Joint Optimization of Detection and Tracking in Adaptive Radar Systems - Advances in Heuristic Signal Processing and Applications - page 113

a tracker-aware manner so that the performance of the downstream tracker, hence
of the combined target state estimation system, is maximized. This structure con-
stitutes a form of feedback from the downstream tracker to the upstream detector
as illustrated in Fig. 6.1 . We strongly believe that this is an important subarea of
the research consisting of steps that are necessary for the ultimate goal of cognitive
radar [ 25 ] which also includes the upper feedback path in Fig. 6.1 , i.e., adaptive
waveform optimization .
6.1.1 Related Work
The covariance of the filter's estimation error is one of the most important per-
formance measures for the downstream tracking. So, as a good starting point, re-
searchers first attempted to form an objective function which links their optimization
variables 3 to a scalar function of this covariance, e.g., its trace or determinant. How-
ever, the problem with the tracking filters operating under clutter (or measurement
origin uncertainty [ 10 ]) is that their covariance expressions depend on the measure-
ments they received, hence are related to the optimization variables through stochas-
tic recursions. This makes finding a solution to the concerned optimization prob-
lem difficult in two aspects. First, it makes difficult to apply classical optimization
tools to the problem due to the stochastic nature of the objective function. Second,
from the causality point of view, optimizing the variables through measurement-
dependent objective functions makes the resulting solution impractical as this opti-
mal setting of parameters are supposed to produce these measurements again. These
two reasons motivated researchers to seek possibly approximate but measurement-
independent (i.e., deterministic) covariance recursions for these filters. Finding a
deterministic covariance recursion can also be viewed as making a non-simulation
performance prediction (NSPP) for the filter under concern, as such a recursion
helps evaluating (approximately) the performance of the filter without recourse to
time-consuming Monte Carlo runs.
The line of study devoted to the optimization of the radar detector by minimiz-
ing a cost function based on such a deterministic covariance recursion has been
pioneered by Fortmann et al. [ 20 ] where they considered the Probabilistic Data As-
sociation Filter (PDAF) [ 10 ] as a tracking filter. The main contributions of [ 20 ]are
the so-called Modified Riccati Equation (MRE), which provides an approximate
deterministic covariance recursion for the PDAF, and tracker operating character-
istic (TOC) curves, which are by-product of the steady-state solution of the MRE.
Fortmann et al. have shown that for a given SNR, one can determine the optimal
detector operating point by finding the tangential intersection point between TOC
curves of the tracking filter and the corresponding receiver operating characteristic
3 In this chapter, we consider only the detection threshold as our optimization variable. A more
general set including also the transmitting waveform as in the case of cognitive radar [ 25 ] is out
of the scope of the present chapter.