Joint Error Research Articles

Modeling Time-Varying Dependencies Between Positive-Valued High-Frequency Time Series

Multiplicative error models (MEM) became a standard tool for modeling conditional durations of intraday transactions, realized volatilities and trading volumes. The parametric estimation of the corresponding multivariate model, the so-called vector MEM (VMEM), requires a specification of the joint error term distribution, which is due to the lack of multivariate distribution functions on Rd + defined via a copula. Maximum likelihood estimation is based on the assumption of constant copula parameters and therefore, leads to invalid inference, if the dependence exhibits time variations or structural breaks. Hence, we suggest to test for time-varying dependence by calibrating a time-varying copula model and to reestimate the VMEM based on identified intervals of homogenous dependence. This paper summarizes the important aspects of (V)MEM, its estimation and a sequential test for changes in the dependence structure. The techniques are applied in an empirical example.

Self‐Calibrated Energy‐Efficient and Reliable Channels for On‐Chip Interconnection Networks

Energy‐efficient and reliable channels are provided for on‐chip interconnection networks (OCINs) using a self‐calibrated voltage scaling technique with self‐corrected green (SCG) coding scheme. This self‐calibrated low‐power coding and voltage scaling technique increases reliability and reduces energy consumption simultaneously. The SCG coding is a joint bus and error correction coding scheme that provides a reliable mechanism for channels. In addition, it achieves a significant reduction in energy consumption via a joint triplication bus power model for crosstalk avoidance. Based on SCG coding scheme, the proposed self‐calibrated voltage scaling technique adjusts voltage swing for energy reduction. Furthermore, this technique tolerates timing variations. Based on UMC 65 nm CMOS technology, the proposed channels reduces energy consumption by nearly 28.3% compared with that for uncoded channels at the lowest voltage. This approach makes the channels of OCINs tolerant of transient malfunctions and realizes energy efficiency.

Cartesian sliding PID control schemes for tracking robots with uncertain Jacobian

Owing to the fact that desired tasks are usually defined in operational coordinates, inverse and direct kinematics must be computed to obtain joint coordinates and Cartesian coordinates, respectively. However, in order to avoid the ill-posed nature of the inverse kinematics, Cartesian controllers have been proposed. Considering that Cartesian controllers are based on the assumption that the Jacobian is well known, an uncertain Jacobian will produce a non-exact localization of the end-effector. In this paper, we present an alternative approach to solve the problem of Cartesian tracking for free and constrained motion subject to Jacobian uncertainty. These Cartesian schemes are based on sliding PID controllers where the Cartesian errors are mapped into joint errors without any knowledge of robot dynamics. Sufficient conditions for feedback gains and stability properties of the estimate inverse Jacobian are presented to guarantee stability. Experimental results are provided to visualize the real-time stability properties of the Cartesian proposed schemes.

A General Approach for Geometric Error Modeling of Lower Mobility Parallel Manipulators

This paper presents a general and systematic approach for geometric error modeling of lower mobility manipulators. The approach can be implemented in three steps: (1) development of a linear map between the pose error twist and source errors within an individual limb using the homogeneous transformation matrix method; (2) formulation of a linear map between the pose error twist and the joint error intensities of a lower mobility parallel manipulator; and (3) combination of these two models. The merit of this approach lies in that it enables the source errors affecting the compensatable and uncompensatable pose accuracy of the platform to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement achievable by suitable measures, i.e., component tolerancing in design, manufacturing and assembly processes, and kinematic calibration. Three typical and well-known parallel manipulators are taken as examples to illustrate the generality and effectiveness of this approach.

Geometric error compensation of spherical surface grinding system

Kinematics theory for a multi-body system is used to analyse translational joint error, rotational joint error, and quadrature error in a spherical grinding system. A virtual grinding point method is proposed that is based on process features, and the feasibility as well as effectiveness of this method is demonstrated. A volumetric error model of the grinding system is created and the compensation method is coded into a control computer program. A laser interferometer is used to experimentally measure the error both with and without the proposed error compensation scheme. The experimental results validate the proposed approach in that they show that the spherical surface grinding precision is significantly improved.

