CN106815478A - A kind of high ferro settlement observation data predication method based on adaptive Kalman filter - Google Patents

A kind of high ferro settlement observation data predication method based on adaptive Kalman filter Download PDF

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CN106815478A
CN106815478A CN201710034374.9A CN201710034374A CN106815478A CN 106815478 A CN106815478 A CN 106815478A CN 201710034374 A CN201710034374 A CN 201710034374A CN 106815478 A CN106815478 A CN 106815478A
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high ferro
roadbed
data
sedimentation
observes
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CN106815478B (en
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王建敏
黄佳鹏
董宏祥
谢栋平
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Liaoning Technical University
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Liaoning Technical University
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Abstract

The present invention provides a kind of high ferro settlement observation data predication method based on adaptive Kalman filter, and the method is：N high ferro sedimentation roadbed observation data to be analyzed are obtained, the high ferro sedimentation roadbed observation data are high ferro sedimentation roadbed observation height value time series；The pretreatment that variance compensates adaptive Kalman filter is carried out to high ferro sedimentation roadbed observation data x, the filter value that high ferro sedimentation roadbed observes data is obtained；Determine that high ferro settles roadbed data prediction AR models according to the filter value that high ferro settles roadbed observation data；High ferro sedimentation roadbed observation data are predicted using the high ferro sedimentation roadbed data prediction AR models for determining.This method solve and directly complete prediction using high ferro initial data, it is difficult to solve the situation that initial data has error.Adaptive Kalman filter can be modified according to corresponding mathematical method to initial data in real time while being filtered, and can effectively reduce the Divergent Phenomenon that AR models are likely to occur.

Description

A kind of high ferro settlement observation data predication method based on adaptive Kalman filter
Technical field
The invention belongs to high ferro data analysis and electric powder prediction, and in particular to one kind is based on adaptive Kalman filter High ferro settlement observation data predication method.
Background technology
Now, China just builds high-speed railway on a large scale, and stability and the ride comfort of high-speed railway are to ensure passenger safety Property with the premise of comfortableness, this require must under strict control line engineering structure sedimentation and deformation, especially circuit longitudinal direction Differential settlement.So settlement monitoring must be periodically carried out to engineering under the lines such as the roadbed of high-speed railway, tunnel, bridges and culverts, in real time Its deformation is grasped, the security of construction and the operation of high ferro is just can guarantee that.During deformation monitoring, due to by ring The influence of border, instrument and manual measurement so that observed quantity can not accurately reflect the true strain of high-speed railway.Tradition deformation point With forecasting model including hyperbolic function model, exponential Function Model, logarithmic function model etc., conventional model is substantially base for analysis Coefficient correlation is calculated in time series and data characteristics, determines that concrete model is analyzed treatment.For conventional model, Think that subgrade settlement tends towards stability when the coefficient correlation between time and settling amount is more than 0.92.Due to influenceed by constructing with And the error of manual measurement, early stage observation subsidence curve big rise and fall, although high ferro roadbed observation time has reached technical specification Requirement, and posterior settlement is also basicly stable, but coefficient correlation is still less than 0.92.According to traditional analysis forecasting model, also not Settlement stability can be assert, it is impossible to carry out follow-up assessment and the work such as lay a railway track, need to continue to the Settlement Observation, until phase relation Number is up to standard.This not only adds the manpower and materials needed for roadbed monitoring, the progress of high ferro construction is also delayed.
The content of the invention
In view of the shortcomings of the prior art, the present invention proposes a kind of high ferro settlement observation number based on adaptive Kalman filter It is predicted that method.
