The objective of this research was to develop a fundamentally new method for detecting hidden moving targets within noisy and cluttered data-streams using a novel “soliton resonance” effect in nonlinear dynamical systems.
The technique uses an inhomogeneous Korteweg de Vries (KdV) equation containing moving-target information. Solution of the KdV equation will describe a soliton propagating with the same kinematic characteristics as the target. The approach uses the timedependent data stream obtained with a sensor in form of the “forcing function,” which is incorporated in an inhomogeneous KdV equation. When a hidden moving target (which in many ways resembles a soliton) encounters the natural “probe” soliton solution of the KdV equation, a strong resonance phenomenon results that makes the location and motion of the target apparent.
Soliton resonance method will amplify the moving target signal, suppressing the noise. The method will be a very effective tool for locating and identifying diverse, highly dynamic targets with ill-defined characteristics in a noisy environment.
The soliton resonance method for the detection of moving targets was developed in one and two dimensions. Computer simulations proved that the method could be used for detection of singe point-like targets moving with constant velocities and accelerations in 1D and along straight lines or curved trajectories in 2D. The method also allows estimation of the kinematic characteristics of moving targets, and reconstruction of target trajectories in 2D. The method could be very effective for target detection in the presence of clutter and for the case of target obscurations.
This work was done by Igor K. Kulikov of Caltech and Michail Zak of Raytheon for NASA’s Jet Propulsion Laboratory. NPO-48785
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Detection of Moving Targets Using Soliton Resonance Effect
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Overview
The document titled "Detection of Moving Targets Using Soliton Resonance Effect" from NASA's Jet Propulsion Laboratory outlines a novel approach for detecting moving targets through the application of soliton resonance, utilizing the inhomogeneous Korteweg-de Vries (KdV) equation. Originally discovered in 1895, the KdV equation has gained renewed interest due to its mathematical richness and applications in various fields, particularly in modeling shallow water waves.
The KdV equation is a nonlinear partial differential equation that exhibits unique properties, including conservation of total mechanical energy. The document discusses the linear version of the KdV equation, which describes the propagation of waves and their dispersion characteristics. Each Fourier harmonic of an initial profile propagates at a different phase speed, leading to dispersion over time while preserving the total energy.
The focus of the document is on the inhomogeneous version of the KdV equation, which has fewer applications and less literature available. The authors propose a qualitative theoretical approach to guide numerical algorithms for solving this equation, particularly in the context of target detection. The strategy involves formulating the problem and developing numerical methods to analyze the behavior of solitons in response to moving targets.
The document also references numerical experiments that validate the proposed methods, demonstrating the effectiveness of the soliton resonance effect in detecting moving targets. The results indicate that this approach could have significant implications for various technological and scientific applications, particularly in aerospace and defense.
Overall, the document serves as a technical support package that not only provides insights into the mathematical and physical aspects of the KdV equation but also highlights its practical applications in detecting moving targets. It emphasizes the importance of developing robust numerical methods to explore the inhomogeneous KdV equation and its potential for advancing detection technologies. The research is part of NASA's broader efforts to leverage innovative technologies for aerospace-related developments, showcasing the intersection of mathematics, physics, and engineering in solving real-world problems.
