Walk Error Research Articles

An 8 × 8 CMOS Optoelectronic Readout Array of Short-Range LiDAR Sensors.

This paper presents an 8 × 8 channel optoelectronic readout array (ORA) realized in the TSMC 180 nm 1P6M RF CMOS process for the applications of short-range light detection and ranging (LiDAR) sensors. We propose several circuit techniques in this work, including an amplitude-to-voltage (A2V) converter that reduces the notorious walk errors by intensity compensation and a time-to-voltage (T2V) converter that acquires the linear slope of the output signals by exploiting a charging circuit, thus extending the input dynamic range significantly from 5 μApp to 1.1 mApp, i.e., 46.8 dB. These results correspond to the maximum detection range of 8.2 m via the action of the A2V converter and the minimum detection range of 56 cm with the aid of the proposed T2V converter. Optical measurements utilizing an 850 nm laser diode confirm that the proposed 8 × 8 ORA with 64 on-chip avalanche photodiodes (APDs) can successfully recover the narrow 5 ns light pulses even at the shortest distance of 56 cm. Hence, this work provides a potential CMOS solution for low-cost, low-power, short-range LiDAR sensors.

Effects of gait retraining in knee joint position sense

BackgroundJoint position sense (JPS) is crucial for maintaining posture, protecting joints, and carrying out daily activities such as walking. Studies show that exercises to strengthen muscles and improve proprioception can positively impact JPS during passive and less complex activities. Evidence suggests that motor training can effectively enhance sensory function, including JPS, due to the extensive connections between the motor cortex and somatosensory areas. Gait retraining using real-time feedback has improved outcomes among patients with musculoskeletal disorders. The effect of gait retraining on JPS has not been investigated. This study assessed the effects of gait retraining to reduce knee extension in joint position sense in individuals with knee hyperextension walking patterns. MethodsTen women with asymptomatic knee hyperextension (KH) >5° during overground walking participated in this study. Sagittal-plane kinematics were assessed using a three-dimensional (3D) motion analysis system. The JPS was assessed using the Knee Position Active Reproduction Test. The knee with the highest hyperextension was the focus of the gait retraining intervention, which consisted of six 1-h sessions using verbal instructions and visual kinematic feedback. Comparisons of peak knee extension during walking and knee JPS overall error (RMSE) were made using a paired t-test. ResultsGait retraining intervention significantly reduced knee extension angle during walking (83.8 % change; p < 0.001; Cohen's d = −1.6) and improved knee JPS (62 % change; p = 0.023; Cohen's d = 0.8) post-training. In addition, the improvements in joint kinematics (36.7 % change; p = 0.005; Cohen's d = −1.2) and JPS (52.6 % change; p = 0.015; Cohen's d = 0.9) were observed in the untrained knee. SignificanceGait retraining can improve joint position sense. This study addresses a gap in our understanding of how gait retraining can influence JPS. Our results corroborate that gait retraining is an evolving and promising strategy for improving gait outcomes, particularly in individuals with KH walking patterns.

A Low-Power Optoelectronic Receiver IC for Short-Range LiDAR Sensors in 180 nm CMOS.

This paper presents a novel power-efficient topology for receivers in short-range LiDAR sensors. Conventionally, LiDAR sensors exploit complex time-to-digital converters (TDCs) for time-of-flight (ToF) distance measurements, thereby frequently leading to intricate circuit designs and persistent walk error issues. However, this work features a fully differential trans-impedance amplifier with on-chip avalanche photodiodes as optical detectors so that the need of the following post-amplifiers and output buffers can be eliminated, thus considerably reducing power consumption. Also, the combination of amplitude-to-voltage (A2V) and time-to-voltage (T2V) converters are exploited to replace the complicated TDC circuit. The A2V converter efficiently processes weak input photocurrents ranging from 1 to 50 μApp which corresponds to a maximum distance of 22.8 m, while the T2V converter handles relatively larger photocurrents from 40 μApp to 5.8 mApp for distances as short as 30 cm. The post-layout simulations confirm that the proposed LiDAR receiver can detect optical pulses over the range of 0.3 to 22.8 m with a low power dissipation of 10 mW from a single 1.8 V supply. This topology offers significant improvements in simplifying the receiver design and reducing the power consumption, providing a more efficient and accurate solution that is highly suitable for short-range LiDAR sensor applications.