The technical scheme is that：
A kind of high ferro settlement observation data predication method based on adaptive Kalman filter, comprises the following steps：
Step 1：N high ferro sedimentation roadbed observation data to be analyzed are obtained, the high ferro sedimentation roadbed observation data are High ferro sedimentation roadbed observation height value time series；
Step 2：The pretreatment that variance compensates adaptive Kalman filter is carried out to high ferro sedimentation roadbed observation data x, is obtained The filter value of data is observed to high ferro sedimentation roadbedWherein, k=1...n；
Step 2.1：Random noise is added, settling roadbed observation data according to high ferro determines high ferro sedimentation roadbed observation data State variable y, system noise Qk and measurement noise Rk；
The computing formula of the state variable y, system noise Qk and measurement noise Rk of the high ferro sedimentation roadbed observation data It is as follows：
Y=C*x+Vk*v；
Qk=Wk*WkT*Rw；
Rk=Vk*VkT*Rv：
Wherein, x is high ferro sedimentation roadbed observation data time series,Randn (n) is high ferro The normal distribution random number group of the length n of sedimentation roadbed observation data time series x, Vk and Rv is measurement noise parameter, and C is survey Amount systematic parameter, Wk and Rw is system noise parameter；
Step 2.2：Seen according to the system noise Qk and initial time high ferro sedimentation roadbed that high ferro settles roadbed observation data Survey data x (1) and determine that initial time high ferro sedimentation roadbed observes the error covariance P of data1(1)；
The initial time high ferro sedimentation roadbed observes the error covariance P of data1(1) computing formula is as follows：
P1(1)=Ak*P(1)*Ak T+Qk；
Wherein, AkIt is measurement noise parameter, P (1)=var (x (1)) is initial time high ferro sedimentation roadbed observation data Posteriori error covariance；
Step 2.3：The measurement noise Rk and k moment high ferro sedimentation roadbed observation number of roadbed observation data is settled according to high ferro According to error covariance P1K () determines that k moment high ferro sedimentation roadbed observes kalman gain H (k) of data；
The computing formula of kalman gain H (k) of the k moment high ferro sedimentation roadbed observation data is as follows：
H (k)=P1(k)-CT(C*P1(k))*CT+Pk；
Step 2.4：Determine that k moment high ferro is sunk according to kalman gain H (k) that k moment high ferro settles roadbed observation data Drop roadbed observes the filter value of data
The k moment high ferro sedimentation roadbed observes the filter value of dataComputing formula it is as follows：
Wherein,The filter value of data is observed for k-1 moment high ferro sedimentation roadbed,Y (k) is the k moment High ferro sedimentation roadbed observes the state variable of data；
Step 2.5：The error covariance P that roadbed observes data is settled according to k moment high ferro1K () and k moment high ferro are settled Kalman gain H (k) of roadbed observation data updates the posteriori error covariance P that k+1 moment high ferro sedimentation roadbed observes data (k+1)；
The computing formula of posteriori error covariance P (k+1) of the k+1 moment high ferro sedimentation roadbed observation data of the renewal It is as follows：
P (k+1)=(1-H (k) * C) * P1(k)；
Step 2.6：Road is settled according to the k+1 moment high ferro that high ferro settles the system noise Qk of roadbed observation data and updates Posteriori error covariance P (k+1) of base observation data determines that k+1 moment high ferro sedimentation roadbed observes the error covariance P of data1 (k+1)；
The k+1 moment high ferro sedimentation roadbed observes the error covariance P of data1(k+1) computing formula is as follows：
P1(k+1)=Ak*P(k)*Ak T+Qk；
Step 2.7：The filter value that roadbed observes data is settled according to k moment high ferroSeen with k moment high ferro sedimentation roadbed The difference for surveying data x (k) determines that k moment high ferro settles filtering residue L (k) of roadbed data；
The computing formula of filtering residue L (k) of the k moment high ferro sedimentation roadbed observation data is as follows：
Step 2.8：System noise parameter Rw is updated according to filtering residue L (k) that k moment high ferro settles roadbed observation data With the system noise Qk that high ferro sedimentation roadbed observes data；
The system noise parameter Rw of the high ferro sedimentation roadbed observation data of the renewal and the high ferro sedimentation roadbed for updating are seen The computing formula for surveying the system noise Qk of data is as follows：
Rw=(OT*O)-1*OT*E；
Qk=Wk*WkT*Rw；
Wherein, O=C*Ak* Wk, E=L (k)T*L(k)-trace(C*Ak*P(k)*Ak T*C)-Rk；
Step 2.9：Repeat step 2.3 obtains the filter value that high ferro sedimentation roadbed observes data to step 2.8
Step 3：The filter value that roadbed observes data is settled according to high ferroDetermine that high ferro is settled Roadbed data prediction AR models；
Step 3.1：The filter value that roadbed observes data is settled according to high ferroBy a most young waiter in a wineshop or an inn Multiplication obtains the parameter, Δ that high ferro settles roadbed data prediction AR modelsi；
The high ferro settles the parameter, Δ of roadbed data prediction AR modelsiComputing formula it is as follows：
Wherein, i is the exponent number that high ferro settles roadbed data prediction AR models,
Step 3.2：The parameter, Δ of roadbed data prediction AR models is settled according to high ferroiIt is preliminary to set up high ferro sedimentation roadbed number It is predicted that AR models；
The high ferro sedimentation roadbed data prediction AR models of the preliminary foundation are as follows：
