Absolute attitude measurement based on multi-sensor fusion

In the field of positioning and navigation, the measurement and transmission of absolute attitude are often used in the initial calibration process of positioning and navigation equipment. This requires higher absolute attitude measurement accuracy and lower measurement complexity. In order to solve the problems of high complexity and time-consuming of traditional absolute attitude measurement, a multi-sensor fusion absolute attitude measurement method is proposed. This method uses an optical camera to calculate the angle offset, employs a biaxial inclination sensor to measure horizontal angles, and utilizes GNSS differential positioning to introduce true azimuth angle. The experimental results of the prototype show that under the condition of 60 m baseline length, the max uncertainty of yaw, pitch, and roll angle measurement is 14.13”, 4.41”, and 3.53” respectively, and the average single measurement time consumption is 2.73 minutes.


Introduction
One of the main links in the existing absolute attitude measurement calibration process is the introduction of true azimuth and the measurement of horizontal angle.The commonly used absolute attitude measurement methods mainly include gyroscope measurement [1][2][3] and GNSS differential measurement [2,[4][5][6] .
Among them, the gyroscope uses the fixed axis and precession characteristic to measure the true north direction, and the gyroscope can sense the pitch angle and roll angle of its relative horizontal plane, and then calculate the three-axis attitude of the gyroscope itself.Furthermore, the absolute attitude of the measured object can be calculated by calibrating the relative relationship between the measured object and the gyroscope and converting the coordinate system.Limited by the level of manufacturing technology, the volume and weight of the current high-precision gyroscope are often large, and its portability is difficult to guarantee.Although the MEMS gyroscope is light in weight and small in size, its accuracy generally cannot meet the needs of high-precision measurement and calibration.In addition, the gyroscope inevitably has a drift error, which can only be suppressed but not eliminated [7,8] which also affects the measurement accuracy of the gyroscope to a certain extent.One of the methods in GNSS differential measurement is to measure the true azimuth angle of the connection line (baseline) of the two receivers by differentiating two GNSS receivers separated by a certain distance, and then transmit the true azimuth angle and the measured horizontal angle to the measured object through optical targeting equipment such as theodolite, and further calculate the absolute attitude of the measured object.This method needs to ensure that the perpendicular line between the phase center of the GNSS receiver antenna and the ground passes through the straight line where the optical axis of the optical aiming device is located, otherwise, the measurement error will be introduced.Therefore, the horizontal angle of the optical aiming equipment needs to be accurately adjusted to meet the above requirements.Another type of method is to install more than three GNSS receiver antennas on the measured object to form more than two intersecting baselines, and calculate the absolute attitude of the measured object according to the angle information of several baselines [9] .Since the azimuth measurement accuracy is directly related to the baseline length, this method requires a large volume of the measured object itself or a large volume of measurement tooling.The installation position of all antennas needs to be precisely adjusted or pre-calibrated, otherwise, the attitude measurement accuracy will be reduced.
In order to solve the above problems, this paper adopts the measurement method of multi-sensor fusion.The true azimuth information of the differential baseline is obtained by using the principle of GNSS differential positioning, the baseline vector is mapped to the reference hexahedral prism coordinate system by optical imaging [10] .Then, the biaxial inclination angle of the reference hexahedral prism coordinate system relative to the ground is calculated by using the biaxial inclination sensor.Finally, the absolute attitude of the reference hexahedral prism coordinate system relative to the ground is solved by the fusion algorithm [11] , and the attitude is further transmitted to the measured object, so as to realize the high-precision measurement of the absolute attitude of the measured object.As shown in Figure 1, the method measurement device in this paper is mainly composed of two parts: the measurement host and the target.Wherein, the measurement host comprises a horizontally mounted camera and a dual-axis inclination sensor module, the top of the measurement host is equipped with a GNSS mobile station, and the bottom of the measurement host is equipped with a hexahedral prism.The camera is used to image the optical beacon in the distance and calculate the amount of missed target, so as to obtain the mapping relationship between the differential baseline and the camera pointing.The biaxial inclination sensor can obtain the pitch and roll angles of the measurement host and participate in the subsequent fusion solution.The GNSS mobile station can calculate the accurate true azimuth information by differentiating it from the target GNSS reference station.The hexahedral prism is mainly used for calibration work and attitude transfer.The target is mainly composed of a GNSS reference station, an optical beacon, and a leveling pedestal.The GNSS reference station transmits the positioning information to the mobile station for calculation by differentiating it from the mobile station at the end of the measurement host.In order to facilitate the extraction and identification of the measuring host, the distance between the three optical beacons is precisely designed so that they form an isosceles triangle structure, and the extension line of the midline of the isosceles triangle passes through the phase center of the antenna of the reference station.The leveling pedestal is used to adjust the target to be level with the ground.The overall flow of the algorithm is shown in Figure 2.

