CN113361562B - Multi-sensor fusion method and device for power battery reaction control module - Google Patents

Multi-sensor fusion method and device for power battery reaction control module Download PDF

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CN113361562B
CN113361562B CN202110423936.5A CN202110423936A CN113361562B CN 113361562 B CN113361562 B CN 113361562B CN 202110423936 A CN202110423936 A CN 202110423936A CN 113361562 B CN113361562 B CN 113361562B
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CN113361562A (en
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王卓尔
彭峰
邹家喻
郑丽萍
彭斌
周波
高鹏
肖文超
管世辉
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Wuhan Bus Manufacturing Co ltd
Wuhan University of Technology WUT
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Abstract

The invention discloses a multi-sensor fusion method for a power battery reaction control module, which comprises the following steps: s1, defining a true value x t And predicted valueError e 'between' t And a true value x t And the estimated valueError e between t Obtaining a prediction error covariance matrix P' t And an estimation error covariance matrix P t The method comprises the steps of carrying out a first treatment on the surface of the S2, covariance matrix P 'of prediction error' i Substituting, expanding, deriving, finally defining and data fusion operation to obtain a data fusion value with minimum mean square error, and improving the precision and reliability of the system; s3, carrying out actual theoretical calculation deduction based on actual sensor acquisition data, and verifying the effectiveness of the algorithm. The invention also discloses a multi-sensor fusion device for the power battery reaction control module, which comprises: an error definition module; a data fusion module; and a validity verification module. The invention can ensure the accuracy and the system reliability of the sensor signal acquisition system and can be widely applied to the field of sensors.

Description

Multi-sensor fusion method and device for power battery reaction control module
Technical Field
The invention relates to the field of sensors, in particular to a multi-sensor fusion method and device for a power battery reaction control module.
Background
A sensor is a device or apparatus that senses a measured signal and changes it to a usable signal according to a certain rule. As an important means for information acquisition, the three main supports of the information technology are formed together with the communication technology and the computer technology. With the development of modern science, sensing technology is rapidly developed and applied to various fields as an emerging subject closely related to modern science. With the rapid development of intelligent technology, the requirements of the sensing capability and the robust performance of the multi-sensor system are more and more strict. In order to ensure the reliability of the multi-sensor system, the fault tolerance function and the input signal precision of the system are required to be effectively analyzed, so that the accuracy and the system reliability of the sensor acquisition signals are effectively ensured after the sensor acquisition signals are processed.
Disclosure of Invention
The invention aims to overcome the defects of the background technology, and provides a multi-sensor fusion method and device for a power battery reaction control module, which can ensure the accuracy and the system reliability of a sensor signal acquisition system.
The invention provides a multi-sensor fusion method for a power battery reaction control module, which comprises the following steps: s1, defining a true value x t And predicted valueError e 'between' t And a true value x t And estimate +.>Error e between t Obtaining a prediction error covariance matrix P' t And an estimation error covariance matrix P t The method comprises the steps of carrying out a first treatment on the surface of the S2, covariance matrix P 'of prediction error' i Substituting, expanding, deriving, finally defining and data fusion operation to obtain a data fusion value with minimum mean square error, and improving the precision and reliability of the system; s3, carrying out actual theoretical calculation deduction based on actual sensor acquisition data, and verifying the effectiveness of the algorithm.
In the above technical solution, in the step S1, the true value x t And predicted valueError e 'between' t And a true value x t And estimate +.>Error e between t The method comprises the following steps of: />Wherein Q is a measurement matrix, K kalman Is a Kalman gain matrix, v t Is a process noise matrix; the prediction error covariance matrix P' t And an estimation error covariance matrix P t The method comprises the following steps of: /> Wherein E [ v ] t v t T ]＝C，K kalman Is Kalman gain matrix, Q is measurement matrix, x t Is true value +.>Is the predicted value of the true value, P' t For prediction error covariance matrix, P t To estimate the error covariance matrix.
