CN101650428A - Method for detecting chaotic oscillator of submarine weak target signal - Google Patents

Abstract

The invention discloses a method for detecting a chaotic oscillator of a submarine weak target signal, which comprises the following steps: firstly establishing a detection model of the chaotic oscillator by utilizing a Duffing equation; determining a critical point by calculating Lyapunov index; detecting the rough distribution position of characteristic line-spectrum of the submarine target signal according to the critical point; carrying out the second line-spectrum detection every 0.1 Hz based on the rough distribution position of the characteristic line-spectrum; recording corresponding amplitude of the submarine signal each time; taking the minimum value of the recorded amplitude of the submarine signal as detection threshold; detecting accurate distribution position of the characteristic line-spectrum of the submarine target signal according to the detection threshold to realize the detection of the submarine weak target signal. By adopting the detection model of the chaotic oscillator, submarine radiation noise with lower signal noise ratio is detected, so that the method is an effective method for detecting characteristic line spectrum of submarine radiation noise.

Description

The method for detecting chaotic oscillator of submarine weak target signal

Technical field

The present invention relates to a kind of submarine weak target signal detection method, particularly the method for detecting chaotic oscillator of calm type submarine weak target signal under water.

Background technology

In the hydroacoustic electronic warfare field, along with the appearance of calm type submarine, the development of hydroacoustic electronic warfare and novel Undersea Weapon System also faces new challenges.Generally, the noise radiation intensity of calm type submarine can reach zero shellfish even lower, at this moment adds the interference of ambient sea noise, makes traditional time domain, frequency-region signal etection theory be difficult to bear results to it.

Document " the faint square-wave signal that suppresses principle based on parameter off-resonance excitation chaos detects; Acta Physica Sinica; 2007; Vol.56 (9), p5098-5102 " discloses a kind of parameter off-resonance excitation chaos of self-governing chaos system of utilizing and has suppressed the detection method that principle realizes faint square-wave signal under the strong noise background.This method with frequency much larger than the square-wave signal of system features frequency as built-in pumping signal, after the method for average is handled, obtain the parameter equivalent relation between controlled system and the original system, and determine to make system to sport the detected parameters critical value of cycle status by chaos state thus.The numerical simulation result shows that this system can reach extremely low signal to noise ratio (S/N ratio) work lower limit.Than utilizing parameter resonance perturbation chaos to suppress the method that principle realizes Detection of Weak Signals, this scheme can obtain detected parameters estimated value more accurately according to rigorous theoretical analysis.The document has just provided the detection method of faint square-wave signal under the strong noise background, does not provide the detection method of submarine weak any period signal under the strong noise background.

Summary of the invention

In order to overcome the deficiency that prior art is difficult to detect submarine weak any period signal under the strong background noise, the invention provides a kind of method for detecting chaotic oscillator of submarine weak target signal.By setting up the chaotic oscillator detection model, can realize the detection of submarine weak target signal.

The technical solution adopted for the present invention to solve the technical problems: a kind of method for detecting chaotic oscillator of submarine weak target signal is characterized in may further comprise the steps:

(a) have periodic characteristics according to the submarine radiated noise, utilize the Duffing equation to set up the chaotic oscillator detection model;

(b) according to the spectrum distribution of submarine radiated noise, in the chaotic oscillator detection model, the reference frequency of detection signal is set to 20～85Hz; According to the amplitude distribution of submarine radiated noise, amplitude to the chaotic oscillator detection model of adjusting reference signal is in the chaos critical conditions, by calculating Lyapunov index, determines critical point;

(c) the submarine signal is input in the chaotic oscillator detection model, calculating Lyapunov index, and increase the amplitude of submarine signal gradually, double counting Lyapunov index, determine the chaos critical point, the amplitude size of record submarine signal this moment is a foundation with this critical point, detect the rough distribution position of Submarine Target signal characteristic line spectrum, this line spectrum is represented the frequency spectrum of the radiated noise of submarine;

(d) on the basis of feature line spectrum rough position, carry out the line spectrum detection second time every 0.1Hz, the corresponding submarine signal amplitude of each record, with the submarine signal amplitude minimum value noted as detection threshold, with this detection threshold is foundation, detect the accurate distribution position of Submarine Target signal characteristic line spectrum, realize the detection of submarine weak target signal.

