US4956792A — Target signal detecting apparatus

Claim 1

Independent Claim 166 words

A target signal detecting apparatus comprising: logarithmic transformation means for logarithmically transforming a received signal X having an amplitude intensity distribution which follows Weibull distribution having a probability density function Pc(x) given by the expression: ##EQU25## where b and c are constants which are determined by the nature of said received signal; mean-square value computing means for calculating a meansquare value computing means for calculating a meansquare value <y 2 > of an amplitude of said logarithmically transformed received signal y=1nx; square value computing means for calculating a square value <y> 2 of the mean of said logarithmically transformed received signal; distributed parameter computing means for calculating a distributed parameter E in accordance with said mean square value <y 2 > and said square value <y> 2 of said mean, where E follows the expression: ##EQU26## target signal detecting means for comparing said calculated distributed parameter E with a predetermined threshold to detect a target signal when said distributed parameter E is greater than said threshold.

Claim 2

Dependent Claim 166 words

A target signal detecting apparatus comprising: logarithmic transformation means for logarithmically transforming a received signal X having an amplitude intensity distribution which follows Weibull distribution having a probability density function Pc(x) given by the expression: ##EQU25## where b and c are constants which are determined by the nature of said received signal; mean-square value computing means for calculating a meansquare value computing means for calculating a meansquare value <y 2 > of an amplitude of said logarithmically transformed received signal y=1nx; square value computing means for calculating a square value <y> 2 of the mean of said logarithmically transformed received signal; distributed parameter computing means for calculating a distributed parameter E in accordance with said mean square value <y 2 > and said square value <y> 2 of said mean, where E follows the expression: ##EQU26## target signal detecting means for comparing said calculated distributed parameter E with a predetermined threshold to detect a target signal when said distributed parameter E is greater than said threshold.

Claim 3

Dependent Claim 164 words

The apparatus as defined in claim 1, A target signal detecting apparatus comprising: logarithmic transformation means for logarithmically transforming a received signal X having an amplitude intensity distribution following a Weibull distribution with its probability density function Pc(x) given by the following ##EQU27## (where B and C are constants which are determined by the nature of said received signal); mean-square value computing means for calculating a mean-square value <y 2 > of an amplitude of said logarithmically transformed received signal y=1nx; square value computing means for calculating a square value <y> 2 of a mean of said logarithmically transformed received signal; distributed parameter computing means for computing the following distributed parameters in accordance with said mean-square value <y 2> and said square value <y> 2 of said mean ##EQU28## including nonlinear amplifying means for generating said predetermined threshold value as Z=E n by raising said calculated distributed parameter E to nth power (where n is a number greater than or equal to 1 (n≦1).

Claim 4

Dependent Claim 57 words

An apparatus according to claim 2, wherein in accordance with said value Z(Z-E n ) and a variance about a mean <Z> of said value Z(Z=E n ), the threshold of said target signal detecting means is predetermined such that the false alarm rate or the probability of detection of said target signal attains a predetermined value.

Claim 5

Dependent Claim 31 words

An apparatus according to claim 3, wherein said threshold has a value of K19 <Z> obtained by multiplying the mean <Z> of said value Z(Z=E n ) by a constant K.

Claim 6

Dependent Claim 39 words

An apparatus according to claim 3, wherein said threshold has a value of K·√<Z 2 > obtained by multiplying a square root of a mean-square value <Z 2 > of said value Z(Z=E n ) by a constant K.

Claim 7

Dependent Claim 72 words

An apparatus according to claim 3, wherein said threshold has a value of K·√<Z 2 >-<Z> 2 obtained by calculating a variance about the mean <Z> of said value Z (Z=E n ) and then multiplying a square root of said variance by a constant K (where <Z 2 > represents a mean-square value of said value Z and <Z> 2 represents a square value of the mean of said value Z).

Claim 8

Dependent Claim 82 words

An apparatus according to claim 3, wherein said threshold hold has a value of <Z>+K·√<Z 2 ><Z> 2 obtained calculating a variance about the mean <Z> of said value Z (Z=E n ), obtaining a product of a square root of said variance and a constant K and then adding said mean <Z> to said product (where <z 2 > represents a mean-square value of said value Z and <Z> 2 represents a square value of the mean of said value Z).

Claim 9

Dependent Claim 78 words

An apparatus according to claim 3, wherein said threshold has a value of K·{<Z>+√<Z 2 >-<Z> 2 }obtained by calculating a variance about the mean <Z> of said value Z (Z=E n ), adding said mean <Z> to a square root of said variance and then multiplying said sum by a constant K (where <Z 2 > represents a mean-square value of said value Z and <Z> represents a square value of the mean of said value Z).

Claim 10

Dependent Claim 38 words

An apparatus according to claim 3, wherein said threshold has a value of K·<Z>+A obtained by adding a constant A to a product of the mean <Z> of said value Z (Z=E n ) and a constant K.

Claim 11

Dependent Claim 46 words

An apparatus according to claim 3, wherein said threshold has a value of K·√<Z 2 >+A obtained by adding a constant A to a product of a square root of a mean-square value <Z 2 > of said value Z(Z=E n ) and a constant K.

Claim 12

Dependent Claim 83 words

An apparatus according to claim 3, wherein said threshold has a value of K·√<Z 2 > <Z> 2 +A obtained by calculating a variance about the mean <Z> of said value Z(Z=E n ), obtaining a product of a square root of said variance and a constant K and then adding a constant A to said product (where <Z 2 > represents a mean-square value of said value Z and <Z> 2 represents a square value of the mean of said value Z).

