Relative Distance Error Research Articles

BEAD: Bounded error approximate adder with carry and sum speculations

This paper proposes a configurable reduced worst-case error approximate adder, named BEAD (Bounded Error Approximate Adder). The proposed adder is based on segmentation and carry speculation methods to cut long critical paths. Furthermore, a high accuracy speculation method is proposed to calculate the sum bits. However, the data of real-world applications is often not uniformly distributed, which leads to taking values that result in a worst-case error of the approximate adder quite frequently; therefore, considerable distortion occurs at the output. To overcome this, the carry prorogation scheme of the BEAD is such that the error distance is bounded to a given value, which makes it more accurate rather than prior works. Specifically, the BEAD offers a smaller worst-case error in addition to improved mean relative error distance. The results show between 50% and 80% smaller maximum error compared to the related works. Also, by synthesizing the different adders using a 15-nm FinFET technology, the results demonstrate that the BEAD has at least 30% area saving compared to the exact adder in the various studied configurations. The proposed adder achieves the almost lowest figure of cost (FoC) compared to state-of-the-art approximate adders. Moreover, BEAD's evaluation in image processing and DCT applications shows its great superiority over recently proposed structures.

Fast Underwater Optical Beacon Finding and High Accuracy Visual Ranging Method Based on Deep Learning.

Visual recognition and localization of underwater optical beacons is an important step in autonomous underwater vehicle (AUV) docking. The main issues that restrict the use of underwater monocular vision range are the attenuation of light in water, the mirror image between the water surface and the light source, and the small size of the optical beacon. In this study, a fast monocular camera localization method for small 4-light beacons is proposed. A YOLO V5 (You Only Look Once) model with coordinated attention (CA) mechanisms is constructed. Compared with the original model and the model with convolutional block attention mechanisms (CBAM), and our model improves the prediction accuracy to 96.1% and the recall to 95.1%. A sub-pixel light source centroid localization method combining super-resolution generative adversarial networks (SRGAN) image enhancement and Zernike moments is proposed. The detection range of small optical beacons is increased from 7 m to 10 m. In the laboratory self-made pool and anechoic pool experiments, the average relative distance error of our method is 1.04 percent, and the average detection speed is 0.088 s (11.36 FPS). This study offers a solution for the long-distance fast and accurate positioning of underwater small optical beacons due to their fast recognition, accurate ranging, and wide detection range characteristics.

Comprehensive and clinically accurate head and neck cancer organs-at-risk delineation on a multi-institutional study

Accurate organ-at-risk (OAR) segmentation is critical to reduce radiotherapy complications. Consensus guidelines recommend delineating over 40 OARs in the head-and-neck (H&N). However, prohibitive labor costs cause most institutions to delineate a substantially smaller subset of OARs, neglecting the dose distributions of other OARs. Here, we present an automated and highly effective stratified OAR segmentation (SOARS) system using deep learning that precisely delineates a comprehensive set of 42 H&N OARs. We train SOARS using 176 patients from an internal institution and independently evaluate it on 1327 external patients across six different institutions. It consistently outperforms other state-of-the-art methods by at least 3–5% in Dice score for each institutional evaluation (up to 36% relative distance error reduction). Crucially, multi-user studies demonstrate that 98% of SOARS predictions need only minor or no revisions to achieve clinical acceptance (reducing workloads by 90%). Moreover, segmentation and dosimetric accuracy are within or smaller than the inter-user variation.

High-performance, energy-efficient, and memory-efficient FIR filter architecture utilizing 8x8 approximate multipliers for wireless sensor network in the Internet of Things

