Method and apparatus for communication with chaotic and other waveforms

• US 6,216,093 B1
• Filed: 05/01/1998
• Issued: 04/10/2001
• Est. Priority Date: 11/17/1995
• Status: Expired due to Fees

• Current Assignee: Dynetics Incorporated (Leidos Holdings, Inc.)
• Original Assignee: Dynetics Incorporated (Leidos Holdings, Inc.)
• Inventors: Corron, Ned J., Hahs, Daniel W.
• Primary Examiner(s): WACHSMAN, HAL D
• Application Number:
  US09/071,556
• Time in Patent Office: 1,075 Days
• Field of Search: 702/57, 702/73-76, 702/190, 702/17, 702/62, 702/69, 702/70, 702/106, 702/107, 702/111, 702/122, 702/191, 702/194, 702/195, 702/197, 702/199, 702/117, 702/118, 702/124, 702/126, 702/FOR.107, 702/FOR.108, 702/FOR.110, 702/FOR.155, 702/FOR.164, 702/FOR.166, 702/FOR.167, 329/315-317, 455/143, 331/44, 331/1.R, 331/41, 331/78, 395/500.34, 395/500.35, 395/500.41, 708/300, 708/309, 708/311, 708/444, 708/815, 708/819, 708/823, 708/824, 708/250, 324/613, 324/612, 324/614, 324/620, 324/76.17, 324/76.23, 324/76.93, 324/76-4-, 380/263, 703/2-4, 703/13, 703/14, 703/18
• US Class Current: 702/57
• CPC Class Codes: H03B 29/00 Generation of noise currents and voltages gasfilled discharge tubes with solid cathode specially adapted as noise generators H01J17/005
• CPC Class Codes: H04L 27/001 using chaotic signals for secret or secure communication H04L9/001

Abstract

A method and apparatus for communicating with chaotic and other waveforms employs a filter for estimating a parameter that describes a property of a signal. The filter is constructed by defining a system that models the source of the signal. The system is partitioned into a first subsystem that contains the parameter and a second subsystem that does not contain the parameter, the second subsystem including a term that makes the second subsystem stable and synchronizable with the signal. The signal is introduced as input to the second subsystem and an element of the second subsystem is substituted into a corresponding element of the first subsystem, thereby generating a signal-activated subsystem. An integration factor is introduced to the signal-activated subsystem to cause the parameter to behave as a constant when the signal-activated subsystem with the integration factor is integrated with respect to time. The signal-activated subsystem is integrated with respect to time with the integration factor, generating an equation of integrals in which the parameter is brought out of any of the integrals containing the parameter. The equation of integrals is solved for the parameter so that a multiple of the parameter is expressed as a combination of integrals, which is applied to a low-pass filter to inhibit any singularities in the combination of integrals, thereby generating a filtered combination of integrals. A circuit is constructed from a plurality of circuit elements, each circuit element being an analog of an integral of the filtered combination of integrals.

Claims

1. A method of generating a filtered combination of integrals of combinations of states of a system used in estimating a value of a parameter that describes a property of a signal from a source, comprising a combination of circuit elements wherein each circuit element is an analog of one of a plurality of mathematical integrals of said filtered combination of integrals, the method comprising the steps of:

a. defining a system that models the source of the signal, wherein the system is described by various states that evolve with respect to time;

b. partitioning the system into a first subsystem that contains the parameter and a second subsystem that does not contain the parameter, the second subsystem including a term so as to make the second subsystem stable and synchronizable with the signal;

c. introducing the signal as input to the second subsystem;

d. substituting at least one state of the second subsystem into at least one corresponding state of the first subsystem, thereby generating a signal-activated subsystem;

e. introducing an integration factor of the signal-activated subsystem to the signal-activated subsystem so as to cause the parameter to behave as a constant when the signal-activated subsystem with the integration factor is integrated with respect to time;

f. integrating with respect to time the signal-activated subsystem with the integration factor, thereby generating an equation of integrals of combinations of states of the first subsystem in which the parameter is brought out of any of the integrals containing the parameter;

g. solving the equation of integrals for the parameter so that a term proportional to the parameter is expressed as a combination of integrals derived from the equation of integrals; and

h. applying the combination of integrals as an input to an equation for a low-pass filter so as to inhibit any singularities in the combination of integrals, thereby generating a filtered combination of integrals.

2. The method of claim 1, wherein the term is a decaying feedback term.

3. A method of creating a circuit for estimating a parameter that describes a property of a signal from a source, comprising the steps of:

a. defining a system that models the source of the signal, wherein the system is described by various states that evolve with respect to time;

b. partitioning the system into a first subsystem that contains the parameter and a second subsystem that does not contain the parameter, the second subsystem including a term so as to make the second subsystem stable and synchronizable with the signal;

c. introducing the signal as input to the second subsystem;

d. substituting at least one state of the second subsystem into at least one corresponding state of the first subsystem, thereby generating a signal-activated subsystem;

e. introducing an integration factor of the signal-activated subsystem to the signal-activated subsystem so as to cause the parameter to behave as a constant when the signal-activated subsystem with the integration factor is integrated with respect to time;

f. integrating with respect to time the signal-activated subsystem with the integration factor, thereby generating an equation of integrals of combinations of states of the first subsystem in which the parameter is brought out of any of the integrals containing the parameter;

g. solving the equation of integrals for the parameter so that a term proportional to the parameter is expressed as a combination of integrals derived from the equation of integrals;

h. applying the combination of integrals as an input to an equation for a low-pass filter so as to inhibit any singularities in the combination of integrals, thereby generating a filtered combination of integrals; and

i. constructing a circuit comprising a plurality of circuit elements, wherein each circuit element is an analog of a mathematical integral of the filtered combination of integrals of combinations of the states of the system.

4. The method of claim 3, wherein the term is a decaying feedback term.