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Identifying linear time-variant (LTV) systems has been of great interest for many decades already and an important problem in many engineering applications. This paper proposes to use a double periodic system approximation for the characterization of LTV radar channels. Hereby, a two-dimensional Fourier series is used to approximate the time-variant transfer function in both time and frequency domain. By observing the system's response corresponding to an appropriate input signal, this paper presents a mathematical derivation of how to determine the Fourier coefficients. In practice, these Fourier coefficients are often approximated by assuming the LTV system to be piecewise constant in time domain. This paper establishes an analytical relationship between the original Fourier coefficients and the approximated ones and it investigates how the Fourier coefficients get distorted due to this assumption. Further, this paper provides practical measures to evaluate and control the degree of distortion in advance by adjusting the input signal modulation. This is illustrated by simulation results that are carried out for a double periodic system model with fictitious Fourier coefficients. Consequently, it is shown how the provided results are applied to chirp sequence modulated radar systems and how the radar signals can be interpreted from a system-theoretical perspective.
Automotive radar sensors have been used for measurements of time-varying scenarios for several years and the demands on their performance are increasing continuously. For the development of future signal processing algorithms, it is useful to investigate the problem of linear system identification as a generalized radar scenario. This paper provides a method for the approximation of a wireless transmission channel and derives how such a linear time-variant system can be identified using an FMCW radar. This universal approach enables the introduction of system functions, each characterizing the system's behavior in different time and frequency representation. These system functions of a wireless transmission channel are illustrated by radar measurements of a radially approaching cyclist, which deliver a profound interpretation of the wireless channel.
When charging electric vehicles inductively, living objects must be prevented from being exposed to the magnetic field. Therefore, additional sensors are used to detect endangered objects under the vehicle. This ensures that the charging process can be stopped immediately if endangered objects stay inside the hazardous zone. To prevent the system from unintended charging switch-offs, it is preferable to detect also life-signs for a reliable differentiation between living and non-living objects. In this paper, we propose a method for Doppler-based detection of respiration movements using a chirp sequence modulated radar sensor. We also provide system-theoretical background concerning the identification of linear time-variant systems. This delivers a clear problem statement and facilitates the understanding of the proposed method. Consequently, the theoretical results are applied to measurements for the detection of respiration movements. The results enhance an existing approach for living object protection using a radar sensor on the vehicle side.
As battery capacities become suitable for the mass market, there is an increasing demand on technologies to charge electric vehicles. Wireless charging is regarded as the most promising technique for automatic and convenient charging. Especially in publicly accessible parking spaces, foreign objects are able to enter the large air gap between the charging coils easily. Since the evoked magnetic field does not meet regulations, wireless charging systems are demanded to take further precautions related to the protection of endangered objects. Thus, additional sensors are required to protect primarily living objects by preventing them from being exposed to the magnetic field. In this paper, we propose a new approach for monitoring the air gap under the vehicle underbody using an automotive radar sensor on the vehicle side. The concept feasibility is evaluated with the help of a prototypical implementation. Further, two-dimensional signal processing techniques are applied to meet the requirements of inductive charging systems. Consequently, this paper provides measurement data for relevant use cases frequently discussed in the community of inductive charging.
Optimal Wiener filtering is a popular method for the estimation of stationary processes which can be completely derived system-theoretically. Although there exist several optimal filtering concepts for non-stationary processes, there is still a lack of fundamental time-variant system theory that describes the problem statement for non-stationary process estimation. This paper provides an intuitively understandable theory for the fundamental optimal filtering concept. By interpreting cross- and autocorrelations as a time-variant impulse response of a linear system, the problem statement can be illustrated with a network of linear systems. This paper introduces a double periodic system model that approximates a time-variant transfer function in both time and frequency domain which leads to an analytic solution for the optimal time-variant filter. The presented results are generally applicable and degenerate for simplified process properties (e.g. stationarity) to the well known results. We also present how the problem statement can easily be extended due to the fundamental and uniform theoretical approach.
Measurement performance evaluation of real and virtual automotive light detection and ranging (LiDAR) sensors is an active area of research. However, no commonly accepted automotive standards, metrics, or criteria exist to evaluate their measurement performance. ASTM International released the ASTM E3125-17 standard for the operational performance evaluation of 3D imaging systems commonly referred to as terrestrial laser scanners (TLS). This standard defines the specifications and static test procedures to evaluate the 3D imaging and point-to-point distance measurement performance of TLS. In this work, we have assessed the 3D imaging and point-to-point distance estimation performance of a commercial micro-electro-mechanical system (MEMS)-based automotive LiDAR sensor and its simulation model according to the test procedures defined in this standard. The static tests were performed in a laboratory environment. In addition, a subset of static tests was also performed at the proving ground in natural environmental conditions to determine the 3D imaging and point-to-point distance measurement performance of the real LiDAR sensor. In addition, real scenarios and environmental conditions were replicated in the virtual environment of a commercial software to verify the LiDAR model’s working performance. The evaluation results show that the LiDAR sensor and its simulation model under analysis pass all the tests specified in the ASTM E3125-17 standard. This standard helps to understand whether sensor measurement errors are due to internal or external influences. We have also shown that the 3D imaging and point-to-point distance estimation performance of LiDAR sensors significantly impacts the working performance of the object recognition algorithm. That is why this standard can be beneficial in validating automotive real and virtual LiDAR sensors, at least in the early stage of development. Furthermore, the simulation and real measurements show good agreement on the point cloud and object recognition levels.
