CN103595405A - Phase-locked loop implementation method based on particle filtering - Google Patents

Abstract

The invention relates to a phase-locked loop implementation method based on particle filtering, and belongs to the technical field of communication signal processing. The phase-locked loop implementation method based on the particle filtering has the advantages of being wider in application range compared with a traditional phase-locked loop, and can be applied to nonlinearity and non-Gaussian occasions.

Description

A kind of phase-locked loop implementation method based on particle filter

Technical field

The present invention relates to a kind of phase-locked loop implementation method based on particle filter, belong to signal of communication processing technology field.

Background technology

PHASE-LOCKED LOOP PLL TECHNIQUE is applied to the tracking of airbound target in universe and remote measurement.Phase-locked loop be take the locking phase place of input carrier signal and a kind of carrier wave ring way of realization that frequency is target, yet in conventional phase locked loops, what loop filter adopted is low pass filter, belong to linear unit, can only solve linear problem, adopt in the present invention particle filter to substitute low pass filter, can be so that the range of application of phase-locked loop be more extensive

Particle filter can solve non-linear, and the problem of non-Gaussian Systems, so applied range day by day become the study hotspot of academia.In recent years, particle filter causes that signal is processed and the attention of the communications field gradually.And the present invention is applied to particle filter method to improve in phase-locked loop the performance of phase-locked loop, expand the range of application of phase-locked loop.

Summary of the invention

The object of the invention is can not to be applied to for improving existing phase-locked loop the defect in non-linear non-Gauss's situation, propose a kind of phase-locked loop implementation method based on particle filter, expand the scope that phase-locked loop can be used.

The object of the invention is to be achieved through the following technical solutions.

A kind of phase-locked loop implementation method based on particle filter of the present invention, implementation step is as follows:

Step 1, by input digital signal u _iinput enters phase discriminator, and what another port of phase discriminator was inputted is the signal of upper one phase-locked loop output constantly, is designated as u _o.Result through phase discriminator output is u _d.If initial condition, u _oit can be the signal of the device rough estimate of phase-locked loop front end.

Step 2, generation particle.

According to the probability distribution π setting (it is 0 that π chooses an average conventionally, and the Gaussian that variance is very large distributes, and can determine according to concrete condition, in this case, is generally considered as being uniformly distributed), sampling obtains k particle collection constantly

i=1,2 ..., N, wherein subscript i represents sample sequence number, i=1,2 ..., N, subscript k is symbol period sequence number, k=1,2 ...

Step 3, determine state transition equation and observational equation.

The state equation of particle filter is as the formula (1):

x _k+1=Φx _k+Ψe _k+Γu _k （1）

Wherein, $x_k=\left[\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_k\\ {\stackrel{\·}{\mathrm{\θ}}}_k\end{array}\right],$ General x _krepresent the now state of filter; $\mathrm{\Φ}=\left[\begin{array}{cc}-1& 0\\ a_1& -1\end{array}\right],$ A wherein ₁=T(T is loop filter interval update time); $\mathrm{\Ψ}=\left[\begin{array}{c}{a}_2\\ a_2+a_3\end{array}\right],$ A wherein ₂=ω ³ _nptk(ω _npfor 1.2 times of loop equivalent noise, k is the coefficient of setting according to actual conditions), a ₃=2 ω ² _nptk; $\mathrm{\Γ}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right];$ $u_k=\left[\begin{array}{c}{\stackrel{\·\·}{u}}_k\\ {\stackrel{\·}{u}}_k\end{array}\right]$

with

what represent is the noise producing in loop filtering process.

The observational equation of particle filter is as the formula (2):

$y_{k+1}=\left[\begin{array}{cc}0& 1\end{array}\right]{\hat{x}}_{k+1}+a_4{\hat{e}}_k+v_{k+1}---\left(2\right)$

Wherein, a ₄=2 ω _npk; v _k+1be illustrated in the noise producing in observation process.