Wherein, x ' (n+k ') is the predicted value that the n-th+k ' moment high ferro settles roadbed data；
Step 3.3：The high ferro for calculating different rank respectively settles the predicted value of roadbed data prediction AR models, and calculates not The high ferro sedimentation roadbed observation data at the predicted value corresponding moment of roadbed data prediction AR models are settled with the high ferro of exponent number Residual values, the minimum high ferro of its gained residual values sum is settled into roadbed data prediction AR model orders and is settled as the high ferro The exponent number of roadbed data prediction AR models, determines that high ferro settles the final form of roadbed data prediction AR models；
Described exponent number is 1~15；
Step 4：High ferro sedimentation roadbed observation data are carried out using the high ferro sedimentation roadbed data prediction AR models for determining Prediction.
Beneficial effects of the present invention：
The present invention proposes a kind of high ferro settlement observation data predication method based on adaptive Kalman filter, uses variance Compensation adaptive Kalman filter carries out pretreatment to initial data and can reduce error for the adverse effect predicted, solves Directly prediction is completed using high ferro initial data, it is difficult to solve the situation that initial data has error.Adaptive Kalman filter While being filtered, initial data can be modified according to corresponding mathematical method in real time, can effectively dropped The Divergent Phenomenon that low AR models are likely to occur.Adaptive Kalman filter is compensated using variance to complete at the denoising of high ferro data Reason, reduces the noise for existing for the influence that high ferro is built, and reduction is dropped in the manpower, material resources and financial resources in terms of high ferro sedimentation.
Brief description of the drawings
Fig. 1 is the high ferro settlement observation data prediction side based on adaptive Kalman filter in the specific embodiment of the invention The flow chart of method；
Fig. 2 observes the filter value and height of data for the different high ferro sedimentation roadbed obtained in the specific embodiment of the invention Iron sedimentation roadbed observes the correlation curve of data；
Wherein, (a) is the filter value and high ferro sedimentation roadbed observation data of the high ferro sedimentation roadbed observation data of embodiment 1 Correlation curve；
B () is right with high ferro sedimentation roadbed observation data for the filter value of the high ferro sedimentation roadbed observation data of embodiment 2 Compare curve；
C () is right with high ferro sedimentation roadbed observation data for the filter value of the high ferro sedimentation roadbed observation data of embodiment 3 Compare curve；
D () is right with high ferro sedimentation roadbed observation data for the filter value of the high ferro sedimentation roadbed observation data of embodiment 4 Compare curve；
E () is right with high ferro sedimentation roadbed observation data for the filter value of the high ferro sedimentation roadbed observation data of embodiment 5 Compare curve；
F () is right with high ferro sedimentation roadbed observation data for the filter value of the high ferro sedimentation roadbed observation data of embodiment 6 Compare curve；
Fig. 3 is settled for the filter value for observing data using high ferro sedimentation roadbed in the specific embodiment of the invention as high ferro The input of roadbed data prediction AR models predict the outcome and using high ferro sedimentation roadbed observation data as input obtain it is pre- Survey comparative result figure；
Wherein, (a) is to settle roadbed number as high ferro using the filter value of the high ferro sedimentation roadbed observation data of embodiment 1 It is predicted that the input of AR models being predicted the outcome and obtained as input using the high ferro sedimentation roadbed observation data of embodiment 1 Predict the outcome comparison diagram；
B () is pre- as high ferro sedimentation roadbed data using the filter value of the high ferro sedimentation roadbed observation data of embodiment 2 Survey AR models input predict the outcome and using embodiment 2 high ferro sedimentation roadbed observation data as the prediction that obtains of input Comparative result figure；
C () is pre- as high ferro sedimentation roadbed data using the filter value of the high ferro sedimentation roadbed observation data of embodiment 3 Survey AR models input predict the outcome and using embodiment 3 high ferro sedimentation roadbed observation data as the prediction that obtains of input Comparative result figure；
D () is pre- as high ferro sedimentation roadbed data using the filter value of the high ferro sedimentation roadbed observation data of embodiment 4 Survey AR models input predict the outcome and using embodiment 4 high ferro sedimentation roadbed observation data as the prediction that obtains of input Comparative result figure；
E () is pre- as high ferro sedimentation roadbed data using the filter value of the high ferro sedimentation roadbed observation data of embodiment 5 Survey AR models input predict the outcome and using embodiment 5 high ferro sedimentation roadbed observation data as the prediction that obtains of input Comparative result figure；
F () is pre- as high ferro sedimentation roadbed data using the filter value of the high ferro sedimentation roadbed observation data of embodiment 6 Survey AR models input predict the outcome and using embodiment 6 high ferro sedimentation roadbed observation data as the prediction that obtains of input Comparative result figure.