A Methodology to Model the Rain and Fog Effect on the Performance of Automotive LiDAR Sensors
(2023)
In this work, we introduce a novel approach to model the rain and fog effect on the light detection and ranging (LiDAR) sensor performance for the simulation-based testing of LiDAR systems. The proposed methodology allows for the simulation of the rain and fog effect using the rigorous applications of the Mie scattering theory on the time domain for transient and point cloud levels for spatial analyses. The time domain analysis permits us to benchmark the virtual LiDAR signal attenuation and signal-to-noise ratio (SNR) caused by rain and fog droplets. In addition, the detection rate (DR), false detection rate (FDR), and distance error derror of the virtual LiDAR sensor due to rain and fog droplets are evaluated on the point cloud level. The mean absolute percentage error (MAPE) is used to quantify the simulation and real measurement results on the time domain and point cloud levels for the rain and fog droplets. The results of the simulation and real measurements match well on the time domain and point cloud levels if the simulated and real rain distributions are the same. The real and virtual LiDAR sensor performance degrades more under the influence of fog droplets than in rain.
This work introduces a process to develop a tool-independent, high-fidelity, ray tracing-based light detection and ranging (LiDAR) model. This virtual LiDAR sensor includes accurate modeling of the scan pattern and a complete signal processing toolchain of a LiDAR sensor. It is developed as a functional mock-up unit (FMU) by using the standardized open simulation interface (OSI) 3.0.2, and functional mock-up interface (FMI) 2.0. Subsequently, it was integrated into two commercial software virtual environment frameworks to demonstrate its exchangeability. Furthermore, the accuracy of the LiDAR sensor model is validated by comparing the simulation and real measurement data on the time domain and on the point cloud level. The validation results show that the mean absolute percentage error (MAPE) of simulated and measured time domain signal amplitude is 1.7%.
In addition, the MAPE of the number of points Npoints and mean intensity Imean values received from the virtual and real targets are 8.5% and 9.3%, respectively. To the author’s knowledge, these are the smallest errors reported for the number of received points Npoints and mean intensity Imean values up until now. Moreover, the distance error derror is below the range accuracy of the actual LiDAR sensor, which is 2 cm for this use case. In addition, the proving ground measurement results are compared with the state-of-the-art LiDAR model provided by commercial software and the proposed LiDAR model to measure the presented model fidelity. The results show that the complete signal processing steps and imperfections of real LiDAR sensors need to be considered in the virtual LiDAR to obtain simulation results close to the actual sensor. Such considerable imperfections are optical losses, inherent detector effects, effects generated by the electrical amplification, and noise produced by the sunlight.
Possible interference sources for our aerosol lidar setup with transient recorders have been assessed. This was done by two methods: a spectrum analysis of the lidar signals in order to detect radio-frequency interference and measurements of the electromagnetic interference caused by the laser power supply. We found disturbances in the analog channels of the transient recorders, presumably caused by ageing effects of our older recorders. An easy method on how the signal-to-noise-ratio can be improved retrospectively is presented. We also show that the usage of two-way radio at our location leads to a visible radio-frequency interference in the lidar profiles. Further, we present measurements of the electromagnetic interference caused by the laser power sup- ply, which may lead to disturbances in the lidar profiles if the transient recorders are placed next to it.
Many modern automated vehicle sensor systems use light detection and ranging (LiDAR) sensors. The prevailing technology is scanning LiDAR, where a collimated laser beam illuminates objects sequentially point-by-point to capture 3D range data. In current systems, the point clouds from the LiDAR sensors are mainly used for object detection. To estimate the velocity of an object of interest (OoI) in the point cloud, the tracking of the object or sensor data fusion is needed. Scanning LiDAR sensors show the motion distortion effect, which occurs when objects have a relative velocity to the sensor. Often, this effect is filtered, by using sensor data fusion, to use an undistorted point cloud for object detection. In this study, we developed a method using an artificial neural network to estimate an object’s velocity and direction of motion in the sensor’s field of view (FoV) based on the motion distortion effect without any sensor data fusion. This network was trained and evaluated with a synthetic dataset featuring the motion distortion effect. With the method presented in this paper, one can estimate the velocity and direction of an OoI that moves independently from the sensor from a single point cloud using only one single sensor. The method achieves a root mean squared error (RMSE) of 0.1187 m s−1 and a two-sigma confidence interval of [−0.0008 m s−1, 0.0017 m s−1] for the axis-wise estimation of an object’s relative velocity, and an RMSE of 0.0815 m s−1 and a two-sigma confidence interval of [0.0138 m s−1, 0.0170 m s−1] for the estimation of the resultant velocity. The extracted velocity information (4D-LiDAR) is available for motion prediction and object tracking and can lead to more reliable velocity data due to more redundancy for sensor data fusion.