Joint Optimization of Detection and Tracking in Adaptive Radar Systems - Advances in Heuristic Signal Processing and Applications - page 115

optimization schemes given in Fig. 6.2 has been presented in [ 2 ]. Apart from a com-
prehensive experimental survey, the primary contribution of [ 2 ] was the establish-
ment of a unified experimental and theoretical framework to categorize and compare
these schemes as static or dynamic threshold optimization as given in Fig. 6.2 .
It is worth noting that another fundamentally different approach to the detection
threshold optimization problem has been considered in the literature by Willett et
al. [ 68 ]. This method, while being a perfectly valid alternative approach, differs
from all NSPP-based approaches in that it is based on an optimal Bayesian detector
framework where the prior hypothesis probabilities required by the detector are fed
back from the posterior information state 4 of the PDAF.
In all aforementioned studies, which are the NSPP-based methods in Fig. 6.2 ,
i.e., [ 2 , 5 , 20 , 22 , 48 ], and the one presented in [ 68 ], it is implicitly assumed that the
model describing the target motion dynamics is fairly well known to the filter ( non-
maneuvering target assumption). This assumption has been relaxed in [ 3 ] where a
threshold optimization problem is formulated and solved for tracking maneuvering
targets by extending the previous ideas applicable to the PDAF to multiple model
filtering structures which use PDAFs as modules. A recent study on the same line
has been presented by Wang et al. in [ 66 ] where instead of a Gaussian mixture as in
[ 3 ], a moment-matched single Gaussian has been used in the cost function.
A line of recent articles [ 17 , 23 , 26 , 27 ] show the growing interest into the con-
cept of cognitive radar [ 24 , 25 ], which aims to make a radar system smarter and
more adaptive by dynamically optimizing the “transmitter” as well. We should note,
however, that steps towards this goal are not entirely new. In the context of overall
system optimization, the optimization of transmitter waveforms was first introduced
in [ 39 ] and applied to the PDAF in [ 41 ]. Another study was [ 32 ] where the design of
the waveform and detection threshold for range and range-rate tracking in clutter is
formulated and numerically solved as a finite horizon optimization problem. A good
summary of waveform optimization for tracking is given in [ 67 ].

6.1.2 Chapter Outline

In the present chapter, we consider these exciting theoretical and experimental steps
towards the goal of spatially and temporally adaptive radar. In particular, we focus
on the interaction between the detector and the tracker subsystems and consider the
problem of tracker-aware optimization of detector threshold per target track and per
resolution cell. We build on two important NSPP techniques for the PDAF, namely,
MRE of Fortmann [ 20 ] and HYCA of Li [ 46 ]. There are two common properties
of the optimization problems that we consider: First, they all aim at maximizing
the performance of a tracking filter over detection thresholds. 5

Second, the cost

4 See, e.g., [ 9 , pp. 373].
5 This in essence results in a feedback from the tracker to the detector as illustrated in Fig. 6.1 .