IoT uses wireless sensor networks (WSN) to deploy many sensors to track environmental and physical parameters. The WSN measurements are frequently contaminated and altered by noise. The noise in the signal increases the sensor node’s computation and energy utilization, resulting in less longevity of the sensor node. The Finite Impulse Response (FIR) filter is commonly employed in WSN to pre-process sensed signals to remove noise from the sensed signals using delay elements, multipliers, and adders. Traditional multiplier-based FIR filter designs result in hardware-intensive multipliers that consume a lot of energy, and area and have low computation speed. These drawbacks make them unsuitable for IoT-based WSN systems with stringent power efficiency necessities. Approximate computing enhances the energy efficiency of an FIR filter. Arithmetic circuits utilizing approximate computing improve the hardware performance, with some loss of accuracy to save energy utilization and boost speed. A novel approximate multiplier architecture employing a fast and straightforward approximation adder is proposed in this study. Approximate multiplier M1 using OR gate and approximate multiplier M2 using proposed approximate adders are compared. The proposed approximate adder is suited for building an adder tree to accumulate partial product (PP) because it is less complicated than traditional adders. Compared to a one-bit-full adder, the critical path delay (CPD) is reduced significantly in the proposed methods. The accuracy comparison of M1. M2 and Wallace tree using the normalized mean error distance (NMED), the mean relative error distance (MRED), the maximum error (ME), and the error rate (ER) with the number of bits utilized for reducing error. For the area (delay) optimized circuit, when the bit used is 4, the delay is 0.4 ns for M1, 0.43 ns for M2, and 1.08 ns for the Wallace tree multiplier. For the delay (area) optimized circuit, when the bit used is 4, the delay is 0.16 ns for M1, 0.16 ns for M2, and 0.40 ns for the Wallace tree multiplier. To more accurately evaluate performance at the circuit level, the PDP and ADP are computed. The NMED, MRED, ME, and ER versus PDP and ADP are computed. The proposed multipliers M1 and M2 are compared with existing approximate multipliers. When an equivalent MRED, NMED, or ER is taken into account, M1 has the smallest ADP and PDP among other multipliers. The very low likelihood of a significant ED occurring is indicated by the small values of NMED and MRED in M1 and M2. The proposed solutions effectively reduce delay, area, and power while maintaining increased accuracy and performance.

Improved blur circle detection method for geometric calibration of multifocus light field cameras

Multifocus light field cameras are increasingly gaining attention in the field of computational imaging and machine vision due to their ability to capture spatial and angular information of light rays. Accurate calibration of the geometric parameters of multifocus light field cameras is the prerequisite for implementing computational imaging techniques, such as digital refocusing, depth reconstruction, and three-dimensional reconstruction. We propose an improved blur circle detection method for the calibration of multifocus light field cameras. The circular Hough transform-based circle detection method is used to obtain the subimage centers accurately in white raw images. On this basis, the subimages in the checkerboard images are classified, and the image corners are detected to determine the clusters of image corners corresponding to checkerboard corners. Then, the centers of plenoptic disc features are used as projection points of checkerboard corners on the light field image to calculate the camera pose. Levenberg–Marquardt method is further used to solve the calibration model. Finally, the calibration experiments of multifocus light field cameras are carried out to evaluate the improved blur circle detection method. Experimental results indicated that the improved blur circle detection method has higher calibration accuracy of multifocus light field camera than the blur circle detection method, while the mean reprojection error of the microlens centers and the image corners are 0.12 and 0.33 pixels, and the mean relative distance error between adjacent checkerboards is 2.53%.

An Energy-Efficient Approximate Divider Based on Logarithmic Conversion and Piecewise Constant Approximation

Approximate computing (AC) has been considered as a promising paradigm to improve the energy-efficiency of computing hardware for error-tolerant applications, with negligible quality degradation to the output. Dividers frequently limit the performance of a computing system; however, they have not received as much attention as multipliers and adders in AC. In this paper, an energy-efficient and high-performance approximate divider is proposed based on logarithmic conversion and piecewise constant approximation. In this design, the range for the conversion between binary and logarithmic numbers is first expanded from <inline-formula> <tex-math notation="LaTeX">$\mathbf {[{0,1}]}$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$\mathbf {[-0.5,1]}$ </tex-math></inline-formula>. A heuristic search algorithm is then devised to find the most accurate constant set to approximate the reciprocal of the divisor, by minimizing a statistical error. The hardware implementation is presented for both floating-point (FP) and integer dividers. With a high configurability, the proposed divider results in a mean relative error distance (MRED) from 2.78&#x0025; to 0.046&#x0025;, indicating a high accuracy among state-of-the-art approximate dividers. Compared to the half-precision FP divider, the proposed divider with a MRED of 0.74&#x0025; can achieve nearly <inline-formula> <tex-math notation="LaTeX">$\mathbf {90\times }$ </tex-math></inline-formula> improvement in PDP. Moreover, compared to state-of-the-art approximate dividers, the proposed design is in the Pareto Frontier in terms of power delay product (PDP) and MRED. The three image processing application results demonstrate that the proposed divider can result in the highest peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) even with truncation.

