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The Universal Lidar Error Model
Abstract
Methods to adjust multiple lidar datasets, to adjust lidar with other modalities, and to quantify lidar accuracy are limited. While lidar sensor modeling, error propagation, and data adjustment exist in literature, there are no known implementations supporting all three operations within existing file formats and processing architectures. The Universal Lidar Error Model (ULEM) has been developed to meet the community’s need for rigorous error propagation and data adjustment. ULEM exploitation allows one to develop predicted error covariance at single points and full covariance among multiple points. It defines a standardized set of adjustable parameters, provides for the modeling and storage of correlations and cross-correlations among parameters, and stores the data within existing file formats. This paper provides an introduction to ULEM, its metadata requirements, and its model exploitation methods. It concludes with an example of ULEM error modeling, showing the predicted uncertainty agrees well with errors calculated from surveyed control.
... The LiDAR systems used in vegetation monitoring usually exploit near-infrared light to scan vegetation stands, single components (e.g., trees), or even subcomponents (e.g., branches and leaves) [10,11]. In fact, a narrow laser beam can map physical features with very high spatial resolution, e.g., an aircraft can map the target at decimetric resolution [12]. A 3-dimensional (3D) dense cloud of laser pulses resulting from a typical ALS campaign represents a collection of numerous 3D points, each having, at least, geographic position and height information. ...
... Remote Sens. 2020,12, 1877 ...
... Remote Sens. 2020, 12, 1877 ...
Protection and recovery of natural resource and biodiversity requires accurate monitoring at multiple scales. Airborne Laser Scanning (ALS) provides high-resolution imagery that is valuable for monitoring structural changes to vegetation, providing a reliable reference for ecological analyses and comparison purposes, especially if used in conjunction with other remote-sensing and field products. However, the potential of ALS data has not been fully exploited, due to limits in data availability and validation. To bridge this gap, the global network for airborne laser scanner data (GlobALS) has been established as a worldwide network of ALS data providers that aims at linking those interested in research and applications related to natural resources and biodiversity monitoring. The network does not collect data itself but collects metadata and facilitates networking and collaborative research amongst the end-users and data providers. This letter describes this facility, with the aim of broadening participation in GlobALS.
... The results show that the targets can be accurately located within point clouds from typical scanning parameters to <2 cm σ, and that including observation weights in the algorithm based on propagated point position uncertainty leads to more accurate results. , and fusing it with other geospatial datasets, such as photography [5]. Accuracy assessment of geospatial data typically involves the use of check-points, independently surveyed targets, or features within the captured scene, to produce statistical measures of accuracy often reported using the root mean square error (RMSE). ...
... The covariance matrix of the target template transformation parameters, Σ ∆∆ , may be calculated using Equation (5). The elements of Σ ∆∆ . ...
Lidar from small unoccupied aerial systems (UAS) is a viable method for collecting geospatial data associated with a wide variety of applications. Point clouds from UAS lidar require a means for accuracy assessment, calibration, and adjustment. In order to carry out these procedures, specific locations within the point cloud must be precisely found. To do this, artificial targets may be used for rural settings, or anywhere there is a lack of identifiable and measurable features in the scene. This paper presents the design of lidar targets for precise location based on geometric structure. The targets and associated mensuration algorithm were tested in two scenarios to investigate their performance under different point densities, and different levels of algorithmic rigor. The results show that the targets can be accurately located within point clouds from typical scanning parameters to <2 cm σ , and that including observation weights in the algorithm based on propagated point position uncertainty leads to more accurate results.
... ;Habib et al. (2008);Rodarmel et al. (2015)). Thus, a full uncertainty analysis is not repeated here; only the effect of heading uncertainty on the positional uncertainty of a point cloud is discussed to provide the theoretical foundation for the experiment of this study.The coordinates of a point observed by a UAS-lidar system can be expressed within a local level reference frame (north-east-down) by: the fundamental rotations around the x, y, z axes of a frame, respectively; , , are the roll, pitch, and heading angles, respectively, of the navigation (n) reference frame of the GNSS/INS sensor relative to the local level (l) frame;represents the boresight rotations from the lidar sensor (s) frame to the n frame; , , are the range, horizontal angle, and vertical angle, respectively, from the lidar sensor to the observed point (p) in the s frame; , , are the x, y, z lever-arm offsets, respectively, from the center of the GNSS/INS sensor (i.e., center of the IMU) to the origin of the lidar sensor measured in the n frame; , , are the X, Y, Z coordinates of the center of the GNSS/INS sensor in the l frame, respectively. ...
Three-dimensional mapping of natural and built environments using lidar sensors and digital cameras onboard unoccupied aerial systems has gained wide interest within academic research and industrial applications. This research uses case studies to showcase the development of the first complete and virtually fully open-source lidar and imagery-based mobile mapping system that is low-cost, adaptable, and has been proven to produce high-accuracy geospatial data.
