Automatic calibration of airborne LiDAR installation angle based on point cloud conjugate matching

Airborne LiDAR plays an important role in island detection, shallow ocean topography mapping and intertidal zone detection. The installation angle error usually leads to deviation between overlapping strips, which affects the accuracy of LiDAR point cloud data. However, previous methods had complex requirements for routes and calibration field, leading to inefficient calibration. This paper proposes an automatic installation angle error calibration algorithm based on point cloud conjugate matching, which does not require strict route design and field selection. In the algorithm, the conjugated point cloud is extracted by selecting routes and processing point cloud, and the installation angle error is calculated by matching the conjugate point cloud. Airborne LiDAR data from Shanghai Institute of Optics and Fine Mechanics is utilized to verify the method which show that the overlap degree of conjugate point clouds can reach 90% in different routes. This method is expected to dramatically improve the efficiency of system calibration and the convenience of measurement.


Introduction
High precision and high efficiency underwater terrain detection is an important work for marine environment protection[1-6] and resource utilization.Airborne LiDAR [7,8] has become a new measurement technology developed rapidly in recent years.The accuracy of airborne LiDAR point cloud data is subject to measurement errors of each module, system errors [5,9,10] such as installation angle error [11,12], laser beam alignment tolerance [13] ， environmental errors such as wave refraction [14] and water scattering [15].In order to generate high-precision point cloud data, it is necessary to reduce the system error as much as possible.The installation angle error correction is an indispensable calibration procedure.The coordinate system of Inertial Measurement Unit (IMU) cannot completely coincide with the laser emission coordinate system.There is a small angle deviation, which is called the installation angle error.It is difficult to obtain the exact value of this deviation by direct measurement.
Installation angle error has a great influence on the accuracy of airborne LiDAR point cloud data, which usually leads to the displacement deviation and deformation of the overlapping strip.In previous studies, researchers calibrated the installation angle error by establishing the point-to-point relationship of the point cloud and simplifying the approximation of the system parameters.However, these methods have strict requirements on the selection of the calibration field and flight route.Calibration fields needs to contain an area with straight roads and spire architecture.Aircraft need to follow parallel and vertical flight paths.These requirements result in a complex and inefficient airborne LiDAR system calibration process.
In this paper, an automatic calibration method is proposed based on point cloud conjugate matching.The conjugated point cloud is extracted by selecting routes and processing point cloud, and the installation angle error is calculated by matching the conjugate point cloud.Airborne LiDAR data from Mapper5000[16] developed by Shanghai Institute of Optics and Fine Mechanics is used to verify the convenience of the method.This method is expected to effectively improve the correction of system calibration and improve the efficiency of researchers using LiDAR to detect shallow sea terrain.

Coordinate system
The installation angle error is difficult to obtain the error value by direct measurement.Therefore, it is necessary to arrange the calibration field to obtain the feature point cloud for error correction.Most airborne LiDAR systems adopt the palmer scanner [17].On ground, an approximately elliptical scanning pattern can be observed.The coordinate system of airborne LiDAR sensor is established, and the initial point cloud without error correction is calculated.We choose the east-north-up (ENU) system as the local cartesian coordinates coordinate.The coordinate origin is at the center of the mirror.The X axis is perpendicular to the direction of flight of the aircraft, the Y axis is along the direction of flight, and the Z axis is vertically upward.The unit vector P of the emerging light under the lidar sensor can be expressed as: sin( )cos( ) sin( )sin( ) cos( ) Where  is the azimuth angle;  is the zenith angle.The aircraft attitude angle matrix can be expressed as: Where pitch 、 roll 、 heading are the aircraft attitude data.The unit vector can be expressed as: Where P is the unit vector of the emerging light after the aircraft attitude angle changes.The initial point cloud without error correction is calculated by using the laser ranging results, the unit vector of the emerging light and the current latitude and longitude values.
The installation angle correction matrix is the same as that of the aircraft attitude.Then the unit vector of the emerging light can be expressed as: The point cloud can be obtained by bringing the error values of pitch angle, roll angle and heading angle into calculation.

Route selection and point cloud processing
The results of point cloud deviation caused by errors of heading angle, pitch angle and roll angle are different.The pitch angle error mainly causes the point cloud displacement deviation of the real position of the scanned object in parallel to the flight direction of the aircraft.The roll angle error causes the point cloud displacement deviation of the scanned object in perpendicular to the flight direction of the aircraft.The heading angle error will cause the scanned object to deform.Therefore, the route selection of heading angle, pitch angle and roll angle is divided into two categories.For heading angle, select areas with visible structures on a flight route.The two time point clouds before and after the elliptic scanning trajectory are distinguished as conjugate point clouds.For pitch angle and roll angle, the selected routes are required to fly in opposite directions and overlap.Select areas with visible buildings on the route.The point cloud of the same building in the two routes is selected as the conjugate point cloud.
The extracted conjugated point cloud was processed by cloth filtering [18] and threshold filtering.Then we extract the aircraft attitude data corresponding to the point cloud.The brief application steps of cloth filtering can be summarized as follows: select the appropriate scene model according to the point cloud information; set the appropriate mesh size according to the point cloud density; set the number of iterations required by the algorithm; and set the classification threshold of ground points and non-ground points.Threshold filtering can select the actual height of the building point cloud, set an appropriate height threshold, and extract the point cloud data larger than the set threshold.The aircraft attitude angle data corresponding to the point cloud is extracted, as well as the corresponding laser ranging results and latitude and longitude values.

