Systolic Algorithms and Architectures for High-Throughput Processing Applications

Real-time reconstruction of the time-dependent heat flux and temperature distribution in participating media by using the Kalman filtering technique

The protection of sensitive and confidential data become a challenging task in the present scenario as more and more digital data is stored and transmitted between the end users. The privacy is vitally necessary in case of medical data, which contains the important information of the patients. In this article, a novel biometric inspired medical encryption technique is proposed based on newly introduced parameterized all phase orthogonal transformation (PR-APBST), singular value, and QR decomposition. The proposed technique utilizes the biometrics of the patient/owner to generate a key management system to obtain the parameters involved in the proposed technique. The medical image is then encrypted employing PR-APBST, QR and singular value decomposition and is ready for secure transmission or storage. Finally, a reliable decryption process is employed to reconstruct the original medical image from the encrypted image. The validity and feasibility of the proposed framework have been demonstrated using an extensive experiments on various medical images and security analysis.

This paper is an updated and extended version of the paper "The QR Decomposition and the Singular Value Decomposition in the Symmetrized Max-Plus Algebra" (B. De Schutter and B. De Moor, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 378--406). The max-plus algebra, which has maximization and addition as its basic operations, can be used to describe and analyze certain classes of discrete-event systems, such as flexible manufacturing systems, railway networks, and parallel processor systems. In contrast to conventional algebra and conventional (linear) system theory, the max-plus algebra and the max-plus-algebraic system theory for discrete-event systems are at present far from fully developed, and many fundamental problems still have to be solved. Currently, much research is going on to deal with these problems and to further extend the max-plus algebra and to develop a complete max-plus-algebraic system theory for discrete-event systems. In this paper we address one of the remaining gaps in the max-plus algebra by considering matrix decompositions in the symmetrized max-plus algebra. The symmetrized max-plus algebra is an extension of the max-plus algebra obtained by introducing a max-plus-algebraic analogue of the $-$-operator. We show that we can use well-known linear algebra algorithms to prove the existence of max-plus-algebraic analogues of basic matrix decompositions from linear algebra such as the QR decomposition, the singular value decomposition, the Hessenberg decomposition, the LU decomposition, and so on. These max-plus-algebraic matrix decompositions could play an important role in the max-plus-algebraic system theory for discrete-event systems.

An estimation fusion algorithm based on a group of hybrid coordinate (HC) filters is presented to the position and velocity estimation using angle-only measurements extracted from multiple maneuverable aircrafts with onboard passive sensor. The algorithm is a hierarchical architecture which consists of several local processors and a global processor. In each local processor, an extended Kalman (EK) filter utilizes the reference Cartesian coordinate (RCC) system for state and state covariance extrapolation and utilizes the modified spherical coordinate (MSC) system for state and state covariance updating. In the global processor, a recursive least squares (RLS) estimator sequentially computes a global estimate in the local inertial Cartesian coordinate (LICC) system. The estimator is developed by utilizing RCC updated state covariance to compute each filter weight for combining the outputs of local processors. The typical case of target motion analysis is investigated through computer simulation. In simulation study the proposed algorithm is compared to each HC EK filter. The EK filter encounters slow convergence problem under both circular arc and waving flight scenarios. By using a RLS estimator, the convergence is greatly accelerated. The algorithm markedly improves the tracking accuracy as well.

In many circumstances involving heat and mass transfer issues, it is considered impractical to measure the input flux and the resulting state distribution in the domain. Therefore, the need to develop techniques to provide solutions for such problems and estimate the inverse mass flux becomes imperative. Adaptive state estimator (ASE) is increasingly becoming a popular inverse estimation technique which resolves inverse problems by incorporating the semi-Markovian concept into a Bayesian estimation technique, thereby developing an inverse input and state estimator consisting of a bank of parallel adaptively weighted Kalman filters. The ASE is particularly designed for a system that encompasses independent unknowns and /or random switching of input and measurement biases. The present study describes the scheme to estimate the groundwater input contaminant flux and its transient distribution in a conjectural two-dimensional aquifer by means of ASE, which in particular is because of its unique ability to efficiently handle the process noise giving an estimation of keeping the relative error range within 10% in 2-dimensional problems. Numerical simulation results show that the proposed estimator presents decent estimation performance for both smoothly and abruptly varying input flux scenarios. Results also show that ASE enjoys a better estimation performance than its competitor, Recursive Least Square Estimator (RLSE) due to its larger error tolerance in greater process noise regimes. ASE’s inherent deficiency of being slower than the RLSE, resulting from the complexity of algorithm, was also noticed. The chosen input scenarios are tested to calculate the effect of input area and both estimators show improved results with an increase in input flux area especially as sensors are moved closer to the assumed input location.

A conditional fuzzy c-means (CFCM)-based fuzzy adaptive neuro-fuzzy system (ANFS) by on-line learning is proposed in this paper. In the structure identification, the optimal or near optimal number of fuzzy rules is determined by a CFCM clustering with TSK-type fuzzy rules based on the criterion. In the parameter identification. The consequent parameters are tuned by least squares estimator (LSE) and the premise parameters are tuned by back-propagation algorithm in off-line learning. Then on-line learning by recursive least squares estimator (RLSE) and back-propagation algorithm is used to cope with time varying plant dynamics. Finally, we show its capability for a CFCM-based on-line ANFS to control the temperature of a water path.