Approximate Multipliers Using Static Segmentation: Error Analysis and Improvements

Approximate multipliers are used in error-tolerant applications, sacrificing the accuracy of results to minimize power or delay. In this paper we investigate approximate multipliers using static segmentation. In these circuits a set of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> contiguous bits (a segment of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> bits) is extracted from each of the two <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -bits operand, the two segments are in input to a small <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m\times m$ </tex-math></inline-formula> internal multiplier whose output is suitably shifted to obtain the result. We investigate both signed and unsigned multipliers, and for the latter we propose a new segmentation approach. We also present simple and effective correction techniques that can significantly reduce the approximation error with reduced hardware costs. We perform a detailed comparison with previously proposed approximate multipliers, considering a hardware implementation in 28 nm technology. The comparison shows that static segmented multipliers with the proposed correction technique have the desirable characteristic of being on (or close to) the Pareto-optimal frontier for both power vs normalized mean error distance and power vs mean relative error distance trade-off plots. These multipliers, therefore, are promising candidates for applications where their error performance is acceptable. This is confirmed by the results obtained for image processing and image classification applications.

Smart vector-inspired optical vision guiding method for autonomous underwater vehicle docking and formation.

A smart vector-inspired optical vision guiding (VIOVG) method for autonomous underwater vehicle (AUV) docking and formation is proposed. Unlike traditional optical guiding methods based on LED arrays, the method is inspired by a vector, and uses four laser diodes to form a wing-light pattern to realize smart optical guiding for AUVs. Due to the light scattering effect from water, the four laser diodes can emit four bright and slim laser beams in water, which can be captured by underwater cameras. The intersections of the laser beams form wing-lights as markers for AUV distance and pose estimation. The wing-light pattern is easily tuned and extended by changing the propagation direction and the power of the laser beams beyond the limitation of the physical size of the AUV or docking station. The simulations and experiments show that the proposed method can achieve high precision positioning. A relative distance error of 3.35% is achieved in a positioning experiment at ∼10 m. It has great potential for AUV docking and formation, especially for small AUVs.

Tracking the Traveled Distance of Capsule Endoscopes along a Gastrointestinal-Tract Model Using Differential Static Magnetic Localization.

The traveled distance and orientation of capsule endoscopes for each video frame are not available in commercial systems, but they would be highly relevant for physicians. Furthermore, scientific approaches lack precisely tracking the capsules along curved trajectories within the typical gastrointestinal tract. Recently, we showed that the differential static magnetic localisation method is suitable for the precise absolute localisation of permanent magnets assumed to be integrated into capsule endoscopes. Thus, in the present study, the differential method was employed to track permanent magnets in terms of traveled distance and orientation along a length trajectory of 487.5 mm, representing a model of the winding gastrointestinal tract. Permanent magnets with a diameter of 10 mm and different lengths were used to find a lower boundary for magnet size. Results reveal that the mean relative distance and orientation errors did not exceed 4.3 ± 3.3%, and 2 ± 0.6, respectively, when the magnet length was at least 5 mm. Thus, a 5 mm long magnet would be a good compromise between achievable tracking accuracy and magnet volume, which are essential for integration into small commercial capsules. Overall, the proposed tracking accuracy was better than that of the state of the art within a region covering the typical gastrointestinal-tract size.

