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

Toothless tiger, sleeping dragon : implied freedoms, internet filters and the growing culture of internet censorship in Australia

The internet by its very nature challenges an individual’s notions of propriety, moral acuity and social correctness. A tension will always exist between the censorship of obscene and sensitive information and the freedom to publish and/or access such information. Freedom of expression and communication on the internet is not a static concept: ‘Its continual regeneration is the product of particular combinations of political, legal, cultural and philosophical conditions’.

Accurate urban road model reconstruction from high resolution remotely sensed imagery based on Support Vector Machine and Gabor filters

In this paper, we presented an automatic system for precise urban road model reconstruction based on aerial images with high spatial resolution. The proposed approach consists of two steps: i) road surface detection and ii) road pavement marking extraction. In the first step, support vector machine (SVM) was utilized to classify the images into two categories: road and non-road. In the second step, road lane markings are further extracted on the generated road surface based on 2D Gabor filters. The experiments using several pan-sharpened aerial images of Brisbane, Queensland have validated the proposed method.

Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Fat and thin adaptive HMM filters for vision based detection of moving targets

Computer vision is an attractive solution for uninhabited aerial vehicle (UAV) collision avoidance, due to the low weight, size and power requirements of hardware. A two-stage paradigm has emerged in the literature for detection and tracking of dim targets in images, comprising of spatial preprocessing, followed by temporal filtering. In this paper, we investigate a hidden Markov model (HMM) based temporal filtering approach. Specifically, we propose an adaptive HMM filter, in which the variance of model parameters is refined as the quality of the target estimate improves. Filters with high variance (fat filters) are used for target acquisition, and filters with low variance (thin filters) are used for target tracking. The adaptive filter is tested in simulation and with real data (video of a collision-course aircraft). Our test results demonstrate that our adaptive filtering approach has improved tracking performance, and provides an estimate of target heading not present in previous HMM filtering approaches.

Driving speed is altered by monocular Neutral Density filters : the Enright phenomenon

Introduction: An observer, looking sideways from a moving vehicle, while wearing a neutral density filter over one eye, can have a distorted perception of speed, known as the Enright phenomenon. The purpose of this study was to determine how the Enright phenomenon influences driving behaviour. Methods: A geometric model of the Enright phenomenon was developed. Ten young, visually normal, participants (mean age = 25.4 years) were tested on a straight section of a closed driving circuit and instructed to look out of the right side of the vehicle and drive at either 40 Km/h or 60 Km/h under the following binocular viewing conditions: with a 0.9 ND filter over the left eye (leading eye); 0.9 ND filter over the right eye (trailing eye); 0.9 ND filters over both eyes, and with no filters over either eye. The order of filter conditions was randomised and the speed driven recorded for each condition. Results: Speed judgments did not differ significantly between the two baseline conditions (no filters and both eyes filtered) for either speed tested. For the baseline conditions, when subjects were asked to drive at 60 Km/h they matched this speed well (61 ± 10.2 Km/h) but drove significantly faster than requested (51.6 ± 9.4 Km/h) when asked to drive at 40 Km/h. Subjects significantly exceeded baseline speeds by 8.7± 5.0 Km/h, when the trailing eye was filtered and travelled slower than baseline speeds by 3.7± 4.6 Km/h when the leading eye was filtered. Conclusions: This is the first quantitative study demonstrating how the Enright effect can influence perceptions of driving speed, and demonstrates that monocular filtering of an eye can significantly impact driving speeds, albeit to a lesser extent than predicted by geometric models of the phenomenon.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

A framework for a dense matching algorithm : Results using matching metrics and order statistic filters

An algorithm for computing dense correspondences between images of a stereo pair or image sequence is presented. The algorithm can make use of both standard matching metrics and the rank and census filters, two filters based on order statistics which have been applied to the image matching problem. Their advantages include robustness to radiometric distortion and amenability to hardware implementation. Results obtained using both real stereo pairs and a synthetic stereo pair with ground truth were compared. The rank and census filters were shown to significantly improve performance in the case of radiometric distortion. In all cases, the results obtained were comparable to, if not better than, those obtained using standard matching metrics. Furthermore, the rank and census have the additional advantage that their computational overhead is less than these metrics. For all techniques tested, the difference between the results obtained for the synthetic stereo pair, and the ground truth results was small.

