<p>The problem of estimating the states of a dynamical system on the basis of output measurements is considered in detail. Some of the existing nonlinear estimation techniques are critically surveyed, these include the extended Kalman filter, the second-order filter, the innovations approach, and the invariant imbedding nonlinear filter. A new algorithm for nonlinear estimation is proposed which combines the invariant imbedding approach and the stochastic approximation algorithm for adaptively estimating the filter gain. The new algorithm is an iterative scheme which does not require knowledge of a priori input and measurement noise statistics. The proposed algorithm and the other techniques are used for the recursive state estimation of a satellite orbital trajectory. The results of simulation indicate the efficiency and reliability of the new algorithm. Convergence to the true state is achieved with much less computation when compared to the other methods.</p> / Doctor of Philosophy (PhD)

<p>This thesis is mainly directed towards the developement of new techniques that can be used in the analysis of normal and pathological gaits. The kinematic aspects of human gait are studied, and a new technique for the derivation of spatial trajectories of joints from electrogoniometric measurements is presented. The technique relies on the fact that at any point in time, there is at least one point of either foot in contact with the floor. This point is used as an instantaneous reference from which the positions of the joints are calculated. The procedure is repeated for various points of contact during the walk cycles.</p> <p>The spatial trajectories are used in the study of the kinetics of gait. Forces and moments acting at the joints are computed by considering the equations of motion of the segments of the lower extremity. Rates of energy exchange between the muscles crossing the joints and the segments connected by these joints are estimated, and the total energy expenditure by the leg muscles during swing is obtained. The relation between the speed of walking and energy expenditure by the muscles is studied for normal subjects and hemiplegic patients. The outcome of this study is a new method that can be used in the assessment of normal and pathological gaits.</p> <p>A study of the various electromyographic processing strategies is presented. The different processors are evaluated, and the processor that is most suitable for the analysis of gait is determined. This processor is used on EMG signals from various muscles, and the processed signals are used as inputs to systems whose outputs are the muscle torques at the joints. The transfer-function models of these systems are obtained for the swing phase, and then the same models are used to predict muscle torques and floor-reaction forces during the stance phase.</p> / Doctor of Philosophy (PhD)

<p>The subject of this study is the development of a computer-aided-design tool that filter designers could use to obtain nonlinear phase and nonsymmetric amplitude responses for surface acoustic wave devices. To accomplish this, a design algorithm was developed that uses a Fast Fourier Transform to realize the time domain transform of the frequency domain specifications required by the designer. From this time domain solution an interdigital transducer (IDT) is synthesized that will approximate the design specifications. The next step in the algorithm is to analyse the synthesized IDT using an accurate charge distribution model for the IDT (the charge distribution model is developed in this thesis which gives the frequency domain response for the IDT). The frequency response is then compared to the input specifications so as to generate an error function. This error function is then used to predistort the input frequency domain specifications and the whole synthesis/analysis procedure is repeated iteratively until an acceptable solution is obtained. The algorithm is programmed and used to design 2 filters (3 separate IDT designs) for the nonlinear phase and nonsymmetric amplitude specifications for television intermediate frequency (TVIF) specifications. Using these designs, two filters were fabricated and tested to show the validity of the algorithm.</p> / Doctor of Philosophy (PhD)

<p>This thesis concerns itself with the design and implementation of an electron beam lithography system. A novel microcomputer-controlled vector-scan pattern generator was constructed and interfaced to a commercially available scanning electron microscope (SEM). A software monitor program was incorporated into the 8-bit microcomputer, which allows pattern data entry in decimal coordinates via a keyboard/display interface, and subsequent storage of the coded data on cassette tape.</p> <p>The usable scan field size for accurate pattern exposure in the Stereoscan Mark II A SEM has been determined to be 1mm x 1mm. The electron beam lithography system was used to scan a 1 GHz surface acoustic wave (SAW) delay line pattern, which featured a total of 480 fingers, each 7,680 Å in width. Polymethylmethacrylate (PMMA) electron-sensitive resist was used for the pattern exposures, and a linear charge density of 1 x 10ˉ⁸ C/cm was used. The lift-off fabrication process was used to obtain the final device circuit features. The resulting delay line exhibited an untuned insertion loss of 24.3 dB, and was subsequently incorporated into the feedback loop of an amplifier with excess gain to form a SAW oscillator.</p> <p>Several other circuit patterns were scanned, including a 2 GHz SAW delay line with 3000 Å linewidths, and sub-micron bubble memory T-I bar circuits. Details of all the scanning parameters are given, along with the pattern exposure results.</p> / Doctor of Philosophy (PhD)

