Monocular image-based time to collision and closest point of approach estimation

Abstract

Abstract-This paper deals with monocular image-based time-to-collision (TTC) and closest point of approach (CPA) estimation for aircraft sense and avoid. First, it proposes a disc-based pinhole camera projection model which can better represent a real 3D object. Then it proposes simple least squares optimal line fitting-based techniques for TTC and CPA estimation based-on measurable image parameters only. Possible errors in the image are considered through design nomograms and a collision decision threshold selection technique is presented. Theoretical results are verified through software-in-the-loop simulation and real flight test results. To the best of the author's knowledge the disc-based projection model and the line fit-based TTC and CPA estimation are new contributions in this field.

Three Dimensional Intruder Closest Point of Approach Estimation Based-on Monocular Image Parameters in Aircraft Sense and Avoid

“…Unfortunately x and S x can not be directly related to intruder distances X C , Z C from the own aircraft in the camera frame. However, their transformed valuesS x ,x has a close connection to X C , Z C as shown in (1) (for details see [4]). S…”

“…In the figure (X,Z) is the (aircraft) body frame and (X C , Z C ) is the camera frame rotated by β C angle relative to the body. The disc represents the intruder aircraft (with half size r = R/2) (original derivation of the disc projection model can be found in [4]). Before deriving the details of the projection model the possible measurable parameters of the intruder image in the image plane should be defined in Fig.…”

“…In the literature there are several works dealing with TTCPA estimation based-on optic flow or first order motion models such as [6], [19], [24] however, it is hard to find references for CPA estimation ( [24] makes a decision about the collision based-on the epipole position). Consequently, previous efforts of the authors [2], [3], [4] focused on the estimation of TTCPA and CPA values together with the direction of CPA from solely the monocular image parameters in the horizontal plane. In these previous works we referenced TTCPA as TTC (time to collision) however TTCPA better describes the meaning of this parameter.…”

“…The proposed solution is a least squares (LS) optimal line fit based very simple algorithm which well fits real-time execution needs. Error analysis considering image pixelization errors was done in [4].…”

“…However, the evaluation of the collision situation should be done in the vertical plane also as two aircraft can be very close in the horizontal plane though very far vertically which means a clear situation (no chance of collision). The extension of the formulae derived in [2], [3] and [4] into the vertical dimension is the first topic of this article. If one can evaluate the situation both in the horizontal and vertical planes the question arise if the three dimensional (3D) minimum distance between the aircraft can be determined from these parameters.…”