Article
Target Tracking in 3-D Using Estimation Based
Nonlinear Control Laws for UAVs
†
Mousumi Ahmed and Kamesh Subbarao *
Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, 211 Woolf Hall,
Box 19018, 500 W. First St., Arlington, TX 76010, USA; mousumi.ahmed@mavs.uta.edu
* Correspondence: subbarao@uta.edu; Tel.: +1-817-272-7467
† This paper is an extended version of our paper published in IEEE Multi-conference on Systems and
Control, Denver, CO, USA, 28–30 September 2011.
Academic Editor: David Anderson
Received: 21 December 2015; Accepted: 20 January 2016; Published: 1 February 2016
Abstract: This paper presents an estimation based backstepping like control law design for an
Unmanned Aerial Vehicle (UAV) to track a moving target in 3-D space. A ground-based sensor
or an onboard seeker antenna provides range, azimuth angle, and elevation angle measurements to
a chaser UAV that implements an extended Kalman filter (EKF) to estimate the full state of the target.
A nonlinear controller then utilizes this estimated target state and the chaser’s state to provide
speed, flight path, and course/heading angle commands to the chaser UAV. Tracking performance
with respect to measurement uncertainty is evaluated for three cases: (1) stationary white noise; (2)
stationary colored noise and (3) non-stationary (range correlated) white noise. Furthermore, in an
effort to improve tracking performance, the measurement model is made more realistic by taking
into consideration range-dependent uncertainties in the measurements, i.e., as the chaser closes in on
the target, measurement uncertainties are reduced in the EKF, thus providing the UAV with more
accurate control commands. Simulation results for these cases are shown to illustrate target state
estimation and trajectory tracking performance.
Keywords: backstepping; control; UAVs; estimation; kalman filter; 3D target tracking
1. Introduction
Target tracking by Unmanned Aerial Vehicles (UAVs) is an important area of study, especially
when it applies to tracking a target in 3-D space. Tracking capabilities of a UAV depend on
many factors but we focus on how accurately it can obtain the target state information using
onboard sensors, and how effectively it can generate its control commands so as to achieve tracking.
For control laws that require full state information of a target, it is thus necessary that the target
state information be reconstructed based on limited measurements observed by the chaser UAV.
These measurements are often corrupted by external disturbances (wind gust, turbulence). In a
target state estimation problem, the choice of the appropriate model to represent the target motion
is also not clear. The classical approaches either use a constant velocity model leading to an α-β
tracking filter [1,2], or a constant acceleration model that leads to the α-β-γ tracking filter [1,2].
Mehrotra et al. [3] have proposed the use of a constant jerk model that allows for changes in
acceleration of the target thereby accommodating a richer class of target maneuvers. This research
focuses on an extended state kinematic model for the target with the objective to determine the
location, flight path angle and course/heading of the target vehicle when full state information is
not available or achievable due to limitation of sensors and their capabilities. In this study, the
Aerospace 2016, 3, 5; doi:10.3390/aerospace3010005 www.mdpi.com/journal/aerospace
