠性比较高等优点。正是由于以上优点，它在航空、航天、航海和很多民用领域得到了广泛应用。In the strapdown inertial navigation system, all inertial measurement elements are directly installed on the carrier, and the output of the inertial elements is the angular velocity and acceleration of the carrier relative to the inertial space, and the computer converts the acceleration data measured in the carrier coordinate system to navigation coordinates The system then performs navigation calculations, which is equivalent to using the output data of the gyroscope to build a mathematical platform in the computer as a reference for navigation calculations. Since the strapdown system does not have a platform frame and a connected servo mechanism, the hardware is simplified. Compared with the platform inertial navigation system, it has the advantages of small size, light weight, low cost, and relatively high reliability. It is because of the above advantages that it has been widely used in aviation, aerospace, navigation and many civil fields.

旋转调制技术是惯性导航系统的一种自校正方法。调制型捷联惯性导航系统在捷联惯导系统的外面加上转动机构和测角装置，导航解算仍采用捷联惯导算法。它不需要引入外部校正信息，能够自动对系统中惯性器件的常值偏差进行平均，达到抵消漂移对系统精度的影响。因而可以提高惯性导航系统长时间工作的精度，充分发挥惯性导航“自主式”的优点。应用旋转调制技术，还可以应用较低精度的惯性器件，构成较高精度的惯性导航系统，有利于降低惯性导航系统的成本，同时由于引入外界运动可以有效地提高惯导系统部分参数的可观测度。The rotational modulation technique is a self-calibration method of the inertial navigation system. The modulation type strapdown inertial navigation system adds a rotating mechanism and an angle measuring device to the outside of the strapdown inertial navigation system, and the navigation solution still uses the strapdown inertial navigation algorithm. It does not need to introduce external correction information, and can automatically average the constant value deviation of the inertial device in the system to offset the influence of drift on the system accuracy. Therefore, the long-time working precision of the inertial navigation system can be improved, and the "autonomous" advantage of the inertial navigation system can be fully utilized. The application of rotational modulation technology can also use lower-precision inertial devices to form a higher-precision inertial navigation system, which is conducive to reducing the cost of the inertial navigation system. At the same time, the introduction of external motion can effectively improve the observability of some parameters of the inertial navigation system. Spend.

初始姿态误差是惯性导航系统主要的误差源之一，初始姿态的误差对系统误差的影响不仅表现在姿态指标上，而且表现在速度和位置信息的获取上。初始姿态确定的精度直接影响着导航的精度。按基座的运动状态来分，惯导系统的初始姿态确定方法可以分为两类，即静基座初始姿态确定和动基座初始姿态确定。所谓静基座初始姿态确定是指惯性测量组合在载体完全静止的情况下确定载体的初始姿态信息。目前，该技术已经比较成熟，通过多位置法和卡尔曼滤波已经能够达到相当高的精度。但是，静基座初始姿态确定技术对于众多的机载和舰载武器系统来说已经不能适应它们快速反应的要求，所以当前研究的重点主要集中在动基座初始姿态确定方法。所谓动基座初始姿态确定是指惯性测量组合在载体运动或者外界扰动的情况下完成。其难点在于构造快速、稳定、鲁棒性强的滤波器，并且对滤波器状态的可观测性和可观测度进行评价，从而设计最优滤波器。根据使用外部信息的情况，可以将动基座初始姿态确定方法分为三类：外部阻尼式、传递式和外部辅助姿态信息式。The initial attitude error is one of the main error sources of the inertial navigation system. The influence of the initial attitude error on the system error is not only reflected in the attitude index, but also in the acquisition of speed and position information. The accuracy of initial attitude determination directly affects the accuracy of navigation. According to the motion state of the base, the initial attitude determination methods of the inertial navigation system can be divided into two categories, that is, the initial attitude determination of the static base and the initial attitude determination of the dynamic base. The so-called determination of the initial attitude of the static base means that the inertial measurement unit determines the initial attitude information of the carrier when the carrier is completely still. At present, the technology has been relatively mature, and the multi-position method and Kalman filtering have been able to achieve quite high precision. However, the initial attitude determination technology of the static base can no longer meet the requirements of rapid response for many airborne and shipborne weapon systems, so the current research focus is mainly on the determination method of the initial attitude of the moving base. The so-called determination of the initial attitude of the moving base refers to the completion of the inertial measurement combination under the condition of carrier motion or external disturbance. The difficulty lies in constructing a fast, stable and robust filter, and evaluating the observability and observability of the filter state, so as to design the optimal filter. According to the use of external information, the initial attitude determination methods of the moving base can be divided into three categories: external damping method, transfer method and external auxiliary attitude information method.

滤波器的功能就是允许某一部分频率的信号顺利的通过，而另外一部分频率的信号则受到较大的抑制，它实质上是一个选频电路。无限冲击响应(IIR)滤波器属于经典滤波器，即假定输入信号中的有用成分和希望除去的成分各自占有不同的频带。这种假定在一定程度上符合了客观规律，对于高通滤波器来说，采样序列的高频部分包含有用信号，而低频部分则主要是由舒勒周期振荡控制。因此通过设计合理的高通滤波器，就可以达到去除舒勒周期振荡的目的。The function of the filter is to allow the signal of a certain part of the frequency to pass smoothly, while the signal of the other part of the frequency is greatly suppressed. It is essentially a frequency selection circuit. The infinite impulse response (IIR) filter belongs to the classical filter, that is, it is assumed that the useful components in the input signal and the components to be removed occupy different frequency bands. This assumption conforms to the objective law to a certain extent. For the high-pass filter, the high-frequency part of the sampling sequence contains useful signals, while the low-frequency part is mainly controlled by the Schuler periodic oscillation. Therefore, by designing a reasonable high-pass filter, the purpose of removing the Schuler periodic oscillation can be achieved.

(三)发明内容 (3) Contents of the invention

本发明的技术解决问题是：克服现有技术的不足，提供一种无外观测量的调制型捷联系统组合姿态确定方法。The technical problem of the present invention is to overcome the deficiencies of the prior art, and provide a method for determining the combined posture of a modulated strapdown system without appearance measurement.

