CN101714963A - Symbolic vector dynamics based self-adaption estimation method of chaotic noise signal - Google Patents

Abstract

The invention discloses a symbolic vector dynamics based self-adaption estimation method of a chaotic noise signal, comprising the following steps of: (A1) mapping xn+1=H(xn) according to a n+1 moment (next moment) chaotic system, and determining chaotic mapping by sn; (A2) knowingly receiving a vector sequence (yi)i=0L, and signifying into (s'i)i=0L, and randomly selecting Eta as an initial vector rxL; (A3) selecting minimum rx''s as an estimate value rxl-1 under the condition of various symbolic vectors s; and (A4) repeating the step 1 and the step 2, sequentially solving for rxL-2 and rxL-2 to rx1, wherein the rx1 is the estimate value x'1. The invention has the advantages of fast analysis and high accuracy.

Description

Based on the dynamic (dynamical) self-adaption estimation method of chaotic noise signal 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 " Estimation of Coupled Map Lattices Using Symbolic Vector Dynamics " (KaiWang, Wenjiang Pei, Haishan Xia, Yiu-ming Cheung, Physics Letters A, Accecpt) 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, by comparing by distinct symbols s ' _iProduce follow-up vectorial rx _I-1With observation signal y _I-1Come self-adapting correction observation symbolic vector sequence, and then propose one based on the symbolic vector dynamics initial value algorithm for estimating that has from the error correction function.

Summary of the invention

The present invention seeks at the defective that prior art exists provide a kind of be applicable to chaos system the noise cancellation signal method of estimation arranged, this method utilizes the chaos symbol sebolic addressing with the one-to-one relationship between actual power sequence, by relatively by distinct symbols s ' _iProduce follow-up vectorial rx _I-1With observation signal y _I-1Come self-adapting correction observation symbolic vector sequence, and then observation sequence is estimated.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 based on the dynamic (dynamical) self-adaption estimation method of chaotic noise signal 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 its chaos inverse mapping

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 rx _L, wherein η is the traversal interval purpose amount of taking up an official post, L is an observation vector length;

(A3) according under various symbolic vector s situations

And select to make

Minimum rx " _sAs estimated value rx _L-1, wherein

I=1 ..., N represents the lattice point position, N represents lattice point size, rx " _sBe the estimated value of coupling reflection grid under distinct symbols vector situation, vector x=[x arbitrarily ₁, x ₂..., x _N] ^T, y=[y ₁, y ₂..., y _N] ^T, symbol T represents that vector changes order, function d () is defined as follows:

$d(x,y)={\left|\right|x-y\left|\right|}_2={\left({\mathrm{\Σ}}_{i=1}^N{(x_i-y_i)}^2\right)}^{1/2}.$

(A4) repeating step 1～step 2 is obtained rx successively _L-2, rx _L-2..., rx ₁, rx wherein ₁Be estimated value x ' ₁

Because the dynamic (dynamical) algorithm of symbolic vector pays close attention to noise W more to the influence between acknowledge(ment) signal Y location, rather than the size of W itself, so has higher noiseproof feature.In fact, in big signal to noise ratio snr situation, only otherwise influence the symbol of received signal, these noises all will be left in the basket so, and this is just feasible can work under lower state of signal-to-noise based on symbolic vector dynamics method of estimation.

Description of drawings

Fig. 1 multi-user's modulation and demodulation of the present invention algorithm block diagram.

Embodiment

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

As shown in Figure 1, the present invention includes following steps:

(A1) according to chaos system type x _N+1=H (x _n), utilize s _nDetermine its chaos inverse mapping S wherein _nBe n symbolic vector sequence constantly.

(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 rx _L

(A3) according to enumerating respectively under various symbolic vector s situations

And select to make

Minimum rx " _sAs estimated value rx _L-1, wherein

$d(x,y)={\left|\right|x-y\left|\right|}_2={\left({\mathrm{\Σ}}_{i=1}^N{(x_i-y_i)}^2\right)}^{1/2}.$

(A4) repeating step 1～step 2 is obtained rx successively _L-2, rx _L-2..., rx ₁Rx wherein ₁Be estimated value x ' ₁In steps A 1, we consider that 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] be the unimodal map function.At n constantly, note Above-mentioned coupling reflection grid can extensively be x _N+1=H (x _n), and one dimension chaos x _N+1=f (x _n) can regard the simplest special case of coupling reflection grid in coupling coefficient ε=0 o'clock as.

