Method for filtering signals from nonlinear dynamical systems

• US 20020178193A1
• Filed: 05/24/2002
• Published: 11/28/2002
• Est. Priority Date: 11/18/1997
• Status: Active Grant

• Current Assignee: Samsung Electronics Co. Ltd.
• Original Assignee: Samsung Electronics Co. Ltd.
• Inventors: Lee, Chung-Yong
• Granted Patent: US 6,766,340 B2
• Time in Patent Office: Days
• US Class Current: 708/300
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: H03H 17/0261 Non linear filters

Abstract

A method for filtering signals from a nonlinear dynamical system is provided. An initial enhanced point is set to a noisy point obtained from the signals. An intermediate enhanced point is estimated. A new enhanced point is calculated using the estimated point and a weighting constant. Estimation of an intermediate enhanced point and calculation of a new enhanced point are iterated until the computed point converges to a true enhanced point which represents a noise reduced signal to provide filtered signals, wherein the new enhanced point is computed by the equation

{circumflex over (x)}_n⁽ⁱ⁾={circumflex over (x)}_n⁽ⁱ⁻¹⁾=K₃[{circumflex over (x)}_n^(i,temp)−{circumflex over (x)}_n⁽ⁱ⁻¹⁾]

wherein {circumflex over (x)}_n⁽ⁱ⁾ is the new enhanced point, {circumflex over (x)}_n^(i-temp) is the intermediate enhanced point for iteration i, {circumflex over (x)}_n⁽ⁱ⁻¹⁾ is the enhanced point at iteration i−1, and K₃ is a weighing constant.

Claims

1. A method for filtering signals from a nonlinear dynamical system, comprising the steps of:

(a) setting an initial enhanced point to a noisy point obtained from the signals;

(b) estimating an intermediate enhanced point;

(c ) computing a new enhanced point using the estimated point and a weighting constant; and

(d) iterating the steps (b) and (c) until the computed point converges to a true enhanced point which represents a noise reduced signal to provide filtered signals,

wherein the new enhanced point is computed by the equation

${\hat{x}}_n^{\left(i\right)}={\hat{x}}_n^{\left(i-1\right)}+K_3<br><br>\left[{\hat{x}}_n^{\left(i,\mathrm{temp}\right)}-{\hat{x}}_n^{\left(i-1\right)}\right]$

wherein {circumflex over (x)}_n⁽ⁱ⁾ is the new enhanced point, {circumflex over (x)}_n<sup>(i−

temp)</sup> is the intermediate enhanced point for iteration i, {circumflex over (x)}_n<sup>(i−

1)</sup> is the enhanced point at iteration i−

1, and K₃ is a weighing constant.

2. The method for filtering signals from a nonlinear dynamical system as recited in claim 1, wherein the step of estimating the intermediate enhanced point includes the step of estimating an intermediate enhanced point in accordance with

{circumflex over (x)}^(i,temp)=g({circumflex over (x)}⁽ⁱ⁻

1),y_n)

wherein signal {circumflex over (x)}_n<sup>(i−

temp)</sup> is the intermediate enhanced point for iteration i, g is a non-linear function, {circumflex over (x)}_n<sup>(i−

1)</sup> is the enchanced point at iteration i−

1 for point n, and y_n is a noise point at point n.

3. A system for filtering signals from a nonlinear dynamical system, comprising:

a processor having an associated stored program including means for setting an initial enhanced point to a noisy point obtained from the signals;

means for estimating an intermediate enhanced point; and

means for iteratively computing a new enhanced point using the estimated point and a weighting constant until the computed point converges to a true enhanced point which represents a noise reduced signal to provide filtered signals,

wherein the new enhanced point is computed by the equation

${\hat{x}}_n^{\left(i\right)}={\hat{x}}_n^{\left(i-1\right)}+K_3<br><br>\left[{\hat{x}}_n^{\left(i,\mathrm{temp}\right)}-{\hat{x}}_n^{\left(i-1\right)}\right]$

wherein {circumflex over (x)}_n⁽ⁱ⁾ is the new enhanced point, {circumflex over (x)}_n<sup>(i−

temp)</sup> is the intermediate enhanced point for iteration i, {circumflex over (x)}_n<sup>(i−

1)</sup> is the enhanced point at iteration i−

1, and K, is a weighing constant.

4. The system as recited in claim 3, wherein the means for estimating the intermediate enhanced point includes an intermediate enhanced point computed in accordance with

{circumflex over (x)}_n^(i,temp)=g({circumflex over (x)}⁽ⁱ⁻

1),y_n)

wherein signal {circumflex over (x)}_n<sup>(i−

temp)</sup> is the intermediate enhanced point for iteration i, g is a non-linear function, {circumflex over (x)}_n<sup>(i−

1)</sup> is the enchanced point at iteration i−

1 for point n, and y_n is a noise point at point n.