Order statistic filters for image matching

The rank and census are two filters based on order statistics which have been applied to the image matching problem for stereo pairs. Advantages of these filters include their robustness to radiometric distortion and small amounts of random noise, and their amenability to hardware implementation. In this paper, a new matching algorithm is presented, which provides an overall framework for matching, and is used to compare the rank and census techniques with standard matching metrics. The algorithm was tested using both real stereo pairs and a synthetic pair with ground truth. The rank and census filters were shown to significantly improve performance in the case of radiometric distortion. In all cases, the results obtained were comparable to, if not better than, those obtained using standard matching metrics. Furthermore, the rank and census have the additional advantage that their computational overhead is less than these metrics. For all techniques tested, the difference between the results obtained for the synthetic stereo pair, and the ground truth results was small.

Efficient articulated trajectory reconstruction using dynamic programming and filters

This paper considers the problem of reconstructing the motion of a 3D articulated tree from 2D point correspondences subject to some temporal prior. Hitherto, smooth motion has been encouraged using a trajectory basis, yielding a hard combinatorial problem with time complexity growing exponentially in the number of frames. Branch and bound strategies have previously attempted to curb this complexity whilst maintaining global optimality. However, they provide no guarantee of being more efficient than exhaustive search. Inspired by recent work which reconstructs general trajectories using compact high-pass filters, we develop a dynamic programming approach which scales linearly in the number of frames, leveraging the intrinsically local nature of filter interactions. Extension to affine projection enables reconstruction without estimating cameras.

Analysis of organic aerosols collected on filters by Aerosol Mass Spectrometry for source identification

Aerosol mass spectrometers (AMS) are powerful tools in the analysis of the chemical composition of airborne particles, particularly organic aerosols which are gaining increasing attention. However, the advantages of AMS in providing on-line data can be outweighed by the difficulties involved in its use in field measurements at multiple sites. In contrast to the on-line measurement by AMS, a method which involves sample collection on filters followed by subsequent analysis by AMS could significantly broaden the scope of AMS application. We report the application of such an approach to field studies at multiple sites. An AMS was deployed at 5 urban schools to determine the sources of the organic aerosols at the schools directly. PM1 aerosols were also collected on filters at these and 20 other urban schools. The filters were extracted with water and the extract run through a nebulizer to generate the aerosols, which were analysed by an AMS. The mass spectra from the samples collected on filters at the 5 schools were found to have excellent correlations with those obtained directly by AMS, with r2 ranging from 0.89 to 0.98. Filter recoveries varied between the schools from 40 -115%, possibly indicating that this method provides qualitative rather than quantitative information. The stability of the organic aerosols on Teflon filters was demonstrated by analysing samples stored for up to two years. Application of the procedure to the remaining 20 schools showed that secondary organic aerosols were the main source of aerosols at the majority of the schools. Overall, this procedure provides accurate representation of the mass spectra of ambient organic aerosols and could facilitate rapid data acquisition at multiple sites where AMS could not be deployed for logistical reasons.

Vision-based estimation of airborne target pseudobearing rate using hidden Markov model filters

The problem of estimating pseudobearing rate information of an airborne target based on measurements from a vision sensor is considered. Novel image speed and heading angle estimators are presented that exploit image morphology, hidden Markov model (HMM) filtering, and relative entropy rate (RER) concepts to allow pseudobearing rate information to be determined before (or whilst) the target track is being estimated from vision information.

Faster parameter estimation using risk-sensitive filters

In this paper, we propose a risk-sensitive approach to parameter estimation for hidden Markov models (HMMs). The parameter estimation approach considered exploits estimation of various functions of the state, based on model estimates. We propose certain practical suboptimal risk-sensitive filters to estimate the various functions of the state during transients, rather than optimal risk-neutral filters as in earlier studies. The estimates are asymptotically optimal, if asymptotically risk neutral, and can give significantly improved transient performance, which is a very desirable objective for certain engineering applications. To demonstrate the improvement in estimation simulation studies are presented that compare parameter estimation based on risk-sensitive filters with estimation based on risk-neutral filters.