Joint Optimization of Detection and Tracking in Adaptive Radar Systems - Advances in Heuristic Signal Processing and Applications - page 114

Fig. 6.2 The algorithmic space of NSPP-based tracker-aware detector threshold optimization
schemes for tracking a nonmaneuvering target with the PDAF. Here, the abbreviations TOC, LUT,
LS, and CF correspond to the “tracker operating characteristic”, “look-up table”, “line search”, and
“closed-form”, respectively [ 2 ]

(ROC) curve of the detector. The introduced MRE provides a steady-state NSPP
for the PDAF in clutter, very similar to how the standard Riccati equation (SRE)
does for the Kalman filter in clutter-free environments. We call this approach to
tracker-aware detector threshold optimization as NSPP-based static [ 2 ] approach
(called STATIC-MRE-TOC in Fig. 6.2 ). Belonging to the same category is a set
of studies by Li et al. [ 46 ] where they have improved the idea in [ 20 ]byintro-
ducing a different deterministic covariance recursion (an NSPP tool) for the PDAF,
called the Hybrid Conditional Averaging (HYCA) algorithm. Interestingly its ap-
plication to optimization of detection thresholds using a look-up-table procedure
(called STATIC-HYCA-LU TinFig. 6.2 ) has made limited use of the results [ 48 ].
A neat comparison of MRE-based and HYCA-based static threshold optimization
using TOC curves has been recently made in [ 2 ].
When the steady-state analysis is inappropriate, such as in time-varying or non-
linear systems, a suggested solution is to apply the same methodology by iterating
the MRE or HYCA not to their steady-state but for n steps into the future. In the
case of n 1, this leads to a dynamic [ 2 ] (also called adaptive [ 22 ]) threshold op-

timization scheme. In [ 22 ], Gelfand et al. proposed two such problems, namely,
prior and posterior threshold optimization, where they minimize the mean-square
state estimation error over detection thresholds, based on the measurements up to
the previous (prior) and current (posterior) time steps, respectively. It was further
shown that for the prior case the problem reduces into a single line search [ 22 ]
( DYNAMIC-MRE-LS in Fig. 6.2 ). Due to the claimed mathematical intractability
of obtaining a full closed-form solution, in [ 22 ] this problem was solved using iter-
ative numerical optimization techniques, such as the Golden-Section and Fibonacci
Search methods [ 11 ]. In [ 5 ], the same problem is solved in an approximate closed-
form ( DYNAMIC-MRE-CF in Fig. 6.2 ). The solution was applicable for a special
case of Neyman-Pearson (NP) detector and based on a functional approximation in-
troduced by [ 40 ]. It was shown that this approximate closed-form solution leads to
considerable reduction in computational complexity without any notable loss in per-
formance [ 4 , 5 ]. A comparison of aforementioned NSPP-based detector threshold

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