CN105180971A - Noise variance measurement method based on alpha-beta-gamma filtering and second-order mutual difference - Google Patents

Abstract

The invention discloses a noise variance measurement method based on alpha-beta-gamma filtering and second-order mutual difference. The noise variance measurement method measures pseudo redundancy of a measurement signal through an alpha-beta-gamma filtering structure, selects a slowly-varying or linear-varying part in the measurement signal by adopting a data selection algorithm, and calculates to obtain noise variance by adopting a second-order mutual difference method. The noise variance measurement method can be used for estimating noise variance of any signal in real time, and can effectively improve the filtering precision in Kalman filtering.

Description

A kind of noise variance measuring method of dividing based on alpha-beta-γ filtering and second order mutual deviation

Technical field

The present invention relates to a kind of noise variance measuring method, can measuring-signal noise variance exactly.In Kalman filter application, can effective adaptive measuring noise variance matrix, improve filtering accuracy, suppression filtering divergence.

Background technology

In Practical Project, the scarcity of prior imformation and measuring method causes the statistical property of noise to obtain.For ensureing precision and the convergence of Kalman filter, method the most common in engineering is by adaptive method, obtains the estimation to noise statistics, reaches raising filtering accuracy, suppresses the object of filtering divergence.

At present, the adaptable Kalman filter of domestic and international design regulates measurement noises variance matrix mainly through newly breath or residual error, mainly contains Sage-Husa method, robust self-adaptation Sage filtering, based on the Kalman filter algorithm of fuzzy self-adaption, mobile fenestration etc.These methods effectively cannot solve the filtering divergence problem under filtering lag situation.For overcoming this problem, also researching and proposing and directly signal variance having been measured, mainly contained the method for estimation of adaptive approach based on envelope and the mutual differential pair noise variance of second order.And the former can only for white Gaussian noise, the latter needs redundant measurement condition.

When there being two kinds of heterogeneitys to measure to same measurer, the method computation and measurement noise variance that second order mutual deviation can be used to divide, and under single measuring condition, do not meet the redundant measurement condition that second order mutual deviation divides, cannot noise variance be recorded.

Summary of the invention

The object of the invention is to solve the problem, overcome the deficiency that second order mutual deviation point condition is excessively strong, provide a kind of noise variance measuring method of dividing based on alpha-beta-γ filtering and second order mutual deviation, second order mutual deviation is divided and is generalized in the measurement of single system noise variance, have more universal significance.By the present invention, the noise variance of single system can be measured exactly in real time, in Kalman filter application, can filtering accuracy be improved, suppress filtering divergence.

A kind of noise variance measuring method of dividing based on alpha-beta-γ filtering and second order mutual deviation of the present invention, is realized by following steps:

Step one: utilize the data under typical service condition to carry out offline design to alpha-beta-γ wave filter.Utilize the method for envelope to try to achieve raw measured signal noise amplitude and filter output noise amplitude, by adjusting the parameter h of wave filter, the noise amplitude that smooth type alpha-beta-γ wave filter is exported is 1/10 ~ 1/20 of raw measured signal noise amplitude.The h value of getting following-up type alpha-beta-γ wave filter is 10 ~ 100 times of smooth type;

Step 2: after constructing suitable smooth type and following-up type alpha-beta-γ wave filter, can measure the noise variance of the live signal of sensor collection.The signal of sensor Real-time Collection is raw measured signal, uses the smooth type alpha-beta-γ wave filter designed and following-up type alpha-beta-γ wave filter is online respectively carries out filtering to it, is length of window, by sequence segment with m;

Step 3: usage data selection algorithm screens exporting in following-up type alpha-beta-γ wave filter and smooth type alpha-beta-γ filtering window, selects tempolabile signal or linear change signal.Tempolabile signal or linear signal may be used for calculating noise variance;

Step 4: the gradual or former measuring-signal of linear change part that step 3 filters out, exports with the smooth type alpha-beta-γ wave filter in corresponding moment the virtual redundancy measurement formed and carries out the mutual calculus of differences of second order, obtain noise variance.

