Adaptive instantaneous frequency estimation: Techniques and algorithms

This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent

Theory of radar imaging using time-frequency distribution

The concept of radar was developed for the estimation of the distance (range) and velocity of a target from a receiver. The distance measurement is obtained by measuring the time taken for the transmitted signal to propagate to the target and return to the receiver. The target's velocity is determined by measuring the Doppler induced frequency shift of the returned signal caused by the rate of change of the time- delay from the target. As researchers further developed conventional radar systems it become apparent that additional information was contained in the backscattered signal and that this information could in fact be used to describe the shape of the target itself. It is due to the fact that a target can be considered to be a collection of individual point scatterers, each of which has its own velocity and time- delay. DelayDoppler parameter estimation of each of these point scatterers thus corresponds to a mapping of the target's range and cross range, thus producing an image of the target. Much research has been done in this area since the early radar imaging work of the 1960s. At present there are two main categories into which radar imaging falls. The first of these is related to the case where the backscattered signal is considered to be deterministic. The second is related to the case where the backscattered signal is of a stochastic nature. In both cases the information which describes the target's scattering function is extracted by the use of the ambiguity function, a function which correlates the backscattered signal in time and frequency with the transmitted signal. In practical situations, it is often necessary to have the transmitter and the receiver of the radar system sited at different locations. The problem in these situations is 'that a reference signal must then be present in order to calculate the ambiguity function. This causes an additional problem in that detailed phase information about the transmitted signal is then required at the receiver. It is this latter problem which has led to the investigation of radar imaging using time- frequency distributions. As will be shown in this thesis, the phase information about the transmitted signal can be extracted from the backscattered signal using time- frequency distributions. The principle aim of this thesis was in the development, and subsequent discussion into the theory of radar imaging, using time- frequency distributions. Consideration is first given to the case where the target is diffuse, ie. where the backscattered signal has temporal stationarity and a spatially white power spectral density. The complementary situation is also investigated, ie. where the target is no longer diffuse, but some degree of correlation exists between the time- frequency points. Computer simulations are presented to demonstrate the concepts and theories developed in the thesis. For the proposed radar system to be practically realisable, both the time- frequency distributions and the associated algorithms developed must be able to be implemented in a timely manner. For this reason an optical architecture is proposed. This architecture is specifically designed to obtain the required time and frequency resolution when using laser radar imaging. The complex light amplitude distributions produced by this architecture have been computer simulated using an optical compiler.

Analytical modeling and sensitivity analysis for travel time estimation on signalized urban networks

This paper presents a model for estimation of average travel time and its variability on signalized urban networks using cumulative plots. The plots are generated based on the availability of data: a) case-D, for detector data only; b) case-DS, for detector data and signal timings; and c) case-DSS, for detector data, signal timings and saturation flow rate. The performance of the model for different degrees of saturation and different detector detection intervals is consistent for case-DSS and case-DS whereas, for case-D the performance is inconsistent. The sensitivity analysis of the model for case-D indicates that it is sensitive to detection interval and signal timings within the interval. When detection interval is integral multiple of signal cycle then it has low accuracy and low reliability. Whereas, for detection interval around 1.5 times signal cycle both accuracy and reliability are high.

Urban dynamic origin-destination matrices estimation

The aim of this paper is to explore a new approach to obtain better traffic demand (Origin-Destination, OD matrices) for dense urban networks. From reviewing existing methods, from static to dynamic OD matrix evaluation, possible deficiencies in the approach could be identified: traffic assignment details for complex urban network and lacks in dynamic approach. To improve the global process of traffic demand estimation, this paper is focussing on a new methodology to determine dynamic OD matrices for urban areas characterized by complex route choice situation and high level of traffic controls. An iterative bi-level approach will be used, the Lower level (traffic assignment) problem will determine, dynamically, the utilisation of the network by vehicles using heuristic data from mesoscopic traffic simulator and the Upper level (matrix adjustment) problem will proceed to an OD estimation using optimization Kalman filtering technique. In this way, a full dynamic and continuous estimation of the final OD matrix could be obtained. First results of the proposed approach and remarks are presented.