In the above technical solution, the specific process of step S2 is as follows: s21, covariance matrix P 'of prediction error' t Substituting to obtain P t ＝(I-K kalman Q)P′ t (I-K kalman Q) T +K kalman CK kalman T (5) Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix; s22, while Kalman filtering is basically minimum mean square error estimation, spreading the equation (5) and tracing to obtain tr (P t )＝tr(P′ t )-2tr(K kalman QP′ t )+tr(K kalman (QP′ t Q T +C)K kalman T ) (6) wherein K kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix; s23, optimal estimation K kalman Let tr (P) t ) Minimum, deriving both sides of formula (6) to be equal to 0 to obtain K kalman ＝P′ t Q T (QP′ t Q T +C) -1 (7) Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is a measurement matrix, and the value is debugged according to the system; by collating the above-mentioned derivation processesP′ t ＝P t -K kalman HP t ＝(I-K kalman H)P t (9) Wherein->Predicted value being true value, +.>Estimated value for true value, +.>K is the predicted value of the observed value kalman Is Kalman gain matrix, H is process excitation noise covariance matrix, P t To estimate the error covariance matrix, P' t A covariance matrix of the prediction error; s24, finally defining the calculation process of Kalman filtering as +.>Wherein A is a state transition matrix, B is an input gain matrix,predicted value, u, being the true value of the previous state t-1 For the input of the previous state prediction model, P' t For prediction error covariance matrix, P t-1 Estimating an error covariance matrix for the previous state, wherein H is a process excitation noise covariance matrix; the correction procedure of the Kalman filter is defined as +.>Wherein z is t For observations->For the predicted value of the observed value, Q is the measurement matrix,>k is the predicted value of the true value kalman Is a Kalman gain matrix, P' t For prediction error covariance matrix,>estimated value for true value, +.>To measure the margin; s25, for various kinds ofAnd data fusion is carried out on the data of the sensor to obtain a data fusion value with minimum mean square error, so that the accuracy and reliability of the system are improved.
In the above technical solution, the specific process of step S25 is as follows: s251, supposing that n sensors independent of each other exist, wherein the state of the ith sensor is X i (i=1,., n), the error of the i-th sensor is MSE i (i=1,., n), where the data of each sensor is fused by a weighted average fusion method, it is obtained(12) Wherein ω is i (i=1,., n) is the weight assigned to each sensor, X aver Representing the fused average sensor state; s252, introducing a total mean square error MSE>Wherein omega i Is the weight on the ith sensor, X aver X is the fused average sensor state i Or X j Status of the ith or jth sensor; s253, according to the limit theory, the weight corresponding to the minimum mean square error MSE is calculated as +.>Wherein MSE i MSE for mean square error of the ith sensor j Is the mean square error of the jth sensor.
The invention also provides a multi-sensor fusion device for the power battery reaction control module, which comprises the following parts: and an error definition module: definition of the true value x t And predicted valueError e 'between' t And a true value x t And estimate +.>Error e between t Obtaining the prediction errorDifference covariance matrix P' t And an estimation error covariance matrix P t The method comprises the steps of carrying out a first treatment on the surface of the And a data fusion module: covariance matrix P 'of prediction error' i Substituting, expanding, deriving, finally defining and data fusion operation to obtain a data fusion value with minimum mean square error, and improving the precision and reliability of the system; and a validity verification module: the effectiveness of the algorithm is verified by performing actual theoretical calculation deduction based on the actual sensor acquisition data.
In the above technical solution, the error definition module includes the following parts: error definition unit: the true value x t And predicted valueError e 'between' t And a true value x t And estimate +.>Error e between t The method comprises the following steps of: /> Wherein Q is a measurement matrix, K kalman Is a Kalman gain matrix, v t Is a process noise matrix; error covariance matrix unit: the prediction error covariance matrix P' t And an estimation error covariance matrix P t The method comprises the following steps of: />
Wherein E [ v ] t v t T ]＝C，K kalman Is Kalman gain matrix, Q is measurement matrix, x t To be a true value of the value,is the predicted value of the true value, P' t For prediction error covariance matrix, P t To estimate the error covariance matrix.