By above method, construct the pseudo-redundant measurement sequence for raw measured signal, in gradual data segment, cancellation actual value trend is divided by mutual deviation, by the system deviation of self difference cancellation relative to actual value, obtain the sequence reflecting raw measured signal measurement noises, realize the real-time estimation of signal noise.In Kalman filter, effectively can improve filtering accuracy.

The invention has the advantages that:

(1) the present invention is by using the redundant measurement of alpha-beta-γ filter design raw measured signal, second order mutual deviation is divided and has been generalized to single measurement system noise variance evaluation from being applicable to dual system measurement, reduce the applicable elements that second order mutual deviation divides noise statistics to estimate, have more universal significance;

(2) the inventive method is without the need to the Changing Pattern of known signal;

(3) the inventive method is by effective selection of data, relatively existing adaptive filter algorithm, improves the accuracy that noise statistics is estimated;

(4) the inventive method is simple, calculates accurately, is easy to realize.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the inventive method;

Fig. 2 is the original signal actual value that the present invention emulates;

Fig. 3 is the measurement signal value that the present invention emulates;

Fig. 4 is the smooth type wave filter output of certain emulation and the result of data selection;

Fig. 5 is that the noise variance using Monte Carlo method to obtain measures relative error distribution.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

The present invention is a kind of noise variance measuring method of dividing based on alpha-beta-γ filtering and second order mutual deviation, and flow process, as schemed as indicated with 1, comprises following step:

Step one: utilize the data under typical service condition to carry out offline design to alpha-beta-γ wave filter.Utilize the method for envelope to try to achieve raw measured signal noise amplitude and filter output noise amplitude, by adjusting the parameter h of wave filter, the noise amplitude that smooth type alpha-beta-γ wave filter is exported is 1/10 ~ 1/20 of raw measured signal noise amplitude.The h value of getting following-up type alpha-beta-γ wave filter is 10 ~ 100 times of smooth type:

Specifically comprise:

A. alpha-beta-γ filter model is set up

$\stackrel{\·}{X}\left(t\right)=A\left(t\right)X\left(t\right)+F\left(t\right)\·W\left(t\right)$

Z(t)＝H(t)X(t)+V(t)

Wherein: $X\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]$ For the quantity of state of reflected signal change, x ₁(t), x ₂(t), x ₃t () is element in quantity of state.W (t) is system noise, Z ( _t) be observed reading, V (t) is observation noise. $A\left(t\right)=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$ For state matrix, $F\left(t\right)=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]$ For noise inputs matrix, H (t)=[100] are observing matrix.

In Kalman filter formula:

$\stackrel{\·}{\hat{X}}\left(t\right|t)=A\left(t\right)\hat{X}\left(t\right|t)+K\left(t\right)(Z\left(t\right)-H\left(t\right)\hat{X}\left(t\right|t))$

K(t)＝P(t|t)H ^T(t)R ^-1(t)

$\stackrel{\·}{P}\left(t\right|t)=A\left(t\right)P\left(t\right|t)+P\left(t\right|t)A^T\left(t\right)-P\left(t\right|t)H^T\left(t\right)R^{-1}\left(t\right)H\left(t\right)P\left(t\right|t)+F\left(t\right)Q\left(t\right)F^{-1}\left(t\right)$

Wherein: for the state estimation of t, for the state estimation derivative of t, R (t) is observation noise covariance matrix, and Q (t) is system noise covariance battle array, and P (t|t) is filter noise variance matrix, for the derivative of filter noise variance matrix, K (t) is gain matrix.

