Page 176 - Radar Technology Encyclopedia

error, geodetic error model 166

data. It is usually a component of the platform-dependent
x
error. DKB
Glint error refers to the random tracking error component of
a radar operating against a complex target, resulting from Random Systematic
component
interference between reflections form different scattering cen- component
ters of the target. The glint error may exceed the physical
extent of the target, as a result of ripples in the phase front
received at the radar antenna. DKB
Ref.: Skolnik (1970), Ch. 28; Barton (1969), pp. 167–171.
t
Indicator (measurement error) is an error in parameter esti-
mation due to indicator (usually display) equipment errors. Figure E8 Radar measurement error.
Indicator errors arise for the following reasons. Errors caused
by synchronization inaccuracy are determined by the error
The complete description of x(t) requires knowledge of
time between start of the indicator scan and radar transmitter
the nth-order probability distribution function, F x ()
from
n
signal, those arising in parameter estimation, and those due to
which one can determine the basic parameters of the error: its
scale and method of calculating the measured parameter. In
mathematical expectation (mean value), m ; variance, D (and
x
x
modern radar, automatic coordinate measurement is used, and
rms value, s = D x ); correlation function, K (t ,t ); and
x 1 2
x
as a result indicator error does not affect parameter evalua-
power spectrum, G (w). In practice, the nth-order pdf is sel-
x
tion. AIL
dom available, and these parameters are estimated from the
Ref.: Dymova (1975), p. 129.
samples, z(tn) of the function x(t) at N moments of time
Instrumentation error is the error in evaluating radar accu- n = 0, ..., N. The function x(t) is usually assumed to be sta-
racy that actually results from optical or other test instrumen- tionary and ergodic. In that case, convenient expressions to
tation used as a tracking reference, rather than from the radar estimate the basic error parameters are
itself. When a boresight telescope is used as a reference, it is
subject to parallax error relative to the radar tracking axis, as N N 2
1
1
2
well as to errors in stability of the optics and reading of the D = ------------- å [ x n Dt )] -------------------- 2 å x n Dt )
(
×
(
×
–
x
film. Similar errors may arise in use of external reference N + 1 ( N + 1 )
n = 0 n = 0
instrumentation. DKB
Ref.: Barton (1964), p. 325.
Nm
–
Lag error refers to the failure of a tracking system to keep up 1
(
[
K m Dt ) ----------------------- å x n Dt )x n + m ) D t ]
×
×
(
×
=
×
(
with target velocity, acceleration, or higher derivatives of x N + 1 – m
motion in radar coordinates. The conventional servo error Nm n = 0
–
analysis expresses total lag error in terms of a Taylor expan- 1
å
(
×
– ------------------------------- 2 å x n Dt ) ( x n Dt )
×
sion of the target trajectory, each term being reduced by an ( N + 1 – m )
appropriate error constant: n = 0 n
· ··
x x x
e = ------ + ------ + ------ + ¼ N – 1
K K K
×
p v a K 0 () D t 1 æ m ö
x
G w() ------------------------ += --- å K m Dt ) cos ( × ---- Dt
w m Dtw ) 1 –
×
(
where K is the position error constant (normally infinite), K x x è
p v 2p p N ø
is the velocity error constant, K is the acceleration error con- m = 1
a
stant, and higher order terms are generally negligible. The
velocity error constant can be made arbitrarily high, although N
1
transient effects limit its practical value. This error is also m = ------------- å x n Dt )
×
(
x N + 1
called dynamic error. See also acceleration error. DKB
n = 0
Ref.: Barton (1988), pp. 463–466.
where Dt is the sampling interval. When these parameters are
An error model is a mathematical description representing determined, the measurement error can be described in terms
radar measurement error as a function of the radar and envi- of its magnitude (mean value m and rms value s ) and its
x
x
ronmental parameters causing the error. The error is described temporal behavior (i.e., whether it is a slow or fast function of
as a random process (i.e., as a random function of time): time, as determined by the correlation interval, t , derived
c
x = xpt , ) from K (t)). The final model of error can then be written as
(
x
where is the vector of parameters causing the specified
p
3
error type (see angular error, doppler error, range error).
×
[
x t () = å [ m ( pt , ) + spt , ] h t ()]
Measurement errors usually include both systematic (bias) x i x i i
and random (noise) components (Fig. E8). i = 1