Linear Error Research Articles

Diagnostics for partially linear measurement error models

Partially linear models are useful tools to analyze data from economic, genetic, and other fields. Similar to other data analyses, the identification of influential observations that may be potential outliers is an important step beyond estimation in such models. The objective of this article is to develop some diagnostic measures for identifying influential observations in partially linear models when some of the covariates are measured with errors. Deletion measures are developed based on case deletion, mean shift outlier models, and the corrected likelihood of Nakamura (1990). The performance of the methods is illustrated by an artificial example and a real example.

Decoding Quantum Tanner Codes

We introduce sequential and parallel decoders for quantum Tanner codes. When the Tanner code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain a family of asymptotically good quantum low-density parity-check codes. In this case, our decoders provably correct arbitrary errors of weight linear in the code length, respectively in linear or logarithmic time. The same decoders are easily adapted to the expander lifted product codes of Panteleev and Kalachev. Along the way, we exploit recently established bounds on the robustness of random tensor codes to give a tighter bound on the minimum distance of quantum Tanner codes.

Deep Learning OFDM Receivers for Improved Power Efficiency and Coverage

In this article, we propose multiple machine learning (ML) based physical-layer receiver solutions for demodulating orthogonal frequency-division multiplexing (OFDM) signals that are subject to high level of nonlinear distortion. Specifically, three novel deep learning based convolutional neural network receivers are devised, containing layers in time- and/or frequency-domains, allowing to demodulate and decode the transmitted bits reliably despite the high error vector magnitude (EVM) in the transmit signal. Applicable training procedures are also described, such that the learned layers in the receiver processing properly generalize over different nonlinear distortion and multipath channel characteristics. Extensive set of numerical results is provided, in the context of 5G NR uplink (UL) incorporating also measured terminal power amplifier (PA) characteristics. The obtained results show that the proposed receiver systems are able to clearly outperform the classical linear minimum mean-squared error (LMMSE) receiver as well as the existing ML receiver approaches, especially when the EVM is high compared to modulation order. This is particularly so when the devised ML receiver is of hybrid nature with layers both in time and frequency. The proposed ML receivers can thus facilitate pushing the terminal PA systems deeper into saturation, and thereon improve the terminal power-efficiency, radiated power and network coverage. Through combining the obtained radio link performance results with link budget calculations, all carried out at the 28 GHz mmWave band, it is shown that the proposed ML receivers can enhance the network coverage in terms of maximum UL link distances by close to 100%, when compared to classical LMMSE receiver based networks.

A study on nuclear binding energy and beta decay energy using deep neural networks

The Artificial Neural Network (ANN) is one of the innovative methods for predicting the structural and dynamic properties of atomic nuclei. In this work, we employed machine learning based on the Deep Neural Network (DNN) technique to find the ground state binding energy and beta decay energy of various nuclei. 3560 experimental nuclear data sets have been used for training and validating the DNN model. Neutron number (N), proton number (Z), the pairing term (δ), a magic number greater than or equal to N and Z, asymmetry factor (a) and promiscuity factor (P) are used as input parameters. The Rectified Linear Unit (ReLU) function and Mean Absolute Error (MAE) are used as activation and Loss functions for the training process. We perform the predictions of ground state binding energy per nucleon and beta decay energies in Zinc and Promethium isotopes using the DNN model, which is in good agreement with experimental results.

Data-Aided CSI Estimation Using Affine-Precoded Superimposed Pilots in Orthogonal Time Frequency Space Modulated MIMO Systems