When filtering reaches stable, the P (t|t) in Kalman filter does not change, and K (t) keeps definite value K:

$K=\left[\begin{array}{c}2\sqrt[3]{h}\\ 2\sqrt[3]{h^2}\\ h\end{array}\right]$

$h=\frac{q}{r}$

Wherein: q is system noise variance, r is measurement noises variance, and h is system noise variance and the ratio of state-noise variance, is gain matrix K parameter.

B. appoint and get h value, use alpha-beta-γ wave filter to follow the tracks of raw measured signal, build the alpha-beta-γ Filtering Model of discretize:

X(k+1)＝Φ·X(k)+W

Z(k+1)＝H·X(k+1)+V

Wherein: X (k+1), Z (k+1) are respectively state value and the observed reading in k+1 moment, and Φ is state-transition matrix, and W is system noise matrix, and H is observing matrix, and V is observation noise matrix, and value is respectively:

$\mathrm{\Φ}=\left[\begin{array}{ccc}1& T& \\ & 1& T\\ & & 1\end{array}\right]$

$W=\left[\begin{array}{c}0\\ 0\\ w\end{array}\right]$

H＝[100]

V＝v

Wherein, T is sampling interval, the white noise of w to be noise variance be q, the white noise of v to be noise variance be r;

Alpha-beta-γ filtering is calculated by following formula:

$\hat{X}\left(k\right)=\mathrm{\Φ}(k,k-1)\hat{X}(k-1)+K(Z\left(k\right)-H\mathrm{\Φ}(k,k-1)\hat{X}(k-1))$

Wherein: for the state estimation in k moment.

C. envelope identification is carried out to smooth type alpha-beta-γ filter output value, obtains the noise amplitude of wave filter | V ₁|:

$\left|V_1\right|=\frac{\Σ({\mathrm{upperEnv}}_{1k}-{\mathrm{lowerEnv}}_{1k})}{2m_1}$

Wherein: m ₁for the data bulk of whole raw measured signal, upperEnv _1kand lowerEnv _1kfor wave filter is at the upper and lower envelope point of k moment point;

D. Envelope Analysis is carried out to whole raw measured signal, obtains the noise amplitude of raw measured signal | V ₂|:

$\left|V_2\right|=\frac{\Σ({\mathrm{upperEnv}}_{2k}-{\mathrm{lowerEnv}}_{2k})}{2m_1}$

Wherein: upperEnv _2kand lowerEnv _2kfor raw measured signal is at the upper and lower envelope point of k moment point;

E. adjust wave filter h value, repeat B and C two step, until filter noise amplitude | V ₁| with raw measured signal noise amplitude | V ₂| meet:

$\frac{1}{10}\≤\frac{\left|V_1\right|}{\left|V_2\right|}\≤\frac{1}{20}$

The h value of F. getting now is the h value h of smooth type alpha-beta-γ wave filter _s, get h _s10 ~ 100 times be the alpha-beta-γ wave filter h value h of following-up type _t;

Step 2: after constructing suitable smooth type and following-up type alpha-beta-γ wave filter, can measure the noise variance of the live signal of sensor collection.The signal of sensor Real-time Collection is raw measured signal, uses the smooth type alpha-beta-γ wave filter designed and following-up type alpha-beta-γ wave filter is online respectively carries out filtering to it, obtains smooth type filtered sequence with following-up type filtered sequence be length of window with m, in sequence with middle slip respectively obtains data segment, the tract started with the k moment with for:

${\hat{X}}_S{|}_k^{k+m}={\left[\begin{array}{ccc}{\hat{x}}_S\left(k\right)& {\hat{x}}_S(k+1)...& {\hat{x}}_S(k+m)\end{array}\right]}^T$

${\hat{X}}_T{|}_k^{k+m}={\left[\begin{array}{ccc}{\hat{x}}_T\left(k\right)& {\hat{x}}_T(k+1)...& {\hat{x}}_T(k+m)\end{array}\right]}^T$

Wherein: with the smooth type wave filter and the following-up type wave filter that are respectively the k moment export.

