CN101707575A - Chaotic noise signal estimating method based on symbolic vector dynamics - Google Patents

Abstract

The invention discloses a chaotic noise signal estimating method based on symbolic vector dynamics, comprising the following steps: (A1) according to n+1 moment, namely, next moment, mapping that xn+1 is equal to H(xn) by a chaotic system, and utilizing sn to determine n moment, namely, current moment, carrying out inverse mapping chaotically, wherein sn is a symbol vector sequence of the n moment; (A2) if the received vector sequence: (yi)i is equal to 0L, is received and symbolized to that (s'i)i is equal to 0L, randomly selecting eta as an initial vector; and (A3) at any n moment, according to an evaluation algorithm based on symbol vector sequence, figuring out explanatory evaluation value n equaling to 0,1 and the like. based on S'. The estimating method has fast analysis speed and high accuracy.

Description

A kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector

Technical field

The invention belongs to nonlinear signal processing technology, based on the signal estimation method of a kind of chaotic signal at the affix white Gaussian noise of design, but extensive use is based on the signal processing of chaos, fields such as message transmission and secure communication.

Background technology

In signals transmission, inevitably will introduce noise, therefore be necessary to study the validity of chaotic signal algorithm for estimating under the situation of making an uproar.At present, various have the proposition of the signal algorithm for estimating of one dimension chaos under the condition of making an uproar to provide strong reference and reference for carrying out of this research work.Wherein the structure thought of a class algorithm comes from Design of Filter, promptly extracts immediate signal trajectory by optimizing some cost from noise cancellation signal is arranged; The structure thinking of another kind of algorithm then derives from symbolic dynamics, promptly utilizes the corresponding relation between symbol sebolic addressing and Chaos dynamic system, has noise cancellation signal to estimate the initial value or the Control Parameter of actual chaotic maps by symbolism.

At paper " Estimating initial conditions in coupled map lattices from noisy time series usingsymbolic vector dynamics " (Kai Wang, Wenjiang Pei, Zhenya He, Yiu-ming Cheung, PhysicsLetters A, 367 (2007) 316-321) in, we propose a kind of based on the dynamic (dynamical) self adaptation chaotic noise signal of symbolic vector algorithm for estimating, this method utilizes the chaos symbol sebolic addressing with the one-to-one relationship between actual power sequence, with observation signal y _iSymbolism estimates that chaos has noise cancellation signal.

Summary of the invention

The present invention seeks to provides a kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector at the defective that prior art exists.This method utilizes the chaos symbol sebolic addressing with the one-to-one relationship between actual power sequence, with observation signal y _iSymbolism estimates that chaos has noise cancellation signal.It is fast that it has analysis speed, the characteristics that accuracy is high.

The present invention adopts following technical scheme for achieving the above object:

The present invention is a kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector, it is characterized in that comprising the steps:

(A1) be next x of chaos system mapping constantly constantly according to n+1 _N+1=H (x _n), utilize s _nDetermine that its n is the inverse mapping of current time chaos constantly

S wherein _nBe n symbolic vector sequence constantly, H () is that extensive coupling reflection grid produces function;

(A2) known reception sequence vector { y _i} _I=0 ^L, and symbol turn to s ' _i} _I=0 ^L, picked at random η is as initial vector, i=1 wherein ..., N represents the lattice point position, and N represents the lattice point size, and η is the traversal interval purpose amount of taking up an official post, and L is an observation vector length;

(A3) at any n constantly,, calculate estimated value based on S ' according to algorithm for estimating based on the symbolic vector sequence N=0,1 ..., n express time step number, wherein S ' is the symbolic vector sequence of observation.

Beneficial effect of the present invention is as follows: one, itself has fault-tolerance algorithm.Since algorithm for estimating only relevant with symbol sebolic addressing s ' _n} _N=0 ^∞, to actual signal sequence { y _n} _N=0 ^∞Irrelevant.Suppose constantly the symbol s ' of observation at i node n _n ⁱWith actual symbol s _n ⁱIdentical, noise signal w so _n ⁱInfluence can ignore; Its two since estimated value x ' (n|L) only with back L bit sign sequence s ' _N+i} _I=0 ^L-1Relevant, if supposition n bit sign makes a mistake, L position estimated value before so only can influencing x ' _N+k} _K=1-L ⁰Precision.Thereby avoided the index of evaluated error to increase.

