With the proliferation of wireless networks and the declining cost of wireless devices there is increasing interest in the development of location aware applications. These applications include robotics, context aware systems to collect or disseminate information, duress alarms in institutions such as hospitals and prisons and security of the wireless network. There are many technologies that may be used to sense the location of mobile devices or personnel, including those based on infrared, ultrasonic, radio frequency tags and magnetic sensing. Most of these technologies require the deployment of devices specifically placed to support the location system. This paper focuses on a location system based on the RSSI of packets on the IEEE 802.11b wireless network. This technique has the great advantage that it may be implemented using off the shelf hardware that is generally already deployed to support the data network. A simple wireless network was deployed in the School of Computing Building at the Newnham Campus of the University of Tasmania and used to test the location performance of a location system based on Bayesian filtering of detected signal strengths.

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In the 1950's and early 1960's a considerable amount of effort was devoted by Dr. H.A. Whale and others at the Seagrove Radio Research Station (now the Radio Research Centre, University of Auckland), to the examination of some of the problems involved in HF radio propagation. Among these were the evaluation of the effects of large-scale ionospheric tilts, the scattering which occurs at the earth and ionosphere, and the measurement and prediction of incoming bearing and elevation angles of signals from distant stations. In the latter stages of this work it became obvious that little was known about effects occurring at antipodal distances, so attempts were made to examine these and to postulate a propagation model consistent with the effects observed. The results presented in this thesis are a logical extension of this early work, and comprise investigations in three main areas: (1) The shape and size of the antipodal focussing area, (2) The development of a more general and less idealised propagation model, (3) The shape of the incoming angular power spectrum at antipodal distances. A summary of the theory and experimental results contained in chapters 4, 5, 6 and 7 has been published (Bold, 1969), and that contained in chapters 8 and 9 will be submitted for publication shortly.

In the 1950's and early 1960's a considerable amount of effort was devoted by Dr. H.A. Whale and others at the Seagrove Radio Research Station (now the Radio Research Centre, University of Auckland), to the examination of some of the problems involved in HF radio propagation. Among these were the evaluation of the effects of large-scale ionospheric tilts, the scattering which occurs at the earth and ionosphere, and the measurement and prediction of incoming bearing and elevation angles of signals from distant stations. In the latter stages of this work it became obvious that little was known about effects occurring at antipodal distances, so attempts were made to examine these and to postulate a propagation model consistent with the effects observed. The results presented in this thesis are a logical extension of this early work, and comprise investigations in three main areas: (1) The shape and size of the antipodal focussing area, (2) The development of a more general and less idealised propagation model, (3) The shape of the incoming angular power spectrum at antipodal distances. A summary of the theory and experimental results contained in chapters 4, 5, 6 and 7 has been published (Bold, 1969), and that contained in chapters 8 and 9 will be submitted for publication shortly.

In the 1950's and early 1960's a considerable amount of effort was devoted by Dr. H.A. Whale and others at the Seagrove Radio Research Station (now the Radio Research Centre, University of Auckland), to the examination of some of the problems involved in HF radio propagation. Among these were the evaluation of the effects of large-scale ionospheric tilts, the scattering which occurs at the earth and ionosphere, and the measurement and prediction of incoming bearing and elevation angles of signals from distant stations. In the latter stages of this work it became obvious that little was known about effects occurring at antipodal distances, so attempts were made to examine these and to postulate a propagation model consistent with the effects observed. The results presented in this thesis are a logical extension of this early work, and comprise investigations in three main areas: (1) The shape and size of the antipodal focussing area, (2) The development of a more general and less idealised propagation model, (3) The shape of the incoming angular power spectrum at antipodal distances. A summary of the theory and experimental results contained in chapters 4, 5, 6 and 7 has been published (Bold, 1969), and that contained in chapters 8 and 9 will be submitted for publication shortly.

In the 1950's and early 1960's a considerable amount of effort was devoted by Dr. H.A. Whale and others at the Seagrove Radio Research Station (now the Radio Research Centre, University of Auckland), to the examination of some of the problems involved in HF radio propagation. Among these were the evaluation of the effects of large-scale ionospheric tilts, the scattering which occurs at the earth and ionosphere, and the measurement and prediction of incoming bearing and elevation angles of signals from distant stations. In the latter stages of this work it became obvious that little was known about effects occurring at antipodal distances, so attempts were made to examine these and to postulate a propagation model consistent with the effects observed. The results presented in this thesis are a logical extension of this early work, and comprise investigations in three main areas: (1) The shape and size of the antipodal focussing area, (2) The development of a more general and less idealised propagation model, (3) The shape of the incoming angular power spectrum at antipodal distances. A summary of the theory and experimental results contained in chapters 4, 5, 6 and 7 has been published (Bold, 1969), and that contained in chapters 8 and 9 will be submitted for publication shortly.