Step 3: usage data selection algorithm screens exporting in following-up type, smooth type alpha-beta-γ filtering window, selects tempolabile signal or linear change signal.Tempolabile signal or linear signal may be used for calculating noise variance;

Channel selection algorithm filters out detailed process that is gradual or linear change data:

A., in gradual or linear course, signal approximation is in linearly.Set up linear least-squares model:

${\hat{X}}_S{|}_k^{k+m}=H_l\left[\begin{array}{c}{a}_S\left(k\right)\\ b_S\left(k\right)\end{array}\right]$

${\hat{X}}_T{|}_k^{k+m}=H_l\left[\begin{array}{c}{a}_T\left(k\right)\\ b_T\left(k\right)\end{array}\right]$

$H_l=\left[\begin{array}{cc}1& 1\\ 2& 1\\ .& .\\ .& .\\ .& .\\ m& 1\end{array}\right]$

Wherein: H _lfor least square observing matrix, a _s(k), b _s(k) and a _t(k), b _tk () is the valuation of a, b of fitting a straight line x (k+i)=ai+b.

B. least-squares estimation a is used _s(k), b _s(k) and a _t(k), b _t(k):

$\left[\begin{array}{c}{a}_S\left(k\right)\\ b_S\left(k\right)\end{array}\right]={\left(H_l^T{H}_l\right)}^{-1}{H_l}^T{\hat{X}}_S{|}_k^{k+m}$

$\left[\begin{array}{c}{a}_T\left(k\right)\\ b_T\left(k\right)\end{array}\right]={\left(H_l^T{H}_l\right)}^{-1}{H_l}^T{\hat{X}}_T{|}_k^{k+m}$

C. data in window are temporally divided into two sections, front and back, centered by fitting a straight line, in adding up every section respectively the A of average amplitude up and down ₁, A ₂, A ₃, A ₄:

$A_1=mean\{{\hat{x}}_S(k+i)-a_S\left(k\right)i-b_S|{\hat{x}}_S(k+i)\≥a_S\left(k\right)i-b_S,i\∈(0,m/2)\}$

$A_2=mean\{{\hat{x}}_S(k+i)-a_S\left(k\right)i-b_S|{\hat{x}}_S(k+i)<a_S\left(k\right)i-b_S,i\&Element;(0,m/2)\}$

$A_3=mean\{{\hat{x}}_S(k+i)-a_S\left(k\right)i-b_S|{\hat{x}}_S(k+i)\&GreaterEqual;a_S\left(k\right)i-b_S,i\&Element;\&lsqb;m/2,m\left)\right\}$

$A_4=mean\{{\hat{x}}_S(k+i)-a_S\left(k\right)i-b_S|{\hat{x}}_S(k+i)<a_S\left(k\right)i-b_S,i\&Element;\&lsqb;m/2,m\left)\right\}$

Wherein: mean represents the function of averaging.

D. the absolute value of angle theta between two fitting a straight lines is calculated | θ |:

|θ|＝|arctan(a _S(k))-arctan(a _T(k))|

E. A is judged ₁, A ₂, A ₃, A ₄whether one angle between two fitting a straight lines of making peace is enough little:

$\left\{\begin{array}{c}\left|\frac{A_1}{A_2}\right|,\left|\frac{A_1}{A_3}\right|,\left|\frac{A_3}{A_4}\right|\&Element;(1-th\_amp,1+th\_amp)\\ \left|\mathrm{\&theta;}\right|<th\_ang\end{array}\right.$

Wherein: th_amp and th_ang is respectively the threshold value of amplitude and angle.

Work as A ₁, A ₂, A ₃, A ₄the ratio of absolute value is within scope (1-th_amp, 1+th_amp) and the absolute value of fitting a straight line angle | θ | when being less than threshold value th_ang, think A ₁, A ₂, A ₃, A ₄consistent and between fitting a straight line angle less, then this data segment is gradual or the data segment of linear course, may be used for calculating noise variance.Otherwise data segment, for become process soon, can not be used for calculating noise variance.

