# Performance Evaluation of MEMS-Based Automotive LiDAR Sensor and Its Simulation Model as per ASTM E3125-17 Standard

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## Abstract

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## 1. Introduction

**Figure 1.**ADAS used in modern vehicles, source: adapted with permission from [5].

## 2. Background

#### Working Principle of MEMS LiDAR Sensor

## 3. Devices Under Test

#### LiDAR FMU Model

## 4. ASTM E3125-17

#### 4.1. Specification of Targets

#### 4.2. Inside Test

#### 4.3. Symmetric Test

#### 4.4. Asymmetric Test

#### 4.5. Relative Range Test

#### 4.6. User-Selected Tests

## 5. Data Analysis

#### 5.1. Calculation of Sphere Target Derived Points Coordinates

- Initial segmentation: The measured data corresponding to sphere targets shall be segmented from the surroundings since the DUT measures every object in its work volume [22]. The exemplary point clouds before and after the initial segmentation are shown in Figure 13. The points obtained after the initial segmentation are regarded as ${S}_{i}$.
- Initial estimation: The initial estimation is used to find the coordinate of the derived point, which is the center of the point set ${S}_{i}$ received from the surface of the sphere target [22]. Several methods are introduced in the standard for the initial estimation, including manual estimation, the software provided by the DUT manufacturer, and the closest point method [22]. In this work, we have used the closest point method to estimate the derived point, as shown in Figure 14. First, the Euclidean distances of all the LiDAR points in data set ${S}_{i}$ to the origin of DUT are calculated. ${r}_{1}$ is determined as the median of the M closest distances of points from the DUT origin, as shown in Figure 14a). Afterward, the ${r}_{2}$ distance is calculated by adding the half radius $R/2$ of the sphere target to ${r}_{1}$, as illustrated in Figure 14b). The points within the radius ${r}_{2}$ are represented by ${S}_{r}$ [22].
- Initial least squares sphere fit: A non-linear, orthogonal, least squares sphere fit (LSSF) is used on the ${S}_{r}$ points to determine the initial derived point ${O}_{1}$. The general equation of the sphere can be expressed as follows [37]:$${(x-{x}_{c})}^{2}+{(y-{y}_{c})}^{2}+{(z-{z}_{c})}^{2}={R}^{2},$$$${x}^{2}+{y}^{2}+{z}^{2}=2x{x}_{c}+2y{y}_{c}+2z{z}_{c}+{R}^{2}-{x}_{c}^{2}-{y}_{c}^{2}-{z}_{c}^{2}.$$To apply the least squares fit on all points obtained from the sphere surface, Equation (3) can be expressed in vector/matrix notation for all points in the data set as given in [37]$$\overrightarrow{f}=\left(\right)open="["\; close="]">\begin{array}{c}{x}_{i}^{2}+{y}_{i}^{2}+{z}_{i}^{2}\\ {x}_{i+1}^{2}+{y}_{i+1}^{2}+{z}_{i+1}^{2}\\ \vdots \\ {x}_{n}^{2}+{y}_{n}^{2}+{z}_{n}^{2}\end{array}$$$$A=\left(\right)open="["\; close="]">\begin{array}{cccc}2{x}_{i}& 2{y}_{i}& 2{z}_{i}& 1\\ 2{x}_{i+1}& 2{y}_{i+1}& 2{z}_{i+1}& 1\\ \vdots & \vdots & \vdots & \vdots \\ 2{x}_{n}& 2{y}_{n}& 2{z}_{n}& 1\end{array}$$$$\overrightarrow{c}=\left(\right)open="["\; close="]">\begin{array}{c}{x}_{c}\\ {y}_{c}\\ {z}_{c}\\ {R}^{2}-{x}_{c}^{2}-{y}_{c}^{2}-{z}_{c}^{2}\end{array}$$$$\overrightarrow{f}=A\overrightarrow{c}.$$Here, the terms ${x}_{i}$, ${y}_{i}$, and ${z}_{i}$ represent the initial points of the data set, and ${x}_{n}$, ${y}_{n}$, and ${z}_{n}$ show the last points of the data set. Vector $\overrightarrow{f}$, matrix A, and vector $\overrightarrow{c}$ contain the expanded terms of the sphere, Equation (3). The vector $\overrightarrow{f}$ is the least squares fit method used to calculate the vector $\overrightarrow{c}$ that contains the sphere’s center coordinates and radius R. We used the Python Numpy library [38] least squares function to calculate the vector $\overrightarrow{c}$ that returns the sphere’s center ${O}_{1}$ coordinates and radius R. We can fit a sphere to our original data set by using the output of vector $\overrightarrow{c}$.
- Cone cylinder method: As recommended in the standard, in the next step, we refine the derived point ${O}_{1}$ coordinates through the cone cylinder method for the sphere target, as shown in Figure 15. A straight line ${O}_{1}O$ is drawn between the origin of DUT O and the initial derived point ${O}_{1}$ given in Figure 15a. A new point data set ${S}_{1}$ is generated from the initial segmented points ${S}_{i}$, which lie within both cones shown in Figure 15b,c [22].
- Second least squares sphere fit: Furthermore, an orthogonal non-linear LSSF is applied to the ${S}_{1}$ data set to find the updated derived point ${O}_{2}$ of the sphere target [22].
- Calculation of residuals and standard deviation: Afterward, the residual and standard deviation of every point within ${S}_{1}$ is calculated. The residual is the difference between the sphere-updated derived point ${O}_{2}$ and the points in the set ${S}_{1}$. In the next step, a new point set ${S}_{2}$ is defined, including the points whose absolute residual value is less than three times the standard deviation [22].
- Third least squares sphere fit: On the new set ${S}_{2}$, another LSSF is performed to find the updated derived point ${O}_{3}$ [22].
- Calculation of final derived point coordinates: The final derived point ${O}_{f}$ is determined after at least four more times repeating the previous procedures on ${S}_{i}$ as recommended in the standard. The newly derived point ${O}_{3}$ of the prior task is regarded as ${O}_{1}$ in the subsequent iteration tasks [22]. The comparison between the sphere’s point cloud after initial ${S}_{i}$ and final ${S}_{f}$ LSSF is given in Figure 16.