The invention has the beneficial effects as follows:

(a) nonequilibrium phase transition of chaotic oscillator detection model has susceptibility to weak periodic signal, and has very strong immunity to white noise with the bigger periodic interference signals of reference signal frequency difference.Therefore, utilize the chaotic oscillator detection model to solve the input of calm type submarine under the complicated marine environment, promptly solved the detection difficult problem of weak target signal under water.

(b) the Lyapunov index determines exactly as the chaos criterion whether the chaotic oscillator detection model is in the chaos critical conditions, from quantitatively having provided the foundation of chaotic oscillator detection model dynamic behavior phase transformation.

(c) the submarine radiated noise signals detection method based on the chaotic oscillator detection model has realized that directly the submarine radiated noise being carried out line spectrum on time domain detects, owing to adopted the chaotic oscillator detection model, detected the lower submarine radiated noise of signal to noise ratio (S/N ratio), therefore, be a kind of effective ways that detect submarine radiated noise feature line spectrum.

Below in conjunction with embodiment the present invention is elaborated.

Embodiment

The chaos detection that embodiment 1:A type submarine line spectrum is analyzed, its step is as follows:

(a) utilize the Duffing equation to set up the chaotic oscillator detection model.

The Duffing equation is a second order differential equation that contains cube item, and it externally encourages down and vibrates, and produces periodic motion and chaotic motion.Its Holmes type Duffing equation is:

x ⁿ(t)+kx′(t)-x(t)+x ³(t)＝Fcos(t) (1)

In the formula, x (t) is the system equation variable, and k is a damping ratio, and Fcos (t) is a cycle driving force reference signal, and F is a hormetic amplitude of cycle ,-x (t)+x ³(t) be non-linear restoring power.When external signal was determined, the characteristic of system depended primarily on the nonlinear restoring force of system.Take all factors into consideration from the many-sides such as proof of Detection of weak lower limit, chaos system detection signal-to-noise ratio, system's chaos criterion, nonlinear restoring force is changed into-x ³(t)+x ⁵(t), promptly

x ⁿ(t)+kx′(t)-x ³(t)+x ⁵(t)＝Fcos(t) (2)

But the detection system based on formula (2) also has certain limitation: (i) can only detect the periodic signal that frequency is ω=1rad/s.(ii) can only detect the signal that has same waveform as with reference signal cos (t).Solution: the first, in formula (2), make t=ω τ, then

$\frac{d^{2}x}{d^2\mathrm{\τ}}+\mathrm{k\ω}\frac{\mathrm{dx}}{\mathrm{d\τ}}-{\mathrm{\ω}}^2{x}^3+{\mathrm{\ω}}^2{x}^5={\mathrm{\ω}}^{2}F\cos \left(\mathrm{\ω\τ}\right)---\left(3\right)$

Formula (3) is compared with formula (2), and phase velocity has improved ω doubly, but fork character is constant.In formula (2), add coefficient c ₁, c ₂, c ₃, c ₄, then

x″(t)+kc ₁x′(t)-c ₂x ³(t)+c ₃x ⁵(t)＝c ₄Fcos(ωt) (4)

Make c ₁=ω, c ₂=c ₃=c ₄=ω ², the property of system of formula (4) and formula (2) is just identical.Like this, formula (4) can detect the sinusoidal signal of optional frequency, but can't detect the periodic signal of random waveform.The second, the method for utilizing chaos to suppress is constructed the chaos detection model.In the Duffing EQUATION x ⁵Add a weak cycle perturbation item in the coefficient of item, equation becomes

x″+kωx′-ω ²x ³+ω ²[1+as(ωt)]x ⁵＝ω ²Fcos(ωt) (5)

Wherein as (ω t) is a weak periodic signal to be measured.Work as a=0, be i.e. during printenv perturbation, system placed the chaos critical conditions, add non-linear x this moment ⁵The weak cycle perturbation of item coefficient just can curb chaos state, enters the large scale cycle status, thereby arbitrarily weak periodic signal is detected.The kinetics equation of formula (5) is:

$\left\{\begin{array}{c}{x}^{\′}=\mathrm{\ωv}\\ v^{\′}={\mathrm{\ω}}^2\{-\mathrm{kv}+x^3-[1+\mathrm{as}\left(\mathrm{\ωt}\right)]x^5+F\cos \left(\mathrm{\ωt}\right)\}\end{array}\right.---\left(6\right)$

Set up chaotic oscillator detection system realistic model by formula (6);

(b) reference signal frequency is made as 20～30Hz, amplitude to the chaotic oscillator detection model of adjusting reference signal is in the chaos critical conditions, by calculating Lyapunov index, determines critical point;