An orthogonal affine-precoded superimposed pilot (AP-SIP)-based architecture is developed for the cyclic prefix (CP)-aided single input single output (SISO) and multiple input multiple output (MIMO) orthogonal time frequency space (OTFS) systems relying on arbitrary transmitter-receiver (Tx-Rx) pulse shaping. The data and pilot symbol matrices are affine-precoded and superimposed in the delay Doppler (DD)-domain followed by the development of an end-to-end DD-domain relationship for the input-output symbols. At the receiver, the decoupled pilot and data symbol are extracted by employing orthogonal precoder matrices, which eliminates the mutual interference. Furthermore, a novel pilot-aided Bayesian learning (PA-BL) technique is conceived for the channel state information (CSI) estimation of SISO OTFS systems based on the expectation-maximization (EM) technique. Subsequently, a data-aided Bayesian learning (DA-BL)-based joint CSI estimation and data detection technique is proposed, which beneficially harnesses the estimated data symbols for improved CSI estimation. In this scenario our sophisticated data detection rule also integrates the CSI uncertainty of channel estimation into our the linear minimum mean square error (LMMSE) detectors. The AP-SIP framework is also extended to MIMO OTFS systems, wherein the DD-domain input matrix is affine-precoded for each transmit antenna (TA). Then an EM algorithm-based PA-BL scheme is derived for simultaneous row-group sparse CSI estimation for this system, followed also by our data-aided DA-BL scheme that performs joint CSI estimation and data detection. Moreover, the Bayesian Cramer-Rao bounds (BCRBs) are also derived for both SISO as well as MIMO OTFS systems. Finally, simulation results are presented for characterizing the performance of the proposed CSI estimation techniques in a range of typical settings along with their bit error rate (BER) performance in comparison to an ideal system having perfect CSI.

A power efficient actively shielded two-channel transverse MRI gradient coil numerical design

Large and fast electrical current pulses are typically applied to conventional single-channel transverse MR gradient coils. However, these pulses result in a significant amount of power losses and heating of the coils. Previously, we presented a cylindrical multi-channel Z-gradient coil design that has better power efficiency compared to the single-channel design. In this work, we further investigate the DC power advantage for a two-channel actively-shielded transverse cylindrical gradient coil over the single-channel design. The conventional coil quadrants are radially divided into two sections, one for each channel, for both the primary and shielding surfaces. The symmetric inner sections of both the primary and shielding coils are assigned to the first channel, while the outer enclosing sections for each quadrant are assigned to the second channel. Discrete wire design is employed, where quasi-elliptic functions are used to parameterize the turns of each section. The coil geometric parameters, section size, number of turns, and turn locations are used as the design optimization parameters. The coils are optimized to maximize the coil’s efficiency while keeping the linearity error less than 10% and the shielding ratio above 85%. The design procedure is employed to design both the single and two-channel transverse gradient coils for comparison. Eleven different two-channel configurations having different section sizes were investigated. Results show that the power used to drive the most power-efficient two-channel coil is less than that of the single-channel design by ∼25%. Moreover, the two-channel configuration showed slightly better shielding efficiency.

Inference for the VEC(1) model with a heavy-tailed linear process errors*

This article studies the first-order vector error correction (VEC(1)) model when its noise is a linear process of independent and identically distributed (i.i.d.) heavy-tailed random vectors with a tail index . We show that the rate of convergence of the least squares estimator (LSE) related to the long-run parameters is n (sample size) and its limiting distribution is a stochastic integral in terms of two stable random processes, while the LSE related to the short-term parameters is not consistent. We further propose an automated approach via adaptive shrinkage techniques to determine the cointegrating rank in the VEC(1) model. It is demonstrated that the cointegration rank r 0 can be consistently selected despite the fact that the LSE related to the short-term parameters is not consistently estimable when the tail index . Simulation studies are carried out to evaluate the performance of the proposed procedure in finite samples. Last, we use our techniques to explore the long-run and short-run behavior of the monthly prices of wheat, corn, and wheat flour in the United States.

Torque-Based Control of a Bio-Inspired Modular Climbing Robot

This article presents a generalizable, low computational cost, simple, and fast gravity compensation method for legged robots with a variable number of legs. It is based on the static problem, which is a reduction in the dynamic model of the robot that takes advantage of the low velocity of climbing robots. To solve it, we propose a method that computes the torque to be applied by each actuator to compensate for the gravitational forces without using the Jacobian matrix for the forces exerted by the end-effector and without using analytical methods for the gravitational components of the model. We compare our method with the most popular method and conclude that ours is twice as fast. Using the proposed gravity compensator, we present a torque-based PD controller for the position of the leg modules, and a body velocity control without dynamic compensation. In addition, we validate the method with both hardware and a simulated version of the ROMERIN robot, a modular legged and climbing robot. Furthermore, we compare our controller with the usual kinematic inverse controllers, demonstrating that the mean angular and linear error is significantly reduced, as well as the power requirements of the actuators.