#### Test Acceptance Criteria

- According to the specifications of the DUT, the value of the distance MPE is equal to 20 $\mathrm{m}$$\mathrm{m}$. The distance error ${d}_{error}$ shall be less than 20 $\mathrm{m}$$\mathrm{m}$ [22]. The distance error ${d}_{error}$ between the two derived points can be written as:$${d}_{error}={d}_{meas}-{d}_{ref}.$$$${d}_{meas}=\sqrt{{({x}_{t}-{x}_{s})}^{2}+{({y}_{t}-{y}_{s})}^{2}+{({z}_{t}-{z}_{s})}^{2}},$$$${d}_{ref}=\sqrt{{({x}_{t}-{x}_{RI})}^{2}+{({y}_{t}-{y}_{RI})}^{2}+{({z}_{t}-{z}_{RI})}^{2}},$$
- In the case of the sphere target, the number of points in the ${S}_{2}$ data set shall be greater than 300 [22].

#### 5.2. Calculating Coordinates of Derived Point for the Plate Target

- Initial data segmentation: The DUT provides point clouds from all the objects within its work volume. Therefore, all points received from the objects of no interest need to be filtered, as shown in Figure 18. After initial segmentation, the rest of the points are regarded as the points set ${P}_{i}$ [22].
- Point selection for plane fit: Afterward, as required in the standard, the measured points from the edges of a rectangular plate are removed to fit a plane. This new point set is designated as ${P}_{1}$ [22].
- Least squares plane fit: The least squares plane fit (LSPF) method is applied on the point set ${P}_{1}$ defined in [42] to determine the location and orientation of the plate target. In addition, the standard deviation s of residual q of the plane fit is measured at each position of the plate target, as required in the standard. The plane fit residuals q are the orthogonal distances of every measured point of the plate target to its respective plane [22].
- Second data segmentation: The points whose residuals q are greater than double the corresponding standard deviation s were eliminated to visualize the best plane fit, as suggested in the standard. The updated point set is regarded as ${P}_{2}$. The number of points in ${P}_{2}$ should be more than 95% of all measured points from the plate target. The distance error ${d}_{error}$ and the root mean square (RMS) dispersion of the residuals q in ${P}_{2}$ are calculated using Equation (11) at the reference and each test position.$${q}_{rms}=\sqrt{\frac{{\sum}_{j=1}^{n}{q}_{j}^{2}}{N}},$$
- Derived point for plate target: Although the plate target has a fiducial mark, it was still challenging to determine a derived point precisely at the center of the plate target. Because of that, we use the 3D geometric center method on the point set ${P}_{2}$ to determine the derived point of the plate target, as recommended in the standard [22].

