CN112013873A - A Fast Alignment Method for Static Base Based on Gradient Descent Optimization - Google Patents

Abstract

The invention discloses a static base self-alignment method based on gradient descent optimization. Firstly, establishing a corresponding model by utilizing self-accelerometer and gyroscope information to replace latitude information to realize estimation calculation of the spin angular velocity vector of the earth under a navigation system; secondly, in order to improve the noise suppression capability, the problem of non-latitude alignment of a static base is converted into the problem of Wahba attitude determination, and a target function in the least square sense is constructed by using multiple measurement vectors; and finally, obtaining a least square solution of the target function by using batch gradient descent optimization, so that the target function can be updated by fully utilizing all previous measurement information after each attitude quaternion is updated, and the target function is only related to the latest attitude quaternion, thereby accelerating the alignment convergence speed. The invention solves the problem of fast high-precision alignment of ships under the condition of unknown latitude.

Description

A Fast Alignment Method for Static Base Based on Gradient Descent Optimization

technical field

The invention relates to the technical field of strapdown inertial navigation, in particular to a method for rapid alignment of static bases based on gradient descent optimization.

Background technique

Inertial navigation system is an autonomous navigation system based on the principle of inertia. The strapdown inertial navigation system directly fixes the gyroscope and accelerometer on the carrier to measure the angular motion and linear motion information of the carrier, and calculates the speed, position, attitude and heading information of the carrier relative to the earth through integral operation. The initial alignment is a key technology of the strapdown inertial navigation system. The accuracy of the alignment directly affects the accuracy of the navigation system, and the time to complete the alignment directly affects the rapid response capability of the system.

For the relatively simple application condition of static base alignment, the research on traditional static base alignment algorithm is relatively mature, and the theoretical alignment accuracy of the algorithm is close to the limit value of device error. Although the traditional inertial framed base alignment method can be used for static base alignment, the alignment time is long, and the alignment error will increase with time, so that the alignment accuracy is not as good as the traditional static base analytical alignment method. In addition, analytical alignment uses the spatial relationship between the earth's rotation angular velocity and the gravitational acceleration vector to directly determine the initial attitude matrix, which has the advantages of simple principle, fast alignment speed, and meets the initial alignment requirements under arbitrary attitude conditions. There is a disadvantage that alignment accuracy is easily affected by device noise interference.

Traditional static base alignment techniques can usually be divided into three categories: analytical alignment, compass alignment, and Kalman filter combination alignment based on optimal estimation. The local latitude information needs to be input externally during initial alignment, which will reduce the efficiency of the alignment. Autonomy and safety of joint attitude systems. In addition, the combined alignment of compass alignment and Kalman filter is mainly aimed at the case where the initial attitude angle is small, such as the fine alignment process, due to the limitations of the application conditions, it cannot complete the initial alignment task under the condition of any heading angle . In addition, the combined alignment process of compass alignment and Kalman filter usually takes a long time, and it is difficult to adapt to the fast alignment requirements of the static base. For the initial alignment of the static base in tunnels, deep mountains, jungles and seabeds where GPS positioning information cannot be obtained, the traditional static base initial alignment technology cannot complete the alignment task, which further limits the strapdown attitude system in complex environments. application below.

In view of the above problems, the present invention designs a static base fast alignment method based on gradient descent optimization, and uses batch gradient descent optimization to determine the least squares solution of the objective function, so that it can be fully utilized after each attitude quaternion update. All previous measurement information updates the objective function to ensure that the objective function is only related to the latest attitude quaternion, thereby accelerating the alignment convergence speed; at the same time, by using all the measurement information to construct the objective function, the device noise interference can be effectively suppressed. It can be used for fast and high-precision alignment when the latitude of the ship is unknown, which improves the environmental adaptability of alignment.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a fast and high-precision transfer alignment method that can be applied in the case of unknown latitude.