The first case study examines the position and orientation accuracy of the specific GNSS/INS sensor used within the mobile mapping system developed as part of this work. The study investigates the impacts of using a single-antenna versus a dual-antenna GNSS/INS sensor for UAS-lidar mapping applications. Specifically, the impact heading orientation uncertainty has on the spatial accuracy of directly georeferenced point clouds is analyzed. Results indicate that substantial improvements in heading accuracy and spatial accuracy can be realized with a dual-antenna GNSS/INS sensor.
The second case study examines the accuracy of the specific lidar sensor used within the mobile mapping system developed as part of this work. The study investigates the angular observation model of Risley prism beam steering mechanisms for applications within lidar-based laser scanning systems. Specifically, methods for assessing the accuracy of the angular observations and estimating calibration parameters for the lidar sensor are developed. Results indicate that angular observations from the specific lidar sensor are more accurate than specified by the manufacturer and that estimating new calibration parameters can improve the spatial accuracy of the sensor observations.
The third case study examines the novel hardware integration and software development aspects of the mobile mapping system developed as part of this work. The study investigates the manufacturing techniques, calibration procedures, data collection operations, and data processing paradigms involved with mobile mapping systems. Specifically, a complete process is developed that produces a mobile mapping hardware sensor and data processing software. Results indicate the solution is robust and produces high-accuracy geospatial data.
This research showcases the engineering aspects from multiple disciplines that are involved in the design, production, operation, and assessment of mobile mapping systems for unoccupied aerial systems. A fully comprehensive description of a novel lidar and imagery-based mobile mapping solution is developed to enable replication and thus decrease the barriers to entry and increase global access to geospatial data which can impact scientific discovery in a wide variety of applications.
... In this section, the influence of intercorrelation is simulated assuming identical correlation coefficients ranging from 0.1 to 1.0, with an increment of 0.1 [see (7)]. We recall here that intercorrelation in LiDAR point clouds has not been studied in detail in the literature [23]. Though the assumption of identical intercorrelation may not reflect the actual case for an airborne LiDAR data, the test in this section will show how large this influence is, which motivates further studies on this topic in the future, because it is a significant source of additional uncertainty. ...
Airborne light detection and ranging (lidar) has been widely applied to terrain modelling, but a gridded Digital Elevation Model (DEM) is usually adopted for most applications. The lidar point cloud is transformed to grids by interpolation methods, with Triangulated Irregular Network (TIN) linear interpolation most widely used. Both horizontal and vertical uncertainties exist in a point cloud dataset, and should therefore be propagated to grid points during spatial interpolation. Studies in the literature have either considered the vertical component only, or both components separately. This article proposes to apply the general law of propagation of variances (GLOPOV) to estimate vertical uncertainties at grid points for TIN linear interpolation considering both horizontal and vertical uncertainties of the point cloud simultaneously. The experimental results with an airborne lidar dataset indicate that underestimation of grid point vertical uncertainties may be derived if only vertical uncertainties of the point cloud are considered; the amount of underestimation depends on the terrain slope. This article suggests that both horizontal and vertical uncertainties of point cloud should be considered during TIN linear spatial interpolation. The effect of correlated errors between lidar points is also examined. It is shown that if significant correlation between points is ignored, the resulting propagated TIN error is underestimated by a factor of almost two.
... As a result, evaluating the mapping accuracy of a GNSS/INS sensor based on the manufacturer's specifications can be difficult. Several published works have rigorously analyzed the effects of trajectory errors on point cloud coordinate accuracies for both UAS-based (e.g., [14]) and occupied aircraftbased laser scanning systems (e.g., [22][23][24]). Thus, a full error analysis is not repeated here; only the effect of heading precision on the positional precision of a point cloud is discussed in order to provide the theoretical foundation for the experiment of this study. ...
Data collected from a moving lidar sensor can produce an accurate digital representation of the physical environment that is scanned, provided the time-dependent positions and orientations of the lidar sensor can be determined. The most widely used approach to determining these positions and orientations is to collect data with a GNSS/INS sensor. The use of dual-antenna GNSS/INS sensors within commercial UAS-lidar systems is uncommon due to the higher cost and more complex installation of the GNSS antennas. This study investigates the impacts of using a single-antenna and dual-antenna GNSS/INS MEMS-based sensor on the positional precision of a UAS-lidar generated point cloud, with an emphasis on the different heading determination techniques employed by each type of GNSS/INS sensor. Specifically, the impacts that sensor velocity and acceleration (single-antenna), and a GNSS compass (dual-antenna) have on heading precision are investigated. Results indicate that at the slower flying speeds often used by UAS (≤5 m/s), a dual-antenna GNSS/INS sensor can improve heading precision by up to a factor of five relative to a single-antenna GNSS/INS sensor, and that a point of diminishing returns for the improvement of heading precision exists at a flying speed of approximately 15 m/s for single-antenna GNSS/INS sensors. Additionally, a simple estimator for the expected heading precision of a single-antenna GNSS/INS sensor based on flying speed is presented. Utilizing UAS-lidar mapping systems with dual-antenna GNSS/INS sensors provides reliable, robust, and higher precision heading estimates, resulting in point clouds with higher accuracy and precision.