#### Test Acceptance Criteria

- The plate target should yield a minimum of 100 points in the point cloud [22].

## 6. Tests Setup and Results

#### 6.1. Inside Test

#### 6.2. Symmetric Test

#### 6.3. Asymmetric Tests

#### 6.4. Relative Range Tests

#### 6.5. Uncertainty Budget for ASTM E3125-17 Tests

#### 6.5.1. Uncertainty Budget of Real Measurements

- Contribution of RI (external influences): The RI has a range accuracy of ±$1.0$ $\mathrm{m}$$\mathrm{m}$, from $0.1$ $\mathrm{m}$ to 10 $\mathrm{m}$, with a confidence level of 95%. That is why we consider a $1.0$ $\mathrm{m}$$\mathrm{m}$ range uncertainty due to the RI for the ASTM E3125-17 tests because we place the targets within the 10 $\mathrm{m}$.
- Contribution of misalignment between the target and RI center (external influences): We aligned the center of the targets and the laser tracker of RI manually, and it is tough to always aim the laser tracker in the center of the sphere compared to the plate target. The highest standard uncertainty due to this factor was $3.9$ $\mathrm{m}$$\mathrm{m}$ for the top sphere of test position C of symmetric tests. However, for all the other tests, the standard uncertainty due to this factor is less than $3.9$ $\mathrm{m}$$\mathrm{m}$.
- Contribution of environmental conditions (external influences): All the tests were performed in the lab; therefore, environmental conditions’ influence on the measurements is negligible.
- Contribution of DUT internal influences (internal influences): The ranging error ${d}_{error}$ due to the internal influences of the DUT is $5.4$ $\mathrm{m}$$\mathrm{m}$ for all the tests. These internal influences include the ranging error ${d}_{error}$ due to the internal reflection of the sensor, detector losses, peak detection algorithm, and precision loss due to the spherical coordinates conversion to the cartesian coordinates. It should be noted that the distance error ${d}_{error}$ due to the sensor’s internal influences may vary depending on the temperature (see point 3 above).

#### 6.5.2. Uncertainty Budget of Simulation

- Contribution of DUT (internal influences): As given above, the LiDAR FMU simulation model considers the exact scan pattern, signal processing chain, and sensor-related effect of Blickfeld Cube 1. Therefore, the uncertainty due to the internal influences of the sensor model is $5.4$ $\mathrm{m}$$\mathrm{m}$ (see 4 above).
- Contribution of environmental conditions effect model (external influences): Environmental conditions effects are not modeled for these tests.

#### 6.6. Comparison of Simulation and Real Measurements Results

#### 6.7. User-Selected Tests

#### 6.8. Influence of ASTM Standard KPIs on Object Detection

## 7. Conclusions

## 8. Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ACC | Adaptive cruise control |

AOS | Average orientation similarity |

ADAS | Advanced driver-assistance system |

BSD | Blind-spot detection |

DUT | Device under test |

Effect Engine | FX engine |

FMU | Functional mock-up unit |

FMI | Functional mock-up interface |

FCW | Forward collision warning |

FoV | Field of view |

GNSS | Global navigation satellite system |

INS | Inertial navigation system |

LDWS | Lane departure warning system |

LiDAR | Light detection and ranging |

LDM | Laser and detector module |

LSSF | Least square sphere fit |

LSPF | Least square plane fit |

MPE | Maximum permissible error |

MEMS | Micro-electro-mechanical systems |

MAPE | Mean absolute percentage error |

OSI | Open simulation interface |

OEMs | Original equipment manufacturers |

OSMP | OSI sensor model packaging |

OPA | Optical phased array |

ODCS | Object detection confidence score |

RADAR | Radio detection and ranging |

RTDT | Round-trip delay time |

RI | Reference instrument |

RMS | Root mean square |

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**Figure 2.**Block diagram of MEMS LiDAR sensor, source: adapted with permission from [31].