Specific embodiment
The specific embodiment of the invention is described in detail below in conjunction with the accompanying drawings.
A kind of high ferro settlement observation data predication method based on adaptive Kalman filter, as shown in figure 1, including following Step：
Step 1：N high ferro sedimentation roadbed observation data to be analyzed are obtained, the high ferro sedimentation roadbed observation data are High ferro sedimentation roadbed observation height value time series.
Step 2：The pretreatment that variance compensates adaptive Kalman filter is carried out to high ferro sedimentation roadbed observation data x, is obtained The filter value of data is observed to high ferro sedimentation roadbedWherein, k=1...n.
Step 2.1：Random noise is added, settling roadbed observation data according to high ferro determines high ferro sedimentation roadbed observation data State variable y, system noise Qk and measurement noise Rk.
In present embodiment, shown in the computing formula such as formula (1) of the state variable y of high ferro sedimentation roadbed observation data：
Y=C*x+Vk*v (1)
Wherein, x is high ferro sedimentation roadbed observation data time series,Randn (n) is high ferro The normal distribution random number group of the length n of sedimentation roadbed observation data time series x, Rv=10^ (- 10) joins for measurement noise Number, C=1 is measuring system parameter.
Shown in the computing formula such as formula (2) of the system noise Qk of high ferro sedimentation roadbed observation data：
Qk=Wk*WkT*Rw (2)
Wherein, Wk=1 is system noise parameter, and Rw=10^ (- 10) is system noise parameter.
Shown in the computing formula such as formula (3) of the measurement noise Rk of high ferro sedimentation roadbed observation data：
Rk=Vk*VkT*Rv (3)
Wherein, Vk=1 is measurement noise parameter.
Step 2.2：Seen according to the system noise Qk and initial time high ferro sedimentation roadbed that high ferro settles roadbed observation data Survey data x (1) and determine that initial time high ferro sedimentation roadbed observes the error covariance P of data1(1)。
In present embodiment, initial time high ferro sedimentation roadbed observes the error covariance P of data1(1) computing formula As shown in formula (4)：
P1(1)=Ak*P(1)*Ak T+Qk (4)
Wherein, Ak=0.97 is measurement noise parameter, and P (1)=var (x (1)) is the sedimentation roadbed observation of initial time high ferro The posteriori error covariance of data.
Step 2.3：The measurement noise Rk and k moment high ferro sedimentation roadbed observation number of roadbed observation data is settled according to high ferro According to error covariance P1K () determines that k moment high ferro sedimentation roadbed observes kalman gain H (k) of data.
In present embodiment, the computing formula such as formula of kalman gain H (k) of k moment high ferro sedimentation roadbed observation data (5) shown in：
H (k)=P1(k)-CT(C*P1(k))*CT+Pk (5)
Step 2.4：Determine that k moment high ferro is sunk according to kalman gain H (k) that k moment high ferro settles roadbed observation data Drop roadbed observes the filter value of data
In present embodiment, k moment high ferro sedimentation roadbed observes the filter value of dataComputing formula such as formula (6) institute Show：
Wherein,The filter value of data is observed for k-1 moment high ferro sedimentation roadbed,Y (k) is the k moment High ferro sedimentation roadbed observes the state variable of data.