Improved echo signal detection for pseudo-random single-photon counting laser ranging

In this paper, a new echo signal detection method, to the best of our knowledge, for pseudo-random single-photon counting ranging (PSPCR) LiDAR systems is proposed, which is applied for long distances, low repetition rates, and system cost reduction. First, in order to achieve a comparable temporal resolution as that in time-correlated single-photon counting (TCSPC) systems, we extend the pseudo-random code to discriminate the minimal time slot in time correlation. Second, we use the full width at half maxima (FWHM) in the duration of each pseudo-random code for correlation to reduce the impact of pulse width variation and timing jitters on ranging accuracy. Third, we study the bias and errors caused by using synchronous signals as the “START” signal, and propose to use the time of flight (ToF) at half energy to reduce the walk error. Simulation results show that, compared with existing PSPCR methods, the proposed method improves ranging accuracy with a lower repetition rate and lower peak and average power—centimeter-level ranging accuracy over tens of kilometers can be achieved using a laser with a repetition rate of 400 kHz, peak power of up to 1 kW, and average power of up to 1 W.

Real-Time Walk Error Compensation Method Using Echo Signal Magnitude Measurement in ToF Laser Scanners.

The rapid advancement of mobile laser scanner technology used for terrain mapping, among other things, imposes increasing requirements for scanning frequency and distance measurement accuracy. To meet these requirements, rangefinder modules are expected to operate with high echo signal dynamics and to allow accurate distance measurement even based on single-laser-pulse echo detection. Such performance can be potentially achieved using pulsed time-of-flight (ToF) laser rangefinders (LRF). In conventional ToF modules, however, the STOP signal (for time counter interruption) is generated using a straightforward fixed-threshold comparator method. Unfortunately, it corresponds to the so-called walk error, i.e., the dependence of the measured time of flight on the magnitude of the echo signal. In most ranging applications, however, the LRF detection channel can be exposed to an extremely large span of received echo power levels, which depend on the distance measured, type of target surface, atmospheric transmission, etc. Thus, the walk error is an inseparable element of the conventional ToF technique and creates a fundamental limit for its precision. This article presents a novel method of walk error compensation in real time. By using our authorial electronic circuit for measuring the magnitude of the echo signal, it is possible to effectively compensate for the walk error even when the echo signal brings the detection channel amplifiers into saturation. In addition, the paper presents a laboratory method for calibrating the walk error compensation curve.

Modeling, Prediction, and Results Correction of PDSH Circuits for Nanosecond Pulse Peak Detection

The peak detect and sample hold (PDSH) circuit is an important component of the light detection and ranging (LiDAR) system, because the PDSH circuit can correct the walk error of the time discriminator, and distinguish different objects at the same location. However, due to the requirement for high-precision measurement of nanosecond-scale pulse signals, the design of the PDSH circuit presents significant challenges. This paper accomplishes the modeling of the PDSH circuit, including the modeling of the PDSH measurement speed and the voltage step, quantifies various factors that affect the PDSH circuit measurement results, and makes predictions based on the model. Through the derivation and simplification of the rise process in the PDSH circuit, this study establishes a mathematical model to predict the performance of the PDSH circuit. Furthermore, this study also investigates the effect of circuit delay time on the measurement speed of the PDSH circuit. Meanwhile, this study analyzes the voltage step process, and an equivalent circuit model is derived through theoretical analysis. By utilizing a fitting method, the equivalent capacitance value of the diode is obtained. The simulation and experiment results show that the errors between the measurement speed model of the PDSH circuit and the actual circuit are no more than 1.98 ns and 2.03 ns, respectively. Thus, the measurement speed model can accurately predict whether the PDSH circuit meets the requirements. Moreover, the maximum absolute error of the equivalent circuit model is 19.87 mV, which can significantly reduce the error caused by the voltage step.