本发明的技术解决方案为：一种无外观测量的调制型捷联系统组合姿态确定方法，其特征在于采用惯性测量单元单轴四位置转停，提出载体瞬时速度的提取方法，根据瞬时速度的误差特性，采用无限冲击响应(IIR)数字高通滤波器滤除载体速度中的舒勒周期，将滤波后的速度信息和惯导解算出的速度信息作差后作为系统的观测量，采用卡尔曼滤波技术实现捷联惯导系统的组合姿态，其具体步骤如下：The technical solution of the present invention is: a method for determining the combined posture of a modulated strapdown system without appearance measurement, which is characterized in that an inertial measurement unit is used to rotate and stop at four positions on a single axis, and a method for extracting the instantaneous velocity of the carrier is proposed. Error characteristics, using an infinite impulse response (IIR) digital high-pass filter to filter out the Schuler period in the carrier velocity, and taking the difference between the filtered velocity information and the velocity information calculated by the inertial navigation solution as the observation of the system, using the Kalman The filtering technology realizes the combined attitude of the strapdown inertial navigation system, and the specific steps are as follows:

(1)通过GPS确定载体的初始位置参数，将它们装订至导航计算机中；(1) Determine the initial position parameters of the carrier by GPS, and bind them into the navigation computer;

(2)调制型捷联惯导系统进行预热准备，采集光纤陀螺仪和石英加速度计输出的数据并对数据进行处理；(2) The modulated strapdown inertial navigation system is preheated, and the data output by the fiber optic gyroscope and the quartz accelerometer are collected and processed;

(3)IMU采用4个转停次序为一个旋转周期的转位方案(如附图2)；(3) The IMU adopts an indexing scheme in which four rotation-stop sequences are one rotation cycle (as shown in Figure 2);

次序1，IMU由位置A出发，顺时针旋转180°到位置B，并在位置B停留时间T_s；次序2，IMU由位置B出发，顺时针旋转90°到达位置C，并在位置C停留时间T_s；次序3，IMU由位置C出发，逆时针旋转180°到位置D，在位置D停留时间T_s；次序4，IMU由位置D出发逆时针旋转90°回到位置A，并在位置A停留时间T_s；然后按照次序1～4的顺序循环运动。Sequence 1, IMU starts from position A, rotates 180° clockwise to position B, and stays at position B for a time T _s ; Sequence 2, IMU starts from position B, rotates 90° clockwise to reach position C, and stays at position C Time T _s ; Sequence 3, the IMU starts from position C, rotates 180° counterclockwise to position D, and stays at position D for a time T _s ; Sequence 4, IMU starts from position D and rotates 90° counterclockwise to return to position A, and Position A stay time T _s ;

IMU每次转动180°或90°间隔进行。从一个位置转动180°到对称位置，在这两个相互对称的位置上，水平方向上惯性敏感元件的常值漂移在进行导航计算的时候能够相互抵消掉。通过旋转90°到达另外一个新位置。The IMU rotates at intervals of 180° or 90° each time. Rotate 180° from one position to a symmetrical position. In these two mutually symmetrical positions, the constant drift of the inertial sensor in the horizontal direction can cancel each other out when performing navigation calculations. Go to another new position by rotating 90°.

(4)将加速度计的输出转换到载体半固定坐标系，利用调制型捷联惯导系统中的积分环节提取载体瞬时线速度信息；(4) Convert the output of the accelerometer to the semi-fixed coordinate system of the carrier, and use the integral link in the modulated strapdown inertial navigation system to extract the instantaneous linear velocity information of the carrier;

1)引入载体半固定坐标系1) Introduce the semi-fixed coordinate system of the carrier

以舰船重心为载体半固定坐标系原点，纵轴OY_d指向舰船的主行向方向，横轴OX_d垂直于纵轴平行于水平面，在舰船无纵摇运动时指向右舷方向。垂直轴OZ_d与前两轴垂直，沿船只竖轴向上为正(如附图3)。其中ψ_G为主航向角，γ角为航向摇摆角(即艏摇角定义其与主航向角同向为正)。载体半固定坐标系的引入使得测量结果和角运动基本脱离，可以准确地描述舰船的瞬时线运动，因此采用载体半固定坐标系作为研究舰船瞬时线运动或称为平动的基础坐标系。Taking the center of gravity of the ship as the origin of the semi-fixed coordinate system of the carrier, the vertical axis OY _d points to the main row direction of the ship, and the horizontal axis OX _d is perpendicular to the longitudinal axis and parallel to the horizontal plane, pointing to the starboard direction when the ship has no pitch motion. The vertical axis OZ _d is perpendicular to the first two axes, and is positive along the vertical axis of the ship (as shown in Figure 3). Among them, ψ _G is the main heading angle, and γ angle is the heading swing angle (that is, the yaw angle defines that it is positive in the same direction as the main heading angle). The introduction of the semi-fixed coordinate system of the carrier makes the measurement results and the angular motion basically separated, and can accurately describe the instantaneous line motion of the ship. Therefore, the semi-fixed coordinate system of the carrier is used as the basic coordinate system for studying the instantaneous line motion of the ship or called translation. .

2)建立惯性测量单元坐标系与载体半固定坐标系的转换矩阵2) Establish the conversion matrix between the inertial measurement unit coordinate system and the carrier semi-fixed coordinate system

首先建立载体坐标系与载体半固定坐标系之间相差三个旋转角，可视为半固定坐标系经三次旋转后与载体坐标系重合，三个角度分别为：纵摇角α、横摇角β及艏摇角γ(如附图4)。载体坐标系(b系)转换到载体半固定坐标系(d系)的方向余弦矩阵 Firstly, the difference between the carrier coordinate system and the carrier semi-fixed coordinate system is established by three rotation angles, which can be regarded as the semi-fixed coordinate system coincides with the carrier coordinate system after three rotations. The three angles are: pitch angle α, roll angle β and yaw angle γ (as shown in Figure 4). The direction cosine matrix of the carrier coordinate system (b system) converted to the carrier semi-fixed coordinate system (d system)

${C C}_{b b}^{d d} = = [\begin{matrix} cos cos γ γ cos cos β β & sin sin γ γ cos cos α α + + cos cos γ γ sin sin β β sin sin α α & sin sin γ γ sin sin α α - - cos cos γ γ sin sin β β cos cos α α \\ - - sin sin γ γ cos cos β β & cos cos γ γ cos cos α α + + sin sin γ γ sin sin β β sin sin α α & cos cos γ γ sin sin α α - - sin sin γ γ sin sin β β cos cos α α \\ sin sin β β & - - cos cos β β sin sin α α & cos cos β β cos cos α α \end{matrix}]$

现有的惯性导航系统已经可以提供较为精确的姿态角信息，其中水平两个姿态角信息即为纵摇角信息和横摇角信息，而航向信息提供的是航向角信息ψ，这有别于艏摇角γ，但舰船的操纵者可以提供准确的主航向信息ψ_G，可得The existing inertial navigation system can already provide more accurate attitude angle information. The two horizontal attitude angle information are pitch angle information and roll angle information, while the heading information provides heading angle information ψ, which is different from Yaw angle γ, but the operator of the ship can provide accurate main heading information ψ _G , we can get

γ＝ψ-ψ_G γ=ψ- _ψG

将γ代入的计算方程中，即可得到载体坐标系转换到载体半固定坐标系的方向余弦矩阵。Substitute γ into In the calculation equation, the direction cosine matrix for transforming the carrier coordinate system to the carrier semi-fixed coordinate system can be obtained.

