Timothy L. Molloy

HMM relative entropy rate concepts for vision-based aircraft manoeuvre detection

Machine vision is emerging as a viable sensing approach for mid-air collision avoidance (particularly for small to medium aircraft such as unmanned aerial vehicles). In this paper, using relative entropy rate concepts, we propose and investigate a new change detection approach that uses hidden Markov model filters to sequentially detect aircraft manoeuvres from morphologically processed image sequences. Experiments using simulated and airborne image sequences illustrate the performance of our proposed algorithm in comparison to other sequential change detection approaches applied to this application.

Detection of aircraft below the horizon for vision-based detect and avoid in unmanned aircraft systems

Vision-based aircraft detection technology may provide a credible sensing option for automated detect and avoid in small to medium size fixed-wing unmanned aircraft systems (UAS). Reliable vision-based aircraft detection has previously been demonstrated in sky-region sensing environments. This paper describes a novel vision-based system for detecting aircraft below the horizon in the presence of ground clutter. We examine the performance of our system on a data set of 63 near collision encounters we collected between a camera- equipped manned aircraft, and a below-horizon target. In these 63 encounters, our system successfully detects all aircraft, at an average detection range of 1890m (with a standard error of 43m and no false alarms in 1.1 hours). Furthermore, our system does not require access to inertial sensor data (which significantly reduces system cost), and operates at over 12 frames per second.

Nonlinear

This paper proposes a nonlinear H∞ controller for stabilization of velocities, attitudes and angular rates of a fixed-wing unmanned aerial vehicle (UAV) in a windy environment. The suggested controller aims to achieve a steady-state flight condition in the presence of wind gusts such that the host UAV can be maneuvered to avoid collision with other UAVs during cruise flight with safety guarantees. This paper begins with building a proper model capturing flight aerodynamics of UAVs. Then a nonlinear controller is developed with gust attenuation and rapid response properties. Simulations are conducted for the Shadow UAV to verify performance of the proposed controller. Comparative studies with the proportional-integral-derivative (PID) controllers demonstrate that the proposed controller exhibits great performance improvement in a gusty environment, making it suitable for integration into the design of flight control systems for cruise flight of UAVs.

\boldsymbol{\mathcal{H}}_{\boldsymbol\infty}

Rapid recursive estimation of hidden Markov Model (HMM) parameters is important in applications that place an emphasis on the early availability of reasonable estimates (e.g. for change detection) rather than the provision of longer-term asymptotic properties (such as convergence, convergence rate, and consistency). In the context of vision-based aircraft (image-plane) heading estimation, this paper suggests and evaluates the short-data estimation properties of 3 recursive HMM parameter estimation techniques (a recursive maximum likelihood estimator, an online EM HMM estimator, and a relative entropy based estimator). On both simulated and real data, our studies illustrate the feasibility of rapid recursive heading estimation, but also demonstrate the need for careful step-size design of HMM recursive estimation techniques when these techniques are intended for use in applications where short-data behaviour is paramount.

Control of UAVs for Collision Avoidance in Gusty Environments

In this paper, we propose a novel online hidden Markov model (HMM) parameter estimator based on Kerridge inaccuracy rate (KIR) concepts. Under mild identifiability conditions, we prove that our online KIR-based estimator is strongly consistent. In simulation studies, we illustrate the convergence behaviour of our proposed online KIR-based estimator and provide a counter-example illustrating the local convergence properties of the well known recursive maximum likelihood estimator (arguably the best existing solution).

Short-data recursive HMM parameter estimation for rapid vision-based aircraft heading estimation

We consider the problem of quickly detecting an unknown change in a sequence of independent random variables with unknown transient (or time-varying) prechange and postchange distributions. We pose and solve novel robust versions of the popular Lorden and Bayesian quickest change detection criteria with unknown transients that belong to known uncertainty sets. Simulations of our robust solutions detecting additive changes in linear state-space systems suggest that they can outperform more computationally expensive rules.

Consistent HMM parameter estimation using Kerridge inaccuracy rates

In this note, we consider the problem of computing the parameters (or weights) of an optimal control objective function given optimal closed-loop state and control trajectories. We establish a method of inverse optimal control that exploits the discrete-time minimum principle. Under a testable matrix rank condition, our proposed method is guaranteed to recover the unknown objective-function parameters of finite-horizon discrete-time nonlinear optimal control problems.

Minimax Robust Quickest Change Detection in Systems and Signals with Unknown Transients

Quickly detecting changes in the statistical behavior of measurements is important in many applications of control engineering involving fault detection and process monitoring. In this letter, we pose and solve minimax robust Lorden and Bayesian quickest change detection problems for situations where the cost of detection delays compounds exponentially. We show that the detection rules that solve our robust quickest change detection problems are also the rules that solve the standard (non-robust) problems specified by least favorable distributions from uncertainty classes of possible distributions that satisfy a stochastic boundedness condition. In contrast to previous robust quickest change detection results with nonlinear detection delay penalties, our results with exponential delay penalties are exact (i.e., they hold for any false alarm constraint and not only in the asymptotic regime of few false alarms). We illustrate our results through simulations.

Finite-horizon inverse optimal control for discrete-time nonlinear systems

In this letter, we present a change detection approach for dependent processes based on the output of a mismatched hidden Markov model (HMM) test filter (i.e., an HMM filter applied to observations not generated by its model). The presented approach is intended to be suitable for dependent processes that are significantly undermodelled in the sense that their conditional densities are not known, are too complex, or are otherwise unsuitable for existing change detection techniques. We establish a description of a mismatched HMM test filter’s output when it is applied to sequences generated by a general dependent process. This description is used to motivate the proposal of a novel change detection approach based on monitoring the statistical properties of the mismatched HMM test filter’s output. We examine our proposed approach in an important vision based aircraft detection application where it offers improvements in detection range (mean increase of 276 m) compared to the current state of the art baseline detection approach.

Minimax Robust Quickest Change Detection With Exponential Delay Penalties

We investigate the quickest detection of an unknown change in the distribution of a stochastic process generating independent and identically distributed observations. We develop new bounds on the performance of misspecified cumulative sum (CUSUM) rules, and pose minimax robust versions of the popular Lorden and Pollak criteria with polynomial (or higher order moment) detection delay penalties. By exploiting our results for misspecified CUSUM rules, we identify solutions to our robust quickest change detection problems in the asymptotic regime of few false alarms. In contrast to previous robust quickest change detection treatments, our asymptotic results hold under relaxed conditions on the uncertainty sets of possible prechange and postchange distributions. We illustrate our results in simulations and apply them to the problem of detecting target manoeuvres in low signal-to-noise ratio settings (i.e., dim-target manoeuvre detection).