arXiv subjects

Steven Sandoval

Publications and source records attributed to Steven Sandoval.

8 recordsLinked to original sources

arXiv2025

Globally Asymptotically Stable Trajectory Tracking of Underactuated UAVs using Geometric Algebra

This paper employs Geometric Algebra (GA) tools to model the dynamics of objects in 3-dimensional space, serving as a proof of concept to facilitate control design for trajectory tracking in underactuated systems. For control purposes, the model is structured as a cascade system, where a rotational subsystem drives a translational one. The rotational subsystem is linear, while the translational subsystem follows a linear-plus-perturbation form, thereby reducing the complexity of control design. A control strategy requiring only simple operations, no memory, and no iterative search loops is presented to illustrate the main features of the GA model. By employing GA to model both translations and rotations, a singularity-free and geometrically intuitive representation can be achieved through the use of the geometric product. Closed-loop stability is rigorously established using input-to-state stability methods. Numerical simulations of a quad tilt-rotorcraft performing trajectory tracking in a windy environment validate the controller's stability and performance.

eess.SY↗

arXiv2025

Unifying Common Signal Analyses with Instantaneous Time-Frequency Atoms

In previous work, we presented a general framework for instantaneous time-frequency analysis but did not provide any specific details of how to compute a particular instantaneous spectrum (IS). In this work, we use instantaneous time-frequency atoms to obtain an IS associated with common signal analyses: time domain analysis, frequency domain analysis, fractional Fourier transform, synchrosqueezed short-time Fourier transform, and synchrosqueezed short-time fractional Fourier transform. By doing so, we demonstrate how the general framework can be used to unify these analyses and we develop closed-form expressions for the corresponding ISs. This is accomplished by viewing these analyses as decompositions into AM--FM components and recognizing that each uses a specialized (or limiting) form of a quadratic chirplet as a template during analysis. With a two-parameter quadratic chirplet, we can organize these ISs into a 2D continuum with points in the plane corresponding to a decomposition related to one of the signal analyses. Finally, using several example signals, we compute in closed-form the ISs for the various analyses.

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arXiv2024

Estimation of non-uniform motion blur using a patch-based regression convolutional neural network (CNN)

The non-uniform blur of atmospheric turbulence can be modeled as a superposition of linear motion blur kernels at a patch level. We propose a regression convolutional neural network (CNN) to predict angle and length of a linear motion blur kernel for varying sized patches. We analyze the robustness of the network for different patch sizes and the performance of the network in regions where the characteristics of the blur are transitioning. Alternating patch sizes per epoch in training, we find coefficient of determination scores across a range of patch sizes of $R^2>0.78$ for length and $R^2>0.94$ for angle prediction. We find that blur predictions in regions overlapping two blur characteristics transition between the two characteristics as overlap changes. These results validate the use of such a network for prediction of non-uniform blur characteristics at a patch level.

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arXiv2023

Estimation of motion blur kernel parameters using regression convolutional neural networks

Many deblurring and blur kernel estimation methods use a maximum a posteriori (MAP) approach or deep learning-based classification techniques to sharpen an image and/or predict the blur kernel. We propose a regression approach using convolutional neural networks (CNNs) to predict parameters of linear motion blur kernels, the length and orientation of the blur. We analyze the relationship between length and angle of linear motion blur that can be represented as digital filter kernels. A large dataset of blurred images is generated using a suite of blur kernels and used to train a regression CNN for prediction of length and angle of the motion blur. The coefficients of determination for estimation of length and angle are found to be greater than or equal to 0.89, even under the presence of significant additive Gaussian noise, up to a variance of 10\% (SNR of 10 dB). Using our estimated kernel in a non-blind image deblurring method, the sum of squared differences error ratio demonstrates higher cumulative histogram values than comparison methods, with most test images yielding an error ratio of less than or equal to 1.25.

eess.IV↗

arXiv2023

Deep Learning Estimation of Modified Zernike Coefficients and Recovery of Point Spread Functions in Turbulence

Recovering the turbulence-degraded point spread function from a single intensity image is important for a variety of imaging applications. Here, a deep learning model based on a convolutional neural network is applied to intensity images to predict a modified set of Zernike polynomial coefficients corresponding to wavefront aberrations in the pupil due to turbulence. The modified set assigns an absolute value to coefficients of even radial orders due to a sign ambiguity associated with this problem and is shown to be sufficient for specifying the intensity point spread function. Simulated image data of a point object and simple extended objects over a range of turbulence and detection noise levels are created for the learning model. The MSE results for the learning model show that the best prediction is found when observing a point object, but it is possible to recover a useful set of modified Zernike coefficients from an extended object image that is subject to detection noise and turbulence.

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arXiv2021

WIDEFT: A Corpus of Radio Frequency Signals for Wireless Device Fingerprint Research

Wireless network security may be improved by identifying networked devices via traits that are tied to hardware differences, typically related to unique variations introduced in the manufacturing process. One way these variations manifest is through unique transient events when a radio transmitter is activated or deactivated. Features extracted from these signal bursts have in some cases, shown to provide a unique "fingerprint" for a wireless device. However, only recently have researchers made such data available for research and comparison. Herein, we describe a publicly-available corpus of radio frequency signals that can be used for wireless device fingerprint research. The WIDEFT corpus contains signal bursts from 138 unique devices (100 bursts per device), including Bluetooth- and WiFi-enabled devices, from 79 unique models. Additionally, to demonstrate the utility of the WIDEFT corpus, we provide four baseline evaluations using a minimal subset of previously-proposed features and a simple ensemble classifier.

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arXiv2015

Theory of the Hilbert Spectrum

This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency analysis. We provide a multicomponent model of a signal that enables rigorous definition of instantaneous frequency on a per-component basis. Within our framework, we have shifted all uncertainty of the latent signal to its quadrature. In this approach, uncertainty is not a fundamental limitation of analysis, but rather a manifestation of the limited view of the observer. With the appropriate assumptions made on the signal model, the instantaneous amplitude and instantaneous frequency can be obtained exactly, hence exact representation of a signal in the coordinates of time and frequency can be achieved. However, uncertainty now arises in obtaining the correct assumptions, i.e.~how to correctly choose the quadrature of the components.

math.CV↗

arXiv2015

Latent Signal Analysis and the Analytic Signal

In this paper we present the latent signal analysis problem as a recasting of the complex extension problem. Almost universally, the approach has been to use the Hilbert Transform (HT) to construct Gabor's analytic signal. This approach depends on harmonic correspondence and forces the use of simple harmonic components in the analysis, which may lead to incorrect Instantaneous Amplitude (IA) and Instantaneous Frequency (IF) parameters. We show that by relaxing the harmonic correspondence condition, the resulting complex extension can still be an analytic function and we can arrive at alternate IA/IF parameterizations which may be more accurate at describing the latent signal. However, in relaxing the harmonic correspondence condition there is no longer a unique rule for the complex extension. In addition, we discuss the problems associated with the use of the HT as an AM--FM demodulator for the latent signal. Finally we provide solutions to an example latent signal analysis problem.

math.CV↗