A Low-Cost Measurement Methodology for LiDAR Receiver Integrated Circuits

This paper presents a test methodology to facilitate the measuring processes of LiDAR receiver ICs by avoiding the inherent walk error issue. In a typical LiDAR system, a costly laser diode driver emits narrow light pulses with fast rising edges, and the reflected pulses from targets enter an optical detector followed by an analog front-end (AFE) circuit. Then, the received signals pass through the cascaded amplifiers down to the time-to-digital converter (TDC) that can estimate the detection range. However, this relatively long signal journey leads to the significant decline of rising-edge slopes and the output pulse spreading, thus producing inherent walk errors in LiDAR receiver ICs. Compensation methods requiring complex algorithms and extra chip area have frequently been exploited to lessen the walk errors. In this paper, however, a simpler and lower-cost methodology is proposed to test LiDAR receiver ICs by employing a high-speed buffer and variable delay cells right before the TDC. With these circuits, both START and STOP pulses show very similar pulse shapes, thus effectively avoiding the walk error issue. Additionally, the time interval between two pulses is easily determined by varying the number of the delay cells. Test chips of the proposed receiver IC implemented in a 180-nm CMOS process successfully demonstrate easier and more accurate measurement results.

Finite Length Triple Estimation Algorithm and its Application to Gyroscope MEMS Noise Identification

Abstract The noises associated with MEMS measurements can significantly impact their accuracy. The noises characterised by random walk and bias instability errors strictly depend on temperature effects that are difficult to specify during direct measurements. Therefore, the paper aims to estimate the fractional noise dynamics of the stationary MEMS gyroscope based on finite length triple estimation algorithm (FLTEA). The paper deals with the state, order and parameter estimation of fractional order noises originating from the MEMS gyroscope, being part of the popular Inertial Measurement Unit denoted as SparkFun MPU9250. The noise measurements from x, y and z gyroscope axes are identified using a modified triple estimation algorithm (TEA) with finite approximation length. The TEA allows a simultaneous estimation of the state, order and parameter of fractional order systems. Moreover, as it is well-known that the number of samples in fractional difference approximations plays a key role, we try to show the influence of applying the TEA with various approximation length constraints on final estimation results. The validation of finite length TEA in the noise estimation process coming from MEMS gyroscope has been conducted for implementation length reduction achieving 50% of samples needed to estimate the noise with no implementation losses. Additionally, the capabilities of modified TEA in the analysis of fractional constant and variable order systems are confirmed in several numerical examples.

Improving the Accuracy of TOF LiDAR Based on Balanced Detection Method.

The ranging accuracy of pulsed time-of-flight (TOF) lidar is affected by walk error and jitter error. To solve the issue, the balanced detection method (BDM) based on fiber delay optic lines (FDOL) is proposed. The experiments are carried out to prove the performance improvement of BDM over the conventional single photodiode method (SPM). The experimental results show that BDM can suppress common mode noise and simultaneously shift the signal to high frequency, which reduces the jitter error by approximately 52.4% and maintains the walk error at less than 300 ps with a non-distorted waveform. The BDM can be further applied to silicon photomultipliers.

Correction method for walk error based on the shape of reflective surface in LiDAR

Walk error produced in light detection and ranging (LiDAR) based on the time-of-flight (TOF) leads to loss of ranging accuracy. Walk error, which is systematic and correctable, is mainly attributed to the distance to the target, reflectance, the shape of reflective surface, and so on. In particular, various shapes of received pulse based on the shape of reflective surface have a considerable effect on the ranging accuracy. In this paper an incoherent pulsed laser echo equation for different shapes of reflective surface is established and it is found that parameters that can represent various shapes of received pulse involve received pulse width and slew rate. A measurement method of pulse width and slew rate combining a constant fraction discriminator (CFD) principle with a time over threshold (TOT) is proposed. It is also found that the proposed method is more efficient in walk error correction than the TOT by obtaining walk error corrections corresponding to pulse width and slew rate and determining the corresponding 2D surface polynomial coefficients. The obtained polynomial coefficients are used to ensure the ranging accuracy of the LiDAR within ± 3 cm.

