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.

To sonicate or not to sonicate PM filters: Reactive Oxygen Species generation upon ultrasonic irradiation

In aerosol research, a common approach for the collection of particulate matter (PM) is the use of filters in order to obtain sufficient material to undertake analysis. For subsequent chemical and toxicological analyses, in most of cases the PM needs to be extracted from the filters. Sonication is commonly used to most efficiently extract the PM from the filters. Extraction protocols generally involve 10 - 60 min of sonication. The energy of ultrasonic waves causes the formation and collapse of cavitation bubbles in the solution. Inside the collapsing cavities the localised temperatures and pressures can reach extraordinary values. Although fleeting, such conditions can lead to pyrolysis of the molecules present inside the cavitation bubbles (gases dissolved in the liquid and solvent vapours), which results in the production of free radicals and the generation of new compounds formed by reactions with these free radicals. For example, simple sonication of pure water will result in the formation of detectable levels of hydroxyl radicals. As hydroxyl radicals are recognised as playing key roles as oxidants in the atmosphere the extraction of PM from filters using sonication is therefore problematic. Sonication can result in significant chemical and physical changes to PM through thermal degradation and other reactions. In this article, an overview of sonication technique as used in aerosol research is provided, the capacity for radical generation under these conditions is described and an analysis is given of the impact of sonication-derived free radicals on three molecular probes commonly used by researchers in this field to detect Reactive Oxygen Species in PM.

Preparation of magnetic porous ceramsite and its application in biological aerated filters

Ceramsite plays a significant role as a biological aerated filter (BAF) in the treatment of wastewater. In this study, a mixture of goethite, sawdust and palygorskite clay was thermally treated to form magnetic porous ceramsite (MPC). An optimization experiment was conducted to measure the compressive strength of the MPC. X-ray diffraction (XRD), scanning electron microscopy (SEM), and polarizing microscopy (PM) characterized the pore structure of the MPC. The results show that a combination of goethite, sawdust and palygorskite clay with a mass ratio of 10:2:5 is suitable for the formation of MPC. The compressive strength of MPC conforms to the Chinese national industrial standard (CJ/T 299-2008) for wastewater treatment. The SEM and PM results also show that the uniform and interconnected pores in MPC were well suited for microbial growth. The MPC produced in this study can serve as a biomedium for advanced wastewater treatment.

Extended Kalman filters using explicit and derivative-free local linearizations

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.

Use of narrow-pore filters in He II transfer devices - new results

With the aim of finding simple methods for the fabrication of He II refilling devices, He II flow has been studied through filters made from various fine powders (oxides and metals, grain sizes in the range 0.05–2 μm) by compacting them under pressure. The results obtained for the different states of He II flow, especially in the “breakthrough” and “easy flow” range, are explained by the fountain effect, He II hydrodynamics and the choking effect. According to the results, pressedpowder filters can be classified into three groups with different flow characteristics, of which the “good transfer filters” with a behaviour neatly described by simple theory are suitable for use in He II refilling devices.