Currently, digital signal processing systems typically assume that the signals are bandlimited. This is due to our knowledge based on the uniform sampling theorem for bandlimited signals which was established over 50 years ago by the works of Whittaker, Kotel'nikov and Shannon. However, in practice the digital signals are mostly of finite length. This kind of signals are not strictly bandlimited. Furthermore, advances in electronics have led to the use of very wide bandwidth signals and systems, such as Ultra-Wide Band (UWB) communication systems with signal bandwidths of several giga-hertz. This kind of signals can effectively be viewed as having infinite bandwidth. Thus there is a need to extend existing theory and techniques for signals of finite bandwidths to that for non-bandlimited signals. Two recent approaches to a more general sampling theory for non-bandlimited signals have been published. One is for signals with finite rate of innovation. The other introduced the concept of consistent sampling. It views sampling and reconstruction as projections of signals onto subspaces spanned by the sampling (acquisition) and reconstruction (synthesis) functions. Consistent sampling is achieved if the same discrete signal is obtained when the reconstructed continuous signal is sampled. However, it has been shown that when this generalized theory is applied to the de-interlacing of video signals, incorrect results are obtained. This is because de-interlacing is essentially a resampling problem rather than a sampling problem because both the input and output are discrete. While the theory for the resampling for bandlimited signals is well established, the problem of resampling without bandlimited constraints is largely unexplored. The aim of this thesis is to develop a resampling theory for non-bandlimited discrete signals and explore some of its potential applications. The first major contribution is the the theory and techniques for designing an optimal resampling system for signals in the general Hilbert Space when noise is not present. The system is optimal in the sense that the input of the system can always be obtained from the output. The theory is based on the concept of consistent resampling which means that the same continuous signal will be obtained when either the original or the resampled discrete signal is presented to the reconstruction filter. While comparing the input and output of a sampling/reconstruction system is relatively simple since both are continuous signals, comparing the discrete input and output of a resampling system is not. The second major contribution of this thesis is the proposal of a metric that allows us to evaluate the performance of a resampling system. The performance is analyzed in the Fourier domain as well. This performance metric also provides a way by which different resampling algorithms can be compared effectively. It therefore facilitates the process of choosing proper resampling schemes for a particular purpose. Unfortunately consistent resampling cannot always be achieved if noise is present in the signal or the system. Based on the performance metric proposed, the third major contribution of this thesis is the development of procedures for designing resampling systems in the presence of noise which is optimal in the mean squared error (MSE) sense. Both discrete and continuous noise are considered. The problem is formulated as a semi-definite program which can be solved effciently by existing techniques. The usefulness and correctness of the consistent resampling theory is demonstrated by its application to the video de-interlacing problem, image processing, the demodulation of ultra-wideband communication signals and mobile channel detection. The results show that the proposed resampling system has many advantages over existing approaches, including lower computational and time complexities, more accurate prediction of system performances, as well as robustness against noise.

Chapter 1 Introduction. The magnetic field lines that emerge from the polar regions extend to great distances from the earth. The auroral zone closely approximate the boundary between those field lines that are closed within the magnetosphere and those that form the geomagnetic tail. the field lines int he tail may be open or possibly joined with the interplanetary field. this introduces considerable coupling between the polar ionosphere and the distant regions of the earth's atmosphere. High energy charged particles from the sun and disturbances in the magnetosphere, therefore cause large changes in the polar ionosphere, with auroral displays and regions of increased or irregular ionisation. Increasing attention is therefore, being paid to studies of the polar ionosphere to gain some insight into the changes occurring at great heights.

Work began in March 1967 with the design and construction of the fixed interferometer (described in Chapter 2) for measuring the elevation angle of arrival of 20MHz signals from the satellite Beacon-B. Also during this first year most of the computing was completed for the theoretical calculations on ray paths presented in Chapter 5; these results along with some previously obtained experimental results form the basis of a paper accepted by Radio Science. Records were obtained from the interferometer from April 1968 to the end of the transmitting life of Beacon-B in January 1970. The analysis of the phase traces from the two aperture interferometer was complicated by the automatic antenna switching procedures; each transit had to be annotated and the useful chart delineated manually before the analysts recorded the phase at intervals of a few seconds on a semi-automatic digital recording system. The antenna switching was designed to save electronics and one channel on the chart recorder, but lead to a computer programming effort which may have been more costly in time and lost transits than the saving achieved by avoiding two separate interferometers (Chapter 2). While this programming and analysis were going on, the computing delays on the University’s overworked IBM 1130 gave time to follow up the idea of recording the fast Faraday fading on 20 MHz signals from a satellite near to or even below the horizon. This project was simplified by the availability of an easily converted 20 MHz receiver and a digital recording system. The report on this project is given in Chapter 4 and also in a short paper. The elevation angle measurements from the interferometer were converted to virtual height increment versus equivalent vertical frequency plots and thence to electron density profiles (Chapter 3, Part I). This analysis was developed from ideas given originally by Titheridge (1964). The interpretation of the resulting values of the scale height at the peak (Chapter 3, Part II) in terms of ionosphere morphology depended heavily on the total content hourly values maintained on computer disk by Dr Titheridge. The results and discussion in Chapter 3 will be presented as a separated paper. Chapter 6 is a review of the effects of the ionosphere on transmitted satellite signals and in particular gives a wider view of Faraday fading than is normally taken. Because of its general nature Chapter 6 can serve as an introduction to satellite radio propagation techniques; it appears at the end of this thesis as common ground after the diversions of Chapters 4 and 5. Since this work falls into three separate projects of ray elevation angle measurements, fast Faraday fading, and second order Faraday rotation calculations, the reports on each have been written with minimal cross referencing; this should facilitate reading but has resulted in a small amount of repetition.

The single-polynomial method for ionogram analysis is adapted to give a least-squares procedure in which the number of scaled virtual heights is greater than the number of terms in the real-height polynomial. The general principles are described in detail and the procedure is applied to the valley problem in bottomside ionogram analysis. It is shown that only a single parameter, the integrated valley ionisation, is obtainable from typical ionograms. The least-squares technique is then applied to the problem of topside ionogram analysis where the facility for using any mixture of ordinary and extraordinary ray virtual depth data is very useful. The method is shown to offer many advantages over the more traditional methods. The effects of horizontal ionisation gradients on bottomside and topside ionograms are extensively investigated by a new technique for synthesising ionograms corresponding to a given model of a moving disturbance in the ionosphere. A number of interesting and important ionogram characteristics are identified and explained. Finally, the specific problem of a large disturbance seen on total electron content records during summer nights is briefly re-examined using topside ionogram data. It is suggested that the disturbance is not primarily a topside phenomenon as originally supposed.