由于惯性测量单元相对载体存在绕方位轴的转位运动，因此惯性测量坐标系(s坐标系)与载体坐标系之间的转换矩阵可以利用下式进行计算：Since the inertial measurement unit has an indexing motion around the azimuth axis relative to the carrier, the transformation matrix between the inertial measurement coordinate system (s coordinate system) and the carrier coordinate system can be calculated using the following formula:

${C C}_{s the s}^{b b} = = [\begin{matrix} cos cos ωt ωt & - - sin sin ωt ωt & 00 \\ sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}]$

式中，ωt表示惯性测量单元相对载体坐标系的相对角度关系。因此可以得到惯性测量单元坐标系转换到载体半固定坐标系的方向余弦矩阵：In the formula, ωt represents the relative angular relationship of the inertial measurement unit relative to the carrier coordinate system. Therefore, the direction cosine matrix for transforming the inertial measurement unit coordinate system to the carrier semi-fixed coordinate system can be obtained:

${C C}_{s the s}^{d d} = = {C C}_{b b}^{d d} {C C}_{s the s}^{b b}$

(5)设计合理的无限冲击响应数字高通滤波器(IIR)，将导航系下解算出的载体速度进行高通滤波处理；(5) Design a reasonable infinite impulse response digital high-pass filter (IIR), and perform high-pass filtering processing on the carrier velocity calculated by the lower solution of the navigation system;

1)确定所设计数字高通滤波器的技术指标1) Determine the technical indicators of the designed digital high-pass filter

高通数字滤波器f_p1、f_s1、δ_p、δ_s的技术指标是根据信号特征和采样频率f_s给定的。其中，f_p1为通带截止频率，f_s1为阻带截止频率，δ_p为通带波纹，即滤波器通带内偏离单位增益的最大值，通带边缘增益为1-δ_p，δ_s为阻带波纹，即滤波器阻带内偏离单位增益的最大值，阻带边缘处滤波器的增益为δ_s。通带及阻带的衰减α_p、α_s分别定义为-20log(1-δ_p)、-20log(1-δ_s)。The technical indicators of high-pass digital filters f _p1 , f _s1 , δ _p , and δ _s are given according to signal characteristics and sampling frequency f _s . Among them, f _p1 is the cut-off frequency of the pass band, f _s1 is the cut-off frequency of the stop band, δ _p is the ripple of the pass band, that is, the maximum value of the deviation from unity gain in the pass band of the filter, and the edge gain of the pass band is 1-δ _p , δ _s is the stopband ripple, that is, the maximum deviation from unity gain in the stopband of the filter, and the gain of the filter at the edge of the stopband is δ _s . The attenuation α _p and α _s of the passband and stopband are respectively defined as -20log(1-δ _p ), -20log(1-δ _s ).

舒勒周期振荡信号相对来说属于低频信号，振荡周期是84.4分钟。而舰船瞬时线运动是由海洋环境因素引起的，最主要的产生原因是海浪的影响，所以舰船瞬时线运动是频率与海浪频率大体一致的往复运动。而且舰船瞬时线运动相对于舰船的航行运动，属于高频运动，运动周期比较短，一般在1.5秒～10秒左右，频率为0.67赫兹。根据升沉横荡纵荡运动和舰船常规工作运动的运动特性上的不同，设计所需要的滤波器的技术指标要求，具体设计指标在试验过程中根据滤波效果进行调整，以达到最优滤波效果为准。The Schuler periodic oscillation signal is relatively low-frequency signal, and the oscillation period is 84.4 minutes. The instantaneous linear motion of the ship is caused by marine environmental factors, the most important reason is the influence of the waves, so the instantaneous linear motion of the ship is a reciprocating motion whose frequency is roughly consistent with that of the waves. Moreover, compared with the ship's navigational motion, the instantaneous linear motion of the ship is a high-frequency motion with a relatively short motion period, generally about 1.5 seconds to 10 seconds, and the frequency is 0.67 Hz. According to the difference in the motion characteristics of the heave, sway, and surge motions and the ship’s regular working motion, the technical index requirements of the required filter are designed, and the specific design index is adjusted according to the filtering effect during the test to achieve the optimal filtering The effect shall prevail.

2)将技术指标从数字滤波器转换到模拟滤波器2) Conversion of technical indicators from digital filters to analog filters

技术指标从模拟滤波器到数字滤波器的变换采用双线性Z变换法，设计数字高通滤波器的技术指标为f_p1，f_s1，δ_p，δ_s，t_s＝0.0102。首先应得到数字边缘频率Ω，因为2π对应采样频率f_s，而f_s＝1/t_s，所以有：Technical indicators The conversion from analog filter to digital filter adopts bilinear Z-transform method, and the technical indicators for designing digital high-pass filter are f _p1 , f _s1 , δ _p , δ _s , t _s =0.0102. Firstly, the digital edge frequency Ω should be obtained, because 2π corresponds to the sampling frequency f _s , and f _s =1/t _s , so:

$\frac{{f f}_{p p 11}}{{f f}_{s the s}} = = \frac{{Ω Ω}_{p p 11}}{22 π π}$

$\frac{{f f}_{s the s 11}}{{f f}_{s the s}} = = \frac{{Ω Ω}_{s the s 11}}{22 π π}$

所以求得：So get:

Ω_s1＝2πf_s1/f_s Ω _s1 = 2πf _s1 /f _s

Ω_p1＝2πf_p1/f_s Ω _p1 ＝2πf _p1 /f _s

按照双线性Z变换法的频率转换关系ω＝2f_stan(Ω/2)继续转换有：According to the frequency conversion relationship ω=2f _s tan(Ω/2) of the bilinear Z transformation method, the continuous conversion has:

${Ω Ω}_{p p} = = tan the tan ((\frac{{ω ω}_{p p}}{22}))$

${Ω Ω}_{s the s} = = tan the tan ((\frac{{ω ω}_{s the s}}{22}))$

以此将数字高通滤波器的技术指标就转换成为模拟高通滤波器的技术指标。In this way, the technical index of the digital high-pass filter is converted into the technical index of the analog high-pass filter.