The computing method of Lyapunov index are as follows:

The Lyapunov index is used for measuring the degree that attracts or separate by index percent in time in two different phase paths of phase space starting condition; The Lyapunov index is defined as follows: have for two-dimensional map

$\left\{\begin{array}{c}{x}_{n+1}=X(x_n,y_n),\\ y_{n+1}=Y(x_n,y_n)\end{array}\right.---\left(7\right)$

Its Jacobi matrix is

$J(x_n,y_n)=\left[\begin{array}{cc}\frac{\∂X}{\∂x_n}& \frac{\∂X}{\∂y_n}\\ \frac{\∂Y}{{\∂x}_n}& \frac{\∂Y}{{\∂y}_n}\end{array}\right]---\left(8\right)$

Suppose by initial point p ₀(x ₀, y ₀) point range of shining upon one by one and obtaining of setting out is p ₁(x ₁, y ₁), p ₂(x ₂, y ₂) ..., p _n(x _n, y _n), then the Jacobi matrix at preceding n-1 some place is

J ₀＝J(x ₀，y ₀)，J ₁＝J(x ₁，y ₁)，...，J _n-1＝J(x _n-1，y _n-1) (9)

Make J ⁽ⁿ⁾=J _N-1J _N-2... J ₁J ₀, and establish J ⁽ⁿ⁾The mould of eigenwert is j ₁ ⁽ⁿ⁾And j ₂ ⁽ⁿ⁾, and j ₁ ⁽ⁿ⁾＞j ₂ ⁽ⁿ⁾, then the Lyapunov index is defined by following formula: $L_1=\underset{n\→\∞}{\lim }\sqrt[n]{j_1^{\left(n\right)}},$ $L_2=\underset{n\→\∞}{\lim }\sqrt[n]{j_2^{\left(n\right)}};$

(c) the submarine signal is input in the chaotic oscillator detection model, calculating Lyapunov index, and increase the amplitude of submarine signal gradually, double counting Lyapunov index, determine the chaos critical point, the amplitude a size of record submarine signal this moment, a value size is respectively/, /, /, 20,4.2,3.4,03,06,32, /, /, with a value smaller value of noting 0.3,0.6 be foundation, decidable feature line spectrum rough position is at 26～27Hz, wherein "/" expression measured signal can't make the system under this frequency become the large scale cycle status by chaos, and promptly the signal of the frequency content correspondence that should locate is fainter;

(d) carry out the line spectrum detection second time from 26～27Hz every 0.1Hz, the a value size of at every turn noting is respectively 0.30,0.23,0.21,0.29,0.39,0.45,0.48,0.51,0.56,0.63,0.60, with a value minimum value 0.21 noted is foundation, and the accurate distribution position that can further judge the feature line spectrum is at 26.2Hz.The data of A type submarine line spectrum detection gained are as shown in table 1."/" expression measured signal can't make the system under this frequency become the large scale cycle status by chaos, and promptly the frequency content that should locate is fainter.

The chaos detection that three kinds of Submarine Hull spectrums of table 1 distribute

"/" expression measured signal can't make the system under this frequency become the large scale cycle status by chaos, and promptly the frequency content that should locate is fainter.

The chaos detection that embodiment 2:B type submarine line spectrum is analyzed, its step is as follows:

(a) utilize the Duffing equation to set up the chaotic oscillator detection model.

The Duffing equation is a second order differential equation that contains cube item, and it externally encourages down and vibrates, and produces periodic motion and chaotic motion.Its Holmes type Duffing equation is:

x ⁿ(t)+kx′(t)-x(t)+x ³(t)＝Fcos(t) (1)

In the formula, x (t) is the system equation variable, and k is a damping ratio, and Fcos (t) is a cycle driving force reference signal, and F is a hormetic amplitude of cycle ,-x (t)+x ³(t) be non-linear restoring power.When external signal was determined, the characteristic of system depended primarily on the nonlinear restoring force of system.Take all factors into consideration from the many-sides such as proof of Detection of weak lower limit, chaos system detection signal-to-noise ratio, system's chaos criterion, nonlinear restoring force is changed into-x ³(t)+x ⁵(t), promptly

x ⁿ(t)+kx′(t)-x ³(t)+x ⁵(t)＝Fcos(t) (2)