Consider the unimodal map f of i lattice point _i: I → I, I=[a, b].Utilize threshold value x _c ⁱWith I=[a, b] be divided into two disjoint segments, make at threshold value x _c ⁱBoth sides mapping f _iDull.The symbol value that defines i lattice point is as follows:

$s_n^i=\left\{\begin{array}{ccc}-1& \mathrm{if}& x_n^i<x_c^i\\ 1& \mathrm{if}& x_n^i\&GreaterEqual;x_c^i\end{array}\right.---\left(2\right)$

Make fx _N+1=A ^-1* x _N+1, wherein

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

Symbol s as if this lattice point this moment _n ⁱKnown, because mapping f _iAt threshold value x _c ⁱThe both sides dullness, therefore

Unique definite.Order

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

Then

Therefore work as s _nWhen known,

A ^-1(x _N+1)=x _nUnique definite.Order

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

(B1) known symbol sequence vector S={s ₀, s ₁..., s _n..., we can be by the inverse function number determining the inverse function of coupling reflection grid, progressively invert to obtain a series of dullnesses:

Therefore we can we can estimate actual power track X by S by the following method:

Step 1: optional phase space I ^NGo up vectorial η as initial vector;

Step 2: according to symbolic vector sequence S={s ₀, s ₁..., s _L, by coupling reflection grid inverse iteration process, try to achieve based on the symbolic vector sequence X then " (0|L+1) is the estimated value of initial vector x (0).

(B2) the supposition observation signal is defined as follows: y _n=x _n+ w _n, wherein, N dimensional vector sequence X={ x ₀, x ₁..., x _n... the power track that produces for N node coupling reflection grid iteration, W={w ₀, w ₁..., w _n... be separate N road white Gaussian noise, Y={y ₀, y ₁..., y _n... it is received signal.According to signal estimation approach described in (B1), utilize threshold value x _c ⁱObservation signal Y symbol is turned to symbolic vector sequence S '=s ' ₀, s ' ₁..., s ' _n...Can calculate estimated value by observation symbolic vector sequence S ' based on S ' And then obtain estimating estimate vector sequence RX '.

(B3) estimate requirement according to signal, vectorial estimated sequence X ' need satisfy:

Condition 1: the estimate vector sequence X ' be to estimate under the condition near observation sequence Y at certain;

Condition 2: estimate vector sequence X ' estimate under the condition near real system x at certain _N+1=H (x _n) actual sequence that can produce.

Consider the estimated value RX ' that (B2) given noise signal estimates, with based on mean square error minimized have the noise cancellation signal algorithm for estimating select to satisfy cost function: E (|| X '-Y|| ²) minimum estimated sequence RX ' difference, based on the moving Fang Xue of symbolic vector have the noise cancellation signal algorithm for estimating selected to satisfy cost function: E (|| S _{X '}-S _Y|| ²) minimized estimate vector sequence RX ', wherein S _{X '}And S _YThe symbolic vector sequence of representing sequence RX ' and Y respectively.This algorithm for estimating has following some benefit, one, because sequence vector RX ' is by the generation of coupling reflection grid inverse function iteration, so estimate vector sequence RX ' must be real system x _N+1=H (x _n) in the actual path that produces one.Its two, according to condition 2 as can be known, if observation symbol sebolic addressing identical with the actual symbol sequence:

So

Its three since estimated value rx ' (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 rx ' _N+k} _K=1-L ⁰Precision.Thereby avoided the index of evaluated error to increase.

(B4) strengthen the estimated performance of (B2) given noise signal algorithm for estimating, will reduce the S ' error rate of observation symbolic vector sequence after all exactly as far as possible.Consideration based on the least mean-square error principle minimize cost function E (|| RX '-Y|| ²).When n observes symbol sebolic addressing error code occur constantly, studies show that the least mean-square error estimation technique can only estimate for true sequence { x _i} _I=0 ^∞The poorest, and for receiving sequence { y _i} _I=0 ^∞Best estimation is separated:

It is the effectively error correction of mean square error minimization principle.And the least mean-square error algorithm for estimating can only provide the optimal solution on the statistical significance at most, rather than the optimal solution of real system generation.

We suppose observation sequence { y _N-i} _I=-∞ ^∞And if only if, and error code has appearred in n constantly.From the angle that least mean-square error is estimated, and if only if rx _nBe x _nOr-x _nThe time, $\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{({x^{\&prime;}}_{n+i}-y_{n+i})}^2$ The value minimum.And at n constantly, work as rx _n=-x _nThe time, (x ' _n-y _n) ²Minimum; At n-i constantly, work as rx _n=x _nThe time, $\underset{i=-N}{\overset{-1}{\mathrm{\&Sigma;}}}{({x^{\&prime;}}_{n+i}-y_{n+i})}^2$ The value minimum.Just because of at n constantly, the estimator will be because of the evaluated error that error code caused |-x _n-y _n|, treated as observation error | y _n-x _n|=| w _n|, make mean square error minimize effectively error correction.Therefore in A3, at first define

Judging symbolic vector s ' _iThe time, not with current vectorial y _iAs basis for estimation, only be used in distinct symbols s ' _iProduce follow-up vectorial rx _I-1And y _I-1Relatively as basis for estimation.