In the above technical solution, the data fusion module includes the following parts: the prediction error covariance matrix is substituted into the unit: covariance matrix P 'of prediction error' t Substituting to obtain P t ＝(I-K kalman Q)P′ t (I-K kalman Q) T +K kalman CK kalman T (5) Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix; kalman filter expansion unit: whereas the Kalman filtering is essentially a minimum mean square error estimation, the tr (P) is obtained by expanding and tracing equation (5) t )＝tr(P′ t )-2tr(K kalman QP′ t )+tr(K kalman (QP′ t Q T +C)K kalman T ) (6) wherein K kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix; and a derivation unit: optimal estimation K kalman Let tr (P) t ) Minimum, deriving both sides of formula (6) to be equal to 0 to obtain K kalman ＝P′ t Q T (QP′ t Q T +C) -1 (7) Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is a measurement matrix, and the value is debugged according to the system; by collating the above-mentioned derivation processes P′ t ＝P t -K kalman HP t ＝(I-K kalman H)P t (9) Wherein->Is truePredicted value of real value->Estimated value for true value, +.>K is the predicted value of the observed value kalman Is Kalman gain matrix, H is process excitation noise covariance matrix, P t To estimate the error covariance matrix, P' t A covariance matrix of the prediction error; kalman filter definition unit: the calculation process of the final definition Kalman filter is +.>Wherein A is a state transition matrix, B is an input gain matrix,>predicted value, u, being the true value of the previous state t-1 For the input of the last state prediction model, P t ' is the prediction error covariance matrix, P t-1 Estimating an error covariance matrix for the previous state, wherein H is a process excitation noise covariance matrix; defining the correction process of the Kalman filter asWherein z is t For observations->For the predicted value of the observed value, Q is the measurement matrix,k is the predicted value of the true value kalman Is a Kalman gain matrix, P t ' is the prediction error covariance matrix,>estimated value for true value, +.>To measure the margin; and a data fusion unit: and data fusion is carried out on the data of various sensors to obtain a data fusion value with minimum mean square error, so that the accuracy and reliability of the system are improved.
The multi-sensor fusion method and device for the power battery reaction control module have the following beneficial effects: the intelligent algorithm is introduced, so that the reliability of the multi-sensor system is ensured, and the accuracy and the system reliability of the sensor after the sensor collects signals are effectively ensured by effectively analyzing the fault tolerance function and the input signal accuracy of the system.
Drawings
FIG. 1 is a schematic flow chart of a multi-sensor fusion method for a power cell reaction control module of the present invention;
FIG. 2 is a schematic flow chart of step S2 in the multi-sensor fusion method for a power battery reaction control module according to the present invention;
FIG. 3 is a schematic diagram of a multi-sensor fusion device for a power cell reaction control module according to the present invention;
FIG. 4 is a schematic diagram of an error definition module in a multi-sensor fusion device for a power cell reaction control module according to the present invention;
fig. 5 is a schematic structural diagram of a data fusion module in the multi-sensor fusion device for a power battery reaction control module according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, which should not be construed as limiting the invention.
Referring to fig. 1, the multi-sensor fusion method for a power battery reaction control module of the present invention includes the steps of:
step S1, defining a true value x t And predicted valueError e 'between' t True value x t And the estimated value/>Error e between t Respectively is
Wherein Q is a measurement matrix, K kalman Is a Kalman gain matrix, v t Is a process noise matrix;
obtaining a prediction error covariance matrix P' t Estimating an error covariance matrix P t Respectively is
Wherein E [ v ] t v t T ]＝C，K kalman Is Kalman gain matrix, Q is measurement matrix, x t To be a true value of the value,is the predicted value of the true value, P' t For prediction error covariance matrix, P t For estimating an error covariance matrix;
referring to fig. 2, step S2, a prediction error covariance matrix P 'is obtained' i Substituting and expanding, deriving, final defining and data fusion operation to obtain a data fusion value with minimum mean square error so as to improve the accuracy and reliability of the system, wherein the deduction process is as follows:
covariance matrix P 'of prediction error' t Substitution to obtain
P t ＝(I-K kalman Q)P′ t (I-K kalman Q) T +K kalman CK kalman T (5)，
Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix;
the Kalman filtering is essentially the least mean square error estimation, and the method can be obtained by expanding and tracing the formula (5)
tr(P t )＝tr(P′ t )-2tr(K kalman QP′ t )+tr(K kalman (QP′ t Q T +C)K kalman T ) (6)，
Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix;
optimal estimation K kalman Let tr (P) t ) Minimum, therefore, deriving both sides of formula (6) to be equal to 0 is available
K kalman ＝P′ t Q T (QP′ t Q T +C) -1 (7)，
Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is a measurement matrix, and the value is adjusted according to the system;
by arranging the above-mentioned derivation process
P′ t ＝P t -K kalman HP t ＝(I-K kalman H)P t (9)，
Wherein,predicted value being true value, +.>Estimated value for true value, +.>K is the predicted value of the observed value kalman Is Kalman gain matrix, H is process excitation noise covariance matrix, P t To estimate the error covariance matrix, P' t A covariance matrix of the prediction error;
the calculation process of final definition Kalman filtering is as follows
Wherein A is a state transition matrix, B is an input gain matrix,predicted value, u, being the true value of the previous state t-1 For the input of the previous state prediction model, P' t For prediction error covariance matrix, P t-1 Estimating an error covariance matrix for the previous state, wherein H is a process excitation noise covariance matrix;
defining the correction process of the Kalman filter as
Wherein z is t In order to observe the value of the value,for the predicted value of the observed value, Q is the measurement matrix,>k is the predicted value of the true value kalman Is a Kalman gain matrix, P' t For prediction error covariance matrix,>estimated value for true value, +.>To measure the margin;
and data fusion is required to be carried out on the data of various sensors to obtain a data fusion value with minimum mean square error so as to improve the accuracy and reliability of the system. It is therefore assumed here that there are n sensors independent of each other, where the state of the ith sensor is X i (i=1,., n), the error of the i-th sensor is MSE i (i＝1,...,n)，
The data of each sensor is fused by a weighted average fusion method to obtain
Wherein omega i (i=1,., n) is the weight assigned to each sensor, X aver Representing the state of the fused average sensor, wherein the distribution of weights has great influence on the improvement of the overall performance of the system;
the total mean square error MSE is introduced here
Wherein omega i Is the weight on the ith sensor, X aver X is the fused average sensor state i Or X j Status of the ith or jth sensor;
according to the limit theory, the weight corresponding to the minimum time of the total mean square error MSE can be obtained as
Wherein MSE i MSE for mean square error of the ith sensor j Mean square error for the jth sensor;
the weighting factors obtained by the formula (14) can fuse the numerical sensor data with any precision, so that the measurement precision of the system is effectively improved;
and step S3, carrying out actual theoretical calculation deduction based on the acquired data of the actual sensor, and verifying the effectiveness of the algorithm.
Referring to fig. 3, the multi-sensor fusion device for a power battery reaction control module of the present invention includes the following parts:
and an error definition module: definition of the true value x t And predicted valueError e 'between' t And a true value x t And the estimated valueError e between t Obtaining a prediction error covariance matrix P' t And an estimation error covariance matrix P t As shown in fig. 4, the method comprises the following parts:
error definition unit: the true value x t And predicted valueError e 'between' t And a true value x t And the estimated valueError e between t The method comprises the following steps of:
wherein Q is a measurementQuantity matrix, K kalman Is a Kalman gain matrix, v t Is a process noise matrix;
error covariance matrix unit: the prediction error covariance matrix P' t And an estimation error covariance matrix P t The method comprises the following steps of:
wherein E [ v ] t v t T ]＝C，K kalman Is Kalman gain matrix, Q is measurement matrix, x t To be a true value of the value,is the predicted value of the true value, P' t For prediction error covariance matrix, P t For estimating an error covariance matrix;
and a data fusion module: covariance matrix P 'of prediction error' i Substituting and expanding, deriving, final defining and data fusion operation to obtain a data fusion value with minimum mean square error, and improving the precision and reliability of the system, wherein the method comprises the following steps as shown in fig. 5:
the prediction error covariance matrix is substituted into the unit: covariance matrix P of prediction error t Substitution to obtain