Robot accuracy evaluation using a ball-bar link system

SUMMARYRelatively large errors can exist in industrial robots as a result of mismatch between the controller model and the corresponding physical model. The paper outlines a novel approach for accuracy assessment and adjustment of multiaxis industrial robots through a low-cost ball-bar link system. The features of the ball-bar, which incorporated a 12 mm range digital displacement transducer in conjunction with a PC, are discussed. The ball-bar device was used in both a trammelling and circular mode of operation. This produced data which not only related to the accuracy of the robot but also enabled joint errors to be significantly reduced.

On the (in)security of two Joint Encryption and Error Correction schemes

Joint Encryption and Error Correction (JEEC) is proposed to combine encoding/encryption as one process to boost more compact implementations. In this paper, we provide rigorous investigation on the security of two JECC schemes, namely ECBC and SECC. For ECBC, we found a 3-stage differential-like attack, which breaks it with O(k × 2

Diversity-Multiplexing Tradeoff Analysis for OFDM Systems With Subcarrier Grouping, Linear Precoding, and Linear Detection

We consider the use of linear constellation precoding and linear detection in a multicarrier OFDM system with multiple receive antennas to obtain improved performance over multipath fading channels at a low complexity. We split the full set of subcarriers into smaller groups and spread the data symbols assigned to each group via precoding matrices. We adopt the diversity-multiplexing tradeoff (DMT) framework and derive the DMT-optimal split of the subcarriers (DMT-optimal grouping) and the DMT-optimal number of symbols assigned to each group (DMT-optimal symbol loading). We determine necessary and sufficient precoder design conditions to achieve DMT optimality and give specific constructions of such precoders. Next, we consider a multiuser OFDMA system and derive an algorithm which divides the available subcarriers among the active users in order to maximize the diversity order of the system (or joint) error probability. We also extend our analysis to OFDM systems equipped with multiple transmit antennas. Finally, we obtain important insights on the role of outer codes in an OFDM system employing linear precoding and linear equalization.

Accuracy Analysis and Simulation of Three Degrees of Freedom Parallel Machine Tool

This paper proposes a novel three degrees of freedom parallel machine tool. The parallel machine tool consists of three serial chains and a fixed base and a moving platform which can be moved in a pose space corresponding to the three degrees of freedom. By using matrix methods, a error model of the parallel machine was developed. The explicit solution of the error of joint and the stroke error of telescopic link were solved for analysis of influence factors of error on the position of moving platform. It provided a theoretical foundation for error compensation of parallel machine tool.

Maximum error modeling for fault-tolerant computation using maximum a posteriori (MAP) hypothesis

The application of current generation computing machines in safety-centric applications like implantable biomedical chips and automobile safety has immensely increased the need for reviewing the worst-case error behavior of computing devices for fault-tolerant computation. In this work, we propose an exact probabilistic error model that can compute the maximum error over all possible input space in a circuit-specific manner and can handle various types of structural dependencies in the circuit. We also provide the worst-case input vector, which has the highest probability to generate an erroneous output, for any given logic circuit. We also present a study of circuit-specific error bounds for fault-tolerant computation in heterogeneous circuits using the maximum error computed for each circuit. We model the error estimation problem as a maximum a posteriori (MAP) estimate [28,29], over the joint error probability function of the entire circuit, calculated efficiently through an intelligent search of the entire input space using probabilistic traversal of a binary Join tree using Shenoy–Shafer algorithm [20,21]. We demonstrate this model using MCNC and ISCAS benchmark circuits and validate it using an equivalent HSpice model. Both results yield the same worst-case input vectors and the highest percentage difference of our error model over HSpice is just 1.23%. We observe that the maximum error probabilities are significantly larger than the average error probabilities, and provides a much tighter error bounds for fault-tolerant computation. We also find that the error estimates depend on the specific circuit structure and the maximum error probabilities are sensitive to the individual gate failure probabilities.

ISI mitigation for wireless communications in buildings with diversified turbo equalization

In an indoor wireless communication environment, the effect of multipath fading (or equivalently speaking, intersymbol interference (ISI)) is a significant factor that can degrade communication quality. In this paper, we propose a joint error control and equalization scheme to deal with this problem. We call this scheme by the name of diversified turbo equalization (abbreviated as DTE). It is an extension of the turbo equalization (abbreviated as TE) scheme proposed by Douillard et al., 1995. At the receiver, iterative decoding is applied to equalize the received signal and decode the data bits. We also present an analytical method, based on EXIT (extrinsic information transfer) charts, to predict the BER performance of DTE. Realizing the power of diversity in fighting the fading effect, we generalize the DTE for use in the MIMO (multiple‐input multiple‐output) scenario, where spatial diversity is provided. The resultant scheme is called MIMO‐DTE. Simulation results on DTE show two things. First, the DTE is better (in bit error rate (BER) performance) than the TE when the channel signal‐to‐noise power ratio (SNR) is high enough. Second, the predicted BER's are close to the experimentally obtained results. As to the MIMO‐DTE, simulation results show that its BER performance is better than both the DTE and the TE.

