USA As Represented by Secretary of the Navy

Thomas L Carroll

Louis M Pecora

Graham K Hubler

Gregg A Johnson

Ira B Schwartz

Ioana Triandaf

James F Heagy

Louis L Pecora

Systems and method are provided for using chaotic signals for low probability of detection (LPD) communications. Embodiments of the present disclosure provide systems and methods for synchronizing chaotic systems and then encoding information on a signal in a way that produces little or no signature (e.g., using a bit flipping technique or a chaos control encoding technique). Systems and methods in accordance with embodiments of the present disclosure can work with noise larger than the signal, so they are suitable for communication in noisy environments.

Controlled chaotic system for low probability of detection (LPD) communication

A system and method is provided for estimating a trajectory of an incoming bullet based on the acoustics of the shock wave created as the bullet travels through the air. A first auditory signal representing a direct sound from the shock wave is recorded and its azimuthal direction is determined. Based on this azimuthal direction and other assumptions two possible bullet directions that can cause that shock wave are estimated. A second auditory signal representing a reflection of the shock wave as it travels through the air also is recorded and its azimuthal direction determined. The azimuthal direction of the ground reflection will lie between the azimuthal direction of the first auditory signal and the more correct of the two estimated trajectories, and thus can resolve the ambiguity in the estimated direction of the bullet source.

Direction finder for incoming gunfire

The low-interference communications device uses chaotic signals which are almost periodic. A chaotic circuit driven by a sine wave signal from a function generator is produced which has narrow-band features in the power spectrum. An information signal is encoded on the chaotic signal by modulating the phase of the sine wave that drives the chaotic circuit. Periodic (narrow-band) components are then removed from the chaotic signal and the chaotic signal is transmitted to a receiver device. The chaotic signal is nonlinear, so the narrow band and broad band parts of the chaotic signal have been modulated together. The transmitted signal is relatively flat, so it will not interfere with other communications signals. At the receiver, the nonlinear chaotic signal is restored by performing a nonlinear operation on the received signal, such as squaring or cubing, to remove the narrowband components. Then the information modulated onto the narrow band component is detected. When this is accomplished it is possible to detect variations in the phase of the base frequency.

Low-interference communications device using chaotic signals

A signal generator and signal receiver, as well as method of signal generation and transmission, in which selected unstable periodic orbits of a lossy chaotic system are identified and extracted, and portions of the orbits concatenated together to form a resultant signal. The selected orbits are known to the signal detector a priori. The signal detector detects the transmitted signal by correlation of the received signal with the known extracted orbits, also allowing the detector identify information which the generator imposed onto the signal.

Method and apparatus for signal generation and detection using unstable periodic chaotic orbits

A system for synchronizing chaotic transmitters and receivers that is less sensitive to channel effects than other known chaotic communication methods. The system employs duplicate transmitter and receiving modules and in addition to the chaotic output a synchronizing signal which occupies a reduced bandwidth. The small bandwidth affords the system a greater resistance to the affects of frequency dependent channel distortion and noise. The broad band chaotic signal is transmitted and appears to be noise to an unauthorized listener. The receiving unit employs band pass filtering, and when the signal is received the receiver filters the chaotic signal through band pass filters which eliminate channel noise and make gain control easier to implement.

Synchronizing autonomous chaotic systems using filters

An amplitude insensitive synchronized nonlinear system (AISN) that allows communication between nonlinear systems operating in the chaotic realm which is insensitive to attenuation or signal noise affecting the amplitude of the drive signal, thereby allowing communication between remote systems where the amplitude of the transmitted signal has been varied by an unknown amount.

Amplitude insensitive synchronization of nonlinear systems

A filtered cascaded synchronized nonlinear system includes a nonlinear transmitter having stable first and second subsystems. The first subsystem produces a first transmitter signal for driving the second subsystem, and the second subsystem produces a second transmitter signal for driving the first subsystem. A first filter filters the second transmitter signal to produce a filter output signal. A subtractor subtracts the filter output signal from the second transmitter signal to produce a transmitter output signal which is transmitted to a nonlinear cascaded receiver. The receiver includes an adder for summing the received transmitter output signal with a receiver filter output signal to restore frequencies that were subtracted from the second transmitter signal in order to produce a first receiver drive signal. The receiver includes cascaded third and fourth subsystems that are respective duplicates of the first and second subsystems. The third subsystem is driven by the first receiver drive signal to produce a first receiver signal in synchronization with the first transmitter signal. The fourth subsystem is driven by the first receiver signal to produce a second receiver signal in synchronization with the second transmitter signal. A second filter filters the second receiver signal to produce the receiver filter output signal.