Step 4, particle filter initialization

Step 4.1 during according to formula (1) k=0, can be established x ₀=0, all particles in the particle assembly of step 2 li generation are brought in equation (1), obtain N particle;

Step 4.2, N the particle sample value producing during note i=1 is

, wherein the importance weight of each particle is

Step 4.3, is normalized each particle importance weight of step 4.1 output

$w_1^{\left(i\right)}=\frac{w_1^{*\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_1^{*\left(i\right)}}=\frac{1}{N}---\left(3\right)$

Step 4.4, calculates estimated value

with

${\hat{x}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_1^{\left(i\right)}{w}_1^{\left(i\right)}---\left(4\right)$

${\hat{e}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\hat{e}}_1^{\left(i\right)}{w}_1^{\left(i\right)}---\left(5\right)$

Step 5, according to the estimated value obtaining in step 4

with

obtain this output valve y constantly with observation observational equation ₁.

Step 6, the output valve of step 5 is inputed to voltage controlled oscillator, the result using Output rusults as phase-locked loop feeds back to phase discriminator simultaneously.

Step 7, carry out step 1.

Step 8, particle filter:

Step 8.1, repeating step 2, obtain particle assembly, according to formula (1), all particles in particle assembly can be brought in equation (1), obtains N particle;

Step 8.2, calculate k constantly in, the importance weight of each particle;

$w_k^{*\left(i\right)}=w_{k-1}^{*\left(i\right)}\exp [-\frac{1}{{2\mathrm{\σ}}^2}{(y_k^{\left(i\right)}-\left[\begin{array}{cc}0& 1\end{array}\right]x_k^i-k_4{e}_{k-1}^i)}^2]---\left(6\right)$

Step 8.3, weights normalization are carried out weights normalization after each particle weights have calculated;

${\mathrm{\ω}}_k^{\left(i\right)}={\mathrm{\ω}}_k^{*\left(i\right)}/\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_k^{*\left(i\right)}---\left(7\right)$

Step 8.4 is calculated estimated value

with

${\hat{x}}_k=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_k^{\left(i\right)}{w}_k^{\left(i\right)}---\left(8\right)$

${\hat{e}}_k=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\hat{e}}_k^{\left(i\right)}{w}_k^{\left(i\right)}---\left(9\right)$

Step 9, according to the estimated value obtaining in step 8

with

obtain this output valve y constantly with observation observational equation _k, and result is inputed to voltage controlled oscillator, the output using its result as phase-locked loop, and feed back to phase discriminator, and repeated execution of steps 7～step 9.

Beneficial effect

The inventive method, has than conventional phase locked loops range of application advantage more widely, can be applicable to non-linear, non-Gauss's occasion.

Accompanying drawing explanation

Fig. 1 is the impulse response figure of method particle filter part of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the present invention will be further described.

Embodiment

A phase-locked loop implementation method for particle filter, implementation step is as follows:

Step 1, by input digital signal u _i=sin (2 π * 20t) input enters phase discriminator, and what another port of phase discriminator was inputted is the signal of upper one phase-locked loop output constantly, is designated as u _o, as initial time, there is no the output signal u in a upper moment _o, this is can be according to the information of collecting of front end as u _o, we establish u here _o=cos (2 π * 19.5t).Result through phase discriminator output is

Step 2, generation particle.

According to the probability distribution π setting (it is 0 that π chooses an average conventionally, and the Gaussian that variance is very large distributes, and can determine according to concrete condition, and we set variance is here 1000), sampling obtains k particle collection constantly

i=1,2 ..., N, wherein subscript i represents sample sequence number, i=1,2 ..., N, our value of N is 100 here, gets 1024 particles; Subscript k is symbol period sequence number, k=1, and 2 ...

Step 3, determine state transition equation and observational equation.

The state equation of particle filter is as the formula (1):

x _k+1=Φx _k+Ψe _k+Γu _k （1）

Wherein, $x_k=\left[\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_k\\ {\stackrel{\·}{\mathrm{\θ}}}_k\end{array}\right],$ General x _krepresent the now state of filter; $\mathrm{\Φ}=\left[\begin{array}{cc}-1& 0\\ a_1& -1\end{array}\right],$ A wherein ₁=T(T be loop filter interval update time here, we establish this value for 0.01ms); $\mathrm{\Ψ}=\left[\begin{array}{c}{a}_2\\ a_2+a_3\end{array}\right],$ A wherein ₂=ω ³ _nptk(ω _npfor 1.2 times of loop equivalent noise, here we to establish loop equivalent noise bandwidth be 50Hz, ω _np=60Hz, k is the coefficient of setting according to actual conditions, we are made as 1 by k value), a ₃=2 ω ² _nptk; $\mathrm{\Γ}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right];$ $u_k=\left[\begin{array}{c}{\stackrel{\·\·}{u}}_k\\ {\stackrel{\·}{u}}_k\end{array}\right],$

with

what represent is the noise producing in loop filtering process, and we set with

gaussian distributed N(0 all, 0.01 ²).