<p>In the last two decades, functional electrical stimulation (FES) has been investigated as a means for replacing lost function of limbs resulting from paralysis. Improvement in the gait of hemiplegic patients when gradually varying stimulation sequences were employed to control footdrop during the swing-phase of gait, led to the work presented in this thesis.</p> <p>The material described below is original to the field of FES.</p> <p>Two potential controllers of stimulus intensity and hence ankle joint position on the affected side have been explored. These are: the electromyographic (EMG) activity of the corresponding dorsiflexor and plantarflexor muscles on the contralateral side; and ankle-joint angle variations obtained from the contralateral side. The variance ratio, a statistical descriptor for repeatability, has been invoked to quantify the efficacy of EMG and joint position control. Practical time-constants of averaging have been determined for the processing of control and evoked EMG signals to be used in an FES-based orthosis incorporating feedback. Experiments have indicated that EMG, when used to modulate stimulus strength to effect control of ankle-joint position, is as efficacious as joint-angle-variation control. These experiments revealed that joint-position information is contained in the EMG records obtained from the prime movers during specific movements of the ankle joint.</p> <p>This thesis describes an initial attempt to control the affected ankle-joint position of hemiplegics during locomotion. Corresponding signals available from the contralateral side were used to modulate stimulus intensity on the affected side. A computer-controlled interactive program has been used to impose a delay proportional to the period of stepping between recording of the control signals and activation of the stimulators. Preliminary results obtained from a normal and a hemiplegic subject are presented, and their relevance to future thrusts in the field of FES are discussed.</p> / Doctor of Philosophy (PhD)

<p>The behaviour of certain non-linear oscillatory systems are studied analytically. These systems are of the "separable" type i.e. they can be modelled using linear frequency-dependent networks, frequency independent non-linear resistive networks, and non-linear reactive networks.</p> <p>When the time-lags in an oscillatory system are negligibly small, the system may be described by a non-linear differential equation. If the time-lags cannot be ignored, the system may be described by a non-linear difference-differential equation.</p> <p>The exact analytical solutions of non-linear differential or difference-differential equations are not known, except in rare cases. However, with appropriate restrictions, analytical approximations may be found.</p> <p>In this work, analytical approximations are developed for treating second-order, forced or unforced weakly non-linear oscillatory systems, as well as a restricted class of unforced highly non-linear systems. These systems may be of the degenerative or regenerative type. Also, the case when time-lags exist in the system, has been studied analytically.</p> <p>The analytical results are verified either experimentally or by numerical simulation.</p> / Doctor of Philosophy (PhD)

<p>The electrical control activity in human colon was analyzed using an interactive processor, which was developed and implemented on a NOVA 830 minicomputer, for the analysis of a biological rhythm. The characteristics of the human colonic electrical control activity varied in time and space. The colonic control waves were continuously present with waxing and waning of their amplitudes and they were not continuously phase-locked in either the longitudinal or the circumferential directions. Furthermore, multiple fundamental frequencies along with harmonic frequencies were present whereby the intensity, of a harmonic frequency could be larger than that of a fundamental frequency.</p> <p>An interactive processor for modelling of a biological rhythm by a population of coupled relaxation oscillators was developed and implemented on a NOVA minicomputer, whereby each oscillator could be selectively stimulated.</p> <p>A tubular structure of bidirectionally coupled rings of bidirectionally coupled synthesized relaxation oscillators was used to model the human colonic electrical activity. The computer model qualitatively reproduced the observed characteristics of human colonic electrical control activity. A mathematical investigation of a population of coupled synthesized relaxation oscillators elucidated the nature of waxing and waning of the amplitudes of control waves. Furthermore, it provided the conditions of synchronization of the population which led to the derivation of conditions of entrainment of a synthesized relaxation oscillator by different external stimuli.</p> / Doctor of Philosophy (PhD)