Estimate to compare with the signal that nothing is made an uproar under the situation, this moment because the limited evaluated error of bringing of the symbolic vector sequence length that observes not is the main cause of generation signal errors.As long as the correct sequence length long enough that any value observes, algorithm for estimating can accurately estimate the actual power track { x of coupling reflection grid dynamical system so _n} _N=0 ^∞In fact, the reason that causes evaluated error mainly is because the error code that noise signal causes causes.Under the situation of making an uproar, if being the symbol sebolic addressing of L, the length that observes only have wherein preceding N position correct, Ci Shi estimated value x ' (n|L) just is equivalent to and does not have estimated value x (n|N) under the situation of making an uproar so, and the evaluated error of this moment is also just corresponding when making an uproar with nothing that the observation symbol lengths is N under the situation pairing evaluated error.

Consider the i node, n is symbol s constantly _n ⁱThe error rate as follows: make f _i: I → I, wherein traversal is interval, when

D wherein _k ⁱBe k and divide the subinterval.Observation signal

Then: the error rate

Because { w _n ⁱ} _N=0 ^∞Be white Gaussian noise, make that average is μ, variance is σ ²The error rate then:

$p(s_n^i\≠s_n^{\′i})=\frac{1}{\mathrm{\σ}\sqrt{2\mathrm{\π}}}{{\∫}_{x_{c_{k+1}}^i-x_n^i}^{+\∞}e}^{\frac{-{(t-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}\mathrm{dt}+\frac{1}{\mathrm{\σ}\sqrt{2\mathrm{\π}}}{\∫}_{-\∞}^{x_{c_k}^i-x_n^i}{e}^{\frac{-{(t-\mathrm{\μ})}^2}{2{\mathrm{\σ}}^2}}\mathrm{dt}---\left(2\right)$

Count p _n ⁱIf each node signal { y _n ⁱ} _N=0 ^∞, i=1,2 ..., N is separate.Then symbol vector s _nThe error rate be:

$P=1-{\mathrm{\Π}}_{i=1}^N(1-p_n^i).---\left(3\right)$

According to formula (2-3) as can be known, when Gauss's additive white noise one regularly, the factor that influences the symbolic vector error rate is also counted N with the total node of coupling influence grid except with signal to noise ratio is relevant, and relevant between dividing regions.Shown in (2-3), when between dividing regions

Length narrow more, and when the node number many more, then the error rate is big more.

Description of drawings

Fig. 1 algorithm block diagram of the present invention.

Embodiment

Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:

As shown in Figure 1, a kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector, it is characterized in that comprising the steps:

(A1) be next x of chaos system mapping constantly constantly according to n+1 _N+1=H (x _n), utilize s _nDetermine that its n is the inverse mapping of current time chaos constantly

S wherein _nBe n symbolic vector sequence constantly, H () is that extensive coupling reflection grid produces function;

(A2) known reception sequence vector { y _i} _I=0 ^L, and symbol turn to s ' _i} _I=0 ^L, picked at random η is as initial vector, i=1 wherein ..., N represents the lattice point position, and N represents the lattice point size, and η is the traversal interval purpose amount of taking up an official post, and L is an observation vector length;

(A3) at any n constantly,, calculate estimated value based on S ' according to algorithm for estimating based on the symbolic vector sequence

N=0,1 ..., n express time step number, wherein S ' is the symbolic vector sequence of observation.

Described a kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector, it is characterized in that described in steps A 1, being mapped as unimodal map, coupling reflection grid is as follows under the extensive N node unimodal map:

$x_{n+1}^i=(1-\mathrm{\ϵ})f_i\left(x_n^i\right)+\frac{\mathrm{\ϵ}}{2}[f_{i-1}\left(x_n^{i-1}\right)+f_{i+1}\left(x_n^{i+1}\right)]---\left(1\right)$

I=1 wherein ..., N represents the lattice point position, N represents the lattice point size, and n express time step number, ε represents coupling coefficient; Dynamic system f _i: I → I, I=[a, b] for the unimodal map function is a phase space, in n chaos inverse mapping constantly

Above-mentioned coupling reflection grid can extensively be x _N+1=H (x _n), and one dimension chaos x _N+1=f (x _n) be the special case of coupling reflection grid in coupling coefficient ε=0 o'clock.