Step 2.5：The error covariance P that roadbed observes data is settled according to k moment high ferro1K () and k moment high ferro are settled Kalman gain H (k) of roadbed observation data updates the posteriori error covariance P that k+1 moment high ferro sedimentation roadbed observes data (k+1)。
In present embodiment, the k+1 moment high ferro sedimentation roadbed of renewal observes posteriori error covariance P (k+1) of data Computing formula such as formula (7) shown in：
P (k+1)=(1-H (k) * C) * P1(k) (7)
Step 2.6：Road is settled according to the k+1 moment high ferro that high ferro settles the system noise Qk of roadbed observation data and updates Posteriori error covariance P (k+1) of base observation data determines that k+1 moment high ferro sedimentation roadbed observes the error covariance P of data1 (k+1)。
In present embodiment, k+1 moment high ferro sedimentation roadbed observes the error covariance P of data1(k+1) computing formula As shown in formula (8)：
P1(k+1)=Ak*P(k)*Ak T+Qk (8)
Step 2.7：The filter value that roadbed observes data is settled according to k moment high ferroRoadbed is settled with k moment high ferro The difference of observation data x (k) determines that k moment high ferro settles filtering residue L (k) of roadbed data.
In present embodiment, the computing formula such as formula (9) of filtering residue L (k) of k moment high ferro sedimentation roadbed observation data It is shown：
Step 2.8：System noise parameter Rw is updated according to filtering residue L (k) that k moment high ferro settles roadbed observation data With the system noise Qk that high ferro sedimentation roadbed observes data.
In present embodiment, the computing formula such as formula of the system noise parameter Rw of the high ferro sedimentation roadbed observation data of renewal (10) shown in：
Rw=(OT*O)-1*OT*E (10)
Wherein, O=C*Ak* Wk, E=L (k)T*L(k)-trace(C*Ak*P(k)*Ak T*C)-Rk。
Shown in the computing formula such as formula (11) of the system noise Qk of the high ferro sedimentation roadbed observation data of renewal：
Qk=Wk*WkT*Rw (11)
Step 2.9：Repeat step 2.3 obtains the filter value that high ferro sedimentation roadbed observes data to step 2.8
In present embodiment, the filter value of the different high ferro sedimentation roadbed observation data for obtaining is seen with high ferro sedimentation roadbed The correlation curve for surveying data is as shown in Figure 2.
Step 3：The filter value that roadbed observes data is settled according to high ferroDetermine that high ferro is settled Roadbed data prediction AR models.
Step 3.1：The filter value that roadbed observes data is settled according to high ferroBy a most young waiter in a wineshop or an inn Multiplication obtains the parameter, Δ that high ferro settles roadbed data prediction AR modelsi。
In present embodiment, high ferro settles the parameter, Δ of roadbed data prediction AR modelsiComputing formula such as formula (12) institute Show：
Wherein, i is the exponent number that high ferro settles roadbed data prediction AR models,
Step 3.2：The parameter, Δ of roadbed data prediction AR models is settled according to high ferroiIt is preliminary to set up high ferro sedimentation roadbed number It is predicted that AR models.
In present embodiment, shown in the preliminary high ferro sedimentation roadbed data prediction AR model such as formulas (13) set up：
Wherein, x ' (n+k ') is the predicted value that the n-th+k ' moment high ferro settles roadbed data.
Step 3.3：The high ferro for calculating different rank respectively settles the predicted value of roadbed data prediction AR models, and calculates not The high ferro sedimentation roadbed observation data at the predicted value corresponding moment of roadbed data prediction AR models are settled with the high ferro of exponent number Residual values, the minimum high ferro of its gained residual values sum is settled into roadbed data prediction AR model orders and is settled as the high ferro The exponent number of roadbed data prediction AR models, determines that high ferro settles the final form of roadbed data prediction AR models.
In present embodiment, exponent number from the predicted value of 1 to 15 high ferro sedimentation roadbed data prediction AR models is calculated respectively, The exponent number for obtaining settles the predicted value of roadbed data prediction AR models and the high ferro sedimentation roadbed at corresponding moment from 1 to 15 high ferro Observe the residual values of data, the minimum high ferro of its gained residual values sum is settled roadbed data prediction AR model orders as this High ferro settles the exponent number of roadbed data prediction AR models, determines that high ferro settles the final form of roadbed data prediction AR models.
