Jason T. Parker

Control-Oriented Modeling of an Air-Breathing Hypersonic Vehicle

Full simulation models for flexible air-breathing hypersonic vehicles include intricate couplings between the engine and flight dynamics, along with complex interplay between flexible and rigid modes, resulting in intractable systems for nonlinear control design. In this paper, starting from a high-fidelity model, a control-oriented model in closed form is obtained by replacing complex force and moment functions with curve-fitted approximations, neglecting certain weak couplings, and neglecting slower portions of the system dynamics. The process itself allows an understanding of the system-theoretic properties of the model, and enables the applicability of model-based nonlinear control techniques. Although the focus of this paper is on the development of the control-oriented model, an example of control design based on approximate feedback linearization is provided. Simulation results demonstrate that this technique achieves excellent tracking performance, even in the presence of moderate parameter variations. The fidelity of the truth model is then increased by including additional flexible effects, which render the original control design ineffective. A more elaborate model with an additional actuator is then employed to enhance the control authority of the vehicle, required to compensate for the new flexible effects, and a new design is provided.

Sparsity and Compressed Sensing in Radar Imaging

Remote sensing with radar is typically an ill-posed linear inverse problem: a scene is to be inferred from limited measurements of scattered electric fields. Parsimonious models provide a compressed representation of the unknown scene and offer a means for regularizing the inversion task. The emerging field of compressed sensing combines nonlinear reconstruction algorithms and pseudorandom linear measurements to provide reconstruction guarantees for sparse solutions to linear inverse problems. This paper surveys the use of sparse reconstruction algorithms and randomized measurement strategies in radar processing. Although the two themes have a long history in radar literature, the accessible framework provided by compressed sensing illuminates the impact of joining these themes. Potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights.

Bilinear Generalized Approximate Message Passing—Part I: Derivation

In this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its application to matrix completion, robust PCA, dictionary learning, and related matrix-factorization problems. Here, in Part I of a two-part paper, we derive our Bilinear G-AMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, where central-limit theorem arguments and Taylor-series approximations apply, and under the assumption of statistically independent matrix entries with known priors. In addition, we propose an adaptive damping mechanism that aids convergence under finite problem sizes, an expectation-maximization (EM)-based method to automatically tune the parameters of the assumed priors, and two rank-selection strategies. In Part II of the paper, we will discuss the specializations of EM-BiG-AMP to the problems of matrix completion, robust PCA, and dictionary learning, and we will present the results of an extensive empirical study comparing EM-BiG-AMP to state-of-the-art algorithms on each problem.

Approximate Feedback Linearization of an Air-breathing Hypersonic Vehicle

Abstract : This paper describes the design of a nonlinear control law for an air-breathing hypersonic vehicle. The model of interest includes flexibility effects and intricate couplings between the engine dynamics and flight dynamics. To overcome the analytical intractability of this model, a nominal control-oriented model is constructed for the purpose of feedback control design. Analysis performed on the nominal model reveals the presence of unstable zero dynamics with respect to the output to be controlled, namely altitude and velocity. By neglecting certain weaker couplings and resorting to dynamic extension at the input side, a simplified nominal model with full vector relative degree with respect to the regulated output is obtained. Standard dynamic inversion can then be applied to the simplified nominal model, and this results in approximate linearization of the nominal model. Finally, a robust outer loop control is designed using LQR with integral augmentation in a model reference scheme. Simulation results are provided to demonstrate that the approximate feedback linearization approach achieves excellent tracking performance on the truth model for two choices of the system output. Finally, a brief case study is presented to qualitatively demonstrate the robustness of the design to parameter variations.

A Bayesian perspective on sparse regularization for STAP post-processing

Traditional Space Time Adaptive Processing (STAP) formulations cast the problem as a detection task which results in an optimal decision statistic for a single target in colored Gaussian noise. In the present work, inspired by recent theoretical and algorithmic advances in the field known as compressed sensing, we impose a Laplacian prior on the targets themselves which encourages sparsity in the resulting reconstruction of the angle/Doppler plane. By casting the problem in a Bayesian framework, it becomes readily apparent that sparse regularization can be applied as a post-processing step after the use of a traditional STAP algorithm for clutter estimation. Simulation results demonstrate that this approach allows closely spaced targets to be more easily distinguished.