But the detection system based on formula (2) also has certain limitation: (i) can only detect the periodic signal that frequency is ω=1rad/s.(ii) can only detect the signal that has same waveform as with reference signal cos (t).Solution: the first, in formula (2), make t=ω τ, then

$\frac{d^{2}x}{d^2\mathrm{\τ}}+\mathrm{k\ω}\frac{\mathrm{dx}}{\mathrm{d\τ}}-{\mathrm{\ω}}^2{x}^3+{\mathrm{\ω}}^2{x}^5={\mathrm{\ω}}^{2}F\cos \left(\mathrm{\ω\τ}\right)---\left(3\right)$

Formula (3) is compared with formula (2), and phase velocity has improved ω doubly, but fork character is constant.In formula (2), add coefficient c ₁, c ₂, c ₃, c ₄, then

x″(t)+kc ₁x′(t)-c ₂x ³(t)+c ₃x ⁵(t)＝c ₄Fcos(ωt) (4)

Make c ₁=ω, c ₂=c ₃=c ₄=ω ², the property of system of formula (4) and formula (2) is just identical.Like this, formula (4) can detect the sinusoidal signal of optional frequency, but can't detect the periodic signal of random waveform.The second, the method for utilizing chaos to suppress is constructed the chaos detection model.In the Duffing EQUATION x ⁵Add a weak cycle perturbation item in the coefficient of item, equation becomes

x″+kωx′-ω ²x ³+ω ²[1+as(ωt)]x ⁵＝ω ²Fcos(ωt) (5)

Wherein as (ω t) is a weak periodic signal to be measured.Work as a=0, be i.e. during printenv perturbation, system placed the chaos critical conditions, add non-linear x this moment ⁵The weak cycle perturbation of item coefficient just can curb chaos state, enters the large scale cycle status, thereby arbitrarily weak periodic signal is detected.The kinetics equation of formula (5) is:

$\left\{\begin{array}{c}{x}^{\′}=\mathrm{\ωv}\\ v^{\′}={\mathrm{\ω}}^2\{-\mathrm{kv}+x^3-[1+\mathrm{as}\left(\mathrm{\ωt}\right)]x^5+F\cos \left(\mathrm{\ωt}\right)\}\end{array}\right.---\left(6\right)$

Set up chaotic oscillator detection system realistic model by formula (6);

(b) reference signal frequency is made as 65～75Hz, amplitude to the chaotic oscillator detection model of adjusting reference signal is in the chaos critical conditions, by calculating Lyapunov index, determines critical point;

The computing method of Lyapunov index are as follows:

The Lyapunov index is used for measuring the degree that attracts or separate by index percent in time in two different phase paths of phase space starting condition; The Lyapunov index is defined as follows: have for two-dimensional map

$\left\{\begin{array}{c}{x}_{n+1}=X(x_n,y_n),\\ y_{n+1}=Y(x_n,y_n)\end{array}\right.---\left(7\right)$

Its Jacobi matrix is

$J(x_n,y_n)=\left[\begin{array}{cc}\frac{\∂X}{\∂x_n}& \frac{\∂X}{\∂y_n}\\ \frac{\∂Y}{{\∂x}_n}& \frac{\∂Y}{{\∂y}_n}\end{array}\right]---\left(8\right)$

Suppose by initial point p ₀(x ₀, y ₀) point range of shining upon one by one and obtaining of setting out is p ₁(x ₁, y ₁), p ₂(x ₂, y ₂) ..., p _n(x _n, y _n), then the Jacobi matrix at preceding n-1 some place is

J ₀＝J(x ₀，y ₀)，J ₁＝J(x ₁，y ₁)，...，J _n-1＝J(x _n-1，y _n-1) (9)

Make J ⁽ⁿ⁾=J _N-1J _N-2... J ₁J ₀, and establish J ⁽ⁿ⁾The mould of eigenwert is j ₁ ⁽ⁿ⁾And j ₂ ⁽ⁿ⁾, and j ₁ ⁽ⁿ⁾＞j ₂ ⁽ⁿ⁾, then the Lyapunov index is defined by following formula: $L_1=\underset{n\→\∞}{\lim }\sqrt[n]{j_1^{\left(n\right)}},$ $L_2=\underset{n\→\∞}{\lim }\sqrt[n]{j_2^{\left(n\right)}};$

