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Chapter 3 / Sensors / Radar
_ _
3.8.7 Glint Errors
To the radar a target, far from being a point in space, appears as a set of
multiple reflectors which regularly change their intensity and orientation.
When these reflections are combined at the receiver the result is highly
complex and can result in measurements at a point beyond the target's
physical shape. Frequency agility is often employed in modern radar
designs to eliminate the effects of glint. Glint errors are de-correlated by
changing the transmission frequency between measurements by at least
(0.5c/lT) Hz, where (lt) is the physical size of the target and (c) is the speed
of light. The glint error spectrum is thus broadened to the extent that the
angular glint errors may be obtained from a Gaussian distribution,
⎛
⎜
⎜
⎝
⎛
N ⎜
⎜
⎝
0 ,
T
lt
• jˆ
4 ⋅ P ⋅ 3 ⋅ N
o,
t
( Ψ , Θ )
F
G
⎞
⎟
⎟
⎠
3.8-13
,
G
⎛
N ⎜
⎜
⎝
: =
T
t • k
4 ⋅ P ⋅ 3 ⋅ N
ˆ l
0 ,
o,
t
F
⎞ ⎞
⎟ ⎟
⎟ ⎟
⎠ ⎠
Equation 3.8-47
The error is a function of target range, and the number of frequencies used
by the radar during the dwell time (NF). The target dimensions when
viewed in a plane normal to the target LOS are,
T
t
T
A
A
TV
l : = T ⋅ T ⋅
( ) T
XTV
l 0 0
t
Equation 3.8-48
Glint errors are often modelled as a 1 st order Gauss-Markov process with a
LF bandwidth representing bright spot wander. Nesline [N.7] uses this glint
model with a 3 m output, and a 2 Hz bandwidth. The errors produced by
this simple model are a poor representation of true glint effects and usually
lead to optimistic results, particularly if the state observer includes error
states with these dynamics. Borden [B.11] developed a statistical model that is
a better representation of glint, the errors taken from a more realistic longtailed,
Student-t distribution. In Figure 3-42 the Borden glint model is
compared with a normal distribution. Deviation from the straight line
indicates non-Gaussian statistical outliers. The model represents an infinite
number of reflectors in a line that is adequate for targets turning slowly
through small angles between observations. One of the criticisms of this
model is that it leads to pessimistic results since target tend to have a limited
number of highly reflective points. It provide range and doppler glint which
are ignored. The normalised glint and RCS errors (ξG,σRCS) are related to
the transmission frequency (RDfT) of 4 GHz through the wave number,
RD
k WN : = 2 ⋅ π ⋅ RDf
T
c
Equation 3.8-49