Some Algorithms for Eigensubspace Estimation

An important tool in signal processing is the use of eigenvalue and singular value decompositions for extracting information from time-series/sensor array data. These tools are used in the so-called subspace methods that underlie solutions to the harmonic retrieval problem in time series and the directions-of-arrival (DOA) estimation problem in array processing. The subspace methods require the knowledge of eigenvectors of the underlying covariance matrix to estimate the parameters of interest. Eigenstructure estimation in signal processing has two important classes: (i) estimating the eigenstructure of the given covariance matrix and (ii) updating the eigenstructure estimates given the current estimate and new data. In this paper, we survey some algorithms for both these classes useful for harmonic retrieval and DOA estimation problems. We begin by surveying key results in the literature and then describe, in some detail, energy function minimization approaches that underlie a class of feedback neural networks. Our approaches estimate some or all of the eigenvectors corresponding to the repeated minimum eigenvalue and also multiple orthogonal eigenvectors corresponding to the ordered eigenvalues of the covariance matrix. Our presentation includes some supporting analysis and simulation results. We may point out here that eigensubspace estimation is a vast area and all aspects of this cannot be fully covered in a single paper. (C) 1995 Academic Press, Inc.

A Rotor Flux Estimation During Zero and Active Vector Periods Using Current Error Space Vector From a Hysteresis Controller for a Sensorless Vector Control of IM Drive

This paper proposes a sensorless vector control scheme for general-purpose induction motor drives using the current error space phasor-based hysteresis controller. In this paper, a new technique for sensorless operation is developed to estimate rotor voltage and hence rotor flux position using the stator current error during zero-voltage space vectors. It gives a comparable performance with the vector control drive using sensors especially at a very low speed of operation (less than 1 Hz). Since no voltage sensing is made, the dead-time effect and loss of accuracy in voltage sensing at low speed are avoided here, with the inherent advantages of the current error space phasor-based hysteresis controller. However, appropriate device on-state drops are compensated to achieve a steady-state operation up to less than 1 Hz. Moreover, using a parabolic boundary for current error, the switching frequency of the inverter can be maintained constant for the entire operating speed range. Simple sigma L-s estimation is proposed, and the parameter sensitivity of the control scheme to changes in stator resistance, R-s is also investigated in this paper. Extensive experimental results are shown at speeds less than 1 Hz to verify the proposed concept. The same control scheme is further extended from less than 1 Hz to rated 50 Hz six-step operation of the inverter. Here, the magnetic saturation is ignored in the control scheme.

Incremental-angle and angular velocity estimation using a star sensor

A method is described for estimating the incremental angle and angular velocity of a spacecraft using integrated rate parameters with the help of a star sensor alone. The chief advantage of this method is that the measured stars need not be identified, whereas the identification of the stars is necessary in earlier methods. This proposed estimation can be carried out with all of the available measurements by a simple linear Kalman filter, albeit with a time-varying sensitivity matrix. The residuals of estimated angular velocity by the proposed spacecraft incremental-angle and angular velocity estimation method are as accurate as the earlier methods. This method also enables the spacecraft attitude to be reconstructed for mapping the stars into an imaginary unit sphere in the body reference frame, which will preserve the true angular separation of the stars. This will pave the way for identification of the stars using any angular separation or triangle matching techniques applied to even a narrow field of view sensor that is made to sweep the sky. A numerical simulation for inertial as well as Earth pointing spacecraft is carried out to establish the results.

Lamb wave based identification and parameter estimation of corrosion in metallic plate structure using a circular PWAS array

A circular array of Piezoelectric Wafer Active Sensor (PWAS) has been employed to detect surface damages like corrosion using lamb waves. The array consists of a number of small PWASs of 10 mm diameter and 1 mm thickness. The advantage of a circular array is its compact arrangement and large area of coverage for monitoring with small area of physical access. Growth of corrosion is monitored in a laboratory-scale set-up using the PWAS array and the nature of reflected and transmitted Lamb wave patterns due to corrosion is investigated. The wavelet time-frequency maps of the sensor signals are employed and a damage index is plotted against the damage parameters and varying frequency of the actuation signal (a windowed sine signal). The variation of wavelet coefficient for different growth of corrosion is studied. Wavelet coefficient as function of time gives an insight into the effect of corrosion in time-frequency scale. We present here a method to eliminate the time scale effect which helps in identifying easily the signature of damage in the measured signals. The proposed method becomes useful in determining the approximate location of the corrosion with respect to the location of three neighboring sensors in the circular array. A cumulative damage index is computed for varying damage sizes and the results appear promising.

