Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Enhancing the standard operating range of a placido disk videokeratoscope for corneal surface estimation

Abstract—Corneal topography estimation that is based on the Placido disk principle relies on good quality of precorneal tear film and sufficiently wide eyelid (palpebral) aperture to avoid reflections from eyelashes. However, in practice, these conditions are not always fulfilled resulting in missing regions, smaller corneal coverage, and subsequently poorer estimates of corneal topography. Our aim was to enhance the standard operating range of a Placido disk videokeratoscope to obtain reliable corneal topography estimates in patients with poor tear film quality, such as encountered in those diagnosed with dry eye, and with narrower palpebral apertures as in the case of Asian subjects. This was achieved by incorporating in the instrument’s own topography estimation algorithm an image processing technique that comprises a polar-domain adaptive filter and amorphological closing operator. The experimental results from measurements of test surfaces and real corneas showed that the incorporation of the proposed technique results in better estimates of corneal topography, and, in many cases, to a significant increase in the estimated coverage area making such an enhanced videokeratoscope a better tool for clinicians.

Near real-time prediction of Zenith Tropospheric Delays for position estimation over long-baseline CORS network

This paper presents the preliminary results in establishing a strategy for predicting Zenith Tropospheric Delay (ZTD) and relative ZTD (rZTD) between Continuous Operating Reference Stations (CORS) in near real-time. It is anticipated that the predicted ZTD or rZTD can assist the network-based Real-Time Kinematic (RTK) performance over long inter-station distances, ultimately, enabling a cost effective method of delivering precise positioning services to sparsely populated regional areas, such as Queensland. This research firstly investigates two ZTD solutions: 1) the post-processed IGS ZTD solution and 2) the near Real-Time ZTD solution. The near Real-Time solution is obtained through the GNSS processing software package (Bernese) that has been deployed for this project. The predictability of the near Real-Time Bernese solution is analyzed and compared to the post-processed IGS solution where it acts as the benchmark solution. The predictability analyses were conducted with various prediction time of 15, 30, 45, and 60 minutes to determine the error with respect to timeliness. The predictability of ZTD and relative ZTD is determined (or characterized) by using the previously estimated ZTD as the predicted ZTD of current epoch. This research has shown that both the ZTD and relative ZTD predicted errors are random in nature; the STD grows from a few millimeters to sub-centimeters while the predicted delay interval ranges from 15 to 60 minutes. Additionally, the RZTD predictability shows very little dependency on the length of tested baselines of up to 1000 kilometers. Finally, the comparison of near Real-Time Bernese solution with IGS solution has shown a slight degradation in the prediction accuracy. The less accurate NRT solution has an STD error of 1cm within the delay of 50 minutes. However, some larger errors of up to 10cm are observed.

Robust estimation of tear film surface quality in lateral shearing interferometry

Interferometry is a sensitive technique for recording tear film surface irregularities in a noninvasive manner. At the same time, the technique is hindered by natural eye movements resulting in measurement noise. Estimating tear film surface quality from interferograms can be reduced to a spatial-average-localized weighted estimate of the first harmonic of the interference fringes. However, previously reported estimation techniques proved to perform poorly in cases where the pattern fringes were significantly disturbed. This can occur in cases of measuring tear film surface quality on a contact lens on the eye or in a dry eye. We present a new estimation technique for extracting the first harmonic from the interference fringes that combines the traditional spectral estimation techniques with morphological image processing techniques. The proposed technique proves to be more robust to changes in interference fringes caused by natural eye movements and the degree of dryness of the contact lens and corneal surfaces than its predecessors, resulting in tear film surface quality estimates that are less noisy

Online estimation of distorted power system signal parameters

An algorithm based on the concept of Kalman filtering is proposed in this paper for the estimation of power system signal attributes, like amplitude, frequency and phase angle. This technique can be used in protection relays, digital AVRs, DSTATCOMs, FACTS and other power electronics applications. Furthermore this algorithm is particularly suitable for the integration of distributed generation sources to power grids when fast and accurate detection of small variations of signal attributes are needed. Practical considerations such as the effect of noise, higher order harmonics, and computational issues of the algorithm are considered and tested in the paper. Several computer simulations are presented to highlight the usefulness of the proposed approach. Simulation results show that the proposed technique can simultaneously estimate the signal attributes, even if it is highly distorted due to the presence of non-linear loads and noise.

The applicability of biased estimation in model and model order selection

Biased estimation has the advantage of reducing the mean squared error (MSE) of an estimator. The question of interest is how biased estimation affects model selection. In this paper, we introduce biased estimation to a range of model selection criteria. Specifically, we analyze the performance of the minimum description length (MDL) criterion based on biased and unbiased estimation and compare it against modern model selection criteria such as Kay's conditional model order estimator (CME), the bootstrap and the more recently proposed hook-and-loop resampling based model selection. The advantages and limitations of the considered techniques are discussed. The results indicate that, in some cases, biased estimators can slightly improve the selection of the correct model. We also give an example for which the CME with an unbiased estimator fails, but could regain its power when a biased estimator is used.

Unmanned Aerial Vehicles UAVs attitude, height, motion estimation and control using visual systems

This paper presents an implementation of an aircraft pose and motion estimator using visual systems as the principal sensor for controlling an Unmanned Aerial Vehicle (UAV) or as a redundant system for an Inertial Measure Unit (IMU) and gyros sensors. First, we explore the applications of the unified theory for central catadioptric cameras for attitude and heading estimation, explaining how the skyline is projected on the catadioptric image and how it is segmented and used to calculate the UAV’s attitude. Then we use appearance images to obtain a visual compass, and we calculate the relative rotation and heading of the aerial vehicle. Additionally, we show the use of a stereo system to calculate the aircraft height and to measure the UAV’s motion. Finally, we present a visual tracking system based on Fuzzy controllers working in both a UAV and a camera pan and tilt platform. Every part is tested using the UAV COLIBRI platform to validate the different approaches, which include comparison of the estimated data with the inertial values measured onboard the helicopter platform and the validation of the tracking schemes on real flights.

Labelled silhouettes for human pose estimation

This paper proposes a new method of using foreground silhouette images for human pose estimation. Labels are introduced to the silhouette images, providing an extra layer of information that can be used in the model fitting process. The pixels in the silhouettes are labelled according to the corresponding body part in the model of the current fit, with the labels propagated into the silhouette of the next frame to be used in the fitting for the next frame. Both single and multi-view implementations are detailed, with results showing performance improvements over only using standard unlabelled silhouettes.