(6)根据调制型捷联惯导系统动基座误差方程建立载体系泊状态时的组合姿态误差模型，以高通滤波后得到的速度与调制型捷联惯导系统直接解算出的速度作差后作为系统观测量。利用卡尔曼滤波技术实现调制型捷联惯导系统组合姿态的确定；(6) According to the dynamic base error equation of the modulated strapdown inertial navigation system, the combined attitude error model in the mooring state of the carrier is established, and the speed obtained after high-pass filtering is compared with the speed calculated directly by the modulated strapdown inertial navigation system Then as a system observation. Using the Kalman filter technology to realize the determination of the combined attitude of the modulated strapdown inertial navigation system;

建立以经过高通滤波后的水平速度与调制型捷联惯导系统直接解算出的速度作差后作为观测量的卡尔曼滤波模型；Establish a Kalman filter model that takes the difference between the horizontal velocity after high-pass filtering and the velocity directly calculated by the modulated strapdown inertial navigation system as the observation;

用一阶线性微分方程来描述调制型捷联惯导系统的状态误差：The state error of the modulated SINS is described by a first-order linear differential equation:

$\overset{\cdot &Center Dot;}{X x} = = AX AX + + BW BW$

其中，X为系统的状态向量；A和B分别为系统的状态矩阵和噪声矩阵；W为系统噪声向量；Among them, X is the state vector of the system; A and B are the state matrix and noise matrix of the system respectively; W is the system noise vector;

系统的状态向量为：The state vector of the system is:

系统的白噪声向量为：The white noise vector of the system is:

W＝[a_x a_y ω_x ω_y ω_z 0 0 0 0 0]^T W＝[a _x a _y ω _x ω _y ω _z 0 0 0 0 0] ^T

其中δV_e、δV_n分别表示东向、北向的速度误差；分别为IMU坐标系ox_s、oy_s轴加速度计零偏；ε_x、ε_y、ε_z分别为IMU坐标系ox_s、oy_s、oz_s轴陀螺的常值漂移；a_x、a_y分别为IMU坐标系ox_s、oy_s轴加速度计的白噪声误差；ω_x、ω_y、ω_z分别为IMU坐标系ox_s、oy_s、oz_s轴陀螺的白噪声误差；Among them, δV _e and δV _n represent the speed errors in the east direction and north direction respectively; are the zero bias of the IMU coordinate system ox _s , oy _s axis accelerometer; ε _x , ε _y , ε _z are the constant drift of the IMU coordinate system ox _s , oy _s , oz _s axis gyroscope respectively; a _x , a _{y are} respectively is the white noise error of the IMU coordinate system ox _s , oy _s axis accelerometer; ω _x , ω _y , ω _z are the white noise errors of the IMU coordinate system ox _s , oy _s , oz _s axis gyroscope respectively;

系统的状态转移矩阵为：The state transition matrix of the system is:

$A A = = [\begin{matrix} {F f}_{22 \times \times 22}^{11} & {f f}_{22 \times \times 33} & {\overset{~ ~}{T T}}_{22 \times \times 22} & {O o}_{22 \times \times 33} \\ {F f}_{33 \times \times 22}^{22} & {F f}_{33 \times \times 33}^{33} & {O o}_{33 \times \times 22} & {T T}_{33 \times \times 33} \\ {O o}_{55 \times \times 22} & {O o}_{55 \times \times 33} & {O o}_{55 \times \times 22} & {O o}_{55 \times \times 33} \end{matrix}]$

${F f}_{22 \times \times 22}^{11} = = [\begin{matrix} \frac{{V V}_{N N}}{{R R}_{n no}} tan the tan {L L}^{' '} & 22 {ω ω}_{ie ie} sin sin L L + + \frac{{V V}_{E E.}}{{R R}_{n no}} tan the tan L L \\ - - ((22 {ω ω}_{ie ie} sin sin L L + + \frac{22 {V V}_{E E.}}{{R R}_{n no}} tan the tan L L)) & 00 \end{matrix}]$

${F f}_{33 \times \times 22}^{22} = = \begin{matrix} [\begin{matrix} 00 & - - \frac{11}{{R R}_{m m}} \\ \frac{11}{{R R}_{n no}} & 00 \\ \frac{tan the tan L L}{{R R}_{n no}} & 00 \end{matrix}] \end{matrix}$

${F f}_{33 \times \times 33}^{33} = = [\begin{matrix} 00 & {ω ω}_{ie ie} sin sin L L + + \frac{{V V}_{E E.} tan the tan L L}{{R R}_{n no}} & - - (({ω ω}_{ie ie} cos cos L L + + \frac{{V V}_{E E.}}{{R R}_{n no}})) \\ - - (({ω ω}_{ie ie} sin sin L L + + \frac{{V V}_{E E.} tan the tan L L}{{R R}_{n no}})) & 00 & - - \frac{{V V}_{N N}}{{R R}_{m m}} \\ {ω ω}_{ie ie} cos cos L L + + \frac{{V V}_{E E.}}{{R R}_{n no}} & \frac{{V V}_{N N}}{{R R}_{m m}} & 00 \end{matrix}]$

${f f}_{22 \times \times 33} = = [\begin{matrix} 00 & - - {f f}_{U u} & {f f}_{N N} \\ {f f}_{U u} & 00 & {f f}_{E E.} \end{matrix}]$

${\overset{~ ~}{T T}}_{22 \times \times 22} = = [\begin{matrix} {T T}_{1111} & {T T}_{1212} \\ {T T}_{21 twenty one} & {T T}_{22 twenty two} \end{matrix}]$