Described a kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector, it is characterized in that the unimodal map f of i lattice point _i: I → I, I=[a, b]; If f _iThere is q critical point, then according to critical point

Phase space I is divided into q+1 mutually disjoint subinterval d _k ⁱ, k=0,1 ... q, wherein

And

K ≠ 0, q-1; Set

I lattice point n symbol value constantly is as follows:

At n constantly, (1) formula produces symbolic vector

And (1) formula is designated as S={s from the symbolic vector sequence that 0 moment iteration produces ₀, s ₁..., s _n...;

Fx _N+1=A ^-1* x _N+1, wherein The i lattice point (i=1,2...... N) concern constantly at n:

Order

Be the n moment, symbol s ⁱThe traitor's property of each node is given birth to function when known

Then

Order

Then when symbolic vector sequence S was known, the contrary of reflection grid that be coupled can be abbreviated as:

Described a kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector, it is characterized in that in steps A 2, with received signal vector { y _i} _I=0 ^LAs follows symbol turn to symbolic vector s ' _i} _I=0 ^L:

In n symbolic vector sequence constantly

Then the symbolic vector sequence of observation signal be designated as s ' _i} _I=0 ^L

Symbolic vector dynamics is-symbol dynamics replenishing in the space-time chaos field with perfect.And just because of between the two corresponding relation, make further to expand to the application of symbolic dynamics in the one dimension chaos in the coupling reflection grid [].At present in Chaos Modulation and demodulation field, occurred such as CSK (chaotic shift keying), CPSK (chaotic phase shift keying), DCSK (differential chaos shift keying) etc. are based on the modulation algorithm of symbolic dynamics.Therefore the multinode structure that is had in the coupled system can produce the separate chaotic carrier sequence of multichannel simultaneously, therefore the chaos sequence of each node generation of coupling reflection grid can be distributed to the multi-user and carry out Chaos Modulation and demodulation.By a simple expansion, one is based on the dynamic (dynamical) multi-user's modulation and demodulation of symbolic vector algorithm block diagram as shown in Figure 1:

Suppose that the information vector sequence is B={b ₀, b ₁..., b _m..., wherein m information vector constantly is

M=2 generally speaking.Scale length is the coupling reflection grid sequence vector X of 2L+1 when making n _n={ x _{(n, 0)}, x _{(n, 1)}..., x _{(n, 2L)}, modulating function U, modulation signal

Information vector b then _mBe coupled the constantly modulation of reflection grid sequence vector can be expressed as to n: Z=U (X, b _m).At present in Chaos Modulation and demodulation field, occurred such as CSK (chaotic shiftkeying), CPSK (chaotic phase shift keying), DCSK (differential chaos shift keying) etc. are based on the modulation algorithm of symbolic dynamics, by simple expansion, then can design based on the dynamic (dynamical) modulation algorithm of symbolic vector.

Embodiment 1: the chaos shift keying method

Modulated process: if n time information vector is

Then the note general reflection of coupling reflection grid at this moment is

For

In any one

When

The time,

When

The time,

Wherein

The expression chaotic maps

Different Control Parameter.We are with n-1 moment modulation intelligence x _{(n-1), 2L}As the initial value iteration

The coupling reflection grid sequence vector X that produces _nBe modulation signal

Demodulating process: receiving terminal and transmitting terminal are shared initial value, so receiver section and transmitting terminal produce n-1 x constantly synchronously _(n-1,2L)With x _(n-1,2L)Be initial value, enumerate various coupling reflection grid H _bProduce sequence vector Carry out symbolism for the signal that receives, utilize said method to enumerate various b _mDUAL PROBLEMS OF VECTOR MAPPING under the situation

With the least mean-square error principle, select to make cost

Minimum sequence vector, and according to this moment Recover n information transmitted sign indicating number b constantly _m, and write down this x constantly _{(n, 2L)}As the initial value of modulating next time.The differentiation amount of having a surplus is selected

Therefore L is long more, and discrimination precision is high more, and the error rate is low more.

