Intelligence, Surveillance, and Reconnaissance - Spawar

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INTELLIGENCE, SURVEILLANCE, AND RECONNAISSANCE
on average than the NEKF IMM and 3 meters per
second better on average than the IMM. Figure 4 is
the course error, and it shows, once again, the NEKF
IMM having a much smaller error than the other filters.
The NEKF IMM course error is 9 degrees lower
on average than the EKF and 6 degrees lower on
average than the IMM. Table 1 shows the peak errors
from all four statistics (position, velocity, speed, and
course). The NEKF IMM has the smallest peak error
for position, velocity, and course. What this implies is
that the velocity vectors for the NEKF IMM were
more accurate than the EKF and the IMM filters.
Since the velocity vectors were pointing closer to
truth, the position error for the NEKF IMM was
much smaller than the EKF and IMM filters. For the
peak speed error, the NEKF IMM performed the
poorest. The reason for this was that the neural network
inside the NEKF IMM was over-correcting
the velocity estimates at each prediction. This overcorrection
was due to the lag in adaptation. Never-
theless, the NEKF IMM outperformed the EKF and IMM in all but one
of the error statistics. Figure 5 is a plot that shows the error reduction in
position as time progresses. The plot is an ensemble average of a Monte
Carlo average. Both the IMM and the EKF provide little or no error
reduction in the figure. In fact, they do worse than just following the
noisy measurements. The NEKF IMM continually increases positively
showing that it is consistently performing better than the noisy measurements
alone and performing noise reduction throughout the maneuver.
TABLE 1. Peak errors for 100 Monte Carlo runs.
Peak Errors NEKF IMM IMM EKF
Position (m)
15.9
18.4 23.0
Velocity (m/s) 21.5
16.2 15.5
Speed (m/s)
19.3
9.1
2.9
Course (deg) 11.1
17.0 17.6
CONCLUSIONS
This paper described the NEKF embedded in an IMM architecture for
the target-tracking problem. The NEKF uses a neural network to adapt
online to unmodeled dynamics or nonlinearities in the target trajectory.
This online adaptation provides for a robust state estimation for tracking
applications because the maneuvers do not have to be known beforehand.
The NEKF is a generic state estimator that can be used to estimate any
state vector such as position, velocity, magnetic moment, frequency signatures,
etc. Comparisons were performed with an extended Kalman filter,
a three-model IMM filter, and an NEKF IMM with three models.
The NEKF IMM outperformed the other filters in every case except for
speed error. Further investigation into why the NEKF IMM did not outperform
the filters in speed is now under investigation.
ENSEMBLE AVERAGE STATISTIC (m)
–500
0
500
1000
1500
2000
2500
3000
MONTECARLO AVERAGE OF AN ENSEMBLE AVERAGE
KF
IMM
NEKF IMM
3500
0 100 200 300
TIME (s)
400 500 600
FIGURE 5. NEKF IMM, IMM, and EKF ensemble average for 100
Monte Carlo runs.