Collision Avoidance Strategy for Self-Driving Vehicles Based on Drivers and Environmental Factors

In order to enhance the driving safety, various driving assistant systems are gradually developed and widely used. Based on the safe distance model related to the braking process, one warning/dangerous critical distance model for longitudinal control is proposed in this paper, considering the driver’s style and environment factors. The variable driver response time is obtained by employing fuzzy control theory. The author then establishes the vehicle dynamics model and its inverse model. Through the relative distance error and relative speed error, the upper controller is designed to obtain the expected acceleration based on sliding mode control, and the lower controller based on PID control is designed to track the acceleration. In order to solve the chattering problem of sliding mode controller, the author proposes variable gain coefficient control method. The fixed gain parameter in the expected acceleration formula is related to the negative exponential correlation formula, which can effectively depress the chattering of the expected acceleration. Finally, the author uses CarSim and Simulink to establish a co-simulation model of the collision avoidance warning system, and designs the test simulation conditions for typical traffic test scenarios to verify the control algorithm effectiveness.

A prescribed performance PID control of robotic cars with only posture measurements considering path curvature

This paper addresses the prescribed performance adaptive neural observer-based PID controller for robotic cars by considering the trajectory curvature compensation. Constrained relative distance and angle errors between a car and leader are transformed into a new Euler-Lagrange model of unconstrained errors via prescribed performance technique. Two filtered PID error variables are introduced to propose a neural adaptive robust observer-based controller which obtains the followings: (i) the prescribed performances of tracking errors are ensured, (ii) the controller singularity is avoided, (iii) the trajectory curvature is compensated to avoid unwanted deviations between the leader and follower, (iv) car velocities measurements are not required, and (v) controller compensates uncertainties by combining neural networks and adaptive robust control. Lyapunov's method proves the controller stability. Comparative simulations verify controller advantages.

Online calibration technology for a one-dimensional laser Doppler velocimeter based on a strapdown inertial navigation system.

In the integrated navigation system, which consists of a laser Doppler velocimeter (LDV) and strapdown inertial navigation system, it is necessary to calibrate the LDV. We propose an online calibration method for a LDV based on the strapdown inertial navigation system. This system uses highly accurate output information in the early stage of the inertial navigation system to carry out coarse calibration for the velocimeter and then employs a Kalman filter to correct the results of coarse calibration to achieve high precision calibration for the velocimeter. Experimental results show that the relative distance error of dead reckoning is less than 0.02%, indicating that the proposed online calibration method can achieve high-precision calibration for the velocimeter.

On Dark Gravitational Wave Standard Sirens as Cosmological Inference and Forecasting the Constraint on Hubble Constant using Binary Black Holes Detected by Deci-hertz Observatory

Gravitational wave (GW) signals from compact binary coalescences can be used as standard sirens to constrain cosmological parameters if their redshift can be measured independently by electromagnetic signals. However, mergers of stellar binary black holes (BBHs) may not have electromagnetic counterparts and thus have no direct redshift measurements. These dark sirens may be still used to statistically constrain cosmological parameters by combining their GW measured luminosity distances and localization with deep redshift surveys of galaxies around it. We investigate this dark siren method to constrain cosmological parameters in detail by using mock BBH and galaxy samples. We find that the Hubble constant can be constrained well with an accuracy ≲1% with a few tens or more of BBH mergers at redshift up to 1 if GW observations can provide accurate estimates of their luminosity distance (with relative error of ≲0.01) and localization (≲0.1 deg2), though the constraint may be significantly biased if the luminosity distance and localization errors are larger. We also introduce a simple method to correct this bias and find it is valid when the luminosity distance and localization errors are modestly large. We further generate mock BBH samples, according to current constraints on BBH merger rate and the distributions of BBH properties, and find that the Deci-hertz Observatory (DO) in a half year observation period may detect about one hundred BBHs with signal-to-noise ratio ϱ ≳ 30, relative luminosity distance error ≲0.02 and localization error ≲0.01 deg2. By applying the dark standard siren method, we find that the Hubble constant can be constrained to the ∼0.1%–1% level using these DO BBHs, an accuracy comparable to the constraints obtained by using electromagnetic observations in the near future, thus it may provide insight into the Hubble tension. We also demonstrate that the constraint on the Hubble constant applying this dark siren method is robust and does not depend on the choice of the prior for the properties of BBH host galaxies.