WCET Estimation for Executables in the Presence of Data Caches

This paper describes techniques to estimate the worst case execution time of executable code on architectures with data caches. The underlying mechanism is Abstract Interpretation, which is used for the dual purposes of tracking address computations and cache behavior. A simultaneous numeric and pointer analysis using an abstraction for discrete sets of values computes safe approximations of access addresses which are then used to predict cache behavior using Must Analysis. A heuristic is also proposed which generates likely worst case estimates. It can be used in soft real time systems and also for reasoning about the tightness of the safe estimate. The analysis methods can handle programs with non-affine access patterns, for which conventional Presburger Arithmetic formulations or Cache Miss Equations do not apply. The precision of the estimates is user-controlled and can be traded off against analysis time. Executables are analyzed directly, which, apart from enhancing precision, renders the method language independent.

Time delay to firing of a triggered vacuum gap with barium titanate in trigger gap

The time delay to the firing of a triggered vacuum gap (t.v.g.) containing barium titanate in the trigger gap is investigated as a function of the main gap voltage, main gap length, trigger pulse duration, trigger current and trigger voltage. The time delay decreases steadily with increasing trigger current and trigger voltage until it reaches saturation. The effect of varying the main gap length and voltage on the time delay is not strong. Before `conditioning�¿ the t.v.g. two groups of time delays, long (>100�¿s) and short (<10�¿s), are simultaneously observed when a large number of trials are conducted. After conditioning, only the group of short time delays are present. This is attributed to the marked reduction of the resistance of the trigger gap across the surface of the solid dielectric resulting directly from the conditioning effect.

Digital Dead Time Logic and Protection Circuitry for PWM Voltage Source Converters

Power semiconductor devices have finite turn on and turn off delays that may not be perfectly matched. In a leg of a voltage source converter, the simultaneous turn on of one device and the turn off of the complementary device will cause a DC bus shoot through, if the turn off delay is larger than the turn on delay time. To avoid this situation it is common practice to blank the two complementary devices in a leg for a small duration of time while switching, which is called dead time. This paper proposes a logic circuit for digital implementation required to control the complementary devices of a leg independently and at the same time preventing cross conduction of devices in a leg, and while providing accurate and stable dead time. This implementation is based on the concept of finite state machines. This circuit can also block improper PWM pulses to semiconductor switches and filters small pulses notches below a threshold time width as the narrow pulses do not provide any significant contribution to average pole voltage, but leads to increased switching loss. This proposed dead time logic has been implemented in a CPLD and is implemented in a protection and delay card for 3- power converters.

Adaptive window zero-crossing-based instantaneous frequency estimation

We address the problem of estimating instantaneous frequency (IF) of a real-valued constant amplitude time-varying sinusoid. Estimation of polynomial IF is formulated using the zero-crossings of the signal. We propose an algorithm to estimate nonpolynomial IF by local approximation using a low-order polynomial, over a short segment of the signal. This involves the choice of window length to minimize the mean square error (MSE). The optimal window length found by directly minimizing the MSE is a function of the higher-order derivatives of the IF which are not available a priori. However, an optimum solution is formulated using an adaptive window technique based on the concept of intersection of confidence intervals. The adaptive algorithm enables minimum MSE-IF (MMSE-IF) estimation without requiring a priori information about the IF. Simulation results show that the adaptive window zero-crossing-based IF estimation method is superior to fixed window methods and is also better than adaptive spectrogram and adaptive Wigner-Ville distribution (WVD)-based IF estimators for different signal-to-noise ratio (SNR).

Theoretical estimation of electromigration in metallic carbon nanotubes considering self-heating effect

In this paper, we estimate the solution of the electromigration diffusion equation (EMDE) in isotopically pure and impure metallic single-walled carbon nanotubes (CNTs) (SWCNTs) by considering self-heating. The EMDE for SWCNT has been solved not only by invoking the dependence of the electromigration flux on the usual applied static electric field across its two ends but also by considering a temperature-dependent thermal conductivity (κ) which results in a variable temperature distribution (T) along its length due to self-heating. By changing its length and isotopic impurity, we demonstrate that there occurs a significant deviation in the SWCNT electromigration performance. However, if κ is assumed to be temperature independent, the solution may lead to serious errors in performance estimation. We further exhibit a tradeoff between length and impurity effect on the performance toward electromigration. It is suggested that, to reduce the vacancy concentration in longer interconnects of few micrometers, one should opt for an isotopically impure SWCNT at the cost of lower κ, whereas for comparatively short interconnects, pure SWCNT should be used. This tradeoff presented here can be treated as a way for obtaining a fairly well estimation of the vacancy concentration and mean time to failure in the bundles of CNT-based interconnects. © 2012 IEEE.