**Figure 3.**Exemplary elliptical shape scan pattern of Cube 1. Specifications: $\pm {36}^{\circ}$ horizontal and $\pm {15}^{\circ}$ vertical FoV, 50 scan lines, $0.{4}^{\circ}$ horizontal angle spacing, frame rate $5.4$ $\mathrm{Hz}$, the maximum detection range is 250 $\mathrm{m}$, and the minimum detection range is $1.5$ $\mathrm{m}$.

**Figure 4.**Co-simulation framework of the LiDAR FMU model [23].

**Figure 5.**The sphere target is made of plastic with a special matt-textured varnish. It also has a removable magnetic base (M8 thread).

**Figure 6.**The rectangular laser scanner checkerboard has an area of 450 $\mathrm{m}$$\mathrm{m}$ × 420 $\mathrm{m}$$\mathrm{m}$ with a 1/4 inch adapter. As required in the standard, the LiDAR points from the edges of the plate target should not be considered for the point-to-point distance measurement. That is why the exclusion region is defined for the plate target. As a result, the active area of the plate target becomes 400 $\mathrm{m}$$\mathrm{m}$ × 400 $\mathrm{m}$$\mathrm{m}$. In addition, the fiducial mark is defined at the center of the plate target so the RI can aim directly at it for the reference distance measurement.

**Figure 7.**Inside Test layout. The distance d of both spheres A and B from the DUT shall be equal. The manufacturer should specify the distance d; if in case they do not specify it, the user can choose any value of distance.

**Figure 8.**Measurement method of the symmetric tests for the sphere targets A and B placed in orientations (

**a**–

**d**). $\alpha $ is an angular sweep between two targets, and $\phi $ is the angle between the bar and plane, source: adapted with permission from [22].

**Figure 9.**The layout of asymmetric tests for the sphere targets A and B placed in orientations (

**a**–

**c**). $\alpha $ is an angular sweep between two targets, and $\phi $ is the angle between the bar and plane, source: adapted with permission from [22].

**Figure 10.**Layout of relative range test, source: adapted from [24].

**Figure 11.**(

**a**) Layout of user-selected tests for 10% reflective planar Lambertian target. (

**b**) Layout of user-selected tests for the vehicle target.

**Figure 13.**(

**a**) Exemplary raw point cloud data from every object in the FoV of DUT. (

**b**) Segmented data representing point cloud ${S}_{i}$ of sphere target.

**Figure 14.**Closest point method. (

**a**) ${r}_{1}$ is the median of the M smallest distances of points from the DUT origin. (

**b**) ${r}_{2}={r}_{1}+{\textstyle \frac{R}{2}}$, where R denotes the radius of the sphere target, source: reproduced with permission from [22].

**Figure 15.**Cone cylinder method. (

**a**) A straight line ${O}_{1}O$ is drawn between the origin of the DUT and the initial derived point. (

**b**) A cone with an apex located at ${O}_{1}$ with an opening angle of $120{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$ is constructed. (

**c**) A cylinder collinear to ${O}_{1}O$ with $0.866\phantom{\rule{0.166667em}{0ex}}R$ is drawn, source: reproduced with permission from [22].

**Figure 16.**Comparison between sphere’s point clouds after initial ${S}_{i}$ and final ${S}_{f}$ LSSF. (

**a**) Sphere point cloud after initial LSSF ${S}_{i}$. (

**b**) Sphere point cloud after final LSSF ${S}_{f}$. The initial LSSF ${S}_{i}$ contains 381 points, and a $201.4$ $\mathrm{m}$$\mathrm{m}$ sphere diameter $\varnothing $ is estimated from it. The final LSSF ${S}_{f}$ contains 306 points, and a $201.2$$\mathrm{m}$$\mathrm{m}$ sphere diameter $\varnothing $ is estimated from it.