Principle of installation angle error correction
Figure 1 shows the schematic diagram of the heading angle error correcting principle.When the laser scanning track passes through the ground building, the front and back semicircle of the track will scan the building at different times.The blue and red ovals in the figure represent lidar tracks over different time periods.If there is a heading angle deviation at this time, the point cloud of the target building at different times cannot coincide.According to this principle, a heading angle deviation value arrays are set.Bring this array into the coordinate formula to compute the new conjugate point cloud, and then calculate the overlap area of the conjugate point cloud.When the point cloud overlap area is the smallest, the data used is the installation heading angle.

Results
The method was verified by the Mapper5000 airborne LiDAR system in Haitang Bay experiment in Sanya, Hainan in September 2017.Mapper5000 was developed by Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences [16].The repetition rate of the laser pulse is 5kHz.The scanning shape is ellipsoidal.When the flight altitude is 300m, the ground point density can reach 1.1pts/m 2 .Select a single course according to the above method of heading angle error correction.The typical buildings in the selected area are shown in Figure 3(a).Extract the conjugate point cloud of the front and back semicircles of the scan trajectory passing through the building.As shown in Figure 3(b), the deformation of building point clouds in the presence of heading angle error is shown.Green and red point clouds represent conjugate point clouds.For the same building, due to the heading angle error, the shape of point clouds is deformed, and the conjugate point clouds cannot coincide.Figure 3(c) shows the conjugate point cloud results after correction of heading angle error.The angle value of heading error is 1.5°, and the point cloud overlap degree of buildings after correction is higher.After the heading angle error is corrected, the value of heading angle is brought into the point cloud calculation formula to obtain a new point cloud.There is no shape change for the new point cloud.According to the above method of pitch angle and roll angle correction, select two routes that fly opposite each other.Select two overlapping routes with obvious buildings, and use the point cloud processing method to extract the conjugated point clouds.As shown in Figure 4(a), the typical buildings in the selected area are obvious and relatively empty, which is suitable for the application area of the algorithm.We selected some point cloud data from other route.These routes are also not strictly designed, and most routes are not selected in the calibration field.Table 1 shows that overlapping point clouds of different routes are selected and the heading angle deviation of overlapping point clouds is calculated using the above method.The mean heading angle is 1.5°.Table 2 shows that overlapping point clouds of different routes are selected, and the displacement difference of overlapping point clouds is calculated using the above method, and the corresponding roll angle and pitch angle are calculated.The mean value of roll angle error is 1.19° and the mean value of pitch angle error is 0.31°.
Figure 5 shows the point cloud results of multiple overlapping lanes.The point cloud is in good agreement with the high-resolution map.Compared with the existing detection and calibration technology, this method reduces the need for the calibration field and route design.

Discussion and conclusion
The point cloud density of airborne LiDAR will affect the point cloud shape of buildings.Taking Mapper5000 as an example, when the flight altitude is 300m, the point cloud density is about 1 point per square meter.When a laser scan track passes over a building, it usually creates an unscanned area of about 1m at the edge of the building.When the unscanned area interval is 1m, and the aircraft flies 300m, the accuracy of the calculated installation angle is about 0.1°.Therefore, when the airborne Lidar point cloud density increases, the accuracy of system calibration can be improved.In the subsequent development of LiDAR systems, it is expected to use higher repetition frequency lasers and faster scanning motors to achieve high-density point cloud data.
In this paper, an automatic calibration method is proposed based on point cloud conjugate matching.The conjugated point cloud is extracted by selecting routes and processing point cloud, and the installation angle error is calculated by matching the conjugate point cloud.Using this method can improve the efficiency of the airborne LiDAR system calibration and reduce the requirements of the calibration field and route.This method is expected to effectively improve the correction of system calibration.It is expected to improve the efficiency of researchers using LiDAR to detect shallow sea terrain.

Fig. 1
Fig.1The schematic diagram of the heading angle error.

Figure 2
Figure2shows the schematic diagram of the calibration principle of pitch angle and roll angle.The routes with a certain overlap and opposite flight are selected.If there are roll angle error and pitch angle error at this time, the building point cloud in the overlapping area will have displacement deviation.The blue and red ovals in the figure represent lidar tracks over different routes.According to this principle, a set of displacement deviation array is set, which is divided into two groups of data along the direction of aircraft movement and the vertical direction of aircraft movement.The deviation value is added to the overall conjugate point cloud coordinates to obtain a new set of conjugate point cloud coordinates.The projected area of conjugated point cloud is calculated.When the overlap area of the conjugate point cloud is the smallest, two deviation values x  and y  are calculated.The formula for calculating the pitch angle is as follows:

Fig. 2
Fig.2The schematic diagram of the calibration principle of pitch angle and roll angle.

Fig. 3
Fig. 3 Heading angle error calibration.(a) Selection area (b) The conjugate point cloud results before correction of heading angle error (c) The conjugate point cloud results after correction of heading angle error.
Figure 4(b) shows the building point cloud before the pitch angle and roll angle correction.Green and red point clouds represent point clouds in different routes.It can be seen that due to the errors of the placement pitch angle and roll angle, the conjugate point cloud obviously has the displacement deviation of X axes and Y axes. Figure 4(c) shows the building point cloud after the calibration of the pitch angle and roll angle.The value of the pitch error is 0.3°, and the value of the roll error is 1.2°.After the correction, the building point cloud has a high coincidence degree.headingangle, roll angle and pitch angle error, we calculated the overlap degree of the conjugated point cloud.Before and after calibration, the overlap degree of conjugated point clouds increased from 50% to 90%.

Fig. 4
Fig. 4 Pitch and roll angle error calibration.(a) Selection area (b) The conjugate point cloud results before correction of angle error (c) The conjugate point cloud results after correction of angle error.

Fig. 5
Fig. 5 Point clouds of multiple overlapping flight paths.

Table 1 .
The value of heading angle error.

Table 2 .
The value of roll and pitch angle error.