Improvement of pBRDF Model for Target Surface Based on Diffraction and Transmission Effects

The polarised Bidirectional Reflectance Distribution Function (pBRDF) model relates the properties of target materials to the polarisation information of the incident and reflected light. The Priest–Germer (P-G) model was the first strictly pBRDF model to be officially released; however, some shortcomings remain. In this study, we first analyse the assumption framework of the P-G model, analyse the assumption framework to determine the imperfections in the framework, supplement the boundary conditions of the model for diffraction and transmission effects, and propose and construct a polarised pBTDF model based on the existing P-G model and parameter inversion; the output results of the model are compared with the experimental data through simulation. The results show that the intensity relative error and Degree of Linear Polarisation relative error of the target can be reduced by more than 40%, using the improved model, proving its accuracy and precision.

Tracking Control of Wheeled Mobile Robot Based on MMPC

In order to solve the problems of low tracking accuracy and large steady-state error in track tracking of wheeled mobile robots, a MPC control scheme combining feedforward and feedback control is designed on the basis of Traditional Model Predictive Control (TMPC). First, when establishing the WMR kinematic error model, the linearization error is retained, and the control input and incremental constraints are considered. Secondly, a feedforward controller is designed for a given desired trajectory of wheeled mobile robot; At the same time, the multi constraint model predictive control (MMPC) strategy with speed optimization is added to design the feedback controller. Then, the stability of the designed MMPC controller is analyzed based on Lyapunov theory. Finally, MMPC control scheme is compared with TMPC control scheme and PID control scheme. The results show that compared with TMPC control scheme, MMPC control scheme reduces the lateral error by 17.87%, the longitudinal error by 17.12%, and the heading angle error by 9.81%; Compared with the PID control scheme, the lateral error is reduced by 20.82%, the longitudinal error is reduced by 23.26%, and the heading angle error is reduced by 5.87%.

Development of a linearized model for determining the temperature of thermal objects on the basis of radiation data

A piecewise linearized model has been developed for determining the temperature of thermal objects using their radiation characteristics in the IR range. The task of calculating the temperature of a thermal object is formulated as an optimization problem of a variational type, in which the task is to find such a dependence of the considered wavelength interval ∆λ = λ_2-λ_1 on the central wavelength λ_с =(λ_2-λ_1)/2, at which the value of the objective functional, equivalent to the calculated temperature reaches a minimum when a certain restrictive condition is imposed on the function ∆λ = ψ(λ_с). It is shown that the minimum of the objective functional is possible if the inverse dependence of ∆λ on λ_с is ensured, i.e. with increasing λ_с, ∆λ should decrease, which in turn leads to a decrease in the linearization error.

Linear Active Disturbance Rejection Control for Dual-Stator Winding Induction Generator AC Power System

In this article, a control strategy based on linear active disturbance rejection control (LADRC) is proposed for the dual-stator winding induction generator (DWIG) ac power system, in order to solve the problems of contradiction between tracking ability and dynamic performance with proportional-integral controller. Based on the rotor-flux-oriented coordinate system, the dynamic mathematic model of the output ac voltage of power winding (PW) is established. The load disturbance on the PW side and the variation of the system parameters are regarded as the total disturbance, which is observed and compensated by linear extended state observer (LESO) and linear state error feedback (LSEF), respectively. By analyzing the swiftness and disturbance-rejection ability with different bandwidths of LESO, the ac voltage LADRC controller is first designed for DWIG. The stability and performance analysis with different controller parameters is given and the robustness of the proposed controller under the parameter mismatch is investigated. Both simulation and experiments show that the proposed LADRC has a better tracking ability and dynamic performance. Moreover, the proposed LADRC also has strong robustness under the parameter mismatch.