Autonomic QoS Optimization of Real-Time Internet Audio Using Loss Prediction and Stochastic Control

Quality of Internet audio is highly sensitive to packet loss caused by congestion in links. Packet loss for audio is normally rectified by adding redundancy using Forward Error Correction (FEC). Alternatively, path diversity mechanisms are used to improve reliability and thus session quality. To achieve optimized receiver audio quality for transmissions using single or multiple paths, the authors propose a self-adaptive joint Error and Rate Control framework based on packet loss prediction and on-line quality assessment. The Error Control chooses appropriate FEC proactively to preserve quality with optimal bandwidth, using a Markov Decision Process (MDP) and a stochastic inventory control, a novel approach for multimedia error recovery. The Rate Control uses a quality optimization model to determine the optimal dispersion over single or multiple paths. This paper will present results using simulation and Internet experiments to show the superiority of this mechanism over other similar techniques.

LOWER BOUNDS ON PHOTOMETRIC REDSHIFT ERRORS FROM TYPE Ia SUPERNOVA TEMPLATES

Cosmology with Type Ia supernovae heretofore has required extensive spectroscopic follow-up to establish a redshift. Though tolerable at the present discovery rate, the next generation of ground-based all-sky survey instruments will render this approach unsustainable. Photometry-based redshift determination is a viable alternative, but introduces non-negligible errors that ultimately degrade the ability to discriminate between competing cosmologies. We present a strictly template-based photometric redshift estimator and compute redshift reconstruction errors in the presence of photometry and statistical errors. With reasonable assumptions for a cadence and supernovae distribution, these redshift errors are combined with systematic errors and propagated using the Fisher matrix formalism to derive lower bounds on the joint errors in $\Omega_w$ and $\Omega_w'$ relevant to the next generation of ground-based all-sky survey.

Approximation and asymptotics of eigenvalues of unbounded self-adjoint Jacobi matrices acting in l 2 by the use of finite submatrices

Abstract We consider the problem of approximation of eigenvalues of a self-adjoint operator J defined by a Jacobi matrix in the Hilbert space l 2(ℕ) by eigenvalues of principal finite submatrices of an infinite Jacobi matrix that defines this operator. We assume the operator J is bounded from below with compact resolvent. In our research we estimate the asymptotics (with n → ∞) of the joint error of approximation for the eigenvalues, numbered from 1 to N; of J by the eigenvalues of the finite submatrix J n of order n × n; where N = max{k ∈ ℕ: k ≤ rn} and r ∈ (0; 1) is arbitrary chosen. We apply this result to obtain an asymptotics for the eigenvalues of J. The method applied in this research is based on Volkmer’s results included in [23].

Interpolatory Projection Methods for Parameterized Model Reduction

We provide a unifying projection-based framework for structure-preserving interpolatory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to retain in the reduced-order model. The parameter dependence may be linear or nonlinear and is retained in the reduced-order model. Moreover, we are able to give conditions under which the gradient and Hessian of the system response with respect to the system parameters is matched in the reduced-order model. We provide a systematic approach built on established interpolatory $\mathcal{H}_2$ optimal model reduction methods that will produce parameterized reduced-order models having high fidelity throughout a parameter range of interest. For single input/single output systems with parameters in the input/output maps, we provide reduced-order models that are optimal with respect to an $\mathcal{H}_2\otimes\mathcal{L}_2$ joint error measure. The capabilities of these approaches are illustrated by several numerical examples from technical applications.

Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices

The research included in the paper concerns a class of symmetric block Jacobi matrices. The problem of the approximation of eigenvalues for a class of a self-adjoint unbounded operators is considered. We estimate the joint error of approximation for the eigenvalues, numbered from \(1\) to \(N\), for a Jacobi matrix \(J\) by the eigenvalues of the finite submatrix \(J_n\) of order \(pn \times pn\), where \(N = \max \{k \in \mathbb{N}: k \leq rpn\}\) and \(r \in (0,1)\) is suitably chosen. We apply this result to obtain the asymptotics of the eigenvalues of \(J\) in the case \(p=3\).

