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Millimeter Wave RADAR Power-Range Spectra Interpretation 89

containing reflections from objects with different RCSs at different locations.
The noise statistics in power is obtained during both target presence and
absence.
The angular standard deviation is assumed to be 1 as the RADAR wave is
◦
a pencil beam. The observation model is then given by
T
z i (k + 1) =[R i (k + 1), β i (k + 1),P i (k + 1)] + w i (k + 1)
= h(x(k + 1)) + w i (k + 1) (2.36)

where z i (k + 1) is the observation, and w i (k + 1) is the additive observation
noise given by

T
w i (k + 1) =[v R (k + 1)v β (k + 1)v p (k + 1)] (2.37)

and h is the nonlinear observation function defined by Equation (2.25),
Equation (2.26), and Equation (2.35).

2.9 MULTI-TARGET RANGE BIN PREDICTION —RESULTS
To validate the formulation for realistically predicting multiple line-of-site
target range bins, tests using a RADAR unit from Navtech Electronics were
carried out. Initially the vehicle was positioned at pose x v (k) as demonstrated
in Figure 2.28. The full 360 ◦ RADAR scan obtained from this vehicle location
is shown in Figure 2.25. Range bins obtained from the initial vehicle location
at two different bearing angles are shown in Figure 2.26 and Figure 2.29a.
Figure 2.26 is obtained at azimuth 231 and is indicated by the black line in
◦
Figure 2.25. Features in the environment are marked in the figures. The next
predicted vehicle location is calculated using the vehicle model and system
inputs (Equation [2.24]). This corresponds to the new predicted vehicle pose
ˆ x v (k + 1 | k) in Figure 2.28. The range spectra in all directions are then pre-
dicted from the new predicted vehicle location. For example, in the range bin
predicted at angle ˆ β(k + 1 | k) in Figure 2.28, the predicted values for the
range, bearing and received power of features A and D are calculated according
to Equation (2.25), Equation (2.26), and Equation (2.35).
A single range prediction obtained from the predicted vehicle location
x v (k + 1 | k) is shown in Figure 2.29b having two features down-range.
Equation (2.35) can be used to predict the received power as long as the power
bias as a function of range incorporated into the RADAR electronics is taken
into account. This simply requires knowledge of the RADAR’s high pass filter
circuitry which in an FMCW RADAR compensates for the fourth power of
range loss, expected according to the simple RADAR Equation [15, 21].

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c002” — 2006/3/31 — 17:29 — page 89 — #49