Embodiment 2: the CHAOTIC PHASE keying

Modulated process is if n time information vector is

Coupling reflection grid sequence vector X _n={ x _{(n, 0)}, x _{(n, 1)}..., x _{(n, 2L)}.The sequence that makes the i node produce is

The modulation signal of i node then

Wherein

J=0,1 ..., 2L.Demodulating process: receiving terminal and transmitting terminal are shared initial value, so transmitting terminal produces identical sequence vector X with receiving terminal.Make received signal Y _n={ y _{(n, 0)}, y _{(n, 1)}..., y _{(n, 2L)}.Then remember signal

I road signal wherein

J=0,1 ..., 2L, b ∈ 1 ,-1}.Utilize said method, by symbolism Y _2L ^bEnumerate the recovery vector under each b situation

With the least mean-square error principle, select to make cost

Minimum sequence vector, and recover n information transmitted sign indicating number b constantly according to the b of this moment _m

Claims (4)

1. one kind based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector, it is characterized in that comprising the steps: that (A1) is next x of chaos system mapping constantly according to n+1 constantly _N+1=H (x _n), utilize s _nDetermine that its n is the inverse mapping of current time chaos constantly

S wherein _nBe n symbolic vector sequence constantly, H () is that extensive coupling reflection grid produces function;

(A2) known reception sequence vector { y _i} _I=0 ^L, and symbol turn to s ' _i} _I=0 ^L, picked at random η is as initial vector, i=1 wherein ..., N represents the lattice point position, and N represents the lattice point size, and η is the traversal interval purpose amount of taking up an official post, and L is an observation vector length;

(A3) at any n constantly,, calculate estimated value based on S ' according to algorithm for estimating based on the symbolic vector sequence N=0,1 ..., n express time step number, wherein S ' is the symbolic vector sequence of observation.

2. according to claim 1 a kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector, it is characterized in that described in steps A 1, being mapped as unimodal map, coupling reflection grid is as follows under the extensive N node unimodal map:

$x_{n+1}^i=(1-\mathrm{\ϵ})f_i\left(x_n^i\right)+\frac{\mathrm{\ϵ}}{2}[f_{i-1}\left(x_n^{i-1}\right)+f_{i+1}\left(x_n^{i+1}\right)]---\left(1\right)$

I=1 wherein ..., N represents the lattice point position, N represents the lattice point size, and n express time step number, ε represents coupling coefficient; Dynamic system f _i: I → I, I=[a, b] for the unimodal map function is a phase space, in n chaos inverse mapping constantly

Above-mentioned coupling reflection grid can extensively be x _N+1=H (x _n), and one dimension chaos x _N+1=f (x _n) be the special case of coupling reflection grid in coupling coefficient ε=0 o'clock.

3. according to claim 2 a kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector, it is characterized in that the unimodal map f of i lattice point _i: I → I, I=[a, b]; If f _iThere is q critical point, then according to critical point

Phase space I is divided into q+1 mutually disjoint subinterval d _k ⁱ, k=0,1 ... q, wherein

And

K ≠ 0, q-1; Set I lattice point n symbol value constantly is as follows:

At n constantly, (1) formula produces symbolic vector And (1) formula is designated as S={s from the symbolic vector sequence that 0 moment iteration produces ₀, s ₁..., s _n...;

Fx _N+1=A ^-1* x _N+1, wherein

The i lattice point (i=1,2...... N) concern constantly at n:

Order

Be the n moment, symbol s ⁱThe traitor's property of each node is given birth to function when known

Then Order

I ^N→ I ^N, then when symbolic vector sequence S was known, the contrary of coupling reflection grid was: Wherein Be the contrary of reflection grid that be coupled.

4. according to claim 1 a kind of based on the dynamic (dynamical) chaotic noise signal estimating method of symbolic vector, it is characterized in that in steps A 2, with received signal vector { y _i} _I=0 ^LAs follows symbol turn to symbolic vector s ' _i} _I=0 ^L:

In n symbolic vector sequence constantly

Then the symbolic vector sequence of observation signal be designated as s ' _i} _I=0 ^L

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