Beacon vector calculation
Absolute attitude Figure 2. Algorithm flow chart.

Relationship between coordinate systems
In order to facilitate the calculation, four sets of coordinate systems are established, namely the camera coordinate system ( , , ) X Y Z , the inclination sensor coordinate system ( , , ) a a a X Y Z , the hexahedral prism coordinate system ( , , ) X Y Z , and the world coordinate system ( , , ) The camera coordinate system ( , , ) a a a X Y Z coincide with their sensitive roll and pitch axis, respectively.The three orthogonal normals of the hexahedral prism coordinate system ( , , ) and p Z axis.The world coordinate system ( , , ) w w w X Y Z is often equated with the geocentric coordinate system and the ground coordinate system.

Optical offset measurement and calculation
In order to measure the amount of optical miss, it is necessary to distinguish between the beacon mark and the background environment in the captured image, and to identify the beacon mark below the differential reference station as the final target to participate in the calculation.Furthermore, the precalibrated camera model is used to convert the coordinates of the beacon points into the vector representation of the incident light in the camera coordinate system.The specific process is as follows:  The Tophat operation is used to pre-process the captured images, which can filter a large area of the bright sky background and the complex environmental background with smooth brightness changes.This ensures that only the small connected domain of the highlight is left in the image.By calculating the theoretical spot size of the beacon under the current baseline length and adjusting the Tophat operation template based on this, the size of the bright connectivity domain in the image is not larger than the theoretical spot size of the beacon, which is convenient for subsequent identification and solving. The theoretical brightness value of the beacon spot under the current baseline length is calculated, and the pre-processed image is filtered globally with this brightness as a reference value to remove the interference of some false targets.The 4-connected domain method is used to extract the centroid positions of the remaining spots in the image and arrange them in descending order with brightness, which can effectively avoid the influence of isolated noise. According to the current baseline length and the known three-sided length of the beacon, and then according to the camera focal length and pixel size, the theoretical Euclidean distance between the three beacon imaging points can be calculated, and the Euclidean distance plus a certain tolerance can obtain four recognition thresholds. The extracted centroids are grouped according to the permutation selection, and all centroid groups that meet the recognition threshold are searched and recorded.The brightness sum of each group of centroids that meet the requirements is calculated in groups, and the maximum judgment is the group of centroids corresponding to the beacon. In the identified centroid group, the Euclidean distance between the two centroids is calculated separately, and the centroid corresponding to the top light can be found by comparison. The representation of the top beacon vector in the camera coordinate system c meas  v can be calculated by calibrating the completed camera model.Furthermore, the vector can be converted into the representation in the hexahedral prism coordinate system p meas  v by using the structural calibration results.