(c) the submarine signal is input in the chaotic oscillator detection model, calculating Lyapunov index, and increase the amplitude of submarine signal gradually, double counting Lyapunov index, determine the chaos critical point, the amplitude a size of record submarine signal this moment, a value size is respectively/, 12,1.3,0.2,0.26,4.1,6.3,17, /, /, /, with a value smaller value of noting 0.2,0.26 be foundation, decidable feature line spectrum rough position is at 68～69Hz, wherein "/" expression measured signal can't make the system under this frequency become the large scale cycle status by chaos, and promptly the signal of the frequency content correspondence that should locate is fainter;

(d) carry out the line spectrum detection second time from 68～69Hz every 0.1Hz, the a value size of at every turn noting is respectively 0.20,0.20,0.20,0.18,0.15,0.22,0.23,0.24,0.24,0.24,0.26, with a value minimum value 0.15 noted is foundation, and the accurate distribution position that can further judge the feature line spectrum is at 68.4Hz.The data of B submarine line spectrum detection gained are as shown in table 1."/" expression measured signal can't make the system under this frequency become the large scale cycle status by chaos, and promptly the frequency content that should locate is fainter.

The chaos detection that embodiment 3:C submarine line spectrum is analyzed, its step is as follows:

(a) utilize the Duffing equation to set up the chaotic oscillator detection model.

The Duffing equation is a second order differential equation that contains cube item, and it externally encourages down and vibrates, and produces periodic motion and chaotic motion.Its Holmes type Duffing equation is:

x ⁿ(t)+kx′(t)-x(t)+x ³(t)＝Fcos(t) (1)

In the formula, x (t) is the system equation variable, and k is a damping ratio, and Fcos (t) is a cycle driving force reference signal, and F is a hormetic amplitude of cycle ,-x (t)+x ³(t) be non-linear restoring power.When external signal was determined, the characteristic of system depended primarily on the nonlinear restoring force of system.Take all factors into consideration from the many-sides such as proof of Detection of weak lower limit, chaos system detection signal-to-noise ratio, system's chaos criterion, nonlinear restoring force is changed into-x ³(t)+x ⁵(t), promptly

x ⁿ(t)+kx′(t)-x ³(t)+x ⁵(t)＝Fcos(t) (2)

But the detection system based on formula (2) also has certain limitation: (i) can only detect the periodic signal that frequency is ω=1rad/s.(ii) can only detect the signal that has same waveform as with reference signal cos (t).Solution: the first, in formula (2), make t=ω τ, then

$\frac{d^{2}x}{d^2\mathrm{\τ}}+\mathrm{k\ω}\frac{\mathrm{dx}}{\mathrm{d\τ}}-{\mathrm{\ω}}^2{x}^3+{\mathrm{\ω}}^2{x}^5={\mathrm{\ω}}^{2}F\cos \left(\mathrm{\ω\τ}\right)---\left(3\right)$

Formula (3) is compared with formula (2), and phase velocity has improved ω doubly, but fork character is constant.In formula (2), add coefficient c ₁, c ₂, c ₃, c ₄, then

x″(t)+kc ₁x′(t)-c ₂x ³(t)+c ₃x ⁵(t)＝c ₄Fcos(ωt) (4)

Make c ₁=ω, c ₂=c ₃=c ₄=ω ², the property of system of formula (4) and formula (2) is just identical.Like this, formula (4) can detect the sinusoidal signal of optional frequency, but can't detect the periodic signal of random waveform.The second, the method for utilizing chaos to suppress is constructed the chaos detection model.In the Duffing EQUATION x ⁵Add a weak cycle perturbation item in the coefficient of item, equation becomes

x″+kωx′-ω ²x ³+ω ²[1+as(ωt)]x ⁵＝ω ²Fcos(ωt) (5)

Wherein as (ω t) is a weak periodic signal to be measured.Work as a=0, be i.e. during printenv perturbation, system placed the chaos critical conditions, add non-linear x this moment ⁵The weak cycle perturbation of item coefficient just can curb chaos state, enters the large scale cycle status, thereby arbitrarily weak periodic signal is detected.The kinetics equation of formula (5) is:

$\left\{\begin{array}{c}{x}^{\′}=\mathrm{\ωv}\\ v^{\′}={\mathrm{\ω}}^2\{-\mathrm{kv}+x^3-[1+\mathrm{as}\left(\mathrm{\ωt}\right)]x^5+F\cos \left(\mathrm{\ωt}\right)\}\end{array}\right.---\left(6\right)$

Set up chaotic oscillator detection system realistic model by formula (6);

(b) reference signal frequency is made as 75～85Hz, amplitude to the chaotic oscillator detection model of adjusting reference signal is in the chaos critical conditions, by calculating Lyapunov index, determines critical point;