<p>This thesis is concerned primarily with the spectral analysis of clutter in an air traffic control (ATC) radar environment, which is produced by such objects as weather disturbances and migrating flocks of birds. The aim is to provide a means for the on-line classification of the different forms of clutter in such an environment. With the clutter identified and displayed for the operator, aircraft can be vectored in a way to avoid hazardous areas. This separation and identification of radar echoes may also be useful in studies relating to meteorology and ornithology.</p> <p>Since the mechanisms which give rise to weather clutter and bird echoes are different, it is reasonable to expect that they have different statistical parameters. One of these parameters, spectral spread, provides a convenient measure for comparison. To perform the separation of clutter based on spectral spread, a high resolution method is necessary. In this thesis, the maximum entropy method (MEM) is applied to clutter classification. It is shown that the resolution and stability properties of the MEM are well-suited for the separation of different types of clutter; particularly weather from birds. The analysis is performed on both computer-simulated and actual clutter signals. In each case, the results are compared with those obtained by applying the Welch method of averaged modified periodograms. This comparison has revealed that the Welch method does not have the necessary resolution for the classification of clutter.</p> / Doctor of Philosophy (PhD)

<p>The approximation of linear, time-invariant, dynamical systems by similar systems having fewer state variables is investigated. A class of reduced-order approximants called nonminimal partial realizations is introduced which includes many published methods as special cases, and thus represents a unification of the theory of model reduction. Since the concept of linear state variable feedback is central to many of the design procedures of modern control theory, the behaviour of the approximated system to such feedback laws derived from analysis of the approximating system is studied. The specific results derived give a credibility heretofore nonexistant to the class of reduced models called minimal partial realizations by virtue of the fact that they form a subclass of the nonminimal partial realizations. The use of canonical form state equations is advocated as a means of simplifying the computational procedure for an important class of reduced models termed aggregated partial realizations. Such realizations are shown to be useful for designing suboptimal linear quadratic servomechanism compensators, since guaranteed stability of the large-scale system is possible.</p> / Doctor of Philosophy (PhD)

<p>This thesis is directed generally towards a deeper understanding of normal and pathological biped locomotion. Attention has been focussed mainly on electromyographic (EMG) and kinematic aspects of gait. Emphasizing consistency and repeatability of acquired data, the characteristics of surface EMG signals from m. vastus lateralis and m. rectus femoris during several steps of level walking under controlled repeatable gait conditions at three different speeds for several normal subjects have been studied. The variance ratio, a statistical descriptor for repeatability, has been devised. The findings indicate that the variance ratio offers a simple means for selecting an optimal processor for rectifying and averaging the signals. It is of value also in determining an optimal location for surface electrodes on a muscle.</p> <p>Included in the thesis is original research relating to kinematic information presented in the form of knee-angle/hip-angle diagrams. Cyclic loops which had been utilized in the past mainly for their visual representation have been quantified using a shape recognition technique. Quantitative analyses of angle-angle diagrams associated with 5 normal subjects, an above-knee (A/K) amputee and a cerebral-palsied (C.P.) patient, who had an implanted cerebellar stimulator, were carried out. The quantification and physical interpretations of the parameters extracted from the angle-angle diagrams provided a valuable adjunct to visual assessment of the gaits and elicited significant information regarding overall coordination and control during each gait. Using these methods an in-depth assessment of the efficacy of the cerebellar stimulator implanted in the C.P. patient was accomplished.</p> <p>The thesis also describes an initial attempt, using the methods of time series analysis, at modelling the transfer function between several inputs given by the EMG signals of selected muscle groups and an output which is either the hip or knee angle trajectory. The model was able to suggest which individual muscles were synergistic, whether the inputs chosen were good predictors of the output and the relative contribution of each input in predicting the output.</p> / Doctor of Philosophy (PhD)