Aaron D. Lanterman

Unscented Kalman Filters for Multiple Target Tracking With Symmetric Measurement Equations

The symmetric measurement equation approach to multiple target tracking is revisited using the unscented Kalman filter. The performance of this filter is compared to the original symmetric measurement equation implementation using an extended Kalman filter. Counterintuitive results are presented and explained for two sets of symmetric measurement equations. We find that the performance of the SME approach is dependent on the interaction of the SME equations and filter used. Furthermore, an SME/unscented Kalman filter pairing is shown to have improved performance versus previous approaches while possessing simpler implementation and equivalent computational complexity.

A probability hypothesis density-based multitarget tracker using multiple bistatic range and velocity measurements

A novel multitarget tracking scheme for passive radar, using a particle filter implementation of Ronald Mahlers probability hypothesis density (PHD), is presented. Using range and velocity measurements from a simple non-directional receive antenna and low frequency transmitter pair, a target can be located along an ellipse. To pinpoint a target, multiple such antenna pairs are needed to locate the target at the intersection of the corresponding ellipses. Determining the intersection of these bistatic range ellipses, and resolving the resultant ghost targets, is generally a complex task. However, the PHD is found to provide a convenient and simple means of fusing together the multiple range and velocity measurements into coherent target tracks.

Tracking and recognition of airborne targets via commercial television and FM radio signals

We formulate a Bayesian approach to the joint tracking and recognition of airborne targets via reflected commercial television and FM radio signals measured by an array of sensors. Such passive system may remain covert, whereas traditional active systems must reveal their presence and location by their transmissions. Since the number of aircraft in the scene is not known a priori, and targets may enter and leave the scene at unknown times, the parameters space is a union of subspaces of varying dimensions as well as varying target classes. Targets tracks are parameterized via both positions and orientations, with the orientations naturally represented as elements of the special orthogonal group. A prior on target tracks is constructed from Newtonian equations of motion. This prior results in a coupling between the position and orientation estimates, yielding a coupling between the tracking and recognition problems.

ATR performance of a Rician model for SAR images

Radar targets often have both specular and diffuse scatterers. A conditionally Rician model for the amplitudes of pixels in Synthetic Aperture Radar (SAR) images quantitatively accounts for both types of scatterers. Conditionally Rician models generalize conditionally Gaussian models by including means with uniformly distributed phases in the complex imagery. Qualitatively, the values of the two parameters in the Rician model bring out different aspects of the images. For automatic target recognition (ATR), log-likelihoods are computed using parameters estimated from training data. Using MSTAR data, the resulting performance for a number of four class ATR problems representing both standard and extended operating conditions is studied and compared to the performance of corresponding conditionally Gaussian models. Performance is measured quantitatively using the Hilbert-Schmidt squared error for orientation estimation and the probability of error for recognition. For the MSTAR dataset used, the results indicate that algorithms based on conditionally Rician and conditionally Gaussian models yield similar results when a rich set of training data is available, but the performance under the Rician model suffers with smaller training sets. Due to the smaller number of distribution parameters, the conditionally Gaussian approach is able to yield a better performance for any fixed complexity.

Coherent MIMO radar: The phased array and orthogonal waveforms

Coherent multiple-input multiple-output (MIMO) radar is a natural extension of the phased array antenna that has been used by radar systems for decades. This tutorial unifies concepts from the literature and provides a framework for the analysis of an arbitrary suite of MIMO radar waveforms. A number of gain patterns are introduced, which quantify the antenna performance of a MIMO radar, and the impact of the waveform characteristics (e.g., range sidelobes) is discussed.

Implementation of a modified Richardson-Lucy method for image restoration on a massively parallel computer to compensate for space-variant point spread of a charge-coupled-device camera

Several imaging devices are characterized by a space-variant point-spread function (PSF), such as the wide-field/planetary camera of the Hubble Space Telescope (HST). Several techniques for image recovery that use data from such imagers approximate the space-variant PSF by a space-invariant PSF. A modified Richardson-Lucy method is implemented that accommodates the space-variant PSF of the HST as well as corrections for background counts, nonuniform flat field, and readout noise. The implementation runs on the DEC mppl2000 Sx/Model 200 massively parallel computer. Restorations of simulated HST images are obtained with a space-variant PSF and, for comparison, with a space-invariant approximation. Results of these processing methods are compared, and it is found that a residual artifact appears in restorations when a space-invariant PSF is used owing to the mismatch of the PSF kernel used in the restoration and the space-variant one underlying the image acquired with the telescope. This residual artifact is effectively eliminated when the processing is based on the space-variant PSF.

Multiple target tracking with symmetric measurement equations using unscented Kalman and particle filters

The symmetric measurement equation approach to multiple target tracking is revisited using unscented Kalman and particle filters. The characteristics and performance of these filters are compared to the original symmetric measurement equation implementation relying upon an extended Kalman filter. Counter-intuitive results are presented and explained for two sets of symmetric measurement equations, including a previously unknown limitation of the unscented Kalman filter. The point is made that the performance of the SME approach is dependent on the interaction of the set of SME equations and the filter used.

General Metropolis-Hastings jump diffusions for automatic target recognition in infrared scenes

To locate and recognize ground-based targets in forward- looking IR (FLIR) images, 3-D faceted models with associated pose pa- rameters are formulated to accommodate the variability found in FLIR imagery. Taking a Bayesian approach, scenes are simulated from the emissive characteristics of the CAD models and compared with the col- lected data by a likelihood function based on sensor statistics. This like- lihood is combined with a prior distribution defined over the set of pos- sible scenes to form a posterior distribution. To accommodate scenes with variable numbers of targets, the posterior distribution is defined over parameter vectors of varying dimension. An inference algorithm based on Metropolis-Hastings jump-diffusion processes empirically samples from the posterior distribution, generating configurations of templates and transformations that match the collected sensor data with high prob- ability. The jumps accommodate the addition and deletion of targets and the estimation of target identities; diffusions refine the hypotheses by drifting along the gradient of the posterior distribution with respect to the orientation and position parameters. Previous results on jumps strate- gies analogous to the Metropolis acceptance/rejection algorithm, with proposals drawn from the prior and accepted based on the likelihood, are extended to encompass general Metropolis-Hastings proposal den- sities. In particular, the algorithm proposes moves by drawing from the posterior distribution over computationally tractible subsets of the param- eter space. The algorithm is illustrated by an implementation on a Silicon Graphics Onyx/Reality Engine.

Automated target recognition using passive radar and coordinated flight models

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.

Deconvolution techniques for passive radar imaging

Forming images of aircraft using passive radar systems that exploit illuminators of opportunity, such as commercial television and FM radio systems, involves reconstructing an image from sparse samples of its Fourier transform. For a given flight path, a single receiver-transmitter pair produces one arc of data in Fourier space. Since the resulting Fourier sampling patterns bear a superficial resemblance to those found in radio astronomy, we consider using deconvolution techniques borrowed from radio astronomy, namely the CLEAN algorithm, to form images from passive radar data. Some deconvolution techniques, such as the CLEAN algorithm, work best on images which are well-modeled as a set of distinct point scatterers. Hence, such algorithms are well-suited to high-frequency imaging of man-made targets, as the current on the scatterer surface tends to collect at particular points. When using low frequencies of interest in passive radar, the images are more distributed. In addition, the complex-valued nature of radar imaging presents a complication not present in radio astronomy, where the underlying images are real valued. These effects conspire to present a great challenge to the CLEAN algorithm, indicating the need to explore more sophisticated techniques.