Step 4：High ferro sedimentation roadbed observation data are carried out using the high ferro sedimentation roadbed data prediction AR models for determining Prediction.
In present embodiment, roadbed data prediction is settled as high ferro using the filter value of high ferro sedimentation roadbed observation data The predicted value that the input of AR models is obtained is observed with the residual error of actual high ferro sedimentation roadbed observation data, using high ferro sedimentation roadbed Data observe comparison diagram such as Fig. 3 of the residual error of data as the predicted value that the input of AR models is obtained with actual high ferro sedimentation roadbed It is shown.
Using high ferro sedimentation roadbed observation data road is settled as the predicted value that the input of AR models is obtained with actual high ferro Base observes residual error average value, residual error maximum, the root-mean-square error of data, and the filter of data is observed using high ferro sedimentation roadbed Predicted value and actual high ferro sedimentation roadbed observation number that wave number is obtained as the input of high ferro sedimentation roadbed data prediction AR models According to residual error average value, residual error maximum, the reduced value of root-mean-square error it is as shown in table 1.
The residual error average value of table 1, residual error maximum, the reduced value of root-mean-square error
Using high ferro sedimentation roadbed observation data road is settled as the predicted value that the input of AR models is obtained with actual high ferro Base observes the residual distribution of data, and settles roadbed data as high ferro using the filter value that high ferro sedimentation roadbed observes data Predict that the predicted value that the input of AR models is obtained is as shown in table 2 with the residual distribution of actual high ferro sedimentation roadbed observation data.
The residual distribution of table 2

Claims (3)

1. a kind of high ferro settlement observation data predication method based on adaptive Kalman filter, it is characterised in that including following Step：
Step 1：N high ferro sedimentation roadbed observation data to be analyzed are obtained, the high ferro sedimentation roadbed observation data are high ferro Sedimentation roadbed observation height value time series；
Step 2：The pretreatment that variance compensates adaptive Kalman filter is carried out to high ferro sedimentation roadbed observation data x, height is obtained Iron sedimentation roadbed observes the filter value of dataWherein, k=1...n；
Step 3：The filter value that roadbed observes data is settled according to high ferroDetermine that high ferro settles roadbed Data prediction AR models；
Step 3.1：The filter value that roadbed observes data is settled according to high ferroBy least square method Obtain the parameter, Δ that high ferro settles roadbed data prediction AR modelsi；
The high ferro settles the parameter, Δ of roadbed data prediction AR modelsiComputing formula it is as follows：
Δ i = ( X T * X ) - 1 * ( X T * x ^ ) ;
Wherein, i is the exponent number that high ferro settles roadbed data prediction AR models,
Step 3.2：The parameter, Δ of roadbed data prediction AR models is settled according to high ferroiTentatively set up high ferro sedimentation roadbed data pre- Survey AR models；
The high ferro sedimentation roadbed data prediction AR models of the preliminary foundation are as follows：
x ′ ( n + k ′ ) = Δ 1 x ^ ( n + k ′ - 1 ) + Δ 2 x ^ ( n + k ′ - 2 ) + ... + Δ i x ^ ( n + k ′ - i ) ;
Wherein, x ' (n+k ') is the predicted value that the n-th+k ' moment high ferro settles roadbed data；
Step 3.3：The high ferro for calculating different rank respectively settles the predicted value of roadbed data prediction AR models, and calculates not same order The high ferro sedimentation roadbed at the predicted value corresponding moment of several high ferro sedimentation roadbed data prediction AR models observes the residual of data Difference, settles the minimum high ferro of its gained residual values sum roadbed data prediction AR model orders and settles roadbed as the high ferro The exponent number of data prediction AR models, determines that high ferro settles the final form of roadbed data prediction AR models；
Step 4：High ferro sedimentation roadbed observation data are predicted using the high ferro sedimentation roadbed data prediction AR models for determining.