P t ＝(I-K kalman Q)P′ t (I-K kalman Q) T +K kalman CK kalman T (5)，
Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix;
kalman filter expansion unit: the Kalman filtering is essentially the least mean square error estimation, and the method can be obtained by expanding and tracing the formula (5)
tr(P t )＝tr(P′ t )-2tr(K kalman QP′ t )+tr(K kalman (QP′ t Q T +C)K kalman T ) (6)，
Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix;
and a derivation unit: optimal estimation K kalman Let tr (P) t ) Minimum, deriving both sides of formula (6) to be equal to 0
K kalman ＝P′ t Q T (QP′ t Q T +C) -1 (7)，
Wherein K is kalman Is a Kalman gain matrix, P' t For the prediction error covariance matrix, Q is a measurement matrix, and the value is debugged according to the system;
by collating the above-mentioned derivation processes
P′ t ＝P t -K kalman HP t ＝(I-K kalman H)P t (9)，
Wherein,predicted value being true value, +.>Estimated value for true value, +.>K is the predicted value of the observed value kalman Is Kalman gain matrix, H is process excitation noise covariance matrix, P t To estimate the error covariance matrix, P' t A covariance matrix of the prediction error;
kalman filter definition unit: the calculation process of final definition Kalman filtering is as follows
Wherein A is a state transition matrix, B is an input gain matrix,predicted value, u, being the true value of the previous state t-1 For the input of the previous state prediction model, P' t For prediction error covariance matrix, P t-1 Estimating an error covariance matrix for the previous state, wherein H is a process excitation noise covariance matrix;
defining the correction process of the Kalman filter as
Wherein z is t In order to observe the value of the value,for the predicted value of the observed value, Q is the measurement matrix,>k is the predicted value of the true value kalman Is a Kalman gain matrix, P' t For prediction error covariance matrix,>estimated value for true value, +.>To measure the margin;
and a data fusion unit: data fusion is carried out on the data of various sensors to obtain a data fusion value with minimum mean square error, and the accuracy and the reliability of the system are improved;
it is assumed that there are n sensors independent of each other, wherein the state of the ith sensor is X i (i=1,., n), the error of the i-th sensor is MSE i (i＝1,...,n)，
The data of each sensor is fused by a weighted average fusion method to obtain
Wherein omega i (i=1,., n) is the weight assigned to each sensor, X aver Representing the fused average sensor state;
introducing a total mean square error MSE
Wherein omega i Is the weight on the ith sensor, X aver X is the fused average sensor state i Or X j Status of the ith or jth sensor;
according to the limit theory, the weight corresponding to the minimum time of the total mean square error MSE can be obtained as
Wherein MSE i MSE for mean square error of the ith sensor j Mean square error for the jth sensor;
and a validity verification module: the effectiveness of the algorithm is verified by performing actual theoretical calculation deduction based on the actual sensor acquisition data.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
What is not described in detail in this specification is prior art known to those skilled in the art.

Claims (2)

1. A multi-sensor fusion method for a power battery reaction control module, characterized by comprising the steps of: the method comprises the following steps:
s1, defining a true value x t And predicted valueError e 'between' t And a true value x t And estimate +.>Error e between t Obtaining a prediction error covariance matrix P t ' sum-of-estimated-error covariance matrix P t ；
S2, covariance matrix P of prediction error t ' substituting and expanding, deriving, final definition and data fusion operation are carried out to obtain a data fusion value with minimum mean square error, so that the accuracy and reliability of the system are improved;
s3, carrying out actual theoretical calculation deduction based on actual sensor acquisition data, and verifying the effectiveness of an algorithm;
in the step S1, the true value x t And predicted valueError e 'between' t And a true value x t And estimate +.>Error e between t The method comprises the following steps of:
wherein Q is a measurement matrix, K kalman Is a Kalman gain matrix, v t Is a process noise matrix;
the prediction error covariance matrix P t ' sum-of-estimated-error covariance matrix P t The method comprises the following steps of:
wherein E [ v ] t v t T ]＝C，K kalman Is Kalman gain matrix, Q is measurement matrix, x t To be a true value of the value,predicted value as true value, P t ' is the prediction error covariance matrix, P t For estimating an error covariance matrix;
the specific process of the step S2 is as follows:
s21, covariance matrix P of prediction error t ' substitution to obtain
