In this first case, a sinusoidal speed and

direction angle references were used to test the effectiveness of the PI-based MRAS and the proposed FO-MRAS controller.

The thrust

direction angle [gamma] is the intersection angle from [F.sub.[alpha]] to F.

Figure 6 shows the illustration of FDA antenna's apparent

direction angle and physical

direction angle.

The range of simulations allows consideration of "under-merged" plumes with low plume cone angle and high plume

direction angle, or "over-merged" plumes with high plume cone angle and low plume

direction angle.

The starting point of the path is (0, 0), and

direction angle is 0[degrees].

Base shear, bending moment, and the acceleration response are calculated as function of the

direction angle [alpha], for several damping ratios [xi] (1.0%; 2.0%; and 4.0%) (Figures 7 and 8).

Let a be a point in R2 , and n(8) = ( cos(8), sin(8)) be a unit vector in R2 , where 8 is

direction angle. We consider the partition of R2 given by

The proposed method estimates positioning accuracy based on

direction angle, velocity, and distance using an accurate reference point and long-term averaging, rounding error reduction via coordinate translation, and an invalid data check.

The average bistatic NRCS results versus scattering angles from linear, CWM and Creamer (2) sea surfaces for indent angles of 0[degrees] and 60[degrees] in wind

direction angle of 45[degrees] are shown in Figures 5(a), (b) (wind speed of 3 m/s).

The principal damage values [D.sub.1] and [D.sub.2] for fracture sample are 0.17 for minimum and 0.50 for maximum, and the principal

direction angle [theta] of damage tensor is approximately 105[degrees] which is perpendicular to the direction of principal permeability.

Two six-port networks are used to determine the beam

direction angle. Figure 1 shows the block schematic of a direction finding receiver.