${T T}_{33 \times \times 66} = = [\begin{matrix} - - {T T}_{1111} & - - {T T}_{1212} & - - {T T}_{1313} \\ - - {T T}_{21 twenty one} & - - {T T}_{22 twenty two} & - - {T T}_{23 twenty three} \\ - - {T T}_{3131} & - - {T T}_{3232} & - - {T T}_{3333} \end{matrix}]$

V_E、V_N分别表示东向、北向的速度；ω_x、ω_y、ω_z分别表示陀螺的三个输入角速度；ω_ie表示地球自转角速度；R_m、R_n分别表示地球子午、卯酉曲率半径；L表示当地纬度；L′表示系泊状态初始时刻载体纬度信息；f_E、f_N、f_U分别表示为导航坐标系下东向、北向、天向的比力。V _E , V _N represent the eastward and northward velocities respectively; ω _x , ω _y , ω _z represent the three input angular velocities of the gyroscope; ω _ie represent the earth's rotation angular velocity; R _m , R _n represent the earth's meridian, Radius of curvature; L represents the local latitude; L′ represents the latitude information of the carrier at the initial moment of the mooring state; f _E , f _N , and f _U represent the relative forces in the east, north, and sky directions of the navigation coordinate system, respectively.

2)建立卡尔曼滤波的量测方程：2) Establish the measurement equation of the Kalman filter:

用一阶线性微分方程来描述调制型捷联惯导系统的量测方程如下：The measurement equation of the modulated SINS is described by the first-order linear differential equation as follows:

Z＝HX+VZ=HX+V

其中：Z表示系统的量测向量；H表示系统的量测矩阵；V表示系统的量测噪声；Among them: Z represents the measurement vector of the system; H represents the measurement matrix of the system; V represents the measurement noise of the system;

系统量测矩阵为：The system measurement matrix is:

$H h = = [\begin{matrix} 11 & 00 & 00 & 00 & 00 & 00 & 00 & 00 & 00 & 00 \\ 00 & 11 & 00 & 00 & 00 & 00 & 00 & 00 & 00 & 00 \end{matrix}]$

量测量为调制型捷联惯导系统解算的东向速度V_E、北向速度V_N分别和经过高通滤波处理得到的东向速度北向速度之差：Quantities measured are the eastward velocity V _E and northward velocity V _N calculated by the modulated strapdown inertial navigation system and the eastward velocity obtained through high-pass filtering north speed Difference:

$Z Z = = [\begin{matrix} {V V}_{E E.} - - {\overset{~ ~}{V V}}_{E E.} \\ {V V}_{N N} - - {\overset{~ ~}{V V}}_{N N} \end{matrix}]$

本发明与现有技术相比的优点在于：本发明打破了调制型捷联惯导系统组合姿态确定过程中外部设备提供信息频率与调制型捷联惯导系统提供信息频率不匹配这一问题，在惯性测量单元四位置转停方案下的调制型捷联惯导系统中，利用载体瞬时速度信息中存在低频的舒勒周期信息和载体系泊状态存在的摇摆及荡运动的高频扰动信息这一特性，提出利用IIR数字高通滤波器滤除载体瞬时速度信息中的舒勒周期项，将滤波后的速度和惯导解算速度作差后作为系统的观测量，采用卡尔曼滤波技术实现捷联惯导系统的组合姿态。因此不需要外部设备为其提供参考信息。Compared with the prior art, the present invention has the advantages that: the present invention breaks the problem that the information frequency provided by the external equipment does not match the information frequency provided by the modulated SINS in the process of determining the combined attitude of the modulated SINS, In the modulated strapdown inertial navigation system under the four-position turn-stop scheme of the inertial measurement unit, the low-frequency Schuler period information in the instantaneous velocity information of the carrier and the high-frequency disturbance information of the swaying and oscillating motion in the mooring state of the carrier are used. One feature, it is proposed to use IIR digital high-pass filter to filter out the Schuler periodic term in the instantaneous velocity information of the carrier, and take the difference between the filtered velocity and the inertial navigation solution velocity as the observed quantity of the system, and use the Kalman filter technology to realize the fast Combined attitude of the inertial navigation system. Therefore, no external device is required to provide reference information for it.

对本发明有益的效果说明如下：The beneficial effects of the present invention are described as follows:

在VC++仿真条件下，对该方法进行仿真实验：Under the condition of VC++ simulation, the simulation experiment of this method is carried out:

载体作三轴摇摆运动。载体以正弦规律绕纵摇轴、横摇轴和航向轴摇摆，其数学模型为：The carrier makes a three-axis rocking motion. The carrier swings around the pitch axis, roll axis and yaw axis in a sinusoidal law, and its mathematical model is:

$\{\begin{matrix} θ θ = = {θ θ}_{m m} sin sin (({ω ω}_{θ θ} t t + + {φ φ}_{θ θ})) \\ γ γ = = {γ γ}_{m m} sin sin (({ω ω}_{γ γ} t t + + {φ φ}_{γ γ})) \\ ψ ψ = = {ψ ψ}_{m m} sin sin (({ω ω}_{ψ ψ} t t + + {φ φ}_{ψ ψ})) + + k k \end{matrix}$

其中：θ、γ、ψ分别表示纵摇角、横摇角和航向角的摇摆角度变量；θ_m、γ_m、ψ_m分别表示相应的摇摆角度幅值；ω_θ、ω_γ、ω_ψ分别表示相应的摇摆角频率；φ_θ、φ_γ、φ_ψ分别表示相应的初始相位；ω_i＝2π/T_i，i＝θ、γ、ψ，T_i表示相应的摇摆周期，k为初始航向角。仿真时取：θ_m＝6°，γ_m＝12°，ψ_m＝10°，T_θ＝8s，T_γ＝10s，T_ψ＝6s，k＝0°。Among them: θ, γ, ψ represent the roll angle variables of pitch angle, roll angle and heading angle respectively; _θ _m , _γ _m , _ψ _m represent the corresponding swing angle amplitudes; Indicates the corresponding swing angle frequency; φ _θ , φ _γ , φ _ψ respectively represent the corresponding initial phase; ω _i = 2π/T _i , i = θ, γ, ψ, T _i represents the corresponding swing period, and k is the initial heading horn. During simulation, take: θ _m = 6°, γ _m = 12°, ψ _m = 10°, T _θ = 8s, T _γ = 10s, T _ψ = 6s, k = 0°.