**Figure 18.**Initial data segmentation. (

**a**) Raw point cloud data from every object within the FoV of DUT. (

**b**) Refined data ${P}_{i}$ representing point cloud of plate target. The red dotted points are removed from the edges of the rectangular plate as the standard recommends. The effective width W and length L become 400 $\mathrm{m}$$\mathrm{m}$ × 400 $\mathrm{m}$$\mathrm{m}$.

**Figure 19.**Measurement setup for the inside test. (

**a**) Static simulation scene for the inside test. (

**b**) Real static scene for the inside test. The sphere targets were placed at a distance of $6.7$ $\mathrm{m}$ from the DUT in the simulation and real measurements. The reference distance ${d}_{ref}$ is calculated from the sensor’s origin to the target’s center. The coordinates of simulated and real objects and sensors are the same.

**Figure 20.**(

**a**) Real test setup of symmetric tests for test positions (

**A**–

**D**). (

**b**) Static simulation scenes of symmetric tests for test positions (

**A**–

**D**). The simulated and real sphere targets are placed in front of the sensor approximately at $5.5$ $\mathrm{m}$. The simulated and real bar length is 2 $\mathrm{m}$ long, while the distance between the sphere targets is $1.6$ $\mathrm{m}$. The coordinates of the simulated and actual objects and sensors are the same.

**Figure 21.**(

**a**) Real test setup of asymmetric tests for test positions (

**A**–

**C**). (

**b**) Static simulation scenes of asymmetric tests for test positions (

**A**–

**C**). The simulated and real sphere targets are placed in front of the sensor at approximately 5 $\mathrm{m}$. The simulated and real bar length is 2 $\mathrm{m}$ long, while the distance between the sphere targets is $0.8$ $\mathrm{m}$. The coordinates of the simulated and actual objects and sensors are the same.

**Figure 22.**(

**a**) Real setup for relative range tests. (

**b**) Static simulation scene for relative range tests. The coordinates of the actual and simulated sensor and target are the same.

**Figure 23.**Sunlight intensity is measured on a cloudy day. The intensity of sunlight was recorded with an ADCMT 8230E optical power meter in $\mathrm{W}$, and the sensor window size in $\mathrm{m}$${}^{2}$ is used to calculate the sunlight intensity in $\mathrm{W}$/$\mathrm{m}$${}^{2}$.

**Figure 24.**(

**a**) Simulated static scene of plate target. (

**b**) Static real scene of plate target. (

**c**) Simulated static scene of vehicle target. (

**d**) Real static scene of vehicle target. The ego vehicle is equipped with LiDAR, camera, and GNSS/INS RT3000 v3 from OxTS as a reference sensor with a range accuracy of $0.01$ $\mathrm{m}$. The LiDAR sensor was mounted on the vehicle’s roof, and the camera sensor was mounted on the front windscreen. The 10% reflective plate size is $1.5$ × $1.5$ $\mathrm{m}$. The sensor position in the vehicle’s coordinates is x = 2279 $\mathrm{m}$$\mathrm{m}$, y = 96 $\mathrm{m}$$\mathrm{m}$, and z = 2000 $\mathrm{m}$$\mathrm{m}$. The reference distance is measured from the sensor’s reference point to the center of the Lambertian plate and the target vehicle trunk.

**Figure 25.**Visualization of LiDAR point clouds obtained from the real and simulated Lambertian plate placed at 20 $\mathrm{m}$. We removed the LiDAR points from the edges of the plate for the data analysis, as recommended in the standard. Therefore, the effective area of the plate becomes $1.3$ × $1.3$ $\mathrm{m}$.

**Figure 26.**Visualization of LiDAR point clouds obtained from the real and simulated vehicle placed at 12 $\mathrm{m}$. The actual width and height of the vehicle is $1.76$ × $1.25$ $\mathrm{m}$, the LiDAR FMU and Cube 1 estimate $1.74$ × $1.23$ $\mathrm{m}$ and $1.74$ × $1.22$ $\mathrm{m}$, respectively. The vehicle’s height is calculated from the bottom of the rear bumper to the vehicle’s roof. The red dots in the picture show the difference between the simulated and real point clouds.