Calculating Euler angles of the rotation matrix
It is assumed that the absolute attitude in the current hexahedral prism coordinate system is expanded according to the 3-1-2 rotation, and the triaxial Euler angles are    , respectively.Then the rotation matrix from the hexahedral prism coordinate system to the world coordinate system can be expressed as: At this time, the inclination angles of the inclination sensor in the roll axial direction and the pitch axis are X a   and Z a   respectively.The inclination angles of the roll axis X p   and the pitch axis   in the hexahedral prism coordinate system can be obtained according to the conversion relationship between the inclination sensor and the hexahedral prism coordinate system.These two inclinations are the angles between the axis p X and the axis p Y and the geodetic horizon.
Representation of the axis p Z in the world coordinate system under the hexahedral prism coordinate system: Equation ( 2) is compared with the p Z v representation in the polar coordinate system: Similarly, the representation of the axis p X in the world coordinate system under the hexahedral prism coordinate system: Equation ( 4) is compared with the p X v representation in the polar coordinate system: is represented in the world coordinate system as: According to the matrix form expanded in Equation ( 1), the following known constants are simplified: Equation ( 6) can be rewritten as: According to the definition of azimuth in the polar coordinate system and the true azimuth angle of the baseline in the world coordinate system dir  given from the differential by the GNSS, it can be further obtained:   Finally, according to Equation ( 9), the Euler angle Y  in the rotation matrix can be calculated, and the absolute attitude of the measured object in the world coordinate system can be further obtained.

Experiments and analysis
We have made an embedded platform-based prototype to verify the feasibility of the proposed method, and some of the parameters of the prototype are as Table 1.We placed the target about 60 meters away from the measurement host and set it up according to the process.A complete measurement process of 840 times was performed at the same location.Finally, the gyro-theodolite is used to transmit the true azimuth angle and the two-axis inclination reference to the hexahedral prism system of the measuring host for comparison, and the measurement error of the Euler angle in the rotation matrix is shown in Figure 3. Figure 3 shows that the calculation accuracy of roll angle and pitch angle is close to the output accuracy of the two-axis inclination sensor, and the solution accuracy of azimuth angle is close to that of satellite differential true azimuth measurement.This proves that the proposed method has a high absolute attitude solution accuracy.
In addition, in order to further verify the practicability of the method in this paper, the time consumption on each measurement was recorded during the measurement, as shown in Figure 4.

Conclusion
In this paper, we propose an absolute attitude measurement method based on multi-sensor fusion.It solves the missed target with an optical camera, measures the horizontal angle with a dual-axis inclination sensor, and introduces true azimuth from satellite differential positioning.Experiments show that the proposed method can ensure the accuracy of absolute attitude measurement while taking into account the measurement efficiency, and basically realize the automatic measurement of absolute attitude.
However, due to the limited research time, the current measurement method does not model the spatial relationship between the antenna phase center and the main point of the image sensor, and can only reduce the error as much as possible through structural design.In addition, the spatial relationship between the phase center of the antenna at the target end and the center of the top beacon needs to be modeled, and sensors may need to be added to transmit and measure this spatial relationship.Therefore, the follow-up research direction will mainly focus on these two aspects, so as to further improve the method to improve the accuracy of absolute attitude measurement.
takes the optical center c O of the camera as the origin, and points from the image square focal plane to the object along the optical axis as the coordinate system c Z axis.The image square focal plane is the c c cX O Y plane.The a X axis and a Z axis of the inclination sensor coordinate system ( , , ) to the two-axis angle value of the biaxial inclination sensor, two Euler angles in the absolute attitude of the hexahedral prism coordinate system are obtained, and only the Euler angle Y  that constrains the yaw rotation remains.The baseline vector g meas  v

Figure 3 .
Figure 3. Euler angle measurement error.Figure3shows that the calculation accuracy of roll angle and pitch angle is close to the output accuracy of the two-axis inclination sensor, and the solution accuracy of azimuth angle is close to that of satellite differential true azimuth measurement.This proves that the proposed method has a high absolute attitude solution accuracy.In addition, in order to further verify the practicability of the method in this paper, the time consumption on each measurement was recorded during the measurement, as shown in Figure4.