Claim 13

Dependent Claim 88 words

An apparatus according to claim 3, wherein said threshold has a value of <Z>+K·√Z 2 >-<Z>+A obtained by calculating a variance about the mean <Z> of said value Z(Z=E n ), obtaining a product of a square root of said variance and a constant K, adding said mean <Z > to said product and then adding a constant A to said sum (where <Z 2 > represents a mean-square value of said value Z and <Z> 2 represents a square value of the mean of said value Z).

Claim 14

Dependent Claim 92 words

An apparatus according to claim 3, wherein said threshold has a value of K·{<Z>+√<Z 2 >-<Z> 2 }+A obtained by calculating a variance about the mean <Z> of said value Z (Z=E n ), obtaining a sum of said mean <Z> and a square root of said variance, obtaining a product of said sum and a constant K and then adding a constant A to said product (where <Z 2 > represents a mean-square value of said value Z and <Z> represents a square value of the mean of said value Z).

Claim 15

Independent Claim 167 words

A method of detecting a target signal in a logarithmically transformed signal input (Y) having an amplitude intensity following a Weibull distribution, said method comprising the steps of: logarithmically transforming a received signal having an amplitude intensity distribution following the Weibull distribution having a probability density function Pc(x) given by the following expression: ##EQU29## , where b and c are constants determined by the received signal; calculating a first mean value of said signal input (<Y>); squaring said first mean value to derive a first mean value squared (<Y> 2 ); calculating a second mean value of said signal input squared (<y 2 >); computing a distribution parameter value (E) as a function of the first mean value squared (<Y> 2 ) and the second mean value (<Y 2 >) by the expression ##EQU30## providing a predetermined threshold value; comparing said computed distribution parameter value (E) with said predetermined threshold value; and detecting the target signal when the computed distribution parameter value (E) exceeds the threshold value.

Claim 16

Independent Claim 167 words

A method of detecting a target signal in a logarithmically transformed signal input (Y) having an amplitude intensity following a Weibull distribution, said method comprising the steps of: logarithmically transforming a received signal having an amplitude intensity distribution following the Weibull distribution having a probability density function Pc(x) given by the following expression: ##EQU29## , where b and c are constants determined by the received signal; calculating a first mean value of said signal input (<Y>); squaring said first mean value to derive a first mean value squared (<Y> 2 ); calculating a second mean value of said signal input squared (<y 2 >); computing a distribution parameter value (E) as a function of the first mean value squared (<Y> 2 ) and the second mean value (<Y 2 >) by the expression ##EQU30## providing a predetermined threshold value; comparing said computed distribution parameter value (E) with said predetermined threshold value; and detecting the target signal when the computed distribution parameter value (E) exceeds the threshold value.

Claim 17

Dependent Claim 46 words

The method according to claim 14, wherein the step of providing said predetermined threshold value further comprises the steps of computing the square of said distribution parameter, computing the mean of said squared distribution parameter, and computing the product of said mean and a constant K.

Claim 18

Dependent Claim 55 words

The method according to claim 14, wherein the step of providing predetermined threshold value further comprises the steps of twice computing the square of said distribution parameter, computing the mean of said twice squared distribution parameter, computing the square root of the mean, and computing the product of the square root and a constant K.

Claim 19

Dependent Claim 58 words

The method according to claim 14, wherein said step of providing said predetermined threshold value further comprises the steps of computing the square of said distribution parameter, calculating the mean of said square, computing the variance about said mean, computing the square root of said variance, and multiplying the square root of said variance by a constant K.

Claim 20

Dependent Claim 67 words

The method according to claim 14, wherein the step of providing said predetermined threshold value further comprises the steps of computing the square of said distribution parameter about said mean, computing the mean of said square, computing the variance, computing the square root of the variance, computing the product of the square root of the variance and a constant K, and adding the mean to the product.

Claim 21

Dependent Claim 77 words

The method according to claim 14, wherein said step of providing said predetermined threshold value further comprises the steps of computing the square of said distribution parameter, computing the mean of said square, calculating a variance about the mean, computing the square root of said variance, summing said mean and the square root of said variance, and computing the product of said sum of the mean and the square root of said variance and a constant K.

Claim 22

Dependent Claim 27 words

The method according to claim 19, wherein the step of providing said predetermined threshold value further comprises the step of adding a constant A to said product.

Claim 23

Dependent Claim 57 words

The method according to claim 14, wherein the step of providing said predetermined threshold value further comprises the steps of computing the square of the distribution parameter, computing the mean of the square, computing the product of the mean and a constant K, adding a constant A to the product of the mean and the constant K.

Claim 24

Dependent Claim 71 words

The method according to claim 14, wherein the step of providing said predetermined threshold value further comprises the steps of twice computing the square of said distribution parameter, computing the mean of said twice squared distribution parameter, computing the square root of the mean, computing the product of the square root and a constant A, and adding a constant A to the product of the square root and the constant K.

Claim 25

Dependent Claim 67 words

The method according to claim 14, wherein the step of providing said predetermined threshold value further comprises the steps of computing the square of said distribution parameter, computing the mean of said square, computing the variance about said mean, computing the square root of said variance, computing the product of the square root of the variance and a constant K, adding a constant K to said product.

Claim 26

Dependent Claim 82 words

The method according to claim 14, wherein said step of providing said predetermined threshold value further comprises the steps of computing the square of said distribution parameter, calculating the mean of said square, computing the variance about the mean, computing the square root of said variance, multiplying the square root of said variance by a constant K, summing said mean and the product of said constant K and the square root of said variance, and adding a constant A to said sum.

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	1993-09-10	1994-03-12	1994-09-11	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	1997-09-10	1998-03-12	1998-09-11	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	2001-09-10	2002-03-12	2002-09-11	$7700.00	Window Closed / Lapsed

Target signal detecting apparatus

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