**Figure 27.**(

**a**) Comparison of the number of points ${N}_{points}$ received from the surface of simulated and real $10\%$ Lambertian plate. The simulation and real measurement results are consistent. (

**b**) Comparison of real and virtual LiDAR sensor distance error ${d}_{error}$ for the plate target. The distance error ${d}_{error}$ is below MPE ± 20 $\mathrm{m}$$\mathrm{m}$.

**Figure 28.**(

**a**) Comparison of the number of points ${N}_{points}$ received from the surface of the simulated and real vehicle. (

**b**) Comparison of the real and virtual LiDAR sensor distance error ${d}_{error}$ for the vehicle target. The distance error ${d}_{error}$ is below the MPE ±20 $\mathrm{m}$$\mathrm{m}$.

**Figure 29.**(

**a**) Real point cloud data: Black and red cuboids represent the ground-truth 3D orientation of the object and the 3D orientation of the object estimated by the object detection algorithm, respectively. (

**b**) Synthetic point cloud data: Black and red cuboids represent the ground-truth 3D orientation of the object and the 3D orientation of the object estimated by the object detection algorithm, respectively.

**Figure 30.**(

**a**) Exemplary visualization of accurate LiDAR point cloud obtained from a simulated vehicle at $12.0$ $\mathrm{m}$. (

**b**) Exemplary visualization of inaccurate LiDAR point cloud obtained from a simulated vehicle at $12.0$ $\mathrm{m}$. The actual width and height of the vehicle, $1.76$ × $1.25$ $\mathrm{m}$, can not be estimated from the inaccurate data.

**Figure 31.**Exemplary visualization of inaccurate simulated point cloud data: The object detection score drops to 67.8% from 95.3%, and a −$0.8$ $\mathrm{m}$ offset in position leads to a shift in the 3D bounding box of the object predicted by the object detection algorithm, shown with the red color cuboid. The black cuboid shows the ground-truth 3D orientation of the object.

**Table 1.**Parameter specification of Cube 1 LiDAR sensor [28].

Parameters | Values |
---|---|

Typical application range | 1.5 m–75 $\mathrm{m}$ |

Range resolution | <1 $\mathrm{c}$$\mathrm{m}$ |

Range precision (bias-free RMS, 10 $\mathrm{m}$, 50% reflective target). The standard deviation of range precision is one $\sigma $, which means a coverage of 68.26% [34]. | <2 $\mathrm{c}$$\mathrm{m}$ |

FoV (H × V) | ${70}^{\circ}$ × ${30}^{\circ}$ |

Horizontal resolution | $0.{4}^{\circ}$–${1}^{\circ}$ (user configurable) |

Vertical resolution | 5–400 scan lines per frame (user configurable) |

Frame rate | $1.5$ $\mathrm{Hz}$–50 $\mathrm{Hz}$ (user configurable) |

Laser wavelength | 905 $\mathrm{n}$$\mathrm{m}$ |

**Table 2.**Diameter $\varnothing $ and the cartesian coordinates of derived points of simulated and real sphere targets are obtained by LSSF.

x (mm) | y (mm) | z (mm) | Reference Diameter ${\varnothing}_{\mathit{ref}}$ (mm) | Measured Diameter ${\varnothing}_{\mathit{meas}}$ (mm) | Diameter Error ${\varnothing}_{\mathit{error}}$ (mm) | |
---|---|---|---|---|---|---|

Cube 1 | 1.3 | 6672.1 | 125.5 | 200.9 | 201.2 | 0.3 |

LiDAR FMU | 2.1 | 6672.4 | 121.2 | 200.0 | 200.1 | 0.1 |

Target | No. of Points (1) | Reference Distance to Target ${\mathit{d}}_{\mathit{ref}}$ (mm) | Measured Distance ${\mathit{d}}_{\mathit{meas}}$ (mm) | Distance Error ${\mathit{d}}_{\mathit{error}}$ (mm) | MPE (mm) | Pass/Fail | |
---|---|---|---|---|---|---|---|