The technical solution for realizing the object of the present invention is: a method for rapidly aligning static bases based on gradient descent optimization, comprising the following steps:

Step 1: Complete the estimation of the angular velocity vector of the earth's rotation by using its own accelerometer and gyro measurement information: use the unit quaternion to represent the attitude and coordinate transformation, and it is necessary to normalize the angular velocity of the earth's rotation and the gravitational acceleration vector at the same time;

Step 2: Use multi-measurement vectors to construct an objective function in the sense of least squares to suppress device noise interference;

Step 3: Use the batch gradient descent method to obtain the least squares solution of the pose quaternion.

In step 1, the estimation model of the angular velocity vector of the earth's rotation is as follows:

并对地球自转角速度

和重力加速度矢量

进行归一化处理：unit quaternion

and the angular velocity of the Earth's rotation

and the gravitational acceleration vector

To normalize:

And the three-axis accelerometer and three-axis gyro output values are normalized:

只有y轴和z轴分量不为零。因此，

的通式可以记作：The normalized angular velocity vector of the earth's rotation is projected in the navigation coordinate system

Only the y-axis and z-axis components are not zero. therefore,

The general formula can be written as:

The horizontal attitude angle can be determined using the accelerometer information under static base conditions:

Using the output information of the accelerometer, the horizontal plane and the z _n- axis direction of the navigation coordinate system can be determined (perpendicular to the horizontal plane, satisfying the right-hand coordinate system criterion).

由载体系转换到导航坐标系后得到地球自转角速度矢量

The angular velocity vector of the earth's rotation measured by the three-axis gyro

After the carrier system is converted to the navigation coordinate system, the angular velocity vector of the earth's rotation is obtained

The projected components of the y-axis and z-axis in the navigation coordinate system:

The local latitude L can be determined by the above formula. So far, we use the constraint relationship between the intermediate transformation orthogonal coordinate system and the navigation coordinate system determined by the accelerometer and gyro measurement information to obtain the angular velocity vector of the earth's rotation in the navigation coordinate system.

In step 2, the objective function is constructed using the batch gradient descent optimization idea:

所需要的信息。where r ⁿ and r ^b are the corresponding physical vectors in the navigation reference system and the carrier system, respectively, assuming that they contain the quaternion that determines the attitude

required information.

Further, the optimal value of the pose quaternion in the sense of least squares can be obtained by using gradient descent optimization:

为雅克比矩阵,

且

梯度

每次更新都要使用之前全部量测信息，因而对器件白噪声等干扰具有较强的抑制能力。需要指出的是，

的更新依赖于初值

和迭代步长λ的选取。where λ is the gradient iteration step size,

is the Jacobian matrix,

and

gradient

All previous measurement information is used for each update, so it has a strong ability to suppress interference such as device white noise. It should be pointed out that,

The update depends on the initial value

and the selection of the iterative step size λ.

In step 3, the objective function in step 2 is solved using batch gradient descent optimization:

转换到载体系下，得到First, the normalized gravitational acceleration vector under the navigation system

Convert to the download system, get

The difference between the theoretical value of the gravitational acceleration vector and the actual measured value under the load system is

表示

对

的雅克比矩阵，得到Further, remember

express

right

The Jacobian matrix of , we get

In the same way, the theoretical value of the normalized angular velocity vector of the earth's rotation under the carrier system is obtained

The difference between the theoretical value of the earth's rotation angular velocity vector and the actual measured value under the carrier system is:

Combine the gravitational acceleration vector and the earth's rotation angular velocity vector information to determine the attitude quaternion, and establish a unified equation as follows:

Also get the Jacobian matrix

In practice, device noise from accelerometers and gyroscopes can affect alignment performance. In order to overcome the influence of device noise, the following objective function is constructed based on batch gradient descent optimization:

Among them, k represents the current moment of the alignment process.

The attitude quaternion is determined by gradient descent optimization, and the iterative process is as follows:

Among them, λ _k represents the iterative step size. When setting λ _k , it is recommended to select a time-varying parameter value that gradually decreases with the iterative process, which is conducive to speeding up the convergence speed and improving the accuracy. Due to the existence of errors such as device errors, quaternion normalization needs to be performed in the iterative process to ensure that

Compared with the prior art, the beneficial effects of the present invention are:

When the latitude is unknown, the information transforms the attitude determination problem into the least squares solution problem based on multi-vectors, which can effectively suppress noise interference, does not depend on external latitude, and uses its own accelerometer and gyro measurement information to realize the rotation angular velocity of the earth. On this basis, a fast alignment method of static base based on gradient descent optimization is proposed. Each time the attitude quaternion is updated, the objective function can be updated with the latest quaternion and all previous measurement information, which is beneficial to speed up the convergence speed, so as to realize the autonomy and rapidity of the static base alignment under the condition of no latitude.