... The mainstream idea for the error rectification of point cloud data captured by a LiDAR system is based on the LiDAR georeferencing equations, in which, all the possible error sources of a LiDAR system are considered to build and resolve error equations [18,19,22,23]. The core procedure is the construction of the observation error equation that is usually achieved by tie points, and the error parameters can be solved by a matrix operation. ...
Point cloud rectification is an efficient approach to improve the quality of laser point cloud data. Conventional rectification methods mostly relied on ground control points (GCPs), typical artificial ground objects, and raw measurements of the laser scanner which impede automation and adaptability in practice. This paper proposed an automated rectification method for the point cloud data that are acquired by an unmanned aerial vehicle LiDAR system based on laser intensity, with the goal to reduce the dependency of ancillary data and improve the automated level of the rectification process. First, laser intensity images were produced by interpolating the intensity data of all the LiDAR scanning strips. Second, a scale-invariant feature transform algorithm was conducted to extract two dimensional (2D) tie points from the intensity images; the pseudo tie points were removed by using a random sample consensus algorithm. Next, all the 2D tie points were transformed to three dimensional (3D) point cloud to derive 3D tie point sets. After that, the observation error equations were created with the condition of coplanar constraints. Finally, a nonlinear least square algorithm was applied to solve the boresight angular error parameters, which were subsequently used to correct the laser point cloud data. A case study in Shehezi, Xinjiang, China was implemented with our proposed method and the results indicate that our method is efficient to estimate the boresight angular error between the laser scanner and inertial measurement unit. After applying the results of the boresight angular error solution to rectify the laser point cloud, the planar root mean square error (RMSE) is 5.7 cm and decreased by 1.1 cm in average; the elevation RMSE is 1.4 cm and decreased by 0.8 cm in average. Comparing with the stepwise geometric method, our proposed method achieved similar horizontal accuracy and outperformed it in vertical accuracy of registration.
The use of small unmanned aircraft systems to collect 3-D topographic data for a variety of geophysical applications has exploded in the last decade. These data are often produced from imagery using structure-from-motion (SfM) algorithms with or without ground control. While the accuracy of these data products has been assessed in a number of efforts, comparatively little focus has been placed on estimating spatially varying ground-space uncertainties in final data products using rigorous error propagation methodology and uncertainty estimation. Uncertainty estimates of the final 3-D products would provide users a more complete understanding of the quality of the products and therefore the applicability of the product. This paper illustrates an end-to-end workflow, using direct geopositioning and SfM techniques to create 3-D topographic point clouds with rigorously propagated accuracy estimates. Included is a method to quantify uncertainty in dense matching and incorporate those contributions into the final ground covariance. The uncertainty estimates are captured as metadata in the point cloud file using standard formats for exploitation. These estimates are critical to the downstream analysis, exploitation, and fusion of data sets; especially in scenarios where ground truth is not an option. The testing of this end-to-end process is described; data from a field campaign were processed without using mensurated control, and the resultant point clouds were compared to surveyed points to evaluate the predicted accuracy. Predicted accuracies bounded observed errors in the horizontal and vertical components. Future enhancements are also proposed.
Error estimates of lidar observations are obtained by applying the General Law of Propagation of Variances (GLOPOV) to the direct georeferencing equation. Within the formulation of variance propagation, the most important consideration is the values used to describe the error of
the hardware component observations including the global positioning system, inertial measurement unit, laser ranger, and laser scanner (angular encoder noise and beam divergence). Data tested yielded in general, pessimistic predictions as 85 percent of residuals were within the predicted
error level. Simulated errors for varying scan angles and altitudes produced horizontal errors largely influenced by IMU subsystem error as well as angular encoder noise and beam divergence. GPS subsystem errors contribute the largest proportion of vertical error only at shallow scan angles
and low altitudes. The transformation of the domination of GPS related error sources to total vertical error occurs at scan angles of 23°, 13°, and 8° at flying heights of 1,200 m, 2,000 m, and 3,000 m AGL, respectively.
