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.

An integrated rail track degradation model

There has been a worldwide trend to increase axle loads and train speeds. This means that railway track degradation will be accelerated, and track maintenance costs will be increased significantly. There is a need to investigate the consequences of increasing traffic load. The aim of the research is to develop a model for the analysis of physical degradation of railway tracks in response to changes in traffic parameters, especially increased axle loads and train speeds. This research has developed an integrated track degradation model (ITDM) by integrating several models into a comprehensive framework. Mechanistic relationships for track degradation hav~ ?een used wherever possible in each of the models contained in ITDM. This overcc:mes the deficiency of the traditional statistical track models which rely heavily on historical degradation data, which is generally not available in many railway systems. In addition statistical models lack the flexibility of incorporating future changes in traffic patterns or maintenance practices. The research starts with reviewing railway track related studies both in Australia and overseas to develop a comprehensive understanding of track performance under various traffic conditions. Existing railway related models are then examined for their suitability for track degradation analysis for Australian situations. The ITDM model is subsequently developed by modifying suitable existing models, and developing new models where necessary. The ITDM model contains four interrelated submodels for rails, sleepers, ballast and subgrade, and track modulus. The rail submodel is for rail wear analysis and is developed from a theoretical concept. The sleeper submodel is for timber sleepers damage prediction. The submodel is developed by modifying and extending an existing model developed elsewhere. The submodel has also incorporated an analysis for the likelihood of concrete sleeper cracking. The ballast and subgrade submodel is evolved from a concept developed in the USA. Substantial modifications and improvements have been made. The track modulus submodel is developed from a conceptual method. Corrections for more global track conditions have been made. The integration of these submodels into one comprehensive package has enabled the interaction between individual track components to be taken into account. This is done by calculating wheel load distribution with time and updating track conditions periodically in the process of track degradation simulation. A Windows-based computer program ~ssociated with ITDM has also been developed. The program enables the user to carry out analysis of degradation of individual track components and to investigate the inter relationships between these track components and their deterioration. The successful implementation of this research has provided essential information for prediction of increased maintenance as a consequence of railway trackdegradation. The model, having been presented at various conferences and seminars, has attracted wide interest. It is anticipated that the model will be put into practical use among Australian railways, enabling track maintenance planning to be optimized and potentially saving Australian railway systems millions of dollars in operating costs.