Probing cosmology and galaxy cluster structure with the Sunyaev���Zel'dovich decrement versus X-ray temperature scaling relation

Scaling relations among galaxy cluster observables, which will become available in large future samples of galaxy clusters, could be used to constrain not only cluster structure, but also cosmology. We study the utility of this approach, employing a physically motivated parametric model to describe cluster structure, and applying it to the expected relation between the Sunyaev-Zel'dovich decrement (S_\nu) and the emission-weighted X-ray temperature (T_ew). The slope and normalization of the entropy profile, the concentration of the dark matter potential, the pressure at the virial radius, and the level of non-thermal pressure support, as well as the mass and redshift-dependence of these quantities are described by free parameters. With a suitable choice of fiducial parameter values, the cluster model satisfies several existing observational constraints. We employ a Fisher matrix approach to estimate the joint errors on cosmological and cluster structure parameters from a measurement of S_\nu vs. T_ew in a future survey. We find that different cosmological parameters affect the scaling relation differently: predominantly through the baryon fraction (\Omega_m and \Omega_b), the virial overdensity (w_0 and w_a for low-z clusters) and the angular diameter distance (w_0, w_a for high-z clusters; \Omega_DE and h). We find that the cosmology constraints from the scaling relation are comparable to those expected from the number counts (dN/dz) of the same clusters. The scaling relation approach is relatively insensitive to selection effects and it offers a valuable consistency check; combining the information from the scaling relation and dN/dz is also useful to break parameter degeneracies and help disentangle cluster physics from cosmology.

Maximum-Likelihood Priority-First Search Decodable Codes for Combined Channel Estimation and Error Correction

The coding technique that combines channel estimation and error correction has received attention recently, and has been regarded as a promising approach to counter the effects of multipath fading. It has been shown by simulation that a proper code design that jointly considers channel estimation can improve the system performance subject to a fixed code rate as compared to a conventional system which performs channel estimation and error correction separately. Nevertheless, the major obstacle that prevents the practice of such coding technique is that the existing codes are mostly searched by computers, and subsequently exhibit no apparent structure for efficient decoding. Hence, the operation-intensive exhaustive search becomes the only decoding option, and the decoding complexity increases dramatically with codeword length. In this paper, a systematic construction is derived for a class of structured codes that support joint channel estimation and error correction. It is confirmed by simulation that these codes have comparable performance to the best simulated-annealing-based computer-searched codes. Moreover, the systematically constructed codes can now be maximum-likelihoodly decoded with respect to the unknown-channel criterion in terms of a newly derived recursive metric for use by the priority-first search decoding algorithm. Thus, the decoding complexity is significantly reduced as compared with that of an exhaustive decoder.

Channel Coding For High-Speed Links: A Systematic Look at Code Performance and System Simulation

While channel coding is a standard method of improving a system's energy efficiency in digital communications, its practice does not extend to high-speed links. Increasing demands in network speeds are placing a large burden on the energy efficiency of high-speed links and render the benefit of channel coding for these systems a timely subject. The low error rates of interest and the presence of residual intersymbol interference (ISI) caused by hardware constraints impede the analysis and simulation of coded high-speed links. Focusing on the residual ISI and combined noise as the dominant error mechanisms, this paper analyzes error correlation through concepts of error region, channel signature, and correlation distance. This framework provides a deeper insight into joint error behaviors in high-speed links, extends the range of statistical simulation for coded high-speed links, and provides a case against the use of biased Monte Carlo methods in this setting. Finally, based on a hardware test bed, the performance of standard binary forward error correction and error detection schemes is evaluated, from which recommendations on coding for high-speed links are derived.

Adaptive trajectory control and friction compensation of a flexible-link robot

An adaptive trajectory-tracking controller is developed for a single flexible-link manipulator with presence of friction in the joint and parametric uncertainties. The distributed-parameter dynamic modeling approach is used to design the controller. To eliminate large steady-state tracking error, an adaptive friction compensation technique is proposed based on general static friction model. Reduction of effects of data corruption by noise is obtained using a filtering technique. The global asymptotic stability is guaranteed using the Lyapunov stability theorem. The position tracking performance and link vibration attenuation is verified through experimental results. It also shows that the steady-state joint error is significantly eliminated and the noise effect in the control signal is efficiently reduced.