载体的横荡、纵荡和垂荡引起的线速度为：The linear velocity caused by the sway, surge and heave of the carrier is:

式中，i＝x，y，z为地理坐标系的东向、北向、天向。为[0，2π]上服从均匀分布的随机相位。In the formula, i=x, y, and z are the east, north, and sky directions of the geographic coordinate system. is a random phase that obeys a uniform distribution on [0, 2π].

载体初始位置：北纬45.7796°，东经126.6705°；The initial position of the carrier: 45.7796° north latitude, 126.6705° east longitude;

初始姿态误差角：三个初始姿态误差角均为零；Initial attitude error angle: the three initial attitude error angles are all zero;

赤道半径：R_e＝6378393.0m；Equatorial radius: R _e = 6378393.0m;

椭球度：e＝3.367e-3；Ellipsoid: e=3.367e-3;

由万有引力可得的地球表面重力加速度：g₀＝9.78049；The gravitational acceleration on the earth's surface obtained from the universal gravitation: g ₀ =9.78049;

地球自转角速度(弧度/秒)：7.2921158e-5；Earth rotation angular velocity (rad/s): 7.2921158e-5;

陀螺仪常值漂移：0.01度/小时；Gyroscope constant value drift: 0.01 degrees/hour;

陀螺仪随机游走： Gyroscope random walk:

加速度计零偏：10^-4g₀；Accelerometer zero bias: 10 ^-4 g ₀ ;

加速度计噪声：10^-6g₀；Accelerometer noise: 10 ^-6 g ₀ ;

常数：π＝3.1415926；Constant: π=3.1415926;

IMU四位置转停方案的数学模型参数：Mathematical model parameters of IMU four-position turn-stop scheme:

四个位置的停顿时间：T_s＝5min；Dwell time at four positions: T _s = 5min;

转动180°和90°时消耗的时间：T_z＝12s；Time consumed when turning 180° and 90°: T _z =12s;

转动180°和90°的过程中，每一个转位中的加减速时间各为4s；In the process of turning 180° and 90°, the acceleration and deceleration time in each index is 4s;

利用本发明所述的方法得到调制型捷联系统失准角曲线，如图5所示。结果表明有摇摆干扰条件下，采用本发明方法可以获得较高的对准精度。The misalignment angle curve of the modulated strapdown system is obtained by using the method of the present invention, as shown in FIG. 5 . The results show that under the condition of rocking interference, the method of the invention can obtain higher alignment accuracy.

(四)附图说明 (4) Description of drawings

图1为本发明的一种无外观测量的调制型捷联系统组合姿态确定方法流程图；Fig. 1 is a flow chart of a method for determining the combined attitude of a modulated strapdown system without appearance measurement of the present invention;

图2为本发明的IMU单轴四位置转停；Figure 2 is the IMU single-axis four-position rotation stop of the present invention;

图3为本发明的定义载体半固定坐标系；Fig. 3 is the defined carrier semi-fixed coordinate system of the present invention;

图4为本发明的载体坐标系与载体半固定坐标系的转换关系；Fig. 4 is the conversion relationship between the carrier coordinate system of the present invention and the carrier semi-fixed coordinate system;

图5为本发明的无外观测量的调制型捷联系统卡尔曼滤波估计的失准角曲线。Fig. 5 is a curve of misalignment angle estimated by Kalman filter of the modulated strapdown system without appearance measurement according to the present invention.

(五)具体实施方式 (5) Specific implementation methods

下面结合附图对本发明的具体实施方式进行详细地描述：The specific embodiment of the present invention is described in detail below in conjunction with accompanying drawing:

${C C}_{b b}^{d d} = = [\begin{matrix} cos cos γ γ cos cos β β & sin sin γ γ cos cos α α + + cos cos γ γ sin sin β β sin sin α α & sin sin γ γ sin sin α α - - cos cos γ γ sin sin β β cos cos α α \\ - - sin sin γ γ cos cos β β & cos cos γ γ cos cos α α + + sin sin γ γ sin sin β β sin sin α α & cos cos γ γ sin sin α α - - sin sin γ γ sin sin β β cos cos α α \\ sin sin β β & - - cos cos β β sin sin α α & cos cos β β cos cos α α \end{matrix}] - - - - - - ((11))$

γ＝ψ-ψ_G (2)γ=ψ-ψ _G (2)

由于惯性测量单元相对载体存在绕方位轴的转位运动，因此惯性测量坐标系(s坐标系)与载体坐标系之间的转换矩阵可以利用下式进行计算：Since the inertial measurement unit has an indexing motion around the azimuth axis relative to the carrier, the conversion matrix between the inertial measurement coordinate system (s coordinate system) and the carrier coordinate system can be calculated using the following formula:

${C C}_{s the s}^{b b} = = [\begin{matrix} cos cos ωt ωt & - - sin sin ωt ωt & 00 \\ sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] - - - - - - ((33))$

${C C}_{s the s}^{d d} = = {C C}_{b b}^{d d} {C C}_{s the s}^{b b} - - - - - - ((44))$

$\frac{f_{p 1}}{f_{s}} = \frac{Ω_{p 1}}{2 π}$ (5) $\frac{f_{p 1}}{f_{the s}} = \frac{Ω_{p 1}}{2 π}$ (5)

所以求得：So get:

Ω_s1＝2πf_s1/f_s (6)Ω _s1 ＝2πf _s1 /f _s (6)

Ω_p1＝2πf_p1/f_s Ω _p1 ＝2πf _p1 /f _s

按照双线性Z变换法的频率转换关系ω＝2f_stan(Ω/2)继续转换得到：Continue to convert according to the frequency conversion relationship ω=2f _s tan(Ω/2) of the bilinear Z-transform method to obtain:

$Ω_{p} = \tan (\frac{ω_{p}}{2})$ (7) $Ω_{p} = the tan (\frac{ω_{p}}{2})$ (7)

${Ω Ω}_{s the s} = = tan the tan ((\frac{{ω ω}_{s the s}}{22}))$

1)建立卡尔曼滤波的状态方程：1) Establish the state equation of the Kalman filter:

$\overset{\cdot \cdot}{X x} = = AX AX + + BW BW - - - - - - ((88))$

系统的状态向量为：The state vector of the system is:

系统的白噪声向量为：The white noise vector of the system is:

W＝[a_x a_y ω_x ω_y ω_z 0 0 0 0 0]^T (10)W＝[a _x a _y ω _x ω _y ω _z 0 0 0 0 0] ^T (10)

