Joint Optimization of Detection and Tracking in Adaptive Radar Systems - Advances in Heuristic Signal Processing and Applications - page 124

Fig. 6.4 The flow of static threshold optimization (STOP) for graphical (TOC-curve) approach.
The procedure given in this figure is repeated for different SNR values to obtain the optimum
operating curve in the P FA - P D plane. Then, this optimal operating curve is used together with
ROC curve relation to find the STOP curve which is the ultimate goal of STOP. The STOP curve
provides an SNR-dependent optimum P FA setting which makes the threshold optimization online
possible under varying SNR conditions. A numerical example is given in Sect. 6.4.1

the steady-state covariance matrix P NSPP from ( 6.27 )forthe (P FA ,P i D ) pair where
P i D

f ROC (P FA ,ζ) .
Another alternative is to utilize a graphical (i.e., TOC-curve) approach. In this
case, we first construct the scalar performance measure surface f S (P FA ,P D ) by
evaluating the cost function at each point of a sufficiently fine mesh grid on the
P FA - P D plane. Then, we obtain the contours of this surface, which constitute the
TOC curves [ 20 ]. Finally, for the current SNR value, we find the tangential point
of the corresponding operating ROC curve to the TOC curves. This point is the
optimal ( P FA ,P D ) pair satisfying the ROC curve relation, hence the solution to the
constraint optimization problem defined in ( 6.26 ). The procedure is summarized in
Fig. 6.4 .
Although this graphical technique is computationally more expensive, from the
practical applicability point of view, it is not a problem since we make the optimiza-
tion offline and only once. Furthermore, the graphical approach is more preferable
compared to the direct utilization of the line search algorithms, as it allows easier
interpretation and better insight into the problem. For both approaches, however, at
some points in the P FA - P D plane, cost function evaluation may be problematic due
to non-existence of the limit given in ( 6.27 ). This causes an instability region [ 20 ]
in the P FA - P D plane.
The TOC-curve approach was first used in [ 20 ] for solving the static threshold
optimization based on MRE, leading to the threshold optimization scheme STATIC-
MRE-TOC in Fig. 6.2 . The same approach is applied to the HYCA case in [ 2 ]
which results in the optimization scheme STATIC-HYCA-TOC . A numerical ex-
ample comparing these two approaches is given in Sect. 6.4.1 .