MSTGAN: A Multi-Slot Conditional Generative Adversarial Network Based on Swin Transformer for Channel Estimation

Accurate channel estimation is the key to enhance the transmission performance of communication systems. In this letter, we propose a multi-slot conditional generative adversarial network (cGAN) based on Swin Transformer called MSTGAN for channel estimation in a single-input single-output (SISO) scenario. Specifically, the proposed MSTGAN could learn the temporal correlation feature from continuous channel slots by the 3D convolution and extract the deep feature well by the Swin Transformer to improve the accuracy of channel estimation. The model is trained with data augmentation to reduce the computational cost for offline training. The simulation results demonstrate that the proposed method outperforms the linear minimum mean square error (LMMSE) method and other deep learning methods. Furthermore, extension schemes of the MSTGAN to the multiple-input multiple-output (MIMO) case are also provided.

Interactive Distribution Expansion and Measurement Planning Considering Controlled Partitioning

To model interactions among system expansion, con-trolled partitioning (CP), and observability, an integrated multi-period framework is developed in this paper for simultaneous planning of distribution systems and measurements with CP con-straints (DSMP-CP) in unbalanced multi-phase networks. The proposed framework, employing the network AC model, is formu-lated as a mixed-integer quadratically-constrained programing problem. This problem minimizes investment costs (including the costs of feeder reinforcement, distributed generation (DG) place-ment, and allocation of micro-phasor measurement units and their measuring channels) and operation costs (including the costs of DG operation, energy purchased from the upstream grid (UG), re-dispatching of DG and UG injections, and energy curtailment). A phase-based observability function is also introduced to ensure the observability of all phases of buses. Furthermore, the concept of zero-injection (ZI) property is proposed for ZI groups considering physical connections and mutual impedances among phases to en-hance observability efficiency and avoid suboptimal solutions. To enhance problem tractability and eliminate linearization errors, a duality-based solution approach is proposed employing an exact-ness loop with recursive re-linearization. The performance of the proposed framework is evaluated by testing it on the unbalanced IEEE 111-node and 256-node distribution test systems.

LINEAR AND NON-LINEAR WAVELET APPROXIMATIONS OF FUNCTIONS OF LIPSCHITZ CLASS AND RELATED CLASSES USING THE HAAR WAVELET SERIES

In this paper, linear wavelet approximation of a functions f belonging to Lipξ, and Lip(ξ, p), 1 ≤ p < ∞, have been determined by using Haar scaling function and Haar wavelet series. A non-linear wavelet approximation of function belonging L2(R) and Lipα class has been obtained. The comparison of the order of linear and non-linear approximations have been studied. It is observed that a non-linear approximation error is better and sharper than linear approximation error.

Solution of filtration problems of construction geotechnology in thin water layers

Filtration problems of construction geotechnics during water movement in thin permeable layers of soils and artificial materials are considered. Under such conditions, traditional approaches borrowed from classical hydrogeology give errors. This is due to the fact that under normal conditions of underground aquifers of a sufficiently large depth, in hydrogeological practice, the hydraulic theory of filtration is used, in which the velocities of filtration currents are averaged along the vertical coordinate. The original nonlinear differential equations of filtration flows are subjected to forced linearization by one or another known method. In this case, the method of linearization by introducing the average power (depth) of the filtration flow is widely used. This method was originally developed for aquifers of great depth. In the presented work, an attempt was made to abandon such a linearization and solve some of the problems of unsteady filtration flows in thin aquifers, which are characteristic of building geotechnics, with obtaining analytical solutions of the final form without introducing artificial simplifications. A methodology is proposed for combining analytical and numerical methods in the process of finding solutions to filtration problems of construction geotechnics with obtaining self-similar dependencies. This approach will make it possible to avoid linearization errors and carry out filtration calculations in thin permeable layers of soils and artificial materials more accurately. A review of domestic and foreign scientific publications on the topic of research has shown some stagnation in this direction. The comparison revealed that in thin permeable layers of soils and artificial materials, preference can be given to filtration calculations using the presented method, since it more accurately describes the non-stationary movement of water in construction geotechnics.