系统的状态转移矩阵为：The state transition matrix of the system is:

$A A = = [\begin{matrix} {F f}_{22 \times \times 22}^{11} & {f f}_{22 \times \times 33} & {\overset{~ ~}{T T}}_{22 \times \times 22} & {O o}_{22 \times \times 33} \\ {F f}_{33 \times \times 22}^{22} & {F f}_{33 \times \times 33}^{33} & {O o}_{33 \times \times 22} & {T T}_{33 \times \times 33} \\ {O o}_{55 \times \times 22} & {O o}_{55 \times \times 33} & {O o}_{55 \times \times 22} & {O o}_{55 \times \times 33} \end{matrix}] - - - - - - ((1111))$

${F f}_{22 \times \times 22}^{11} = = [\begin{matrix} \frac{{V V}_{N N}}{{R R}_{n no}} tan the tan {L L}^{' '} & 22 {ω ω}_{ie ie} sin sin L L + + \frac{{V V}_{E E.}}{{R R}_{n no}} tan the tan L L \\ - - ((22 {ω ω}_{ie ie} sin sin L L + + \frac{22 {V V}_{E E.}}{{R R}_{n no}} tan the tan L L)) & 00 \end{matrix}] - - - - - - ((1212))$

${F f}_{33 \times \times 22}^{22} = = \begin{matrix} [\begin{matrix} 00 & - - \frac{11}{{R R}_{m m}} \\ \frac{11}{{R R}_{n no}} & 00 \\ \frac{tan the tan L L}{{R R}_{n no}} & 00 \end{matrix}] - - - - - - ((1313)) \end{matrix}$

${F f}_{33 \times \times 33}^{33} = = [\begin{matrix} 00 & {ω ω}_{ie ie} sin sin L L + + \frac{{V V}_{E E.} tan the tan L L}{{R R}_{n no}} & - - (({ω ω}_{ie ie} cos cos L L + + \frac{{V V}_{E E.}}{{R R}_{n no}})) \\ - - (({ω ω}_{ie ie} sin sin L L + + \frac{{V V}_{E E.} tan the tan L L}{{R R}_{n no}})) & 00 & - - \frac{{V V}_{N N}}{{R R}_{m m}} \\ {ω ω}_{ie ie} cos cos L L + + \frac{{V V}_{E E.}}{{R R}_{n no}} & \frac{{V V}_{N N}}{{R R}_{m m}} & 00 \end{matrix}] - - - - - - ((1414))$

${f f}_{22 \times \times 33} = = [\begin{matrix} 00 & - - {f f}_{U u} & {f f}_{N N} \\ {f f}_{U u} & 00 & {f f}_{E E.} \end{matrix}] - - - - - - ((1515))$

${\overset{~ ~}{T T}}_{22 \times \times 22} = = [\begin{matrix} {T T}_{1111} & {T T}_{1212} \\ {T T}_{21 twenty one} & {T T}_{22 twenty two} \end{matrix}] - - - - - - ((1616))$

${T T}_{33 \times \times 66} = = [\begin{matrix} - - {T T}_{1111} & - - {T T}_{1212} & - - {T T}_{1313} \\ - - {T T}_{21 twenty one} & - - {T T}_{22 twenty two} & - - {T T}_{23 twenty three} \\ - - {T T}_{3131} & - - {T T}_{3232} & - - {T T}_{3333} \end{matrix}] - - - - - - ((1717))$

Z＝HX+V (18)Z＝HX+V (18)

其中：Z表示系统的量测向量H表示系统的量测矩阵；V表示系统的量测噪声；Among them: Z represents the measurement vector of the system, H represents the measurement matrix of the system; V represents the measurement noise of the system;

系统量测矩阵为：The system measurement matrix is:

$H h = = [\begin{matrix} 11 & 00 & 00 & 00 & 00 & 00 & 00 & 00 & 00 & 00 \\ 00 & 11 & 00 & 00 & 00 & 00 & 00 & 00 & 00 & 00 \end{matrix}] - - - - - - ((1919))$

$Z Z = = [\begin{matrix} {V V}_{E E.} - - {\overset{~ ~}{V V}}_{E E.} \\ {V V}_{N N} - - {\overset{~ ~}{V V}}_{N N} \end{matrix}] - - - - - - ((2020))$

Claims

1. A modulation type strapdown system combined attitude determination method without appearance measurement, is characterized in that comprising the following steps:

(1) Determine the initial position parameters of the carrier through GPS, and bind them into the navigation computer;

(2) The modulated strapdown inertial navigation system is preheated, and the data output by the fiber optic gyroscope and the quartz accelerometer are collected and processed;

(3) The IMU adopts an indexing scheme in which four rotation-stop sequences are one rotation cycle;

Sequence 1, IMU starts from position A, rotates 180° clockwise to position B, and stays at position B for a time T _s ; Sequence 2, IMU starts from position B, rotates 90° clockwise to reach position C, and stays at position C Time T _s ; Sequence 3, the IMU starts from position C, rotates 180° counterclockwise to position D, and stays at position D for a time T _s ; Sequence 4, IMU starts from position D and rotates 90° counterclockwise to return to position A, and Position A stays for T _s ; then moves in a cyclical sequence in the order of 1 to 4;

The IMU is rotated at intervals of 180° or 90° each time, from one position to a symmetrical position by 180°. In these two mutually symmetrical positions, the constant value drift of the inertial sensor in the horizontal direction can be compared with each other when performing navigation calculations. Offset; reach another new position by rotating 90°;

(4) Convert the output of the accelerometer to the semi-fixed coordinate system of the carrier, and use the integral link in the modulated strapdown inertial navigation system to extract the instantaneous linear velocity information of the carrier;

1) Introduce the semi-fixed coordinate system of the carrier

Taking the center of gravity of the ship as the origin of the semi-fixed coordinate system of the carrier, the vertical axis OY _d points to the main direction of the ship, the horizontal axis OX _d is perpendicular to the longitudinal axis and parallel to the horizontal plane, and points to the starboard direction when the ship has no pitch motion; vertical The axis OZ _d is perpendicular to the first two axes, and is positive along the vertical axis of the ship; among them, ψ _G is the main course angle, and γ angle is the course swing angle, that is, the yaw angle defines that it is positive in the same direction as the main course angle; the carrier is semi-fixed The introduction of the coordinate system basically separates the measurement results from the angular motion, and can accurately describe the instantaneous linear motion of the ship. Therefore, the semi-fixed coordinate system of the carrier is used as the basic coordinate system for studying the instantaneous linear motion of the ship or called translation;