Receive Antenna Selection for Time-Varying Channels Using Discrete Prolate Spheroidal Sequences

Receive antenna selection (AS) has been shown to maintain the diversity benefits of multiple antennas while potentially reducing hardware costs. However, the promised diversity gains of receive AS depend on the assumptions of perfect channel knowledge at the receiver and slowly time-varying fading. By explicitly accounting for practical constraints imposed by the next-generation wireless standards such as training, packetization and antenna switching time, we propose a single receive AS method for time-varying fading channels. The method exploits the low training overhead and accuracy possible from the use of discrete prolate spheroidal (DPS) sequences based reduced rank subspace projection techniques. It only requires knowledge of the Doppler bandwidth, and does not require detailed correlation knowledge. Closed-form expressions for the channel prediction and estimation error as well as symbol error probability (SEP) of M-ary phase-shift keying (MPSK) for symbol-by-symbol receive AS are also derived. It is shown that the proposed AS scheme, after accounting for the practical limitations mentioned above, outperforms the ideal conventional single-input single-output (SISO) system with perfect CSI and no AS at the receiver and AS with conventional estimation based on complex exponential basis functions.

Models for the estimation of life of stator insulation in large rotating machines

Epoxy resin bonded mica splitting is the insulation of choice for machine stators. However, this system is seen to be relatively weak under time varying mechanical stress, in particular the vibration causing delamination of mica and deboning of mica from the resin matrix. The situation is accentuated under the combined action of electrical, thermal and mechanical stress. Physical and probabilistic models for failure of such systems have been proposed by one of the authors of this paper earlier. This paper presents a pragmatic accelerated failure data acquisition and analytical paradigm under multi factor coupled stress, Electrical, Thermal. The parameters of the phenomenological model so developed are estimated based on sound statistical treatment of failure data.

Relative roles of instruction count and cycles per instruction in WCET estimation

Most of the existing WCET estimation methods directly estimate execution time, ET, in cycles. We propose to study ET as a product of two factors, ET = IC * CPI, where IC is instruction count and CPI is cycles per instruction. Considering directly the estimation of ET may lead to a highly pessimistic estimate since implicitly these methods may be using worst case IC and worst case CPI. We hypothesize that there exists a functional relationship between CPI and IC such that CPI=f(IC). This is ascertained by computing the covariance matrix and studying the scatter plots of CPI versus IC. IC and CPI values are obtained by running benchmarks with a large number of inputs using the cycle accurate architectural simulator, Simplescalar on two different architectures. It is shown that the benchmarks can be grouped into different classes based on the CPI versus IC relationship. For some benchmarks like FFT, FIR etc., both IC and CPI are almost a constant irrespective of the input. There are other benchmarks that exhibit a direct or an inverse relationship between CPI and IC. In such a case, one can predict CPI for a given IC as CPI=f(IC). We derive the theoretical worst case IC for a program, denoted as SWIC, using integer linear programming(ILP) and estimate WCET as SWIC*f(SWIC). However, if CPI decreases sharply with IC then measured maximum cycles is observed to be a better estimate. For certain other benchmarks, it is observed that the CPI versus IC relationship is either random or CPI remains constant with varying IC. In such cases, WCET is estimated as the product of SWIC and measured maximum CPI. It is observed that use of the proposed method results in tighter WCET estimates than Chronos, a static WCET analyzer, for most benchmarks for the two architectures considered in this paper.

Structured Dispersion Matrices From Division Algebra Codes for Space-Time Shift Keying

We propose a novel method of constructing Dispersion Matrices (DM) for Coherent Space-Time Shift Keying (CSTSK) relying on arbitrary PSK signal sets by exploiting codes from division algebras. We show that classic codes from Cyclic Division Algebras (CDA) may be interpreted as DMs conceived for PSK signal sets. Hence various benefits of CDA codes such as their ability to achieve full diversity are inherited by CSTSK. We demonstrate that the proposed CDA based DMs are capable of achieving a lower symbol error ratio than the existing DMs generated using the capacity as their optimization objective function for both perfect and imperfect channel estimation.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov's transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Channel training signal design for reciprocal multiple antenna systems with beamforming

Fast and efficient channel estimation is key to achieving high data rate performance in mobile and vehicular communication systems, where the channel is fast time-varying. To this end, this work proposes and optimizes channel-dependent training schemes for reciprocal Multiple-Input Multiple-Output (MIMO) channels with beamforming (BF) at the transmitter and receiver. First, assuming that Channel State Information (CSI) is available at the receiver, a channel-dependent Reverse Channel Training (RCT) signal is proposed that enables efficient estimation of the BF vector at the transmitter with a minimum training duration of only one symbol. In contrast, conventional orthogonal training requires a minimum training duration equal to the number of receive antennas. A tight approximation to the capacity lower bound on the system is derived, which is used as a performance metric to optimize the parameters of the RCT. Next, assuming that CSI is available at the transmitter, a channel-dependent forward-link training signal is proposed and its power and duration are optimized with respect to an approximate capacity lower bound. Monte Carlo simulations illustrate the significant performance improvement offered by the proposed channel-dependent training schemes over the existing channel-agnostic orthogonal training schemes.