Analysis and Research of Walk Error Based on High-precision Satellite Laser Ranging Data

Analysis and Research of Walk Error Based on High-precision Satellite Laser Ranging Data

An Analog SiPM Based Receiver With On-Chip Wideband Amplifier Module for Direct ToF LiDAR Applications

An analog silicon photomultiplier (SiPM) based receiver with wideband transimpedance amplifier (TIA) is proposed for direct ToF LiDAR applications. The analog SiPM comprises a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$16\times 32$ </tex-math></inline-formula> single photon avalanche diodes (SPADs) array with a 25% fill factor. A fully differential pixel readout circuit is proposed within the pixel cell to facilitate the monolithic integration with the subsequent TIA and reduce the output capacitance of the analog SiPM. The TIA with the multipath feedforward compensation technique is proposed to improve the stability and achieve a wider −3-dB bandwidth. The adder array is used in this design to output the intensity information for the walk error compensation and the target identification. The proposed receiver, which is fabricated in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.18~\mu \text{m}$ </tex-math></inline-formula> HV-CMOS technology, achieves a −3-dB bandwidth of 420 MHz. A maximum detection range of 65 m is obtained with 20 W laser peak power, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.8^{\circ }\times 1.8^{\circ }$ </tex-math></inline-formula> field of view, and 40 mm aperture. A ranging accuracy of ±0.4 cm and precision of 4.5 cm are attained under a condition of 5 klux ambient light based on 1000 measurement results.

Chaos single photon LIDAR and the ranging performance analysis based on Monte Carlo simulation.

With the advent of serial production lidars, single photon lidar faces an increasingly severe threat of crosstalk. In this paper, we first propose the concept of Chaos Single Photon (CSP) lidar and establish the theoretical model. In CSP lidar system, chaos laser replaces pulsed laser, and the physical random sequence generated by a Geiger mode avalanche photodiode (GM-APD) responding to chaos laser substitutes the traditional pseudo-random sequence. The mean density of '1' code of the CSP lidar system can exceed 10 million counts per second (Mcps) with a dead time immunity. The theoretical models of detection probability and false alarm rate are derived and demonstrated based on Poisson distribution. The bit error rate (BER) is introduced into the CSP lidar system for evaluating the range walk error intuitively. Additionally, the simulation results indicate that the CSP lidar system has a robust anti-crosstalk capability. Compared with the traditional pseudo-random single photon (PRSP) lidar system, the CSP lidar system not only overcomes range ambiguity but also has a signal to noise rate (SNR) of 60 times, reaching 10000 when the mean echo photoelectron number is 10 per nanosecond. Benefited from large-scale arrays and extremely high sensitivity properties of GM-APDs, we are looking forward to the applications of the CSP lidar in weak signal detection, remote mapping, autonomous driving, etc.

Multiparticle quantum walk–based error correction algorithm with two-lattice Bose–Hubbard model

When the evolution of discrete time quantum walk is carried out for particles, the ramble state is prone to error due to the influence of system noise. A multiparticle quantum walk error correction algorithm based on the two-lattice Bose–Hubbard model is proposed in this study. First, two point Bose–Hubbard models are constructed according to the local Euclidean generator, and it is proved that the two elements in the model can be replaced arbitrarily. Second, the relationship between the transition intensity and entanglement degree of the particles in the model is obtained by using the Bethe hypothesis method. Third, the position of the quantum lattice is coded and the quantum state exchange gate is constructed. Finally, the state replacement of quantum walk on the lattice point is carried out by switching the walker to the lattice point of quantum error correction code, and the replacement is carried out again. The entanglement of quantum particles in the double-lattice Bose–Hubbard model is simulated numerically. When the ratio of the interaction between particles and the transition intensity of particles is close to 0, the entanglement operation of quantum particles in the model can be realized by using this algorithm. According to the properties of the Bose–Hubbard model, quantum walking error correction can be realized after particle entanglement. This study introduces the popular restnet network as a training model, which increases the decoding speed of the error correction circuit by about 33%. More importantly, the lower threshold limit of the convolutional neural network (CNN) decoder is increased from 0.0058 under the traditional minimum weight perfect matching (MWPM) to 0.0085, which realizes the stable progress of quantum walk with high fault tolerance rate.

