System and method for statistically separating and characterizing noise which is added to a signal of a machine or a system

• US 20060179089A1
• Filed: 04/18/2005
• Published: 08/10/2006
• Est. Priority Date: 02/10/2005
• Status: Active Grant

• Current Assignee: Mineral Lassen LLC (Intellectual Ventures LLC)
• Original Assignee: Nemor Properties LLC (Intellectual Ventures LLC)
• Inventors: Moriya, Netzer
• Granted Patent: US 7,552,154 B2
• Time in Patent Office: Days
• US Class Current: 708/200
• 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

Abstract

Method for finding the probability density function type and the variance properties of the noise component N of a raw signal S of a machine or a system, said raw signal S being combined of a pure signal component P and said noise component N, the method comprising: (a) defining a window within said raw signal; (b) recording the raw signal S; (c) numerically differentiating the raw signal S within the range of said window at least a number of times m to obtain an m order differentiated signal; (d) finding a histogram that best fits the m order differentiated signal; (e) finding a probability. density finction type that fits the distribution of the histogram; (f) determining the variance of the histogram, said histogram variance being essentially the m order variance σ²_(m) of the noise component N; and (g) knowing the histogram distribution type, and the m order variance σ²_(m) of the histogram, transforming the m order variance σ²_m) to the zero order variance σ²₀₎, said σ²₀₎ being the variance of the pdf of the noise component N, and wherein the histogram type as found in step (e) being the probability density function type of the noise component N.

Claims

1. Method for finding the probability density function type and the variance properties of the noise component N of a raw signal S of a machine or a system, said raw signal S being combined of a pure signal component P and said noise component N, the method comprising:

a. defining a window within said raw signal;

b. recording the raw signal S;

c. numerically differentiating the raw signal S within the range of said window at least a number of times m to obtain an m order differentiated signal;

d. finding a histogram that best fits the m order differentiated signal;

e. finding a probability density function type that fits the distribution of the histogram;

f. determining the variance of the histogram, said histogram variance being essentially the m order variance σ

²_(m) of the noise component N; and

g. knowing the histogram distribution type, and the m order variance σ

²_(m) of the histogram, transforming the m order variance σ

²_(m) to the zero order variance σ

²₍₀₎, said σ

²₍₀₎ being the variance of the pdf of the noise component N, and wherein the histogram type as found in step (e) being the probability density function type of the noise component N.

2. Method according to claim 1, which is repeatedly performed as the raw signal S progresses.

3. Method according to claim 2 which is performed in real-time.

4. Method according to claim 1, wherein the probability density function type that fits the distribution of the histogram is the one from a list that found to be best fitting the distribution of the histogram.

5. Method according to claim 2, wherein the list comprises only one probability density function type.

6. Method according to claim 3, wherein the one probability density function type is the Gaussian type.

7. Method according to claim 1, wherein the transform is performed by means of a specific expression suitable for the said fitted probability density finction, wherein said specific expression is derived from the following general expression

$F_{n_i}^{\left(m\right)}={\int }_{}$

D s ⁢

∫

{ ∏

j = 1 m ⁢

 

⁢

S j m ⁢

f ⁡

( ξ

) } ⁢

ⅆ

ξ

( m )

8. Method according to claim 1, wherein when the fitted probability distribution finction is Gaussian, the transform is performed by means of the following specific expression

$\frac{d^{}}{}$

m ⁢

N ⁡

( 0 , σ

0 2 ) ⅆ

i m = α

⁡

( m ) ⁢

N ⁡

( 0 , β

⁡

( m ) ⁢

σ

0 2 )

9. Apparatus for determining the probability density function type and the variance properties of the noise component N of a raw signal S of a machine or a system, said raw signal S being combined of a pure signal component P and said noise component N, the system comprising:

a. differentiating module, for receiving and numerically differentiating the raw signal S within the range of a predefined window at least a number of times m to obtain an m order differentiated signal;

b. a module for finding a histogram that best fits the m order differentiated signal;

c. a list containing at least one type of predefined probability density function;

d. a module for finding one probability density function type from said list that best fits the distribution of the histogram;

e. a module for determining the variance of the histogram, said histogram variance being essentially the m order variance a(m) of the noise component N; and

f. a module for, given the histogram distribution type and the m order variance σ

²_(m) of the histogram, transforming the m order variance σ

²_(m) to the zero order variance σ

²₍₀₎, said σ

²₍₀₎ being the variance of the pdf of the noise component N, wherein the histogram type as found in step (d) being the probability density function type of the noise component N.

10. Apparatus according to claim 9, wherein the apparatus components operate repeatedly to find the updated probability density function type, and the variance properties of the noise component as the signal S progresses.

11. A system for receiving a raw signal S which is combined from a pure signal P and a noise component N, and for outputting a signal which is essentially said pure signal, comprising:

a. Apparatus according to claim 9 for receiving said raw signal and outputting the probability density fuinction and distribution type of said noise component into a filter; and

b. A filter receiving said raw signal and also receiving said probability density function and distribution type of said noise component from said apparatus, and given said received data, processing and outputting a signal which is essentially said pure signal.

12. System according to claim 11, wherein the filter is an adaptive filter.

13. System according to claim 12, wherein the filter is a Kalman Filter.

14. System according to claim 11, for operating continuously in real time.