Description of drawings

Fig. 1 is the basic flow chart of the present invention;

Figure 2 is a comparison of horizontal alignment errors;

Figure 3 is a comparison of the heading alignment errors of the attitude (0°, 0°, 45°);

Figure 4 shows the comparison of heading alignment errors between 0° and 360°.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings.

In order to verify the effectiveness of the present invention, the designed latitude-free self-alignment method of static base based on eigenvalue decomposition is simulated by using Matlab.

The simulation parameters are set as follows:

Gyro drift: 0.01°/h

gyro random walk

Accelerometer bias: 1×10 ^-4 g

Accelerometer measurement noise:

Sampling frequency: 100Hz

initial value

Iterative step λ=βΔt

Among them, β represents the parameters of the system dynamic characteristics, and Δt represents the system sampling period.

Gyroscopic random walk and accelerometer measurement noise are treated as white noise. Under the condition of setting the horizontal attitude (0°, 0°), starting from the 0° heading angle, the inertial device data under the condition of the static base is collected and collected at an interval of 15°, and a total of 24 sets of data are collected. The local latitude is set to 45.7796° (Harbin), the simulation time is 20s, and the difference between the alignment result at the 20s alignment completion time and the set benchmark reference value is taken as the alignment error of a single experiment.

Simulation results:

With the above simulation conditions, the simulation results are shown in Table 1-3 and Figure 2-4.

Figures 2 and 3 show the traditional analytical alignment method (OTRIAD1) relying on latitude information under typical attitude conditions of static base (0°, 0°, 45°), and the traditional latitude-dependent information after data averaging preprocessing. Analytical alignment method (OTRIAD2) and the gradient descent optimization based static base fast alignment method (GDSA) proposed in the present invention are horizontal attitude and heading alignment error curves. Although OTRIAD is one of the analytical alignment methods with the highest theoretical alignment accuracy, its alignment results are easily disturbed by device noise. As shown in Figures 2 and 3, the OTRIAD1 alignment error fluctuates around the theoretical error value due to device noise, while the OTRIAD2 method, which is preprocessed by data averaging, can overcome the device noise interference and quickly converge to the theoretical error value. The alignment convergence process of the GDFA method based on gradient descent optimization is the same as that of OTRIAD2, and the error curves of the two completely overlap, which indicates that the GDFA method has a faster alignment convergence rate.

Table 1 and Table 2 respectively give the results of the roll and pitch alignment errors of each algorithm in the 24 alignment experiments. It can be seen from the table that the horizontal error between OTRIAD1 and the existing static base-free latitude alignment method (ONTRIAD1) is large, and the fluctuation is large, indicating that the algorithm has a weak noise suppression ability; while the horizontal error of GDSA fluctuates very little, and each alignment The results of the quasi-errors are all the same (the standard deviation is close to 0 after only 4 significant digits are kept), and the maximum errors of roll and pitch are 0.0057° and 0.0057° respectively; compared with the existing static base after OTRIAD1 and data averaging preprocessing Using the latitude-free alignment method (ONTRIAD2), the maximum error of GDSA horizontal attitude is reduced by 12.31% respectively. At the same time, the results in Table 1 and Table 2 show that the maximum error of the horizontal attitude of the GDSA method proposed by the present invention is the same as that of OTRIAD2 and ONTRIAD2, both being 0.0057°.