A CMOS AFE With 37-nA rms Input-Referred Noise and Marked 96-dB Timing DR for Pulsed LiDAR

This paper presents an analog front-end (AFE) circuit with marked timing point for pulsed time-of-flight LiDAR that employs either sampling- or event-based timing approach. The proposed AFE adopts a dual-mode structure for its pre-amplifier which can be configured as a charge-sensitive amplifier (CSA) or a gated active load-assisted TIA (GALA-TIA), depending on the intensity of input current. As a result, both the sensitivity and dynamic range (DR) of the AFE have been effectively improved. In addition, the zero-crossing point of the output signal has been marked as the timing point with a built-in pulse shaper, which allows the back-end circuits of LiDAR receiver discriminate the timing conveniently and accurately. The measured input-referred RMS noise current of the proposed AFE is 37 nA. With dual-mode control, a linear output DR of 80 dB and a wide timing DR of 96 dB with walk error no more than ±160 ps have been achieved. For single-shot measurement application, only CSA mode was enabled and the pulse widths of saturated output signals have been measured to compensate the walk errors, which realized a timing DR of 78 dB with accuracy of ±150 ps. The averaged power consumption is 66 mW and the total silicon area is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.79\times 0.42\,\,mm^{2}$ </tex-math></inline-formula> in 0.18- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> CMOS process.

Research on Angle Random Walk Suppression and Error Estimation and Compensation Method Based on Online Weight Distribution of Multi-RINSs

Rotary inertial navigation system(RINS) can suppress constant and slowly varying errors of inertial sensors through rotary modulation technology. However, the angle random walk(ARW) error of gyro can not be modulated, which has become the key factor of restricting the long-term navigation accuracy of RINS. In this paper, the influence of ARW on long-term navigation accuracy of RINS is analyzed. In view of the situation that GPS and other external auxiliary information are not available, an ARW suppression and error estimation and compensation method based on online weight distribution of multi-RINSs is proposed. Considering the disturbance of deflection to attitude and the disturbance of lever arm effect to velocity, the dynamic weighted average of position information of multi-RINSs are selected as the measurement, the equivalent error parameters of each RINS are estimated and compensated by KF filter is proposed. The simulation results show that the navigation errors caused by ARW can be reduced several times by using the proposed suppression method, and the weighted average position information to estimate and compensate the equivalent error of each RINS, which can further improve the navigation accuracy of each RINS by about 3 times, and proved that the proposed method of restraining ARW and error estimation and compensation is effective. It makes the relationship among the RINSs of from backup to auxiliary, which has significant value for further improving the autonomous long-term navigation accuracy.

Towards a Multi-Perspective Time of Flight Laser Ranging Device Based on Mirrors and Prisms

This paper investigates the feasibility of redirecting the field of view (FOV) of a light-based time-of-flight (ToF) ranging device, commonly known as a pulsed lidar, using fixed mirrors and prisms for possible future use in robotics. The emphasis is on configurations where the FOV redirection element is positioned beyond the ranging device’s dead zone. A custom made direct ToF ranging device with time-over-threshold (TOT)-based walk error compensation was used to evaluate the effects of the FOV redirecting optics on range measurement accuracy and precision. The tests include redirecting the FOV with a clean prism with anti-reflective (AR) coating on its legs, as well as with a regular and a first surface mirror in both a clean and dusted state. The study finds the prism to be unsuitable due to parasitic reflections, which ruin the ranging data. The clean mirrors were found to have no noticeable effect on ranging accuracy. When they are dusty, mirrors introduce a negative measurement error. This effect is the most pronounced when a mirror is positioned toward the end of the partial dead zone of the ToF rangefinder, but loses influence as the mirror is moved farther away. The error is attributed to the parasitic reflection off dust on the mirror, which reduces the time of detection of the pulse reflected off the real target, and interferes with the walk error compensation by widening the detected pulse.