Super resolution direction finding technique of vortex electromagnetic wave radar in missing mode

Vortex electromagnetic waves have superior performance over electromagnetic waves. In order to improve the radar super-resolution lateralization technique in its missing modes, this study proposes to start from the perspective of mode missing. The missing modes are reconstructed using the Adaptive Step Size Gradient Descent (ASSGD) method by exploiting the features of the missing modes. The linear minimum mean square error (LMMSE) estimation method is also used to solve the problem of poor reconstruction accuracy due to the Missing Modes. The Missing Modes Iterative Adaptive Approach (MMIAA) algorithm and Missing Modes Sparse Learning via Iterative Minimization (MMSLIM) algorithm are then used. Minimization (MMSLIM) algorithm to recover missing modes. The results showed that the RMSEs of the recovery errors of MMSLIM, MMIAA and ASSGD were 0.16, 0.31 and 0.82 respectively at a modal missing ratio of 0.7, while ASSGD fails to recover the missing modal data at a modal missing ratio of 0.9. The overall data quality of the azimuthally estimated RMSE was average when the signal-to-noise ratio was at [–5, 10] dB. And the curve becomes flatter when it reaches 15 dB or more, indicating that MMSLIM, MMIAA has important theoretical and practical value.

Association between urban greenspace, tree canopy cover and intentional deaths: An exploratory geospatial analysis

Greenspaces can provide restorative experiences, offer opportunities for outdoor recreation, and reduce mental fatigue; all of which may improve community health and safety. Yet few studies have examined the neighborhood-level benefits of greenspace in reducing violent deaths. This study explored the association between three distinct greenspace metrics: public greenspace quantity, public greenspace accessibility, neighborhood tree canopy cover, and intentional deaths (i.e., homicides and suicides). Generalized linear models and spatial error models investigated the association between greenspace, tree canopy and intentional deaths in three geographically distinct cities in North Carolina, USA. Results revealed that increased neighborhood greenspace accessibility and tree canopy cover were associated with reduced intentional deaths in all three urban areas. Neighborhood greenspace accessibility was the most protective factor across all study areas. The association between neighborhood greenspace accessibility and intentional deaths was more significant for non-firearm deaths as compared to firearm deaths, indicating that weapon type may be an important consideration for neighborhood greenspace interventions. Compared to predominantly White neighborhoods, predominantly Black neighborhoods had higher rates of homicide in Asheville and Durham and higher rates of suicide in Charlotte. Future policy and research should focus on improving equitable access to existing and future greenspaces, especially in primarily Black neighborhoods.

Forecast accuracy of the linear and nonlinear autoregressive models in macroeconomic modeling

AbstractMost nonlinear vector autoregressive methods in the econometric literature are based on specific functional forms, such as the smooth transition autoregressive model. This study proposes a general form of the nonlinear vector autoregressive model based on global approximators, such as neural networks, Volterra, and Weiner series. The simulation results of 20 linear and nonlinear multivariate time series processes indicate that nonlinear vector autoregressive methods, especially multi‐output neural networks, are more accurate based on the root mean square error and model confidence set criteria. Applying the global approximator approach to a small‐scale macroeconometric model reveals that the new approach can improve forecast accuracy compared to linear and other nonlinear vector error correction models. In addition, forecasting the relevant variables in a typical exchange rate and monetary policy models based on nonlinear specifications gives more successful results than in the linear case.

Multi-position control of movements of large-sized structural elements during static loading using a laser tracker

One of the most important tasks in the manufacturing of aerospace products is the control of their geometric parameters at various stages of production and assessment of their compliance with the requirements of design documentation. The use of laser automated measuring systems makes it possible to increase the measurement speed and to use the product digital model as a reference point. The best results in solving such problems can be obtained using laser automated measuring systems, such as laser scanners and laser trackers. In this paper a two-position measurement system is applied to control the aluminum alloy fuel component tank of the designed launch vehicle with two modes of static loading, corresponding to different transportation conditions. In this case, the linear dimension error should not exceed 150 m. A mathematical model of a multi-position measuring system is constructed and measurement uncertainty equations are obtained. In this case, the error function value that represents the difference between the errors in determining the coordinates of the reference points and the controlled points of the measurement object should be minimal. This mathematical model will be further used for numerical modeling that will allow selecting the optimal configuration of a measuring system for multi-position control of the tank geometric parameters in the static loading process.