Joint Optimization of Detection and Tracking in Adaptive Radar Systems - Advances in Heuristic Signal Processing and Applications - page 133

Ta b l e 6 . 1 Compared tracking systems
System Name

Desired False Alarm Probability, P FA

10 − 8 PDAKF-HEURISTIC-E8 P FA (k) =

10 − 6

PDAKF-HEURISTIC-E6 P FA (k) =

10 − 4

PDAKF-HEURISTIC-E4 P FA (k) =

PDAKF-STATIC-MRE [ 20 ] P FA (k) is set as given in Eq. ( 6.44 )

PDAKF-STATIC-HYCA [ 2 ] P FA (k) is set as given in Eq. ( 6.45 )

PDAKF-DYNAMIC-MRE [ 22 ] P FA (k) is set as given in Eq. ( 6.30 )

PDAKF-DYNAMIC-HYCA [ 2 ] P FA (k) is set as given in Eq. ( 6.35 )

probabilities are determined using MRE/HYCA-based static/dynamic threshold op-
timization. The dynamic optimizations given in ( 6.30 ) and ( 6.35 ) are solved us-
ing Fibonacci Search where we take the initial interval of uncertainty for P FA as
I P FA [ 10 − 7 .

We choose four different constant SNR scenarios of 5, 10, 15 and 20 dB. In each
scenario, the target follows the corresponding constant SNR trajectory for 200 time
steps as illustrated in Fig. 6.6 . That is, SNR is time-invariant for each scenario, but
from scenario to scenario we considered different constant SNR values. We have
conducted 500 Monte Carlo runs for each scenario and compared the algorithms
on a special performance plane where we consider two measures: the percentage of
lost tracks (a transient performance indicator) and steady-state RMS position error
(a steady-state performance indicator). The Track Loss Percentage (TLP) measure
is defined as TLP

10 − 6 , 10 − 1 and the maximum error tolerance 16 as ΔP FA ]

100 where N TL is the number of Monte Carlo
runs that result in track loss 17 and N MC is the total number of Monte Carlo runs
performed. The other measure, steady-state RMS position error, is obtained by en-
semble averaging over only the “track-loss free” runs. The algorithm performances
on this plane are given in Fig. 6.9 for each SNR scenario considered. In these plots,
the lower left corner represents the ultimate performance, i.e., low TLP and low
steady-state RMS position error. Note that the points (algorithm performances) get
closer and eventually converge to the performance of the Kalman filter with perfect
data association, when SNR increases. We may conclude that threshold optimization
is less critical when the SNR is high, e.g., between 15 and 20 dB. On the other hand,

N TL /N MC ×

16 Given an initial interval of uncertainty,

and the number of function evaluations, N ,the
Fibonacci Search algorithm reduces the length of the uncertainty interval to (b

[ a,b ]

− a)/F N + 1 ,where

F N + 1 is the ( N . Therefore, given the number

N , the length of the final uncertainty interval, so the maximum error in finding the extremum point,
is determined. Here, we do the other way around. That is, we specify the maximum error tolerance
that we are required to have at the end of the algorithm which in turn determines the minimum
required number of function evaluations, N .
17 We accept that the track is lost for the i th Monte Carlo run if ε i POS >ρ where ρ

+ 1)th number in the Fibonacci sequence { 1 , 1 , 2 ,... }

√ tr

{ R } is the

measurement error level and ε i POS is the average position estimation error for the i th run.