Page 139 - Fundamentals of Radar Signal Processing

time using the Levinson-Durbin or similar algorithms (Kay, 1988). Furthermore,

the AR parameters can be used to construct optimal adaptive clutter suppression
filters, as is seen in Chap. 5. The disadvantage is that the calculations rapidly
become computationally intensive as the model order increases.
Another decorrelation model, more recently developed and popular in
studies of detection of ground targets from moving platforms, is the Billingsley
model. This model represents the correlation properties of windblown tree

clutter and other vegetative cover, said to be the “most pervasive” ground
clutter (Billingsley, 2001). This model assumes that the clutter temporal power
spectrum is the sum of a two-sided decaying exponential function and an
impulse at the origin in Doppler frequency space

(2.70)

where the parameter α, which established the ratio of the DC to AC
components, is a function of both wind and radar frequency, while β, which

determines the width of the AC power spectral component, is dependent
primarily on wind conditions. The corresponding autocorrelation function is

(2.71)

Based on extensive measurements, Billingsley proposed empirical
formulas for α and β:

(2.72)

(2.73)

where w is the wind speed in statute miles per hour and F is the radar carrier
0
frequency in GHz.
Note that β and therefore the decorrelation time does not depend on radar
frequency, somewhat in conflict with earlier models. Caution is needed in
applying Eq. (2.73) due to mixed units. Specifically, w is in statute miles per

hour but β is in meters per second.
The “DC term” in Eqs. (2.70) and (2.71) represents a constant, nonrandom
component of the clutter echo that is sometimes called a “persistent component”