Step 4: the gradual or former measuring-signal of linear change part that step 3 filters out, exports with the smooth type alpha-beta-γ wave filter in corresponding moment and carries out the mutual calculus of differences of second order, obtain noise variance.

A. establish and start with moment k, length is the gradual or linear former measuring-signal data segment of m and its smooth type alpha-beta-γ wave filter exports by its respectively self difference obtain:

Δx(k)＝x(k+1)-x(k)

$\mathrm{\&Delta;}{\hat{x}}_S\left(k\right)={\hat{x}}_S\left(k+1\right)-{\hat{x}}_S\left(k\right)$

Wherein, x (k) is signal k moment measured value, for smooth type wave filter is in the output valve in k moment, Δ x (k) and be respectively their autodyne score value, and form self difference sequence with

B. the self difference sequence will obtained with carry out mutual deviation to divide, try to achieve raw measured signal data segment in window noise variance

$Var\left(X{|}_k^{k+m}k\right)=\frac{1}{2}(\mathrm{\&Delta;}X{|}_k^{k+m}k-\mathrm{\&Delta;}{\hat{X}}_S{|}_k^{k+m}){(\mathrm{\&Delta;}X{|}_k^{k+m}-\mathrm{\&Delta;}{\hat{X}}_S|-\mathrm{\&Delta;}{\hat{X}}_S{|}_k^{k+m})}^T$

C. calculate the noise variance of raw measured signal, and the data calculated are weighted obtain:

$\{\begin{array}{c}{d}_i=\left(1-b\right)/\left(1-b^{i+1}\right)\\ Var{\left(X\right)}_i=\left(1-d_i\right)Var\left(X{|}_k^{k+m}\right)+d_{i}Var{\left(X\right)}_{i-1}\end{array}\left(0<b<1\right)$

Wherein: X is raw measured signal sequence, b is forgetting factor, d _ifor weighting coefficient, b ⁱ⁺¹the i+1 power of forgetting factor b, Var (X) _iit is the raw measured signal noise variance calculated for i-th time.

Pass through said method, the virtual redundancy of structure raw measured signal measures sequence, select gradual or linear course wherein, by cancellation actual value and the relative variation relative to actual value, obtain the sequence reflecting raw measured signal noise, finally calculate the variance of raw measured signal noise.This variance may be used for Adaptive Kalman Filtering Algorithm, improves arithmetic accuracy.

In example:

Get signal shown in Fig. 2 to emulate, to add in signal standard deviation be the zero mean Gaussian white noise of 5 as measuring-signal, as shown in Figure 3.

According to above-mentioned steps, as shown in Figure 4, in dotted line frame, data are the tempolabile signal selected to this Case Simulation.Use Monte Carlo method emulates the relative error obtained and distributes as shown in Figure 5.As can be seen from Figure 5, method calculating noise variance error of the present invention is within 20%, and the measuring accuracy of 90.2% is within 10%.Can find out, method of the present invention has higher computational accuracy.

The present invention is on the basis that second order mutual deviation divides, use alpha-beta-γ filter design redundant measurement, by screening data and alpha-beta-γ wave filter, to reach the object meeting second order mutual deviation point condition, the method that final utilization second order mutual deviation divides calculates the variance of measurement noises.