Cube 1 | Front sphere | 354 | 6680.0 | 6689.0 | 9.0 | 20.0 | Pass |

Cube 1 | Back sphere | 358 | 6680.0 | 6686.3 | 6.3 | 20.0 | Pass |

LiDAR FMU | Front sphere | 358 | 6680.0 | 6685.5 | 5.5 | 20.0 | Pass |

LiDAR FMU | Back sphere | 358 | 6680.0 | 6685.5 | 5.5 | 20.0 | Pass |

Test Position | Target | No. of Points (1) | Reference Distance to Target ${\mathit{d}}_{\mathit{ref}}$ (mm) | Measured Distance ${\mathit{d}}_{\mathit{meas}}$ (mm) | Distance Error ${\mathit{d}}_{\mathit{error}}$ (mm) | MPE (mm) | Pass/Fail | |
---|---|---|---|---|---|---|---|---|

Cube 1 | A | Left sphere | 326 | 5050.0 | 5056.2 | 6.2 | 20.0 | Pass |

Cube 1 | A | Right sphere | 319 | 5050.0 | 5059.1 | 9.1 | 20.0 | Pass |

LiDAR FMU | A | Left sphere | 327 | 5050.0 | 5055.7 | 5.7 | 20.0 | Pass |

LiDAR FMU | A | Right sphere | 327 | 5050.0 | 5055.7 | 5.7 | 20.0 | Pass |

Cube 1 | B | Top sphere | 321 | 5050.0 | 5058.2 | 8.2 | 20.0 | Pass |

Cube 1 | B | Bottom sphere | 325 | 5050.0 | 5057.3 | 7.3 | 20.0 | Pass |

LiDAR FMU | B | Top sphere | 322 | 5050.0 | 5055.9 | 5.9 | 20.0 | Pass |

LiDAR FMU | B | Bottom sphere | 323 | 5050.0 | 5055.8 | 5.8 | 20.0 | Pass |

Cube 1 | C | Top sphere | 338 | 5050.0 | 5059.3 | 9.3 | 20.0 | Pass |

Cube 1 | C | Bottom sphere | 343 | 5050.0 | 5058.8 | 8.8 | 20.0 | Pass |

LiDAR FMU | C | Top sphere | 340 | 5050.0 | 5055.6 | 5.6 | 20.0 | Pass |

LiDAR FMU | C | Bottom sphere | 339 | 5050.0 | 5055.8 | 5.8 | 20.0 | Pass |

Cube 1 | D | Top sphere | 333 | 5050.0 | 5058.1 | 8.1 | 20.0 | Pass |

Cube 1 | D | Bottom sphere | 332 | 5050.0 | 5057.8 | 7.8 | 20.0 | Pass |

LiDAR FMU | D | Top sphere | 336 | 5050.0 | 5055.4 | 5.4 | 20.0 | Pass |

LiDAR FMU | D | Bottom sphere | 338 | 5050.0 | 5055.2 | 5.2 | 20.0 | Pass |

Test Position | Target | No. of Points (1) | Reference Distance to Target ${\mathit{d}}_{\mathit{ref}}$ (mm) | Measured Distance ${\mathit{d}}_{\mathit{meas}}$ (mm) | Distance Error ${\mathit{d}}_{\mathit{error}}$ (mm) | MPE (mm) | Pass/Fail | |
---|---|---|---|---|---|---|---|---|

