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(or objective) functions of the optimization problems are all based on an
offline
approximation of the filter's covariance, which is obtained by either MRE or HYCA.
Therefore, in Sect.
6.2
, we briefly present these two important NSPP techniques for
the PDAF. Based on that, in Sect.
6.3
, tracker-aware detector threshold optimization
problems are defined and their solution methodologies are explained. In Sect.
6.4
,
these algorithms are compared through a number of simulation experiments. Finally,
in Sect.
6.5
, the important results of the chapter are summarized and possible future
studies from the present point are discussed.
6.2 Offline Performance Evaluation of Tracking Algorithms
Involving both
continuous
and
discrete
uncertainties,
6
real-world tracking is a
hy-
brid
[
45
] estimation problem. Tracking algorithms which operate under these un-
certainties are necessarily stochastic. As the performance of these algorithms can-
not be evaluated
confidently
with a single run, the common practice for performance
evaluation is to run an extensive number of Monte Carlo simulations and take the
ensemble average of a performance measure over the runs.
Although this methodology is very simple and straightforward, it might be very
time-consuming and costly in some cases. More importantly, if a design, an
opti-
mization
,
7
or sensitivity analysis of a tracking algorithm is of interest, Monte Carlo
simulations based approach does not give much insight into the problem. In that
case, analytical expressions and deterministic tools are much more useful. So, the
techniques for performance evaluation that do not require expensive stochastic sim-
ulations are needed. There are numerous works done in this context in the literature.
However, the available tools for offline evaluation of the performance can roughly
be classified into three categories [
49
]:
•
Error Bounding Techniques:
These techniques are the most popular offline per-
formance evaluation tools. They provide Cramér-Rao like bounds on the perfor-
mance. There are lots of works done under different titles (possibly having much
in common), such as nonlinear filtering [
19
,
38
,
63
,
64
], filtering with intermittent
observations [
14
,
15
,
19
,
28
,
56
,
61
], tracking in clutter [
29
,
34
,
70
], bearing-only
tracking [
16
,
34
,
69
], multitarget tracking [
18
,
33
,
43
,
58
], and maneuvering target
tracking [
30
,
69
]. Rather than predicting the filter performance, these techniques
put some
best-achievable
borders for the problem at hand. The tightness of such
6
Examples of continuous uncertainties are the inaccuracy in the measurements and “small” per-
turbations in the target motion which are usually modeled as an additive measurement noise and
process noise, respectively. These types of uncertainties are well-understood and solved in the lit-
erature over the past four decades under the title of
classical state estimation
[
1
,
9
,
42
]. However,
major challenges of tracking arise from two discrete-valued uncertainties: measurement origin
uncertainty, which is, in the words of Li and Bar-Shalom [
46
], the
crux
of tracking, and target
maneuver which appears as an
abrupt
and “large” deviation in the target motion.
7
In this chapter, we consider this aspect, i.e.,
tracker-aware optimization of detection thresholds
.
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