Compressive sensing under matrix uncertainties: An Approximate Message Passing approach

In this work, we consider a general form of noisy compressive sensing (CS) when there is uncertainty in the measurement matrix as well as in the measurements. Matrix uncertainty is motivated by practical cases in which there are imperfections or unknown calibration parameters in the signal acquisition hardware. While previous work has focused on analyzing and extending classical CS algorithms like the LASSO and Dantzig selector for this problem setting, we propose a new algorithm whose goal is either minimization of mean-squared error or maximization of posterior probability in the presence of these uncertainties. In particular, we extend the Approximate Message Passing (AMP) approach originally proposed by Donoho, Maleki, and Montanari, and recently generalized by Rangan, to the case of probabilistic uncertainties in the elements of the measurement matrix. Empirically, we show that our approach performs near oracle bounds. We then show that our matrix-uncertain AMP can be applied in an alternating fashion to learn both the unknown measurement matrix and signal vector. We also present a simple analysis showing that, for suitably large systems, it suffices to treat uniform matrix uncertainty as additive white Gaussian noise.

Bilinear Generalized Approximate Message Passing—Part II: Applications

In this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case. In Part I of this two-part paper, we derived our Bilinear G-AMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, and proposed an adaptive damping mechanism that aids convergence under finite problem sizes, an expectation-maximization (EM)-based method to automatically tune the parameters of the assumed priors, and two rank-selection strategies. Here, in Part II, we discuss the specializations of BiG-AMP to the problems of matrix completion, robust PCA, and dictionary learning, and present the results of an extensive empirical study comparing BiG-AMP to state-of-the-art algorithms on each problem. Our numerical results, using both synthetic and real-world datasets, demonstrate that EM-BiG-AMP yields excellent reconstruction accuracy (often best in class) while maintaining competitive runtimes.

Wide angle SAR data for target discrimination research

An airborne circular synthetic aperture radar system captured data for a 5 km diameter area over 31 orbits. For this challenge problem, the phase history for 56 targets was extracted from the larger data set and placed on a DVD for public release. The targets include 33 civilian vehicles of which many are repeated models, facilitating training and classification experiments. The remaining targets include an open area and 22 reflectors for scattering and calibration research. The circular synthetic aperture radar provides 360 degrees of azimuth around each target. For increased elevation content, the collection contains two nine-orbit volumetric series, where the sensor reduces altitude between each orbit. Researchers are challenged to further the art of focusing, 3D imaging, and target discrimination for circular synthetic aperture radar.

Preliminary experimental results for RF tomography using distributed sensing

Traditional high-value monostatic imaging systems employ frequency-diverse pulses to form images from small synthetic apertures. In contrast, RF tomography utilizes a network of spatially diverse sensors to trade geometric diversity for bandwidth, permitting images to be formed with narrowband waveforms. Such a system could use inexpensive sensors with minimal ADC requirements, provide multiple viewpoints into urban canyons and other obscured environments, and offer graceful performance degradation under sensor attrition. However, numerous challenges must be overcome to field and operate such a system, including multistatic autofocus, precision timing requirements, and the development of appropriate image formation algorithms for large, sparsely populated synthetic apertures with anisotropic targets. AFRL has recently constructed an outdoor testing facility to explore these challenges with measured data. Preliminary experimental results are provided for this system, along with a description of remaining challenges and future research directions.

Sparse reconstruction methods in RF Tomography for underground imaging

Underground imaging involving RF Tomography is generally severely ill-posed posed. Tikhonov Regularization is perhaps the most common method to address this ill-posedness. The proposed methods are based upon the realistic assumptions that targets (e.g. tunnels) are sparse and clustered in the scene, and have known electrical properties. Therefore, we explore the use of alternative regularization strategies leveraging sparsity of the signal and its spatial gradient, while also imposing physically-derived amplitude constraints. By leveraging this prior knowledge, cleaner scene reconstructions are obtained.