Although laser altimetry has been used for the production of digital elevation models in different countries for several years, the completely automatic derivation of a DEM from the raw laser altimetry measurements is not yet mature. The two major problems are the detection of and correction for systematic errors in the laserscanner data and the separation of ground points from points resulting from reflections on buildings, vegetation or other objects above ground. This paper discusses strategies for dealing with these two steps in the production of a DEM from raw laser altimetry data. Results are shown of experiments with different data sets.
The accuracy of lidar systems and the removal of systematic errors have received growing attention in recent years. The level of accuracy and the additional processing that is needed for making the raw data ready to use are affected directly by the systematic errors in the laser
data. It is evident that calibration of the lidar system, both laboratory and in-flight, are mandatory to alleviate these deficiencies. This paper presents an error recovery model that is based on modeling the system errors and on defining adequate control information. The association of the
observations and control information, and configurations that enhance the reliability of the recovered parameters, are also studied here in detail. The application of the model is demonstrated on two of the main error sources in the system, the mounting and the range bias.
Whether statistically representing the errors in the estimates of sensor metadata associated with a set of images, or statistically representing the errors in the estimates of 3D location associated with a set of ground points, the corresponding “full” multi-state vector error covariance matrix is critical to exploitation of the data. For sensor metadata, the individual state vectors typically correspond to sensor position and attitude of an image. These state vectors, along with their corresponding full error covariance matrix, are required for optimal down-stream exploitation of the image(s), such as for the stereo extraction of a 3D target location and its corresponding predicted accuracy. In this example, the full error covariance matrix statistically represents the sensor errors for each of the two images as well as the correlation (similarity) of errors between the two images. For ground locations, the individual state vectors typically correspond to 3D location. The corresponding full error covariance matrix statistically represents the location errors in each of the ground points as well as the correlation (similarity) of errors between any pair of the ground points. It is required in order to compute reliable estimates of relative accuracy between arbitrary ground point pairs, and for the proper weighting of the ground points when used as control, in for example, a fusion process. This paper details the above, and presents practical methods for the representation of the full error covariance matrix, ranging from direct representation with large bandwidth requirements, to high-fidelity approximation methods with small bandwidth requirements.
Although various rigorous lidar error models already exist and examples of a-posteriori studies of lidar data accuracies verified with field-work can be found in the literature, a simple measure to define a-priori error sizes is not available. In this paper, the lidar error contributions
are described in detail: the basic systematic error sources, the flight-mission-related error sources, and the target-characteristic-related error sources. A review of the different error-source sizes is drawn from the literature in order to define the boundary conditions for each error size.
Schenk’s geolocation equation is used as a basis for deriving a simplified error model. This model enables a quick calculation and gives a-priori plausible values for the average and maximum error size, independent of the scan and heading angles as well as being independent of any specific
lidar system’s characteristics. Additionally, some notes are provided for assistance when ordering lidar data, to enable easier a-posteriori quality control.
The primary purpose of airborne laser altimetry is to determine the ellipsoidal or geoidal coordinates of a series of points on the surface of the Earth. An aircraft that is instrumented with a laser altimeter, an inertial navigation system, and a Global Positioning System (GPS) receiver provides the following data: (1) laser range to the Earth's surface, (2) measurement platform spatial location and orientation, and (3) aircraft kinematic trajectory in ellipsoidal coordinates. These data are sufficient to determine (georeference) the three dimensional coordinates of the points where the beam from a pulsed laser intersects the Earth. We develop the exact equations necessary to georeference the laser points. We also discuss calibrating the laser pulse timing, laser positioning and alignment relative to the local-level reference frame, correcting atmospheric refraction effects on the laser pulse, and time synchronizing the various data streams. We use a laser altimeter mission flown over Lake Crowley in California to demonstrate our methods. For seven passes over the lake, our heights agreed with a local tide gauge at the Lake Crowley dam to better than 10 cm with standard deviations ranging from 1-4 cm. The horizontal accuracy of the georeferenced points is still problematic; we have no three-dimensional control points that the laser has hit. Geometrical considerations indicate that the measured horizontal location of the laser footprint is within two metres of the true location when the aircraft altitude is less than one kilometre above the local surface.
An overview of basic relations and formulas concerning airborne laser scanning is given. They are divided into two main parts, the first treating lasers and laser ranging, and the second one referring to airborne laser scanning. A separate discussion is devoted to the accuracy of 3D positioning and the factors influencing it. Examples are given for most relations, using typical values for ALS and assuming an airplane platform. The relations refer mostly to pulse lasers, but CW lasers are also treated. Different scan patterns, especially parallel lines, are treated. Due to the complexity of the relations, some formulas represent approximations or are based on assumptions like constant flying speed, vertical scan, etc. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Airborne laser scanning; Terminology; Basic relations; Formulas; 3D accuracy analysis 1. Introduction In this article, some basic relations and formulas Z. Z. concerning a laser ranging, and b airborne laser sc...