Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

A process for the management of physical infrastructure

Physical infrastructure assets are important components of our society and our economy. They are usually designed to last for many years, are expected to be heavily used during their lifetime, carry considerable load, and are exposed to the natural environment. They are also normally major structures, and therefore present a heavy investment, requiring constant management over their life cycle to ensure that they perform as required by their owners and users. Given a complex and varied infrastructure life cycle, constraints on available resources, and continuing requirements for effectiveness and efficiency, good management of infrastructure is important. While there is often no one best management approach, the choice of options is improved by better identification and analysis of the issues, by the ability to prioritise objectives, and by a scientific approach to the analysis process. The abilities to better understand the effect of inputs in the infrastructure life cycle on results, to minimise uncertainty, and to better evaluate the effect of decisions in a complex environment, are important in allocating scarce resources and making sound decisions. Through the development of an infrastructure management modelling and analysis methodology, this thesis provides a process that assists the infrastructure manager in the analysis, prioritisation and decision making process. This is achieved through the use of practical, relatively simple tools, integrated in a modular flexible framework that aims to provide an understanding of the interactions and issues in the infrastructure management process. The methodology uses a combination of flowcharting and analysis techniques. It first charts the infrastructure management process and its underlying infrastructure life cycle through the time interaction diagram, a graphical flowcharting methodology that is an extension of methodologies for modelling data flows in information systems. This process divides the infrastructure management process over time into self contained modules that are based on a particular set of activities, the information flows between which are defined by the interfaces and relationships between them. The modular approach also permits more detailed analysis, or aggregation, as the case may be. It also forms the basis of ext~nding the infrastructure modelling and analysis process to infrastructure networks, through using individual infrastructure assets and their related projects as the basis of the network analysis process. It is recognised that the infrastructure manager is required to meet, and balance, a number of different objectives, and therefore a number of high level outcome goals for the infrastructure management process have been developed, based on common purpose or measurement scales. These goals form the basis of classifYing the larger set of multiple objectives for analysis purposes. A two stage approach that rationalises then weights objectives, using a paired comparison process, ensures that the objectives required to be met are both kept to the minimum number required and are fairly weighted. Qualitative variables are incorporated into the weighting and scoring process, utility functions being proposed where there is risk, or a trade-off situation applies. Variability is considered important in the infrastructure life cycle, the approach used being based on analytical principles but incorporating randomness in variables where required. The modular design of the process permits alternative processes to be used within particular modules, if this is considered a more appropriate way of analysis, provided boundary conditions and requirements for linkages to other modules, are met. Development and use of the methodology has highlighted a number of infrastructure life cycle issues, including data and information aspects, and consequences of change over the life cycle, as well as variability and the other matters discussed above. It has also highlighted the requirement to use judgment where required, and for organisations that own and manage infrastructure to retain intellectual knowledge regarding that infrastructure. It is considered that the methodology discussed in this thesis, which to the author's knowledge has not been developed elsewhere, may be used for the analysis of alternatives, planning, prioritisation of a number of projects, and identification of the principal issues in the infrastructure life cycle.

How nonprofit boards monitor, judge and influence organisational performance

The law and popular opinion expect boards of directors will actively monitor their organisations. Further, public opinion is that boards should have a positive impact on organisational performance. However, the processes of board monitoring and judgment are poorly understood, and board influence on organisational performance needs to be better understood. This thesis responds to the repeated calls to open the ‘black box’ linking board practices and organisational performance by investigating the processual behaviours of boards. The work of four boards1 of micro and small-sized nonprofit organisations were studied for periods of at least one year, using a processual research approach, drawing on observations of board meetings, interviews with directors, and the documents of the boards. The research shows that director turnover, the difficulty recruiting and engaging directors, and the administration of reporting, had strong impacts upon board monitoring, judging and/or influence. In addition, board monitoring of organisational performance was adversely affected by directors’ limited awareness of their legal responsibilities and directors’ limited financial literacy. Directors on average found all sources of information about their organisation’s work useful. Board judgments about the financial aspects of organisational performance were regulated by the routines of financial reporting. However, there were no comparable routines facilitating judgments about non-financial performance, and such judgments tended to be limited to specific aspects of performance and were ad hoc, largely in response to new information or the repackaging of existing information in a new form. The thesis argues that Weick’s theory of sensemaking offers insight into the way boards went about the task of understanding organisational performance. Board influence on organisational performance was demonstrated in the areas of: compliance; instrumental influence through service and through discussion and decision-making; and by symbolic, legitimating and protective means. The degree of instrumental influence achieved by boards depended on director competency, access to networks of influence, and understandings of board roles, and by the agency demonstrated by directors. The thesis concludes that there is a crowding out effect whereby CEO competence and capability limits board influence. The thesis also suggests that there is a second ‘agency problem’, a problem of director volition. The research potentially has profound implications for the work of nonprofit boards. Rather than purporting to establish a general theory of board governance, the thesis embraces calls to build situation-specific mini-theories about board behaviour.