LiDAR (Light Detection and Ranging) technology has revolutionized the way we perceive and analyze our surroundings, offering unparalleled accuracy and precision in mapping landscapes. However, like any technology, LiDAR is not immune to errors. Understanding the sources of these errors is crucial for ensuring the reliability and validity of LiDAR data analysis.
The laser rangefinder is the most important core device in the LiDAR system, and laser ranging is influenced by various factors, mainly divided into three categories:
1. Observation errors caused by the rangefinder. Every step in the laser ranging process introduces certain errors, but the main contribution comes from the processing, estimation, and time measurement errors of irregular laser echo signals after they have been reflected from the ground and propagated through space by electronic and optical circuits. These errors can be classified into two types: delay estimation errors and time measurement errors. 2. Atmospheric refraction errors. Similar to GPS signals, lasers passing through the atmosphere are also subject to atmospheric (tropospheric) refraction errors, the extent of which depends on the wavelength of the laser pulse. 3. Errors caused by terrain features. When laser pulse signals are emitted to the ground, different reflections occur due to the different physical characteristics of the terrain. When signals undergo diffuse reflection, a large amount of reflected signals are received, resulting in significant received noise. When signals are emitted to smooth surfaces, specular reflection occurs, which may cause the laser ranging signal to be "lost".
The positioning error of DGPS is the main factor affecting the accuracy of laser footprint. The dynamic positioning error of GPS mainly includes satellite orbit error, satellite clock error, receiver clock error, multipath effect, antenna phase center instability, as well as satellite constellation, observation noise, and correct solution of integer ambiguity. Although GPS positioning error is significant, it varies continuously with changes in the observation environment and is not easily eliminated or modeled. To mitigate the impact of GPS positioning errors, a common approach is to establish multiple uniformly distributed reference stations within the measurement area, ensuring that the distance from the reference station during GPS dynamic positioning calculation is not too far.
Attitude measurement error is one of the factors that affects the positioning accuracy of airborne LiDAR systems. In airborne LiDAR systems, the attitude of the rigid-body IMU (Inertial Measurement Unit) is typically aligned with that of the laser scanner. The accuracy of IMU attitude measurement is influenced by factors such as accelerometer scale errors, velocity sensor constant errors, random drift, and various system drifts of gyroscopes. The accuracy of attitude measurement inevitably affects the results of direct positioning.
Currently, in domestic civilian INS (Inertial Navigation System) systems, the accuracy levels are approximately: yaw 0.1°, roll and pitch 0.05°, and when combined with GPS/INS, the accuracy level is approximately 0.03°. Advanced GPS/INS combinations abroad achieve higher accuracy levels, with yaw at 0.01° and roll and pitch at 0.005°. These advancements in attitude measurement accuracy contribute significantly to improving the overall performance and precision of LiDAR-based positioning systems.
"Scan angle error" refers to deviations from the ideal state of the scanning system's rotational axis due to installation, design, or other reasons. This results in the starting angle of the scan angle not being zero, which is a fixed parameter that can be determined during factory calibration. Additionally, errors in the scan angle can arise from non-uniform rotation of the scanning motor, vibrations in the scanning mirror, and torque errors. These factors contribute to discrepancies between the actual scan angle and the expected scan angle, introducing errors into the calculated results.
The eccentricity error refers to the translation error between the coordinate systems of different instruments. Because each device has a different coordinate system center, it is necessary to accurately determine the relative positions of each device after installation, resulting in certain errors in the observed values. Generally, this kind of error is eliminated during data processing, and its impact is minimal. The eccentricity error mainly involves the measurement error of the distance from the GPS receiver antenna center to the point where the laser beam is emitted on the scanning mirror.
The error generated during instrument installation mainly refers to the systematic error of the laser beam deviating from the nadir point due to mounting, including yaw error, pitch error, and roll error.
In airborne LiDAR systems, the IMU (Inertial Measurement Unit) is tightly coupled with the laser scanner. During installation, efforts are made to ensure that the axes of the IMU and the laser scanner are precisely aligned and parallel. However, in reality, there is a small angular difference between the axes of the IMU and the laser scanner, known as the eccentric angle or mounting angle. During actual production, severe vibrations during aircraft landing may cause instrument displacement and interfere with data. Therefore, it is necessary to study the formation mechanism and impact of this angle and make accurate compensations.
In practical applications, it is essential to calibrate and accurately determine the size of the mounting angle, considering this value in various transformations. This ensures that the attitude data recorded by the IMU can be converted into accurate exterior orientation elements for photogrammetric production. This is particularly crucial in high-precision applications like airborne LiDAR, which directly locates on the ground.
Angular step error is the error generated by the angle recording device when recording angle changes, typically calibrated during factory production.
If we consider the scanning mirror as a rigid body, during rotation and oscillation, due to inertia, the actual angle of rotation will inevitably differ from the expected angle (the recorded value of the recording device). This is known as torque error. It is related to the elasticity and mechanical performance of the scanning mirror's rotation axis. At the edges of the scan swath, when the scanning mirror reaches its maximum acceleration, there is a slight difference between its actual mirror position and the calculated position by the encoder. However, at the center of the swath, there is no torque error because the acceleration is zero at that point.
In airborne LiDAR systems composed of POS (Position and Orientation System) and laser scanning systems, they are independent system components with their own time recording devices, and these times are mutually independent. To determine the three-dimensional coordinates of a laser point, it is essential to ensure that the positions, orientations, and range values of laser emission are observed at the same moment in time. If there is a time deviation or if this deviation cannot be precisely determined, it will result in positional errors. Furthermore, this error is variable and increases with the increasing rate of change in related measurements. For example, during smooth aircraft flight, the influence of time deviation between ranging and attitude measurement is minimal, as the attitude angle generally remains constant or changes very little. However, during turbulent flight, time deviation can significantly affect the measurement error of laser points.
The interpolation error arises from the difference in data recording (sampling) frequencies between the laser scanning ranging system and the POS (Position and Orientation System) system. Generally, the laser scanning ranging system has the highest frequency, up to 150kHz; followed by the IMU (Inertial Measurement Unit) at around 200Hz; and the DGPS (Differential Global Positioning System) has the lowest frequency, only about 20Hz. Therefore, to obtain the position and attitude of each laser footprint, interpolation of the POS data is necessary. Obviously, this introduces interpolation errors.
The data obtained from airborne LiDAR systems are typically based on the WGS-84 coordinate system. However, for most engineering purposes, the coordinates of the laser points need to be transformed into the local coordinate system. Due to anomalies in elevation, this transformation process can introduce errors, known as coordinate transformation errors.
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