Table 1 Roll alignment error results (°)

Table 2 Pitch alignment error results

Table 3 shows the heading alignment error results of each algorithm in the 24 alignment experiments. At the same time, in order to better show the heading alignment results of the algorithm, Fig. 4 shows the heading alignment error curves of OTRIAD2, ONTRIAD2 and GDSA in 24 experiments. Since the heading alignment error is mainly affected by the drift of the equivalent easting gyro under the navigation system, when the heading changes from 0° to 360°, the drift of the equivalent easting gyro will change accordingly, resulting in the periodic change of the heading alignment error. From the graph results, OTRIAD2 can better suppress the device noise, and the alignment result is close to the theoretical error value. Due to the weak noise suppression ability of OTRIAD1 and ONTRIAD1, the alignment results fluctuate up and down with the results of OTRIAD2; the results of GDFA are the same as those of OTRIAD2, the curves are also completely overlapped, and the maximum alignment error is 0.0618°. Compared with the ONTRIAD1 method, the GDSA heading maximum error is reduced by 2.83%.

Table 3 Heading alignment error results

In addition, the maximum heading errors of GDSA and the existing latitude-free alignment method ONTRIAD2 are 0.0618° and 0.0619° respectively. It can be considered that the maximum heading error of GDSA and ONTRIAD2 after data average preprocessing is the same. Further analysis of Table 3 and Figure 4 shows that when the heading is 0°-180°, the maximum error of GDSA and ONTRIAD2 is both 0.0875°, and the maximum error of ONTRIAD2 is smaller than GDSA at this time; and when the heading is 180°-360°, the maximum error of GDSA and ONTRIAD2 is the largest The errors are 0.0875° and 0.0893° respectively, and the maximum error of GDSA heading is smaller than ONTRIAD2 at this time. This shows that the latitude-free alignment method GDSA proposed by the present invention and the existing latitude-free alignment method ONTRIAD2 are mutually beneficial supplements, and corresponding algorithms can be selected for alignment according to different heading range conditions.

Therefore, the simulation results show that the maximum alignment error of the static base latitude-free alignment method GDSA proposed by the present invention is the same as that of OTRIAD2 after data average preprocessing, and is close to the device error limit; compared with the existing latitude-free alignment method ONTRIAD1 , the maximum errors of GDSA roll, pitch and heading are reduced by 12.31%, 12.31%, and 2.83%, respectively, showing good noise suppression ability. In addition, it can be a beneficial complement to the latitude-free alignment method ONTRIAD2 after data average preprocessing, in which the maximum heading error of GDSA is smaller than ONTRIAD2 when the heading is 180°-360°.

Claims (4)

1. A static base rapid alignment method based on gradient descent optimization is characterized by comprising the following steps:

the method comprises the following steps: the estimation of the angular velocity vector of the earth rotation is completed by utilizing self-accelerometer and gyroscope measurement information: representing the posture and coordinate transformation by using a unit quaternion, and simultaneously carrying out normalization processing on the rotation angular velocity and the gravity acceleration vector of the earth;

step two: constructing a target function in the least square sense by using multiple measurement vectors to inhibit noise interference of the device;

step three: a least squares solution of the attitude quaternion is obtained by a batch gradient descent method.

2. The method for fast aligning the static base based on the gradient descent optimization as claimed in claim 1, wherein the projection components of the earth rotation angular velocity vector in the y-axis and the z-axis of the navigation coordinate system are as follows:

speed vector of self-rotation angle of earth under navigation coordinate system

3. The method for fast aligning the static base based on the gradient descent optimization according to claim 1, characterized in that an objective function is constructed by using a batch gradient descent optimization idea:

in the formula rⁿAnd r^bCorresponding physical vectors under the navigation reference system and the carrier system respectively, which are assumed to contain the quaternion for determining the attitude

The required information.

4. The method for fast alignment of a static base based on gradient descent optimization according to claim 1, wherein the following objective function is constructed based on the batch gradient descent optimization by using the batch gradient descent optimization solution:

where k denotes the current moment of the alignment process.

Determining the attitude quaternion by utilizing gradient descent optimization, wherein the iteration process is as follows:

wherein λ is_kRepresents the iteration step size, at setting λ_kAnd time-varying parameter values gradually reduced along with the iteration process are selected, so that the convergence speed is accelerated, and the precision is improved. Because errors such as device errors exist, quaternion normalization is required in the iteration process, and the quaternion normalization is guaranteedCertificate (certificate)

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