Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 106


Sense and Avoid for Unmanned Aircraft Systems
direction is named as Lφ, then obstacle angular dimension can be
expressed as
	(44)
Taking the time derivative, we get
	(45)
and thus
	(46)
The approximation error nullifies for zero dCPA, as before.
If the obstacle area within images is measured at different
times, the derivative can be estimated numerically leading to an
estimate of tCPA. Indeed, applicability of this approach in practical cases is limited by the difficulty in resolving small changes in
object appearance at relatively large ranges, when obstacles typically span a few pixels and their appearance is strongly influenced
by the environmental conditions [40] and attitude with respect to
vision instruments. Thus, scale change techniques may have better
applicability in the case of relatively close, fixed, large obstacles.
A more common approach to conflict detection in vision-based
systems is related to the obstacle LOS rate: the condition of zero
angular rate can be used to infer a collision object (Fig. 20), regardless of intruder angular position (implicitly assuming that the EO
system is also able to detect negative range rates, i.e., approaching
aircraft, based on the variation of intruder's appearance).
Hazard alerting based only on LOS rate resembles the decision making process of the human pilot but presents challenging
aspects. Indeed, as the estimated LOS rate will not be zero in practical cases, a threshold has to be defined. Due to the geometry of
the problem, a simple alerting logic based on a constant LOS rate
threshold has significant limitations, since it is hard to find an acceptable trade-off between false and missed conflict detections
[44].
To partially overcome this limit, a possible approach consists
in including obstacle angular position within threshold definition.
This is done for example in [45], where the threshold is defined
considering a so-called "convergence measure" given by the dot
product of the obstacle image position vector and its rate.
A similar approach is followed in [46] and is recalled here. The
main idea consists in setting an adaptive threshold for the LOS
rate based on realistic/worst case assumptions for unobservable
variables, while also taking ownship motion and intruder angular
position into account.
Starting from (41), in small elevation near collision conditions,
dCPA can be approximated as [36]
	(47)

Fig. 20.

Constant LOS in collision conditions.

An EO-based sensing system has a detection performance that
depends on intruder range; the probability of correct intruder declaration (i.e., firm tracking) increases as range decreases. Thus, it is
possible to define a range threshold rmin at which the probability of
declaration (i.e., of firm tracking) is close enough to 1. This range
threshold rmin can be used as a worst case range estimate in collision detection calculations.
As regards range rate, among other variables it depends on the
obstacle type. However, it is still possible to derive a worst case
estimate considering the fastest possible intruder, and then taking
into account the ownship current speed and the estimated intruder
azimuth with respect to the ownship ground speed vector (which is
calculated using tracker NED estimates and ownship course angle
χ). A worst case range rate estimate
is thus obtained.
LOS rate in stabilized coordinates is in general given by [44]
	(48)
In small elevation near-collision conditions, it is possible to demonstrate that the LOS rate can be approximated as
		

representing the magnitude of the 3D angular-rate vector.
Thus, combining (47) and (49), based on the previous considerations the worst case dCPA for a given LOS rate is

where and are azimuth rate and elevation rate in NED coordinates, respectively, and the considered conditions correspond to
,
,ϑ
1.
106	

(49)

IEEE A&E SYSTEMS MAGAZINE	

	(50)

NOVEMBER 2016, Part II of II



Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine November 2016 Tutorial X

No label
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - No label
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - Cover2
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 1
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 2
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 3
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 4
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 5
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 6
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 7
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 8
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 9
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 10
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 11
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 12
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 13
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 14
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 15
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 16
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 17
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 18
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 19
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 20
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 21
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 22
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 23
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 24
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 25
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 26
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 27
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 28
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 29
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 30
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 31
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 32
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 33
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 34
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 35
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 36
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 37
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 38
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 39
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 40
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 41
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 42
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 43
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 44
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 45
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 46
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 47
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 48
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 49
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 50
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 51
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 52
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 53
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 54
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 55
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 56
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 57
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 58
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 59
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 60
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 61
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 62
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 63
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 64
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 65
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 66
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 67
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 68
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 69
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 70
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 71
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 72
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 73
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 74
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 75
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 76
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 77
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 78
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 79
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 80
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 81
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 82
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 83
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 84
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 85
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 86
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 87
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 88
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 89
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 90
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 91
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 92
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 93
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 94
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 95
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 96
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 97
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 98
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 99
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 100
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 101
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 102
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 103
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 104
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 105
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 106
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 107
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 108
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 109
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 110
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 111
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 112
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 113
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 114
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 115
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 116
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 117
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 118
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 119
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 120
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - Cover3
Aerospace and Electronic Systems Magazine November 2016 Tutorial X - Cover4
http://www.brightcopy.net/allen/aesm/34-2s
http://www.brightcopy.net/allen/aesm/34-2
http://www.brightcopy.net/allen/aesm/34-1
http://www.brightcopy.net/allen/aesm/33-12
http://www.brightcopy.net/allen/aesm/33-11
http://www.brightcopy.net/allen/aesm/33-10
http://www.brightcopy.net/allen/aesm/33-09
http://www.brightcopy.net/allen/aesm/33-8
http://www.brightcopy.net/allen/aesm/33-7
http://www.brightcopy.net/allen/aesm/33-5
http://www.brightcopy.net/allen/aesm/33-4
http://www.brightcopy.net/allen/aesm/33-3
http://www.brightcopy.net/allen/aesm/33-2
http://www.brightcopy.net/allen/aesm/33-1
http://www.brightcopy.net/allen/aesm/32-10
http://www.brightcopy.net/allen/aesm/32-12
http://www.brightcopy.net/allen/aesm/32-9
http://www.brightcopy.net/allen/aesm/32-11
http://www.brightcopy.net/allen/aesm/32-8
http://www.brightcopy.net/allen/aesm/32-7s
http://www.brightcopy.net/allen/aesm/32-7
http://www.brightcopy.net/allen/aesm/32-6
http://www.brightcopy.net/allen/aesm/32-5
http://www.brightcopy.net/allen/aesm/32-4
http://www.brightcopy.net/allen/aesm/32-3
http://www.brightcopy.net/allen/aesm/32-2
http://www.brightcopy.net/allen/aesm/32-1
http://www.brightcopy.net/allen/aesm/31-12
http://www.brightcopy.net/allen/aesm/31-11s
http://www.brightcopy.net/allen/aesm/31-11
http://www.brightcopy.net/allen/aesm/31-10
http://www.brightcopy.net/allen/aesm/31-9
http://www.brightcopy.net/allen/aesm/31-8
http://www.brightcopy.net/allen/aesm/31-7
https://www.nxtbookmedia.com