Fixed-wing attitude estimation using temporal tracking of the horizon and optical flow

In this paper, a method has been developed for estimating pitch angle, roll angle and aircraft body rates based on horizon detection and temporal tracking using a forward-looking camera, without assistance from other sensors. Using an image processing front-end, we select several lines in an image that may or may not correspond to the true horizon. The optical flow at each candidate line is calculated, which may be used to measure the body rates of the aircraft. Using an Extended Kalman Filter (EKF), the aircraft state is propagated using a motion model and a candidate horizon line is associated using a statistical test based on the optical flow measurements and the location of the horizon. Once associated, the selected horizon line, along with the associated optical flow, is used as a measurement to the EKF. To test the accuracy of the algorithm, two flights were conducted, one using a highly dynamic Uninhabited Airborne Vehicle (UAV) in clear flight conditions and the other in a human-piloted Cessna 172 in conditions where the horizon was partially obscured by terrain, haze and smoke. The UAV flight resulted in pitch and roll error standard deviations of 0.42◦ and 0.71◦ respectively when compared with a truth attitude source. The Cessna flight resulted in pitch and roll error standard deviations of 1.79◦ and 1.75◦ respectively. The benefits of selecting and tracking the horizon using a motion model and optical flow rather than naively relying on the image processing front-end is also demonstrated.

Change Point Estimation in Monitoring Survival Time

Precise identification of the time when a change in a hospital outcome has occurred enables clinical experts to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for survival time of a clinical procedure in the presence of patient mix in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change in the mean survival time of patients who underwent cardiac surgery. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. Markov Chain Monte Carlo is used to obtain posterior distributions of the change point parameters including location and magnitude of changes and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time CUSUM control charts for different magnitude scenarios. The proposed estimator shows a better performance where a longer follow-up period, censoring time, is applied. In comparison with the alternative built-in CUSUM estimator, more accurate and precise estimates are obtained by the Bayesian estimator. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

An estimation of crash risks using a log-linear model and the induced exposure technique

Prevention and safety promotion programmes. Traditionally, in-depth investigations of crash risks are conducted using exposure controlled study or case-control methodology. However, these studies need either observational data for control cases or exogenous exposure data like vehicle-kilometres travel, entry flow or product of conflicting flow for a particular traffic location, or a traffic site. These data are not readily available and often require extensive data collection effort on a system-wide basis. Aim: The objective of this research is to propose an alternative methodology to investigate crash risks of a road user group in different circumstances using readily available traffic police crash data. Methods: This study employs a combination of a log-linear model and the quasi-induced exposure technique to estimate crash risks of a road user group. While the log-linear model reveals the significant interactions and thus the prevalence of crashes of a road user group under various sets of traffic, environmental and roadway factors, the quasi-induced exposure technique estimates relative exposure of that road user in the same set of explanatory variables. Therefore, the combination of these two techniques provides relative measures of crash risks under various influences of roadway, environmental and traffic conditions. The proposed methodology has been illustrated using Brisbane motorcycle crash data of five years. Results: Interpretations of results on different combination of interactive factors show that the poor conspicuity of motorcycles is a predominant cause of motorcycle crashes. Inability of other drivers to correctly judge the speed and distance of an oncoming motorcyclist is also evident in right-of-way violation motorcycle crashes at intersections. Discussion and Conclusions: The combination of a log-linear model and the induced exposure technique is a promising methodology and can be applied to better estimate crash risks of other road users. This study also highlights the importance of considering interaction effects to better understand hazardous situations. A further study on the comparison between the proposed methodology and case-control method would be useful.