The computing method of Lyapunov index are as follows:

The Lyapunov index is used for measuring the degree that attracts or separate by index percent in time in two different phase paths of phase space starting condition; The Lyapunov index is defined as follows: have for two-dimensional map

$\left\{\begin{array}{c}{x}_{n+1}=X(x_n,y_n),\\ y_{n+1}=Y(x_n,y_n)\end{array}\right.---\left(7\right)$

Its Jacobi matrix is

$J(x_n,y_n)=\left[\begin{array}{cc}\frac{\∂X}{\∂x_n}& \frac{\∂X}{\∂y_n}\\ \frac{\∂Y}{{\∂x}_n}& \frac{\∂Y}{{\∂y}_n}\end{array}\right]---\left(8\right)$

Suppose by initial point p ₀(x ₀, y ₀) point range of shining upon one by one and obtaining of setting out is p ₁(x ₁, y ₁), p ₂(x ₂, y ₂) ..., p _n(x _n, y _n), then the Jacobi matrix at preceding n-1 some place is

J ₀＝J(x ₀，y ₀)，J ₁＝J(x ₁，y ₁)，...，J _n-1＝J(x _n-1，y _n-1) (9)

Make J ⁽ⁿ⁾=J _N-1J _N-2... J ₁J ₀, and establish J ⁽ⁿ⁾The mould of eigenwert is j ₁ ⁽ⁿ⁾And j ₂ ⁽ⁿ⁾, and j ₁ ⁽ⁿ⁾＞j ₂ ⁽ⁿ⁾, then the Lyapunov index is defined by following formula: $L_1=\underset{n\→\∞}{\lim }\sqrt[n]{j_1^{\left(n\right)}},$ $L_2=\underset{n\→\∞}{\lim }\sqrt[n]{j_2^{\left(n\right)}};$

(c) the submarine signal is input in the chaotic oscillator detection model, calculating Lyapunov index, and increase the amplitude of submarine signal gradually, double counting Lyapunov index, determine the chaos critical point, the amplitude a size of record submarine signal this moment, a value size is respectively/, /, 40,3.0,4.1,2.5,0.6,0.4,0.7,2.0,4.8, with a value smaller value of noting 0.4,0.6 be foundation, decidable feature line spectrum rough position is at 81.5～82.5Hz, wherein "/" expression measured signal can't make the system under this frequency become the large scale cycle status by chaos, and promptly the signal of the frequency content correspondence that should locate is fainter;

(d) carry out the line spectrum detection second time from 81.5～82.5Hz every 0.1Hz, the a value size of at every turn noting is respectively 0.57,0.53,0.56,0.51,0.47,0.40,0.35,0.33,0.49,0.57,0.62, with a value minimum value 0.33 noted is foundation, and the accurate distribution position that can further judge the feature line spectrum is at 82.2Hz.The data of C type submarine line spectrum detection gained are as shown in table 1."/" expression measured signal can't make the system under this frequency become the large scale cycle status by chaos, and promptly the frequency content that should locate is fainter.

Claims (1)

1, a kind of method for detecting chaotic oscillator of submarine weak target signal is characterized in that may further comprise the steps:

(a) have periodic characteristics according to the submarine radiated noise, utilize the Duffing equation to set up the chaotic oscillator detection model;

(b) according to the spectrum distribution of submarine radiated noise, in the chaotic oscillator detection model, the reference frequency of detection signal is set to 20～85Hz; According to the amplitude distribution of submarine radiated noise, amplitude to the chaotic oscillator detection model of adjusting reference signal is in the chaos critical conditions, by calculating Lyapunov index, determines critical point;

(c) the submarine signal is input in the chaotic oscillator detection model, calculating Lyapunov index, and increase the amplitude of submarine signal gradually, double counting Lyapunov index, determine the chaos critical point, the amplitude size of record submarine signal this moment is a foundation with this critical point, detect the rough distribution position of Submarine Target signal characteristic line spectrum, this line spectrum is represented the frequency spectrum of the radiated noise of submarine;

(d) on the basis of feature line spectrum rough position, carry out the line spectrum detection second time every 0.1Hz, the corresponding submarine signal amplitude of each record, with the submarine signal amplitude minimum value noted as detection threshold, with this detection threshold is foundation, detect the accurate distribution position of Submarine Target signal characteristic line spectrum, realize the detection of submarine weak target signal.