Claims (1)

1., based on the noise variance measuring method that alpha-beta-γ filtering and second order mutual deviation divide, comprise following step:

Step one: offline design is carried out to alpha-beta-γ wave filter, the method of envelope is utilized to try to achieve raw measured signal noise amplitude and filter output noise amplitude, by adjusting the parameter h of wave filter, the noise amplitude that smooth type alpha-beta-γ wave filter is exported is 1/10 ~ 1/20 of original signal noise amplitude, and the h value of getting following-up type alpha-beta-γ wave filter is 10 ~ 100 times of smooth type;

Specifically comprise:

A. alpha-beta-γ filter model is set up

$\stackrel{\&CenterDot;}{X}\left(t\right)=A\left(t\right)X\left(t\right)+F\left(t\right)\&CenterDot;W\left(t\right)$

Z(t)＝H(t)X(t)+V(t)

Wherein: $X\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ x_3\left(t\right)\end{array}\right]$ For the quantity of state of reflected signal change, x ₁(t), x ₂(t), x ₃t () is element in quantity of state; W (t) is system noise, and Z (t) is observed reading, and V (t) is observation noise, $A\left(t\right)=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$ For state matrix, $F\left(t\right)=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]$ For noise inputs matrix, H (t)=[100] are observing matrix;

In Kalman filter formula:

$\stackrel{\&CenterDot;}{\hat{X}}\left(t\right|t)=A\left(t\right)\hat{X}\left(t\right|t)+K\left(t\right)\left(Z\right(t)-H(t\left)\hat{X}\right(t|t\left)\right)$

K(t)＝P(t|t)H ^T(t)R ^-1(t)

$\stackrel{\&CenterDot;}{P}\left(t\right|t)=A\left(t\right)P\left(t\right|t)+P\left(t\right|t)A^T\left(t\right)-P\left(t\right|t)H^T\left(t\right)R^{-1}\left(t\right)H\left(t\right)P\left(t\right|t)+F\left(t\right)Q\left(t\right)F^{-1}\left(t\right)$

Wherein: for the state estimation of t, for the state estimation derivative of t, R (t) is observation noise covariance matrix, and Q (t) is system noise covariance battle array, and P (t|t) is filter noise variance matrix, for the derivative of filter noise variance matrix, K (t) is gain matrix;

When filtering reaches stable, K (t) keeps definite value K:

$K=\left[\begin{array}{c}2\sqrt[3]{h}\\ 2\sqrt[3]{h^2}\\ h\end{array}\right]$

$h=\frac{q}{r}$

Wherein: q is system noise variance, r is measurement noises variance, and h is system noise variance and the ratio of state-noise variance, is gain matrix K parameter;

B. appoint and get h value, use alpha-beta-γ wave filter to follow the tracks of signal, build the alpha-beta-γ Filtering Model of discretize:

X(k+1)＝Φ·X(k)+W

Z(k+1)＝H·X(k+1)+V

Wherein: X (k+1), Z (k+1) are respectively state value and the observed reading in k+1 moment, and Φ is state-transition matrix, and W is system noise matrix, and H is observing matrix, and V is observation noise matrix, and value is respectively:

$\mathrm{\&Phi;}=\left[\begin{array}{ccc}1& T& \\ & 1& T\\ & & 1\end{array}\right]$

$W=\left[\begin{array}{c}0\\ 0\\ w\end{array}\right]$

H＝[100]

V＝v

Wherein, T is sampling interval, the white noise of w to be noise variance be q, the white noise of v to be noise variance be r;

Calculate alpha-beta-γ filtering:

$\hat{X}\left(k\right)=\mathrm{\&Phi;}(k,k-1)\hat{X}(k-1)+K\left(Z\right(k)-H\mathrm{\&Phi;}(k,k-1\left)\hat{X}\right(k-1\left)\right)$

Wherein: for the state estimation in k moment;

C. envelope identification is carried out to smooth type alpha-beta-γ filter output value, obtains the noise amplitude of wave filter | V ₁|:

$\left|V_1\right|=\frac{\mathrm{\&Sigma;}({\mathrm{upperEnv}}_{1k}-{\mathrm{lowerEnv}}_{1k})}{2m_1}$

Wherein: m ₁for the data bulk of whole raw measured signal, upperEnv _1kand lowerEnv _1kfor wave filter is at the upper and lower envelope point of k moment point;