Apparatus and method for synchronizing nonlinear systems using filtered

A cascaded synchronized system includes a nonlinear transmitter, a nonlinear cascaded receiver, a phase-detector/controller coupled to the receiver, and a signal generator also coupled to the receiver. The transmitter is responsive to an externally generated transmitter forcing signal for producing and transmitting a chaotic communications signal containing phase information. The cascaded receiver is responsive to a receiver forcing signal and to the chaotic communications signal for producing a chaotic receiver output signal containing phase information. The phase-detector/controller is responsive to the chaotic communications signal and to the receiver output signal for producing a correction signal. The signal generator is responsive to the correction signal for producing the receiver forcing signal in phase with and having the same frequency as the transmitter forcing signal.

Synchronization of nonautonomous chaotic systems

A control system for tracking the operation of a nonlinear system has two parts: a tracking subsystem and a controlling subsystem. The tracking subsystem generates a parametric signal and the controlling subsystem controls and stabilizes the nonlinear system operating under operating conditions corresponding to that parametric signal. The controlling subsystem includes a modulator responsive to the parametric signal and to a feedback signal for producing and applying an input signal to the nonlinear system to cause the nonlinear system to produce an output signal. The controlling subsystem also includes means responsive to the output signal for producing the feedback signal. The controlling subsystem also includes correcting means, operable when the time average of the feedback signal is substantially nonzero, for bringing the time average of the feedback signal from a substantially nonzero value to a substantially zero value, and maintaining means, operable when the time average of the feedback signal is substantially zero, for maintaining the time average of the feedback signal over the selected period of time at a substantially zero value.

Control system for tracking nonlinear systems

A controller is provided for driving at least two systems in synchronization with one another. The controller provides a pseudoperiodic drive to drive the two systems at a desired frequency and to ensure that the two systems are synchronized. The pseudoperiodic drive can be produced by combining a periodic drive with a chaotic drive, noise drive or an incommensurate frequency drive. Any of these types of drives can be combined with the periodic drive by adding to or modulating the periodic drive. Thus, the controller can drive the two systems in phase with one another by using the same pseudoperiodic drive.

Method and apparatus for pseudoperiodic drive

A cascaded synchronized nonlinear system includes a nonlinear transmitter having stable first and second subparts. The first subpart produces a first transmitter signal for driving the second subpart and the second subpart produces a second transmitter signal for driving the first subpart. The nonlinear transmitter transmits the second transmitter signal to a nonlinear cascaded receiver. The receiver, being for producing an output signal in synchronization with the second transmitter signal, includes a first stage (a duplicate of the first subpart) responsive to the second transmitter signal for producing a first receiver signal. The receiver further includes a second stage (a duplicate of the second subpart) responsive to the first receiver signal for producing the output signal. The cascaded synchronized nonlinear system can be used in an information transfer system. The transmitter, responsive to an information signal produces a drive signal for transmission to the receiver. An error detector compares the drive signal and the output signal produced by the receiver to produce an error signal indicative of the information contained in the information signal.

Cascading synchronized chaotic systems

A system for producing two synchronized signals comprises a nonlinear dynamical primary system and a nonlinear dynamical secondary response subsystem. The primary system comprises a nonlinear dynamical drive subsystem for producing at least one drive signal, and a nonlinear dynamical primary response subsystem responsive to said at least one drive signal for producing a primary signal, wherein said primary response subsystem has a complete set of at least one primary sub-Lyapunov exponents, all of said at least one primary sub-Lyapunov exponents being negative. The second response subsystem is responsive to said at least one drive signal for producing a secondary signal in synchronization with said primary signal, said secondary response subsystem being substantially a duplicate of said primary response subsystem, wherein said secondary response subsystem has a complete set of at least one secondary sub-Lyapunov exponents, all of said at least one secondary sub-Lyapunov exponents being negative.

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Alexandria, VA, United States of America

Thomas L Carroll