2. the high ferro settlement observation data predication method based on adaptive Kalman filter according to claim 1, it is special Levy and be, the step 2 is comprised the following steps：
Step 2.1：Random noise is added, settling roadbed observation data according to high ferro determines that high ferro sedimentation roadbed observes the shape of data State variable y, system noise Qk and measurement noise Rk；
The computing formula of the state variable y, system noise Qk and measurement noise Rk of the high ferro sedimentation roadbed observation data is as follows It is shown：
Y=C*x+Vk*v；
Qk=Wk*WkT*Rw；
Rk=Vk*VkT*Rv；
Wherein, x is high ferro sedimentation roadbed observation data time series,Randn (n) is that high ferro settles road The normal distribution random number group of the length n of base observation data time series x, Vk and Rv is measurement noise parameter, and C is measuring system Parameter, Wk and Rw are system noise parameter；
Step 2.2：The system noise Qk and initial time high ferro sedimentation roadbed observation number of roadbed observation data are settled according to high ferro Determine that initial time high ferro sedimentation roadbed observes the error covariance P of data according to x (1)1(1)；
The initial time high ferro sedimentation roadbed observes the error covariance P of data1(1) computing formula is as follows：
P1(1)=Ak*P(1)*Ak T+Qk；
Wherein, AkIt is measurement noise parameter, P (1)=var (x (1)) is the posteriority that initial time high ferro sedimentation roadbed observes data Error covariance；
Step 2.3：The measurement noise Rk and k moment high ferro sedimentation roadbed observation data of roadbed observation data are settled according to high ferro Error covariance P1K () determines that k moment high ferro sedimentation roadbed observes kalman gain H (k) of data；
The computing formula of kalman gain H (k) of the k moment high ferro sedimentation roadbed observation data is as follows：
H (k)=P1(k)-CT(C*P1(k))*CT+Pk；
Step 2.4：Determine that k moment high ferro settles road according to kalman gain H (k) that k moment high ferro settles roadbed observation data Base observes the filter value of data
The k moment high ferro sedimentation roadbed observes the filter value of dataComputing formula it is as follows：
x ^ ( k ) = A k * x ^ ( k - 1 ) + H ( k ) * ( y ( k ) - C * A k x ^ ( k - 1 ) ) ;
Wherein,The filter value of data is observed for k-1 moment high ferro sedimentation roadbed,Y (k) is k moment high ferros Sedimentation roadbed observes the state variable of data；
Step 2.5：The error covariance P that roadbed observes data is settled according to k moment high ferro1K () and k moment high ferro settle roadbed Kalman gain H (k) for observing data updates the posteriori error covariance P (k+ that k+1 moment high ferro sedimentation roadbed observes data 1)；
The computing formula of posteriori error covariance P (k+1) of the k+1 moment high ferro sedimentation roadbed observation data of the renewal is as follows It is shown：
P (k+1)=(1-H (k) * C) * P1(k)；
Step 2.6：Seen according to the k+1 moment high ferro sedimentation roadbed that high ferro settles the system noise Qk of roadbed observation data and updates Posteriori error covariance P (k+1) for surveying data determines that k+1 moment high ferro sedimentation roadbed observes the error covariance P of data1(k+ 1)；
The k+1 moment high ferro sedimentation roadbed observes the error covariance P of data1(k+1) computing formula is as follows：
P1(k+1)=Ak*P(k)*Ak T+Qk；
Step 2.7：The filter value that roadbed observes data is settled according to k moment high ferroWith k moment high ferro sedimentation roadbed observation number Determine that k moment high ferro settles filtering residue L (k) of roadbed data according to the difference of x (k)；
The computing formula of filtering residue L (k) of the k moment high ferro sedimentation roadbed observation data is as follows：
L ( k ) = x ^ ( k ) - x ( k ) ;
Step 2.8：System noise parameter Rw and height are updated according to filtering residue L (k) that k moment high ferro settles roadbed observation data Iron sedimentation roadbed observes the system noise Qk of data；
The system noise parameter Rw of the high ferro sedimentation roadbed observation data of the renewal and the high ferro sedimentation roadbed observation number for updating According to system noise Qk computing formula it is as follows：
Rw=(OT*O)-1*OT*E；
Qk=Wk*WkT*Rw；
Wherein, O=C*Ak* Wk, E=L (k)T*L(k)-trace(C*Ak*P(k)*Ak T*C)-Rk；
Step 2.9：Repeat step 2.3 obtains the filter value that high ferro sedimentation roadbed observes data to step 2.8
3. the high ferro settlement observation data predication method based on adaptive Kalman filter according to claim 1, it is special Levy and be, described exponent number is 1~15.
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