Estimation of travel time on urban networks with midlink sources and sinks

This paper presents a methodology for estimation of average travel time on signalized urban networks by integrating cumulative plots and probe data. This integration aims to reduce the relative deviations in the cumulative plots due to midlink sources and sinks. During undersaturated traffic conditions, the concept of a virtual probe is introduced, and therefore, accurate travel time can be obtained when a real probe is unavailable. For oversaturated traffic conditions, only one probe per travel time estimation interval—360 s or 3% of vehicles traversing the link as a probe—has the potential to provide accurate travel time.

Identification and control of induction machines using artificial neural networks

This paper proposes the use of artificial neural networks (ANNs) to identify and control an induction machine. Two systems are presented: a system to adaptively control the stator currents via identification of the electrical dynamics; and a system to adaptively control the rotor speed via identification of the mechanical and current-fed system dynamics. Various advantages of these control schemes over other conventional schemes are cited and the performance of the combined speed and current control scheme is compared with that of the standard vector control scheme

Estimation of WGEN Weather Generation Parameters in Arid Climates

This research discusses some of the issues encountered while developing a set of WGEN parameters for Chile and advice for others interested in developing WGEN parameters for arid climates. The WGEN program is a commonly used and a valuable research tool; however, it has specific limitations in arid climates that need careful consideration. These limitations are analysed in the context of generating a set of WGEN parameters for Chile. Fourteen to 26 years of precipitation data are used to calculate precipitation parameters for 18 locations in Chile, and 3–8 years of temperature and solar radiation data are analysed to generate parameters for seven of these locations. Results indicate that weather generation parameters in arid regions are sensitive to erroneous or missing precipitation data. Research shows that the WGEN-estimated gamma distribution shape parameter (α) for daily precipitation in arid zones will tend to cluster around discrete values of 0 or 1, masking the high sensitivity of these parameters to additional data. Rather than focus on the length in years when assessing the adequacy of a data record for estimation of precipitation parameters, researchers should focus on the number of wet days in dry months in a data set. Analysis of the WGEN routines for the estimation of temperature and solar radiation parameters indicates that errors can occur when individual ‘months’ have fewer than two wet days in the data set. Recommendations are provided to improve methods for estimation of WGEN parameters in arid climates.

Limited information estimation and evaluation of DSGE models

We advance the proposition that dynamic stochastic general equilibrium (DSGE) models should not only be estimated and evaluated with full information methods. These require that the complete system of equations be specified properly. Some limited information analysis, which focuses upon specific equations, is therefore likely to be a useful complement to full system analysis. Two major problems occur when implementing limited information methods. These are the presence of forward-looking expectations in the system as well as unobservable non-stationary variables. We present methods for dealing with both of these difficulties, and illustrate the interaction between full and limited information methods using a well-known model.

Estimation of the depth focus from wavefront measurements

It is possible to estimate the depth of focus (DOF) of the eye directly from wavefront measurements using various retinal image quality metrics (IQMs). In such methods, DOF is defined as the range of defocus error that degrades the retinal image quality calculated from IQMs to a certain level of the maximum value. Although different retinal image quality metrics are used, currently there have been two arbitrary threshold levels adopted, 50% and 80%. There has been limited study of the relationship between these threshold levels and the actual measured DOF. We measured the subjective DOF in a group of 17 normal subjects, and used through-focus augmented visual Strehl ratio based on optical transfer function (VSOTF) derived from their wavefront aberrations as the IQM. For each subject, a VSOTF threshold level was derived that would match the subjectively measured DOF. Significant correlation was found between the subject’s estimated threshold level and the HOA RMS (Pearson’s r=0.88, p<0.001). The linear correlation can be used to estimate the threshold level for each individual subject, subsequently leading to a method for estimating individual’s DOF from a single measurement of their wavefront aberrations.