Integrated vision-based attitude estimation

For many years, computer vision has lured researchers with promises of a low-cost, passive, lightweight and information-rich sensor suitable for navigation purposes. The prime difficulty in vision-based navigation is that the navigation solution will continually drift with time unless external information is available, whether it be cues from the appearance of the scene, a map of features (whether built online or known a priori), or from an externally-referenced sensor. It is not merely position that is of interest in the navigation problem. Attitude (i.e. the angular orientation of a body with respect to a reference frame) is integral to a visionbased navigation solution and is often of interest in its own right (e.g. flight control). This thesis examines vision-based attitude estimation in an aerospace environment, and two methods are proposed for constraining drift in the attitude solution; one through a novel integration of optical flow and the detection of the sky horizon, and the other through a loosely-coupled integration of Visual Odometry and GPS position measurements. In the first method, roll angle, pitch angle and the three aircraft body rates are recovered though a novel method of tracking the horizon over time and integrating the horizonderived attitude information with optical flow. An image processing front-end is used to select several candidate lines in a image that may or may not correspond to the true horizon, and the optical flow is calculated for each candidate line. Using an Extended Kalman Filter (EKF), the previously estimated aircraft state is propagated using a motion model and a candidate horizon line is associated using a statistical test based on the optical flow measurements and location of the horizon in the image. Once associated, the selected horizon line, along with the associated optical flow, is used as a measurement to the EKF. To evaluate the accuracy of the algorithm, two flights were conducted, one using a highly dynamic Uninhabited Airborne Vehicle (UAV) in clear flight conditions and the other in a human-piloted Cessna 172 in conditions where the horizon was partially obscured by terrain, haze and smoke. The UAV flight resulted in pitch and roll error standard deviations of 0.42° and 0.71° respectively when compared with a truth attitude source. The Cessna 172 flight resulted in pitch and roll error standard deviations of 1.79° and 1.75° respectively. In the second method for estimating attitude, a novel integrated GPS/Visual Odometry (GPS/VO) navigation filter is proposed, using a structure similar to a classic looselycoupled GPS/INS error-state navigation filter. Under such an arrangement, the error dynamics of the system are derived and a Kalman Filter is developed for estimating the errors in position and attitude. Through similar analysis to the GPS/INS problem, it is shown that the proposed filter is capable of recovering the complete attitude (i.e. pitch, roll and yaw) of the platform when subjected to acceleration not parallel to velocity for both the monocular and stereo variants of the filter. Furthermore, it is shown that under general straight line motion (e.g. constant velocity), only the component of attitude in the direction of motion is unobservable. Numerical simulations are performed to demonstrate the observability properties of the GPS/VO filter in both the monocular and stereo camera configurations. Furthermore, the proposed filter is tested on imagery collected using a Cessna 172 to demonstrate the observability properties on real-world data. The proposed GPS/VO filter does not require additional restrictions or assumptions such as platform-specific dynamics, map-matching, feature-tracking, visual loop-closing, gravity vector or additional sensors such as an IMU or magnetic compass. Since no platformspecific dynamics are required, the proposed filter is not limited to the aerospace domain and has the potential to be deployed in other platforms such as ground robots or mobile phones.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Load estimation with uncertainties from opportunistic sampling data: A semiparametric approach

We consider estimating the total load from frequent flow data but less frequent concentration data. There are numerous load estimation methods available, some of which are captured in various online tools. However, most estimators are subject to large biases statistically, and their associated uncertainties are often not reported. This makes interpretation difficult and the estimation of trends or determination of optimal sampling regimes impossible to assess. In this paper, we first propose two indices for measuring the extent of sampling bias, and then provide steps for obtaining reliable load estimates that minimizes the biases and makes use of informative predictive variables. The key step to this approach is in the development of an appropriate predictive model for concentration. This is achieved using a generalized rating-curve approach with additional predictors that capture unique features in the flow data, such as the concept of the first flush, the location of the event on the hydrograph (e.g. rise or fall) and the discounted flow. The latter may be thought of as a measure of constituent exhaustion occurring during flood events. Forming this additional information can significantly improve the predictability of concentration, and ultimately the precision with which the pollutant load is estimated. We also provide a measure of the standard error of the load estimate which incorporates model, spatial and/or temporal errors. This method also has the capacity to incorporate measurement error incurred through the sampling of flow. We illustrate this approach for two rivers delivering to the Great Barrier Reef, Queensland, Australia. One is a data set from the Burdekin River, and consists of the total suspended sediment (TSS) and nitrogen oxide (NO(x)) and gauged flow for 1997. The other dataset is from the Tully River, for the period of July 2000 to June 2008. For NO(x) Burdekin, the new estimates are very similar to the ratio estimates even when there is no relationship between the concentration and the flow. However, for the Tully dataset, by incorporating the additional predictive variables namely the discounted flow and flow phases (rising or recessing), we substantially improved the model fit, and thus the certainty with which the load is estimated.

Robust estimation using the Huber function with a data-dependent tuning constant

Robust estimation often relies on a dispersion function that is more slowly varying at large values than the square function. However, the choice of tuning constant in dispersion functions may impact the estimation efficiency to a great extent. For a given family of dispersion functions such as the Huber family, we suggest obtaining the "best" tuning constant from the data so that the asymptotic efficiency is maximized. This data-driven approach can automatically adjust the value of the tuning constant to provide the necessary resistance against outliers. Simulation studies show that substantial efficiency can be gained by this data-dependent approach compared with the traditional approach in which the tuning constant is fixed. We briefly illustrate the proposed method using two datasets.

Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. The family nests as particular cases several important asymmetric distributions like the Generalized Hyperbolic distribution. The Generalized Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multivariate setting, an extension of the standard location and scale mixture concept is proposed into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm and extended to cover the case of mixtures of such multiple scaled distributions for application to clustering. Assessments on simulated and real data confirm the gain in degrees of freedom and flexibility in modelling data of varying tail behaviour and directional shape.