Real-Time Life-Cycle Monitoring of Composite Structures Using Piezoelectric-Fiber Hybrid Sensor Network.

In this paper, an in situ piezoelectric-fiber hybrid sensor network was developed to monitor the life-cycle of carbon fiber-reinforced plastics (CFRPs), from the manufacturing phase to the life in service. The piezoelectric lead-zirconate titanate (PZT) sensors were inserted inside the composite structures during the manufacturing process to monitor important curing parameters, including the storage modulus of resin and the progress of the reaction (POR). The strain that is related to the storage modulus and the state of resin was measured by embedded fiber Bragg grating (FBG) sensors, and the gelation moment identified by the FBG sensors was very close to those determined by dynamic mechanical analysis (DMA) and POR. After curing, experiments were conducted on the fabricated CFRP specimen to investigate the damage identification capability of the embedded piezoelectric sensor network. Furthermore, a modified probability diagnostic imaging (PDI) algorithm with a dynamically adaptive shape factor and fusion frequency was proposed to indicate the damage location in the tested sample and to greatly improve the position precision. The experimental results demonstrated that the average relative distance error (RDE) of the modified PDI method was 68.48% and 46.97% lower than those of the conventional PDI method and the PDI method, respectively, with an averaged shape factor and fusion frequency, indicating the effectiveness and applicability of the proposed damage imaging method. It is obvious that the whole life-cycle of CFRPs can be effectively monitored by the piezoelectric-fiber hybrid sensor network.

Robust image-based coordinated control for spacecraft formation flying

This paper addresses a coordinated control problem for Spacecraft Formation Flying (SFF). The distributed followers are required to track and synchronize with the leader spacecraft. By using the feature points in the two-dimensional image space, an integrated 6-degree-of-freedom dynamic model is formulated for spacecraft relative motion. Without sophisticated three-dimensional reconstruction, image features are directly utilized for the controller design. The proposed image-based controller can drive the follower spacecraft in the desired configuration with respect to the leader when the real-time captured images match their reference counterparts. To improve the precision of the formation configuration, the proposed controller employs a coordinated term to reduce the relative distance errors between followers. The uncertainties in the system dynamics are handled by integrating the adaptive technique into the controller, which increases the robustness of the SFF system. The closed-loop system stability is analyzed using the Lyapunov method and algebraic graph theory. A numerical simulation for a given SFF scenario is performed to evaluate the performance of the controller.

Denoising of the multi-slit streak tube imaging LiDAR system using a faster non-local mean method.

Combined with the characteristic of the multi-slit streak tube imaging LiDAR (MS-STIL) system where the imaging areas corresponding to each slit do not interfere with each other, we denoised the streak images by an improved fast non-local mean filtering algorithm. Experiments were performed to investigate the effectiveness of the method. The experimental results show that the spatial resolution of the system is improved from 22 to 16 mm; the relative distance error is reduced by an average of 22.76%; and the intensity accuracy improved significantly when the distance is 10 m. Additionally, the overall denoising effect is comprehensively verified by long-range target imaging. The mean square error of the reconstructed depth image and intensity image are reduced from 0.0836, 0.0067 to 0.0433, 0.0037, respectively. The applicability of the proposed method was verified through comparative experiments in different environments.

