Conventional algorithms for track association (termed "correlation" by convention) employ algorithms which are
applied to all sensor tracks at a specific time. The overall value of sensor networks for data fusion is closely
tied to the reliability of correct association of common objects tracked by the sensors. Multisensor architectures
consisting of gaps in target coverage requires that tracks must be propagated substantially forward or backward
to a common time for correlation. This naturally gives rise to the question: at which time should track correlation
be performed? In the conventional approach, a two-sensor correlation problem would be solved by propagating
the first sensor's tracks forward to the update time (current time) of the tracks from the second sensor. We
question this approach by showing simulation results that indicate that the current time can be the worst time
to correlate. In addition, a methodology for calculating the approximate optimal correlation time for linear-Gaussian tracking problems is provided.
Closely-spaced (but resolved) targets pose a significant challenge for single-frame unique measurement-to-track
data association algorithms. This is due to the similarity of the Mahalanobis distances between the closely-spaced
measurements and tracks. Contrary to conventional wisdom, adding target feature information (e.g.,
target amplitude) does not necessarily improve the probability of correctly assigning measurements to tracks.
In this paper, the theoretical limitations of using radar cross section (RCS) data to aid in measurement-totrack
association are reviewed. The results of a high-fidelity simulation assessment of the benefits of RCSaided
measurement-to-track association (using the Signal-to-Noise Ratio) are given and other possibilities for
RCS-aided tracking are discussed. Namely, we show the analytical results of our investigation into using RCS
information to determine the presence of merged measurements.
The interacting multiple model (IMM) estimator, which mixes and blends results of multiple filters according to their
mode probabilities, is frequently used to track targets whose motion is not well-captured by a single model. This paper
extends the use of an IMM estimator to computing impact point predictions (IPPs) of small ballistic munitions whose
motion models change when they reach transonic and supersonic speeds. Three approaches for computing IPPs are
compared. The first approach propagates only the track from the most likely mode until it impacts the ground. Since
this approach neglects inputs from the other modes, it is not desirable if multiple modes have near-equal probabilities.
The second approach for computing IPPs propagates tracks from each model contained in the IMM estimator to the
ground independent of each other and combines the resulting state estimates and covariances on the ground via a
weighted sum in which weights are the model probabilities. The final approach investigated here is designed to take
advantage of the computational savings of the first without sacrificing input from any of the IMM's modes. It fuses the
tracks from the models together and propagates the fused track to the ground. Note that the second and third approaches
reduce to the first if one of the models has a mode probability of one. Results from all three approaches are compared
Closely-spaced (but resolved) targets pose a challenge for measurement-to-track data association algorithms.
Since the Mahalanobis distances between measurements collected on closely-spaced targets and tracks are similar,
several elements of the corresponding kinematic measurement-to-track cost matrix are also similar. Lacking any
other information on which to base assignments, it is not surprising that data association algorithms make
mistakes. One ad hoc approach for mitigating this problem is to multiply the kinematic measurement-to-track
likelihoods by amplitude likelihoods. However, this can actually be detrimental to the measurement-to-track
With that in mind, this paper pursues a rigorous treatment of the hypothesis probabilities for kinematic
measurements and features. Three simple scenarios are used to demonstrate the impact of basing data association
decisions on these hypothesis probabilities for Rayleigh, fixed-amplitude, and Rician targets. The first scenario
assumes that the tracker carries two tracks but only one measurement is collected. This provides insight into
more complex scenarios in which there are fewer measurements than tracks. The second scenario includes two
measurements and one track. This extends naturally to the case with more measurements than tracks. Two
measurements and two tracks are present in the third scenario, which provides insight into the performance of
this method when the number of measurements equals the number of tracks. In all cases, basing data association
decisions on the hypothesis probabilities leads to good results.
Passive radar systems exploit illuminators of opportunity, such as TV and FM radio, to illuminate potential targets. Doing so allows them to operate covertly and inexpensively. Our research seeks to enhance passive radar systems by adding automatic target recognition (ATR) capabilities. In previous papers we proposed conducting ATR by comparing the radar cross section (RCS) of aircraft detected by a passive radar system to the precomputed RCS of aircraft in the target class. To effectively model the low-frequency setting, the comparison is made via a Rician likelihood model. Monte Carlo simulations indicate that the approach is viable.
This paper builds on that work by developing a method for quickly assessing the potential performance of the ATR algorithm without using exhaustive Monte Carlo trials. This method exploits the relation between the probability of error in a binary hypothesis test under the Bayesian framework to the Chernoff information. Since the data are well-modeled as Rician, we begin by deriving a closed-form approximation for the Chernoff information between two Rician densities. This leads to an approximation for the probability of error in the classification algorithm that is a function of the number of available measurements. We conclude with an application that would be particularly cumbersome to accomplish via Monte Carlo trials, but that can be quickly addressed using the Chernoff information approach. This application evaluates the length of time that an aircraft must be tracked before the probability of error in the ATR algorithm drops below a desired threshold.
Passive radar is an emerging technology that offers a number of unique benefits, including covert operation. Many such systems are already capable of detecting and tracking aircraft. The goal of this work is to develop a robust algorithm for adding automated target recognition (ATR) capabilities to existing passive radar systems.
In previous papers, we proposed conducting ATR by comparing the precomputed RCS of known targets to that of detected targets. To make the precomputed RCS as accurate as possible, a coordinated flight model is used to estimate aircraft orientation. Once the aircraft's position and orientation are known, it is possible to determine the incident and observed angles on the aircraft, relative to the transmitter and receiver. This makes it possible to extract the appropriate radar cross section (RCS) from our simulated database. This RCS is then scaled to account for propagation losses and the receiver's antenna gain. A Rician likelihood model compares these expected signals from different targets to the received target profile.
We have previously employed Monte Carlo runs to gauge the probability of error in the ATR algorithm; however, generation of a statistically significant set of Monte Carlo runs is computationally intensive. As an alternative to Monte Carlo runs, we derive the relative entropy (also known as Kullback-Liebler distance) between two Rician distributions. Since the probability of Type II error in our hypothesis testing problem can be expressed as a function of the relative entropy via Stein's Lemma, this provides us with a computationally efficient method for determining an upper bound on our algorithm's performance. It also provides great insight into the types of classification errors we can expect from our algorithm. This paper compares the numerically approximated probability of Type II error with the results obtained from a set of Monte Carlo runs.
Rather than emitting pulses, passive radar systems rely on illuminators of opportunity, such as TV and FM radio, to illuminate potential targets. These systems are particularly attractive since they allow receivers to operate without emitting energy, rendering them covert. Many existing passive radar systems estimate the locations and velocities of targets. This paper focuses on adding an automatic target recognition (ATR) component to such systems. Our approach to ATR compares the Radar Cross Section (RCS) of targets detected by a passive radar system to the simulated RCS of known targets. To make the comparison as accurate as possible, the received signal model accounts for aircraft position and orientation, propagation losses, and antenna gain patterns. The estimated positions become inputs for an algorithm that uses a coordinated flight model to compute probable aircraft orientation angles. The Fast Illinois Solver Code (FISC) simulates the RCS of several potential target classes as they execute the estimated maneuvers. The RCS is then scaled by the Advanced Refractive Effects Prediction System (AREPS) code to account for propagation losses that occur as functions of altitude and range. The Numerical Electromagnetic Code (NEC2) computes the antenna gain pattern, so that the RCS can be further scaled. The Rician model compares the RCS of the illuminated aircraft with those of the potential targets. This comparison results in target identification.