Long-range high-speed laser imaging based on VCSEL array and MPPC array.

Flash LiDAR is a photoelectric system that can acquire a 3D image by emitting a diffuse pulsed laser beam, and hence is suitable for both autopilot and spacecraft flight control. Achieving long-range and high-speed, especially in outdoor applications with strong solar background illumination, are challenging requirements. In this paper, a set of laser imaging prototype based on 2×6 VCSEL array and 32×32 MPPC array image sensor is developed, the range calibration is completed, and relevant experimental research is carried out. The frame rate of the system can reach 10kHz, the detection probability of 120m range can reach 86.23%, and the maximum walk error is about 0.6m under different reflectivity. The 3D imaging of the vehicle can be realized at about 70m, the horizontal spatial resolution is less than 5cm, and the ranging precision after ten shots average is within 10cm by calculating the centroid of a histogram. The detection probability can be improved by using the time-gating method. After multiple measurements, a 120m "laser imaging through window" can be realized in sunlight. This LiDAR system has the advantages of small volume, light weight and fast detection speed.

Detection of the near-field targets by non-coaxial underwater single-photon counting lidar

The strong backscattering of near-field water severely limits the detection ability of the coaxial single-photon counting lidar, especially when the target signal peak overlaps with the background(water) signal peak. Based on the important influence of scattering angle on the distribution of echo photons in the volume scattering function (VSF) of water and the BRDF model of target, a detection efficiency model of non-coaxial underwater single-photon counting lidar is established in this paper. It reveals that when the water attenuation coefficient is a fixed value, the maximum detection efficiency and range walk error (RWE) decrease exponentially with the increase of target distance. The variation of the center distance of the transceiver system has the best detection efficiency, which has little effect on the RWE. Compared with the coaxial system, the target detection efficiency of the non-coaxial underwater single-photon counting lidar remains unchanged while suppressing the strong backscattering of near-field water. Monte Carlo simulation results show that the non-coaxial system has faster searching ability for target signals with high attenuation coefficient and overlapping echo peaks. This research lays a theoretical foundation for the fast target search of single-photon counting lidar in complex underwater environment.

DTOF Image LiDAR With Stray Light Suppression and Equivalent Sampling Technology

This paper presents direct time-of-flight image LiDAR to realize a reliable autopilot system, which consists of hardware architecture and processing algorithm based on field programmable logic array (FPGA). The processing algorithm consists of multi-channel time-to-digital converters (TDCs), equivalent sampling technology consisting of equivalent sampling circuit (ESC) and amplitude fitting algorithm (AFA), correlation slope fitting algorithm (CSFA), and stray light suppression algorithm (SLSA). The TDCs are used to measure the flight time. The ESC is used to record waveforms based on time discrimination circuits, dynamic threshold adjustment circuits, and TDCs. The AFA is used to achieve the amplitude of the echo signal whether it is saturated or not. The CSFA based on the Gauss function is used to eliminate walk error, which does not need to calibrate the compensation coefficient in advance. And the stary light suppression algorithm based on laser pulse signal modulation technology is used to suppress the interference of background light and interference within different LiDAR systems. The LiDAR system can achieve 100 m measurement range with the laser peak power of 120 W. A measurement precision of ~+/−15 mm was achieved with non-cooperative targets when the measurement range was less than 10m. And the measured relative precision was less than 1% for a distance up to 100 m with a 100-klux direct sunlight.