Cube 1 | A | Center sphere | 332 | 5050.0 | 5057.7 | 7.7 | 20 | Pass |

Cube 1 | A | Left sphere | 323 | 5050.0 | 5058.3 | 8.3 | 20 | Pass |

LiDAR FMU | A | Center sphere | 339 | 5050.0 | 5055.7 | 5.7 | 20 | Pass |

LiDAR FMU | A | Left sphere | 325 | 5050.0 | 5055.9 | 5.9 | 20 | Pass |

Cube 1 | B | Top sphere | 319 | 5050.0 | 5058.2 | 8.2 | 20 | Pass |

Cube 1 | B | Center sphere | 328 | 5000.0 | 5006.9 | 6.9 | 20 | Pass |

LiDAR FMU | B | Top sphere | 323 | 5050.0 | 5055.5 | 5.5 | 20 | Pass |

LiDAR FMU | B | Center sphere | 331 | 5000.0 | 5005.4 | 5.4 | 20 | Pass |

Cube 1 | C | Top sphere | 317 | 5000.0 | 5008.8 | 8.8 | 20 | Pass |

Cube 1 | C | left sphere | 322 | 5050.0 | 5057.4 | 7.4 | 20 | Pass |

LiDAR FMU | C | Top sphere | 323 | 5000.0 | 5005.7 | 5.7 | 20 | Pass |

LiDAR FMU | C | Left sphere | 324 | 5050.0 | 5055.5 | 5.5 | 20 | Pass |

Target Position | No. of Points (1) | Reference Distance to Target ${\mathit{d}}_{\mathit{ref}}$ (mm) | Measured Distance ${\mathit{d}}_{\mathit{meas}}$ (mm) | Distance Error ${\mathit{d}}_{\mathit{error}}$ (mm) | MPE (mm) | ${\mathit{q}}_{\mathit{rms}}$ (mm) | Pass/Fail | |
---|---|---|---|---|---|---|---|---|

Cube 1 | AB | 451 | 2000.0 | 2005.7 | 5.7 | 20 | 1.5 | Pass |

Cube 1 | AC | 290 | 3000.0 | 3005.7 | 5.7 | 20 | 1.7 | Pass |

Cube 1 | AD | 208 | 4000.0 | 4007.3 | 7.3 | 20 | 1.8 | Pass |

LiDAR FMU | AB | 462 | 2000.0 | 2005.5 | 5.5 | 20 | 1.1 | Pass |

LiDAR FMU | AC | 298 | 3000.0 | 3005.5 | 5.4 | 20 | 0.6 | Pass |

LiDAR FMU | AD | 217 | 4000.0 | 4005.5 | 5.4 | 20 | 0.3 | Pass |

Target | Distance (m) | ODCS (%) | AOS (%) | |
---|---|---|---|---|

Cube 1 | Vehicle | 12.0 | 94.2 | 98.1 |

Cube 1 | Vehicle | 15.5 | 92.8 | 97.7 |

Cube 1 | Vehicle | 20.0 | 90.6 | 97.2 |

LiDAR FMU | Vehicle | 12.0 | 95.3 | 98.8 |

LiDAR FMU | Vehicle | 15.5 | 94.6 | 98.6 |

LiDAR FMU | Vehicle | 20.0 | 93.3 | 98.5 |

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**MDPI and ACS Style**

Haider, A.; Cho, Y.; Pigniczki, M.; Köhler, M.H.; Haas, L.; Kastner, L.; Fink, M.; Schardt, M.; Cichy, Y.; Koyama, S.;
et al. Performance Evaluation of MEMS-Based Automotive LiDAR Sensor and Its Simulation Model as per ASTM E3125-17 Standard. *Sensors* **2023**, *23*, 3113.
https://doi.org/10.3390/s23063113

**AMA Style**

Haider A, Cho Y, Pigniczki M, Köhler MH, Haas L, Kastner L, Fink M, Schardt M, Cichy Y, Koyama S,
et al. Performance Evaluation of MEMS-Based Automotive LiDAR Sensor and Its Simulation Model as per ASTM E3125-17 Standard. *Sensors*. 2023; 23(6):3113.
https://doi.org/10.3390/s23063113

**Chicago/Turabian Style**

Haider, Arsalan, Yongjae Cho, Marcell Pigniczki, Michael H. Köhler, Lukas Haas, Ludwig Kastner, Maximilian Fink, Michael Schardt, Yannik Cichy, Shotaro Koyama,
and et al. 2023. "Performance Evaluation of MEMS-Based Automotive LiDAR Sensor and Its Simulation Model as per ASTM E3125-17 Standard" *Sensors* 23, no. 6: 3113.
https://doi.org/10.3390/s23063113