2) Establish the conversion matrix between the inertial measurement unit coordinate system and the carrier semi-fixed coordinate system

Firstly, the difference between the carrier coordinate system and the carrier semi-fixed coordinate system is established by three rotation angles, which can be regarded as the semi-fixed coordinate system coincides with the carrier coordinate system after three rotations. The three angles are: pitch angle α, roll angle β and yaw angle γ; the direction cosine matrix of the transformation from carrier coordinate system b to carrier semi-fixed coordinate system d

The existing inertial navigation system can already provide more accurate attitude angle information. The two horizontal attitude angle information are pitch angle information and roll angle information, while the heading information provides heading angle information ψ, which is different from Yaw angle γ, but the operator of the ship can provide accurate main heading information ψ _G , we can get

γ=ψ- _ψG

Substitute γ into In the calculation equation, the direction cosine matrix of the transformation of the carrier coordinate system to the carrier semi-fixed coordinate system can be obtained;

Since the inertial measurement unit has an indexing movement around the azimuth axis relative to the carrier, the conversion matrix between the inertial measurement coordinate system s coordinate system and the carrier coordinate system can be calculated by the following formula:

In the formula, ωt represents the relative angle relationship of the inertial measurement unit relative to the carrier coordinate system; therefore, the direction cosine matrix of the conversion of the inertial measurement unit coordinate system to the carrier semi-fixed coordinate system can be obtained:

(5) Design a reasonable infinite impulse response digital high-pass filter IIR, and perform high-pass filtering processing on the carrier velocity calculated by the lower solution of the navigation system;

1) Determine the technical indicators of the designed digital high-pass filter

The technical indicators of high-pass digital filters f _p1 , f _s1 , δ _p , and δ _s are given according to signal characteristics and sampling frequency f _s , where f _p1 is the cut-off frequency of the pass band, f _s1 is the cut-off frequency of the stop band, and δ _p is the passband ripple, that is, the maximum value that deviates from unity gain in the passband of the filter, and the edge gain of the passband is 1-δ _p , δ _s is the stopband ripple, that is, the maximum value that deviates from unity gain in the filter stopband, and The gain of the filter at the band edge is δ _s , and the attenuation α _p and α _s of the passband and stopband are respectively defined as -20log(1-δ _p ), -20log(1-δ _s );

The Schuler periodic oscillation signal is relatively low-frequency signal, the oscillation period is 84.4 minutes, and the ship's instantaneous line motion is caused by marine environmental factors, the main reason is the influence of waves, so the ship's instantaneous line motion is the frequency The reciprocating motion is roughly consistent with the wave frequency, and the instantaneous linear motion of the ship is high-frequency motion relative to the sailing motion of the ship, and the motion cycle is relatively short, generally about 1.5 seconds to 10 seconds, and the frequency is 0.67 Hz; The difference between the motion characteristics of the swaying motion and the normal working motion of the ship, the technical index requirements of the filter required for design, the specific design index is adjusted according to the filtering effect during the test, and the optimal filtering effect shall prevail ;

2) Convert technical indicators from digital filters to analog filters

The conversion of technical indicators from analog filter to digital filter adopts bilinear Z-transform method, and the technical indicators for designing digital high-pass filter are f _p1 , f _s1 , δ _p , δ _s , t _s =0.0102; firstly, the digital The edge frequency Ω, because 2π corresponds to the sampling frequency f _s , and f _s =1/t _s , so:

So get:

Ω _s1 = 2πf _s1 /f _s

Ω _p1 ＝2πf _p1 /f _s

According to the frequency conversion relationship ω=2f _s tan(Ω/2) of the bilinear Z transformation method, the continuous conversion has:

In this way, the technical index of the digital high-pass filter is converted into the technical index of the analog high-pass filter;

(6) According to the dynamic base error equation of the modulated strapdown inertial navigation system, the combined attitude error model in the mooring state of the carrier is established, and the speed obtained after high-pass filtering is compared with the speed calculated directly by the modulated strapdown inertial navigation system Finally, it is used as the system observation quantity; the Kalman filter technology is used to realize the determination of the combined attitude of the modulated strapdown inertial navigation system;

Establish a Kalman filter model that takes the difference between the horizontal velocity after high-pass filtering and the velocity directly calculated by the modulated strapdown inertial navigation system as the observation;

The state error of the modulated SINS is described by a first-order linear differential equation:

Among them, X is the state vector of the system; A and B are the state matrix and noise matrix of the system respectively; W is the system noise vector;

The state vector of the system is:

The white noise vector of the system is:

W＝[a _x a _y ω _x ω _y ω _z 0 0 0 0 0] ^T

Among them, δV _E and δV _N represent the velocity errors in the east direction and north direction respectively; are the zero bias of the IMU coordinate system ox _s , oy _s axis accelerometer; ε _x , ε _y , ε _z are the constant drift of the IMU coordinate system ox _s , oy _s , oz _s axis gyroscope respectively; a _x , a _{y are} respectively is the white noise error of the IMU coordinate system ox _s , oy _s axis accelerometer; ω _x , ω _y , ω _z are the white noise errors of the IMU coordinate system ox _s , oy _s , oz _s axis gyroscope respectively;

The state transition matrix of the system is:

V _E , V _N represent the eastward and northward velocities respectively; ω _x , ω _y , ω _z represent the three input angular velocities of the gyroscope; ω _ie represent the earth's rotation angular velocity; R _m , R _n represent the earth's meridian, Radius of curvature; L represents the local latitude; L′ represents the latitude information of the carrier at the initial moment of the mooring state; f _E , f _N , and f _U represent the relative forces in the east, north, and sky directions of the navigation coordinate system, respectively;

2) Establish the measurement equation of Kalman filter:

The measurement equation of the modulated SINS is described by the first-order linear differential equation as follows:

Z＝HX+V

Among them: Z represents the measurement vector of the system; H represents the measurement matrix of the system; V represents the measurement noise of the system;

The system measurement matrix is:

Quantities measured are the eastward velocity V _E and northward velocity V _N calculated by the modulated strapdown inertial navigation system and the eastward velocity obtained through high-pass filtering north speed Difference

.