Joint Optimization of Detection and Tracking in Adaptive Radar Systems - Advances in Heuristic Signal Processing and Applications - page 136

Ta b l e 6 . 2 Compared tracking systems
System Name

Desired False Alarm Probability, P FA

PDAF-OP-GOL [ 22 ] P FA (k) = arg max P FA q 2 (λV(k),P D ) (Golden-Section Search)

PDAF-OP-FIB [ 22 ] P FA (k) = arg max P FA q 2 (λV(k),P D ) (Fibonacci Search)

PDAF-OP P FA (k) is set as given in Eq. ( 6.31 )

detect (TBD) literature which proposes using no thresholding under very low SNR
[ 13 , 60 ].
An important aspect of practical applicability of DTOP schemes is their com-
putational complexities. The dynamic approaches are computationally much more
expensive than STOP approaches. This is mainly due to the iterative line search
algorithm involved. In the next experiment, we consider, in particular, MRE-based
dynamic threshold optimization problem and compare the line search based algo-
rithms proposed in [ 22 ] with the approximate closed-form solution of [ 5 ].

6.4.3 Experiment 2: Comparison of MRE-Based DTOP Schemes

The objective of this second experiment is to now make a comparison between on-
line optimal threshold selection methods only, in particular between the iterative
line-search based methods used in [ 22 ] and the approximate closed-form solution
proposed in [ 5 ].
We compare both the overall tracking performance and the computational com-
plexity of three optimal tracking systems given in Table 6.2 . Each tracking system
consists of a PDA tracking filter and an NP front-end detector. In each system, the
optimal P FA value found by threshold optimization is fed to the detector at every
time step. The main differences between these tracking systems are their solution
methodology in solving the optimization problem defined in ( 6.30 ). For example,
PDAF-OP-GOL [ 22 ] and PDAF-OP-FIB [ 22 ] solve this problem using the Golden-
Section and Fibonacci Search methods, respectively. On the other hand, PDAF-OP
[ 5 ] solves the problem approximately in closed-form as given in ( 6.31 ). An example
comparative variation of the true cost function q 2 (λV(k),P D ) , where λ

P FA /V C ,

and its functional approximation q 2 (λV(k),P D ) with respect to P FA is illustrated

in Fig. 6.12 . Here, both cost functions are evaluated on the NP detector ROC curve
given in ( 6.41 ) and for V 10 dB values. Note that the true cost

function q 2 (λV(k),P D ) is unimodal in the P FA range shown in Fig. 6.12 . There-
fore, both line search algorithms converge to the global optimum of this function.
Note also that the global optimum found by the closed-form solution slightly differs
from the one of the actual function. At this point, we seek answers to the following
two questions:
•

= 10 V C and ζ =

Is there any notable loss of tracking performance by solving the approximate
optimization problem rather than the original one?