D. Envelope Analysis is carried out to whole raw measured signal, obtains the noise amplitude of original signal | V ₂|:

$\left|V_2\right|=\frac{\mathrm{\&Sigma;}({\mathrm{upperEnv}}_{2k}-{\mathrm{lowerEnv}}_{2k})}{2m_1}$

Wherein: upperEnv _2kand lowerEnv _2kfor raw measured signal is at the upper and lower envelope point of k moment point;

E. adjust wave filter h value, repeat B and C two step, until filter noise amplitude | V ₁| with raw measured signal noise amplitude | V ₂| meet:

$\frac{1}{10}\&le;\frac{\left|V_1\right|}{\left|V_2\right|}\&le;\frac{1}{20}$

The h value of F. getting now is the h value h of smooth type alpha-beta-γ wave filter _s, get h _s10 ~ 100 times be the alpha-beta-γ wave filter h value h of following-up type _t;

Step 2: after constructing smooth type and following-up type alpha-beta-γ wave filter, the noise variance of the live signal of sensor collection is measured, the signal of sensor Real-time Collection is raw measured signal, use smooth type alpha-beta-γ wave filter and following-up type alpha-beta-γ wave filter is online respectively carries out filtering to it, obtain smooth type filtered sequence with following-up type filtered sequence be length of window with m, in sequence with middle slip respectively obtains data segment, the tract started with the k moment with for:

${\hat{X}}_S{|}_k^{k+m}={\left[\begin{array}{cccc}{\hat{x}}_S\left(k\right)& {\hat{x}}_S(k+1)& \mathrm{...}& {\hat{x}}_S(k+m)\end{array}\right]}^T$

${\hat{X}}_T{|}_k^{k+m}={\left[\begin{array}{cccc}{\hat{x}}_T\left(k\right)& {\hat{x}}_T(k+1)& ...& {\hat{x}}_T(k+m)\end{array}\right]}^T$

Wherein: with the smooth type wave filter and the following-up type wave filter that are respectively the k moment export;

Step 3: usage data selection algorithm screens exporting in following-up type, smooth type alpha-beta-γ filtering window, selects tempolabile signal or linear change signal;

Channel selection algorithm filters out detailed process that is gradual or linear change data:

A. linear least-squares model is set up:

${\hat{X}}_S{|}_k^{k+m}=H_l\left[\begin{array}{c}{a}_S\left(k\right)\\ b_S\left(k\right)\end{array}\right]$

${\hat{X}}_T{|}_k^{k+m}=H_l\left[\begin{array}{c}{a}_T\left(k\right)\\ b_T\left(k\right)\end{array}\right]$

$H_l=\left[\begin{array}{cc}1& 1\\ 2& 1\\ .& .\\ .& .\\ .& .\\ m& 1\end{array}\right]$

Wherein: H _lfor least square observing matrix, a _s(k), b _s(k) and a _t(k), b _tk () is the valuation of a, b of fitting a straight line x (k+i)=ai+b;

B. least-squares estimation a is used _s(k), b _s(k) and a _t(k), b _t(k):

$\left[\begin{array}{c}{a}_S\left(k\right)\\ b_S\left(k\right)\end{array}\right]={\left(H_l^T{H}_l\right)}^{-1}{H}_l^T{\hat{X}}_S{|}_k^{k+m}$

$\left[\begin{array}{c}{a}_T\left(k\right)\\ b_T\left(k\right)\end{array}\right]={\left(H_l^T{H}_l\right)}^{-1}{H_l}^T{\hat{X}}_T{|}_k^{k+m}$

C. data in window are temporally divided into two sections, front and back, centered by fitting a straight line, in adding up every section respectively the A of average amplitude up and down ₁, A ₂, A ₃, A ₄:

$A_1=mean\{{\hat{x}}_S(k+i)-a_S\left(k\right)i-b_S|{\hat{x}}_S(k+i)\&GreaterEqual;a_S\left(k\right)i-b_S,i\&Element;(0,m/2)\}$