In A4, if chaotic maps f has q critical point, the above-mentioned inferior f of 2L (q+1) that needs ^-1Computing can be tried to achieve estimated value x ' ₁, corresponding estimated sequence x ' _i} _I=0 ^M-1Need M f of 2L (q+1) ^-1Computing.When coupling reflection grid that N f coupling forms, calculate as can be known the estimate vector sequence x ' _i} _I=0 ^M-1Need 2L (q+1) ^NM H ^-1Computing.

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.

Example 1: 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.

Example 2: 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

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

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) self-adaption estimation method of chaotic noise signal 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 its chaos inverse mapping

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 rx _L, wherein η is the traversal interval purpose amount of taking up an official post, L is an observation vector length;

(A3) according under various symbolic vector s situations And select to make

Minimum rx " _sAs estimated value rx _L-1, wherein I=1 ..., N represents the lattice point position, N represents lattice point size, rx " _sBe the estimated value of coupling reflection grid under distinct symbols vector situation, vector x=[x arbitrarily ₁, x ₂..., x _N] ^T, y=[y ₁, y ₂..., y _N] ^T, symbol T represents that vector changes order, function d () is defined as follows:

$d(x,y)={\left|\right|x-y\left|\right|}_2={\left({\mathrm{\&Sigma;}}_{i=1}^N{(x_i-y_i)}^2\right)}^{1/2}.$

(A4) repeating step 1～step 2 is obtained rx successively _L-2, rx _L-2..., rx ₁, rx wherein ₁Be estimated value x ' ₁

2. according to claim 1 based on the dynamic (dynamical) self-adaption estimation method of chaotic noise signal 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:

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

I=1 wherein ..., N represents the lattice point position, N represents the lattice point size, n express time step number, ε represents coupling coefficient; Dynamic system f _i: I → I, I=[a, b] be the unimodal map function; At n constantly, note

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

Consider the unimodal map f of i lattice point _i: I → I, I=[a, b].Utilize threshold value x _c ⁱWith I=[a, b] be divided into two disjoint segments, make at threshold value x _c ⁱBoth sides mapping f _iDull.The symbol value that defines i lattice point is as follows:

$s_n^i=\left\{\begin{array}{ccc}-1& \mathrm{if}& x_n^i<x_c^i\\ 1& \mathrm{if}& x_n^i\&GreaterEqual;x_c^i\end{array}\right.---\left(2\right)$

Make fx _N+1=A ^-1* x _N+1, wherein

Consider 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:

Be the contrary of reflection grid that be coupled.

3. according to claim 2 based on the dynamic (dynamical) self-adaption estimation method of chaotic noise signal of symbolic vector, it is characterized in that we can estimate actual power track X by symbolic vector sequence S:

Step 1: optional phase space I ^NGo up vectorial η as initial vector;

Step 2: according to symbolic vector sequence S={s ₀, s ₁..., s _L, by coupling reflection grid inverse iteration process, try to achieve based on the symbolic vector sequence

X then " (0|L+1) is the estimated value of initial vector x (0).

Observation signal is defined as follows: y _n=x _n+ w _n, wherein, N dimensional vector sequence X={ x ₀, x ₁..., x _n... } and the power track that produces for N node coupling reflection grid iteration, W={w ₀, w ₁..., w _n... } and be separate N road white Gaussian noise, Y={y ₀, y ₁..., y _n... } and be received signal, utilize threshold value x _c ⁱObservation signal Y symbol is turned to symbolic vector sequence S '=s ' ₀, s ' ₁..., s ' _n...; Can calculate estimated value by observation symbolic vector sequence S ' based on S ' And then obtain estimating estimate vector sequence RX ';

Estimate requirement according to signal, vectorial estimated sequence X ' need satisfy:

Condition 1: the estimate vector sequence X ' be to estimate under the condition near observation sequence Y;

Condition 2: the estimate vector sequence X ' be to estimate under the condition near real system x _N+1=H (x _n) actual sequence that can produce.

4. according to claim 1 based on the dynamic (dynamical) self-adaption estimation method of chaotic noise signal of symbolic vector, it is characterized in that: in steps A 3, definition

Judging symbolic vector s ' _iThe time, be used in distinct symbols s ' _iProduce follow-up vectorial rx _I-1And y _I-1Relatively as basis for estimation.