Underwater target tracking system can be kept covert using the bearing-only or the bearing-Doppler measurements (passive measurements), which will reduce the risk of been detected. According to the characteristics of underwater target tracking, the square root unscented Kalman filter (SRUKF) algorithm, which is based on the Bayesian theory, was applied to the underwater bearing-only and bearing-Doppler non-maneuverable target tracking problem. Aiming at the shortcomings of the unscented Kalman filter (UKF), the SRUKF uses the QR decomposition and the Cholesky factor updating, in order to avoid that the process noise covariance matrix loses its positive definiteness during the target tracking period. The SRUKF uses sigma sampling to avoid the linearization of the nonlinear bearing-only and the bearing-Doppler measurements. To ensure the target state observability in underwater target tracking, the paper uses single maneuvering observer to track the single non-maneuverable target. The simulation results show that the SRUKF has better tracking performance than the extended Kalman filter (EKF) and the UKF in tracking accuracy and stability, and the computational complexity of the SRUKF algorithm is low.

For each pixel, the values of the unwrapped phase produced by interferometric pairs can be parameterized and phase components, such as height, atmospheric path delay difference for the dates of every interferometric set image acquisition, and unwrapping error can be estimated through the solution of a rank deficient system of equations. There are several state of the art methods for solving rank deficient systems of equations, such as the Lower-Upper method, QR factorization and Singular Value Decomposition (SVD). In a previous work, the improved SVD method, which enables the accurate estimation of phase components, has been proposed. In this study, one alternative method for the estimation of the differential interferometry parameters, the improved QR, is proposed. The method relies on the reorganization of the system of equations by using external meteorological data which correspond to the acquisition dates that are less present in the interferometric SAR data set. All the aforementioned methods were tested and compared. The improved SVD and improved QR methods yield the most satisfactory results for all the phase components. The former estimates the heights by achieving almost GPS accuracy, whereas the latter is more robust, producing results of almost the same accuracy for all the estimated atmospheric path delays. However, the requirement of known values for at least two phase components makes the improved QR method less operational.

Research on improved dynamic load identification method based on Kalman filter under noise interference

This work presents an inverse method based on the input estimation method including the finite-element scheme to estimate unknown heat flux. The input estimation method is comprised of the Kalman filtering technique and a recursive least-squares estimator. This recursive least-squares estimator is weighted by the forgetting factor γ. It is derived using the residual innovation sequence to compute the magnitude of the heat flux, and the discretization is carried out using the finite-element scheme. The superior capabilities of the proposed method are demonstrated in one-dimensional and two-dimensional time-varying estimate cases and by comparison of the proposed algorithm with the conjugate gradient method. Results show that this method has the advantages of stability and good accuracy.

Feature selection using singular value decomposition and QR factorization with column pivoting for text-independent speaker identification

A new approach to linear discriminant analysis that puts the burden of the computational load on solving a linear least squares problem rather than on solving a generalized eigensystem is presented. The problem being solved is that of reducing the dimension of a vector space in which several classes of objects are to have the best possible separation after the dimension reduction. Two similar algorithms using the least squares approach are developed, one based on the singular value decomposition and the other on orthogonal triangularization (QR factorization). The version using the singular value decomposition is more stable, especially in the nearly rank deficient case. The orthogonal triangularization version is faster, and is the preferred method if updating is anticipated.

An algorithm to estimate the tangential and normal accelerations directly using the Doppler radar measurement in an online closed loop form is proposed. Specific works are as follows: first, the tangential acceleration and normal acceleration are taken as the state variables to establish a linear state transition equation; secondly, the decorrelation unbiased conversion measurement Kalman filter (DUCMKF) algorithm is proposed to deal with the strongly nonlinear measurement equation; thirdly, the geometric relationship between the range rate and the velocity direction angle is used to obtain two estimators of the velocity direction angle; finally, the interactive multiple model (IMM) algorithm is used to fuse the estimators of the velocity direction angle and then the adaptive IMM of current statistical model based DUCMKF (AIMM-CS-DUCMKF) is proposed. The simulation experiment results show that the accuracy and stability of DUCMKF are better than the sequential extended Kalman filter algorithm, the sequential unscented Kalman filter algorithm, and converted measurement Kalman filter algorithms; on the other hand they show that the AIMM-CS-DUCMKF can obtain the high accuracy of the tangential and normal accelerations estimation algorithm.

Consideration is given to the problem of mapping systolic array algorithms into efficient algorithms for a fixed-size hypercube architecture. The authors describe in detail several optimal implementations of algorithms given for one-way one- and two-dimensional systolic arrays. Since interprocessor communication is many times slower than local computation in parallel computers built to date, the problem of efficient communication is specifically addressed for these mappings. In order to validate the technique experimentally, five systolic algorithms were mapped in various ways onto a 64-node NCUBE/7 MIMD hypercube machine. The algorithms are for the following problems: the shuffle scheduling problem, finite impulse response filtering, linear context-free language recognition, matrix multiplication, and computing the Boolean transitive closure. Experimental evidence indicates that good performance is obtained for the mappings. >

This paper presents direct field oriented control sensorless speed servo for induction motors where the main contribution is the use of low-cost electrical sensors. It is possible due the use of a linear Kalman filter. The current estimates are used in a recursive least-square speed estimator. Moreover, estimated rotor flux provided by Kalman filter helps to keep the flux and torque decoupling. As it is presented in this paper, with both techniques working together is possible to obtain good speed estimation with low noise level and computation effort, in spite of use current transducer that cost just some cents. Some experimental results are presented to evaluate this proposal.