Energy Efficient Error Resilient Multiplier Using Low-power Compressors

The approximate hardware design can save huge energy at the cost of errors incurred in the design. This article proposes the approximate algorithm for low-power compressors, utilized to build approximate multiplier with low energy and acceptable error profiles. This article presents two design approaches (DA1 and DA2) for higher bit size approximate multipliers. The proposed multiplier of DA1 have no propagation of carry signal from LSB to MSB, resulted in a very high-speed design. The increment in delay, power, and energy are not exponential with increment of multiplier size ( n ) for DA1 multiplier. It can be observed that the maximum combinations lie in the threshold Error Distance of 5% of the maximum value possible for any particular multiplier of size n . The proposed 4-bit DA1 multiplier consumes only 1.3 fJ of energy, which is 87.9%, 78%, 94%, 67.5%, and 58.9% less when compared to M1, M2, LxA, MxA, accurate designs respectively. The DA2 approach is recursive method, i.e., n -bit multiplier built with n/2-bit sub-multipliers. The proposed 8-bit multiplication has 92% energy savings with Mean Relative Error Distance (MRED) of 0.3 for the DA1 approach and at least 11% to 40% of energy savings with MRED of 0.08 for the DA2 approach. The proposed multipliers are employed in the image processing algorithm of DCT, and the quality is evaluated. The standard PSNR metric is 55 dB for less approximation and 35 dB for maximum approximation.

Study of the Error Caused by Camera Movement for the Stereo-Vision System

The stereo-vision system plays an increasingly important role in various fields of research and applications. However, inevitable slight movements of cameras under harsh working conditions can significantly influence the 3D measurement accuracy. This paper focuses on the effect of camera movements on the stereo-vision 3D measurement. The camera movements are divided into four categories, viz., identical translations and rotations, relative translation and rotation. The error models of 3D coordinate and distance measurement are established. Experiments were performed to validate the mathematical models. The results show that the 3D coordinate error caused by identical translations increases linearly with the change in the positions of both cameras, but the distance measurement is not affected. For identical rotations, the 3D coordinate error introduced only in the rotating plane is proportional to the rotation angle within 10° while the distance error is zero. For relative translation, both coordinate and distance errors keep linearly increasing with the change in the relative positions. For relative rotation, the relationship between 3D coordinate error and rotation angle can be described as the nonlinear trend similar to a sine-cosine curve. The impact of the relative rotation angle on distance measurement accuracy does not increase monotonically. The relative rotation is the main factor compared to other cases. Even for the occurrence of a rotation angle of 10°, the resultant maximum coordinate error is up to 2000 mm, and the distance error reaches 220%. The results presented are recommended as practice guidelines to reduce the measurement errors.

Performance analysis of dynamic optimization algorithms using relative error distance

Quantification of the performance of algorithms that solve dynamic optimization problems (DOPs) is challenging, since the fitness landscape changes over time. Popular performance measures for DOPs do not adequately account for ongoing fitness landscape scale changes, and often yield a confounded view of performance. Similarly, most popular measures do not allow for fair performance comparisons across multiple instances of the same problem type nor across different types of problems, since performance values are not normalized. Many measures also assume normally distributed input data values, while in reality the necessary conditions for data normality are often not satisfied. The majority of measures also fail to capture the notion of performance variance over time. This paper proposes a new performance measure for DOPs, namely the relative error distance. The measure shows how close to optimal an algorithm performs by considering the multi-dimensional distance between the vector comprising the normalized performance scores for specific algorithm iterations of interest, and the theoretical point of best possible performance. The new measure does not assume normally distributed performance data across fitness landscape changes, is resilient against fitness landscape scale changes, better incorporates performance variance across fitness landscape changes into a single scalar value, and allows easier algorithm comparisons using established nonparametric statistical methods.

Truncation Based Approximate Multiplier For Error Resilient Applications

ABSTRACT Approximate computing is a promising approach for low power IC design and has recently received considerable research attention. To accommodate dynamic levels of approximation, a few accuracy configurable multiplier designs have been developed in the past. However, these designs consumed considerable area and power. Accuracy, as well as latency, power and area design metrics are used to evaluate our approximate multiplier designs of different bit widths, i.e. 16 x 16, 32 × 32 and 64 × 64. Simulation and synthesis results showed a considerable gain than previous designs since we can change the components required according to the error tolerance. Moreover, we have also proposed a technique, where the system takes charge of the design and makes a call depending on the magnitude of the numbers provided. When compared with the exact multiplier designs, for 16 bit, 32 bit and 64 bit, we achieved a reduction by 24.5%, 71.5% and 85.1% in area; reduction in power by 37.7%, 89.4% and 88.2% and with a mean relative error distance of 0.5393%, 0.5428% and 0.2878% respectively.