Analysis, Quantification, and Discussion of the Approximations Introduced by Pulsed 3-D LiDARs

Abstract

LiDARs are considered essential for the environmental sensing required by most ADAS, including autonomous driving. Such has led to significant investments resulted in the availability of countless measuring systems that are increasingly performing and less expensive. Nevertheless, the extremely high speed of light still leads to a non-negligible quantization error in the direct time-of-flight (ToF) measure at the base of pulsed LiDARs -the leading technology for automotive applications. Hence, pulsed 3D-LiDARs analyze the surrounding by approximating and deforming it on concentric spheres whose radii are quantized with a quantization step that, for most commercial systems, is on the order of some centimeters. The deformation and error introduced by such quantization can thus be significant. In this study, we point out the approximations and assumptions intrinsic to 3D-LiDARs and propose a measurement procedure that, through the analysis of the fine variations of the target position, allows an accurate investigation of the axial resolution and error -probably among the few limitations still affecting this technology. To the best of our knowledge, this is the first study focused on the detailed analysis of the quantization error in 3D-LiDARs. The proposed method has been tested on one of the most popular 3D-LiDARs -namely the MRS 6000 by Sick. The obtained results revealed for the MRS 6000 a quantization step of about 6 cm (ToF quantization of about 0.4 ns) and an axial error normally distributed with experimental standard deviation of about 30 mm.

A simple method for the preliminary analysis and benchmarking of automotive LiDARs in fog

“…4 shows the trends of: i) the estimate of the target distance, d, obtained from the IUT, ii) the absorbance, A, measured by LD and PD and, iii) the contrast, C, measured by the camera as the concentration of the fog droplets inside the fog chamber increases. As described in subsection II-C, for direct ToF LiDARs, the radial distance is a quantized variable that can take on a finite number of values, the bins [5]. As shown in Fig.…”

“…For each acquired PC, the proposed procedure involves analyzing only one of the beams generated by the IUT. Indeed, LiDARs typically scan the surrounding environment by sampling it along a set of predetermined directions (elevation angle ϕ and azimuth angle θ) [5]. The proposed method thus involves extracting the value of the radius of the investigated beam -the distance, d, at which the IUT estimates the fixed target.…”

“…3. For direct time-of-flight (ToF) LiDARs, the radial distance of each point of the PC is a quantized variable that can take on a finite number of values equispaced of the radial quantization step δr [5]. It is, therefore, possible to calculate the empirical probability, P (d j , x i , x i+1 ), that the IUT estimates that the target is at distance d j when the fog level is in the [x i , x i+1 ) interval.…”

“…Assuming that the distance d j is the one that best approximates the true target distance d T , the ideal LiDAR should have a probability equal to 1 for d = d j regardless of the value of x (and the probability for d ≠ d j should be zero). Actually, as discussed by Cattini et al [5], due to the noise, even in the absence of absorbing and scattering particles along the optical path, the estimate of the target distance provided by real LiDARs is not a deterministic variable but a discrete random variable that can assume the value of a certain number of bins in the proximity of the true target distance. Therefore, even in the absence of fog, in general P (d ≠ d j ) > 0.…”

LiDARs detected signal and Target distance estimation: measurement errors from Target reflectance and multiple echos

“…This operation must be carefully carried out, to ensure the correct attribution of the PC values to the Target. Selection of the PC values must take into account that the scanning LiDAR senses the environment sampling it along fixed polar directions (elevation angle ϕ and azimuth angle θ) and due to the noise, the estimated distance retrieved by a LiDAR is a random variable that can assume a value among discrete bins, whose width represents the IUT resolution R, around the actual position of the Target [12]. Therefore, having fixed the distance d T of the Target with known reflectance r, the mean value of the Target distance is estimated as the mean distance of the i − th distance d r T i :…”