AUTOMATIC TARGET
RECOGNITION
Sensor Fusion & Performance Analysis
Ground Based Target Orientation Estimation
Overview
Our work has focused on pose estimation
of ground-based targets viewed via multiple sensors including high resolution
range radar, video imaging systems, and forward-looking infrared
radar systems. Data from these three sensors are simulated using CAD models
for the targets of interest in conjunction with XPATCH simulation software,
Silicon Graphics workstations, and the PRISM simulation package, respectively.
Using a Lie Group representation of the orientation space and a
Bayesian estimation framework, we have quantitatively examined both
pose-dependent variations in performance, and the relative performance
of the three aforementioned sensors. The Bayesian estimation framework
naturally accommodates the use of multiple sensors, and allows us to quantify
performance gains due to sensor fusion. Results of simulations are
presented and discussed. Joint and individual plots of the
expected squared estimation error versus noise level are shown
for the three sensors.
Parameterization Using SO(2)
The orientation of a ground-based target is represented by a single angle
of rotation taking values bewteen [0,2*pi]. We represent this angle using
the special orthogonal group of 2 x 2 rotation matricies, SO(2).
SO(2) is a matrix Lie group on which the Hilbert-Schmidt norm is
a natural metric. We use this norm to measure estimation error, and also
to establish bounds on the performance of estimation schemes. Eleements of
SO(2) are matricies of the form:
where x is an angle in [0,2*pi]. The Hilbert-Schmidt norm is defined as
follows on SO(2):
Bayesian Estimation Framework
As detailed on the The CIS Ground-to-Air ATR
Page, our group's
applies a Bayesian approach to the ATR problem.
Having defined a prameter space using pattern theoretic representatiopns, we may then compute data likelihood functions representing
the probability of a given observation conditioned on an element
of the parameter space. These likelihoods capture the variation
introduced by the sensors used to observe the scene, and are detailed below.
For this problem, the parameter space is [0,2*pi]. Using
databases of simulated data, we compare the observations to
elemements of the databses and evaluate likelihood functions
capturing noise effects of the various sensors.
If we consider the observations generated by different sensors
as independent conditioned on an element of the parameter space.
Then the joint likelihood of the group of observations conditioned
on a given element of the parameter space is a product of
the three individual likelihoods, and the joint log-likelihood
becomes the sum of the individual log-likelihoods.
In the equations above, pi is the logposterior of the parameter x, and
element of SO(2), given the n observations from n sensors, each
a different type of sensor. L represents the loglikelihood of the observations
D given parameter x, and P is a logprior on the paremer space.
Sensor Likelihood Models & Simulation Packages
All the data we used is simulated and available on the The
CIS Research Page. The high-resolution range profile
database conatins 360 rangeprofiles of the tank used at all integer orientations on the circle. The data was generated using the XPATCH simulation program. The optical imaging
sensor data was generated using a Silicon Graphics workstation, again rotating the tank
at all 360 integer orientations on the circle. Lastly, a forward-looking infrared image
database was generated using the PRISM simulation package, again with 360 elements at
the aformentioned orientations.
The likelihood models used were based on deterministic signal and image models in the
presence of white Gaussian noise for all three sensors. Thus the likelihood functions
are computed by summing the likelihoods for each pixel for the images, and for each
range bin for the range profiles. Subsequent experiments have been performed using a
Poisson log-likelihood incorporating CCD camera effects with the FLIR data.
Results
The plot below demonstrates the relative performance of the three sensors in the
presence of increasing noise, as well as the considerable improvment in
performance in the joint orientation estimation case. The Y-Axis represents the
expected squared error, by averaging the Hilbert-Schmidt norm between the
estimated and true orientation at each noiselevel for 50 simulations.
The X-Axis shows the scaled standard deviation of the Gaussian noise added to
the observations of the tank at the correct orientation.
Related Pages:
Contact:
Matthew
Cooper,
mlc@cis.jhu.edu
CIS
(cis@cis.jhu.edu);
page last updated on
Mar 27, 2001.