$A_2=mean\{{\hat{x}}_S(k+i)-a_S\left(k\right)i-b_S|{\hat{x}}_S(k+i)<a_S\left(k\right)i-b_S,i\&Element;(0,m/2)\}$

$A_3=mean\{{\hat{x}}_S(k+i)-a_S\left(k\right)i-b_S|{\hat{x}}_S(k+i)\&GreaterEqual;a_S\left(k\right)i-b_S,i\&Element;\&lsqb;m/2,m\left)\right\}$

$A_4=mean\{{\hat{x}}_S(k+i)-a_S\left(k\right)i-b_S|{\hat{x}}_S(k+i)<a_S\left(k\right)i-b_S,i\&Element;\&lsqb;m/2,m\left)\right\}$

Wherein: mean represents the function of averaging;

D. the absolute value of angle theta between two fitting a straight lines is calculated | θ |:

|θ|＝|arctan(a _S(k))-arctan(a _T(k))|

E. A is judged ₁, A ₂, A ₃, A ₄whether one angle between two fitting a straight lines of making peace is enough little:

$\left\{\begin{array}{c}\left|\frac{A_1}{A_2}\right|,\left|\frac{A_1}{A_3}\right|,\left|\frac{A_3}{A_4}\right|\&Element;(1-th\_amp,1+th\_amp)\\ \left|\mathrm{\&theta;}\right|<th\_ang\end{array}\right.$

Wherein: th_amp and th_ang is respectively the threshold value of amplitude and angle;

Work as A ₁, A ₂, A ₃, A ₄the ratio of absolute value is at scope (1-th_amp, 1+th_amp) and the absolute value of fitting a straight line angle | θ | when being less than threshold value th_ang, then this data segment is gradual or linear original measurement measuring-signal data segment, otherwise, data segment, for become process soon, is given up;

Step 4: gradual or linear original measurement measuring-signal data segment step 3 obtained, exports with the smooth type alpha-beta-γ wave filter in corresponding moment and carries out the mutual calculus of differences of second order, obtain noise variance;

Concrete:

A. establish and start with moment k, length is the gradual or linear original measurement measuring-signal data segment of m and its smooth type alpha-beta-γ wave filter exports by its respectively self difference obtain:

Δx(k)＝x(k+1)-x(k)

$\mathrm{\&Delta;}{\hat{x}}_S\left(k\right)={\hat{x}}_S(k+1)-{\hat{x}}_S\left(k\right)$

Wherein, x (k) is signal k moment measured value, for smooth type wave filter is in the output valve in k moment, Δ x (k) and be respectively their autodyne score value, and form self difference sequence with

B. the self difference sequence will obtained with carry out mutual deviation to divide, try to achieve original signal data segment in window noise variance

$Var\left(X{|}_k^{k+m}\right)=\frac{1}{2}(\mathrm{\&Delta;}X{|}_k^{k+m}-\mathrm{\&Delta;}{\hat{X}}_S{|}_k^{k+1}){({\mathrm{\&Delta;X}}_k^{k+m}-\mathrm{\&Delta;}{\hat{X}}_S{|}_k^{k+m})}^T$

C. calculate the noise variance of original signal, and the data calculated are weighted obtain:

$\left\{\begin{array}{cc}\begin{array}{c}{d}_i=(1-b)/(1-b^{i+1})\\ Var{\left(X\right)}_i=(1-d_i)Var\left(X{|}_k^{k+m}\right)+d_{i}Var{\left(X\right)}_{i-1}\end{array}& (0<b<1)\end{array}\right.$

Wherein: X is original measurement measuring-signal sequence, and b is forgetting factor, d _ifor weighting coefficient, b ⁱ⁺¹the i+1 power of forgetting factor b, Var (X) _iit is the original signal noise variance calculated for i-th time.