The observational equation of particle filter is as the formula (2):

$y_{k+1}=\left[\begin{array}{cc}0& 1\end{array}\right]{\hat{x}}_{k+1}+a_4{\hat{e}}_k+v_{k+1}---\left(2\right)$

Wherein, a ₄=2 ω _npk; v _k+1be illustrated in the noise producing in observation process, we set v _k+1gaussian distributed N(0,0.01 ²).

Step 4, particle filter initialization

Step 4.1 during according to formula (1) k=0, can be established x ₀=0, all particles in the particle assembly of step 2 li generation are brought in equation (1), obtain 1024 particles;

Step 4.2,1024 particle sample values that produce during note i=1 are

, wherein the importance weight of each particle is

Step 4.3, is normalized each particle importance weight of step 4.1 output

$w_1^{\left(i\right)}=\frac{w_1^{*\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_1^{*\left(i\right)}}=\frac{1}{1024}---\left(3\right)$

Step 4.4, calculates estimated value with

${\hat{x}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_1^{\left(i\right)}{w}_1^{\left(i\right)}---\left(4\right)$

${\hat{e}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\hat{e}}_1^{\left(i\right)}{w}_1^{\left(i\right)}---\left(5\right)$

Step 5, according to the estimated value obtaining in step 4

with

obtain this output valve constantly with observation observational equation $y_1=\frac{1}{2}\sin (2\mathrm{\π}\×0.5t).$

Step 6, the output valve of step 5 is inputed to voltage controlled oscillator, the result using Output rusults as phase-locked loop feeds back to phase discriminator Output rusults simultaneously.

Step 7, carry out step 1.

Step 8, particle filter.

Step 8.1, repeating step 2, obtain particle assembly, according to formula (1), all particles in particle assembly can be brought in equation (1), obtains 1024 particles;

Step 8.2, calculate k constantly in, the importance weight of each particle;

$w_k^{*\left(i\right)}=w_{k-1}^{*\left(i\right)}\exp [-\frac{1}{{2\mathrm{\σ}}^2}{(y_k^{\left(i\right)}-\left[\begin{array}{cc}0& 1\end{array}\right]x_k^i-k_4{e}_{k-1}^i)}^2]---\left(6\right)$

Step 8.3, weights normalization are carried out weights normalization after each particle weights have calculated;

${\mathrm{\ω}}_k^{\left(i\right)}={\mathrm{\ω}}_k^{*\left(i\right)}/\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_k^{*\left(i\right)}---\left(7\right)$

Step 8.4 is calculated estimated value

with

${\hat{x}}_k=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_k^{\left(i\right)}{w}_k^{\left(i\right)}---\left(8\right)$

${\hat{e}}_k=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\hat{e}}_k^{\left(i\right)}{w}_k^{\left(i\right)}---\left(9\right)$

Step 9, according to the estimated value obtaining in step 8

with

obtain this output valve y constantly with observation observational equation _k, and result is inputed to voltage controlled oscillator, the output using its result as phase-locked loop, and feed back to phase discriminator, and repeated execution of steps 7～step 9, finally can export the signal consistent with input phase difference, result is cos (2 π * 20t).

Claims (1)

1. the phase-locked loop implementation method based on particle filter, is characterized in that step is as follows:

Step 1, by input digital signal u _iinput enters phase discriminator, and what another port of phase discriminator was inputted is the signal of upper one phase-locked loop output constantly, is designated as u _o; Result through phase discriminator output is u _d; If initial condition, u _oit can be the signal of the device rough estimate of phase-locked loop front end;

Step 2, generation particle;

According to the probability distribution π setting (it is 0 that π chooses an average conventionally, and the Gaussian that variance is very large distributes, and can determine according to concrete condition, in this case, is generally considered as being uniformly distributed), sampling obtains k particle collection constantly

i=1,2 ..., N, wherein subscript i represents sample sequence number, i=1,2 ..., N, subscript k is symbol period sequence number, k=1,2,

Step 3, determine state transition equation and observational equation;

The state equation of particle filter is as the formula (1):

x _k+1=Φx _k+Ψe _k+Γu _k （1）

Wherein, $x_k=\left[\begin{array}{c}{\stackrel{\·\·}{\mathrm{\θ}}}_k\\ {\stackrel{\·}{\mathrm{\θ}}}_k\end{array}\right],$ General x _krepresent the now state of filter; $\mathrm{\Φ}=\left[\begin{array}{cc}-1& 0\\ a_1& -1\end{array}\right],$ A wherein ₁=T(T is loop filter interval update time); $\mathrm{\Ψ}=\left[\begin{array}{c}{a}_2\\ a_2+a_3\end{array}\right],$ A wherein ₂=ω ³ _nptk(ω _npfor 1.2 times of loop equivalent noise, k is the coefficient of setting according to actual conditions), a ₃=2 ω ² _nptk; $\mathrm{\Γ}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right];$ $u_k=\left[\begin{array}{c}{\stackrel{\·\·}{u}}_k\\ {\stackrel{\·}{u}}_k\end{array}\right]$

with

what represent is the noise producing in loop filtering process;

The observational equation of particle filter is as the formula (2):

$y_{k+1}=\left[\begin{array}{cc}0& 1\end{array}\right]{\hat{x}}_{k+1}+a_4{\hat{e}}_k+v_{k+1}---\left(2\right)$

Wherein, a ₄=2 ω _npk; v _k+1be illustrated in the noise producing in observation process;

Step 4, particle filter initialization

Step 4.1 during according to formula (1) k=0, can be established x ₀=0, all particles in the particle assembly of step 2 li generation are brought in equation (1), obtain N particle;

Step 4.2, N the particle sample value producing during note i=1 is

, wherein the importance weight of each particle is

Step 4.3, is normalized each particle importance weight of step 4.1 output

$w_1^{\left(i\right)}=\frac{w_1^{*\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_1^{*\left(i\right)}}=\frac{1}{N}---\left(3\right)$

Step 4.4, calculates estimated value

with

${\hat{x}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_1^{\left(i\right)}{w}_1^{\left(i\right)}---\left(4\right)$

${\hat{e}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\hat{e}}_1^{\left(i\right)}{w}_1^{\left(i\right)}---\left(5\right)$

Step 5, according to the estimated value obtaining in step 4

with

obtain this output valve y constantly with observation observational equation ₁;

Step 6, the output valve of step 5 is inputed to voltage controlled oscillator, the result using Output rusults as phase-locked loop feeds back to phase discriminator simultaneously;

Step 7, carry out step 1;

Step 8, particle filter:

Step 8.1, repeating step 2, obtain particle assembly, according to formula (1), all particles in particle assembly can be brought in equation (1), obtains N particle;

Step 8.2, calculate k constantly in, the importance weight of each particle;

$w_k^{*\left(i\right)}=w_{k-1}^{*\left(i\right)}\exp [-\frac{1}{{2\mathrm{\σ}}^2}{(y_k^{\left(i\right)}-\left[\begin{array}{cc}0& 1\end{array}\right]x_k^i-k_4{e}_{k-1}^i)}^2]---\left(6\right)$

Step 8.3, weights normalization are carried out weights normalization after each particle weights have calculated;

${\mathrm{\ω}}_k^{\left(i\right)}={\mathrm{\ω}}_k^{*\left(i\right)}/\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ω}}_k^{*\left(i\right)}---\left(7\right)$

Step 8.4 is calculated estimated value

with

${\hat{x}}_k=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_k^{\left(i\right)}{w}_k^{\left(i\right)}---\left(8\right)$

${\hat{e}}_k=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\hat{e}}_k^{\left(i\right)}{w}_k^{\left(i\right)}---\left(9\right)$

Step 9, according to the estimated value obtaining in step 8

with obtain this output valve y constantly with observation observational equation _k, and result is inputed to voltage controlled oscillator, the output using its result as phase-locked loop, and feed back to phase discriminator, and repeated execution of steps 7～step 9.

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