P t ＝(I-K kalman Q)P t ′(I-K kalman Q) T +K kalman CK kalman T (5)，
Wherein K is kalman Is a Kalman gain matrix, P t ' is the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix;
s22, the Kalman filtering essence is minimum mean square error estimation, and the equation (5) is unfolded and tracked to obtain
tr(P t )＝tr(P t ′)-2tr(K kalman QP t ′)+tr(K kalman (QP t ′Q T +C)K kalman T ) (6)，
Wherein K is kalman Is a Kalman gain matrix, P t ' is the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix;
s23, optimal estimation K kalman Let tr (P) t ) Minimum, deriving both sides of formula (6) to be equal to 0
K kalman ＝P t ′Q T (QP t ′Q T +C) -1 (7)，
Wherein K is kalman Is a Kalman gain matrix, P t ' is a prediction error covariance matrix, Q is a measurement matrix, and the value is debugged according to the system;
by collating the above-mentioned derivation processes
P t ′＝P t -K kalman HP t ＝(I-K kalman H)P t (9)，
Wherein,predicted value being true value, +.>Estimated value for true value, +.>K is the predicted value of the observed value kalman Is Kalman gain matrix, H is process excitation noise covariance matrix, P t To estimate the error covariance matrix, P t ' is a prediction error covariance matrix;
s24, finally defining the calculation process of Kalman filtering as
Wherein A is a state transition matrix, B is an input gain matrix,predicted value, u, being the true value of the previous state t-1 For the input of the last state prediction model, P t ' is the prediction error covariance matrix, P t-1 Estimating an error covariance matrix for the previous state, wherein H is a process excitation noise covariance matrix;
defining the correction process of the Kalman filter as
Wherein z is t In order to observe the value of the value,for the predicted value of the observed value, Q is the measurement matrix,>k is the predicted value of the true value kalman Is a Kalman gain matrix, P t ' is the prediction error covariance matrix,>estimated value for true value, +.>To measure the margin;
s25, data fusion is carried out on the data of various sensors to obtain a data fusion value with minimum mean square error, and the accuracy and the reliability of the system are improved;
the specific process of step S25 is as follows:
s251, supposing that n sensors independent of each other exist, wherein the state of the ith sensor is X i I=1. Once again, error of the ith sensor is MSE i ，i＝1......n，
The data of each sensor is fused by a weighted average fusion method to obtain
Wherein omega i I=1. Once again, n is, to weight each sensor, X aver Representing the fused average sensor state;
s252, introducing a total mean square error MSE
Wherein omega i Is the weight on the ith sensor, X aver X is the fused average sensor state i Or X j Status of the ith or jth sensor;
s253, according to the limit theory, obtaining the weight corresponding to the minimum MSE as
Wherein MSE i MSE for mean square error of the ith sensor j Is the mean square error of the jth sensor.
2. A multi-sensor fusion device for a power cell reaction control module, characterized by: comprises the following parts:
and an error definition module: definition of the true value x t And predictionValue ofError e 'between' t And a true value x t And estimate +.>Error e between t Obtaining a prediction error covariance matrix P t ' sum-of-estimated-error covariance matrix P t ；
And a data fusion module: covariance matrix P of prediction error t ' substituting and expanding, deriving, final definition and data fusion operation are carried out to obtain a data fusion value with minimum mean square error, so that the accuracy and reliability of the system are improved;
and a validity verification module: carrying out actual theoretical calculation deduction based on the data acquired by the actual sensor, and verifying the effectiveness of the algorithm;
the error definition module comprises the following parts:
error definition unit: the true value x t And predicted valueError e 'between' t And a true value x t And estimate +.>Error e between t The method comprises the following steps of:
wherein Q is a measurement matrix, K kalman Is a Kalman gain matrix, v t Is a process noise matrix;
error covariance matrix unit: the prediction error covariance matrix P t ' sum-of-estimated-error covariance matrix P t The method comprises the following steps of:
wherein E [ v ] t v t T ]＝C，K kalman Is Kalman gain matrix, Q is measurement matrix, x t To be a true value of the value,predicted value as true value, P t ' is the prediction error covariance matrix, P t For estimating an error covariance matrix;
the data fusion module comprises the following parts:
the prediction error covariance matrix is substituted into the unit: covariance matrix P of prediction error t ' substitution to obtain
P t ＝(I-K kalman Q)P t ′(I-K kalman Q) T +K kalman CK kalman T (5)，
Wherein K is kalman Is a Kalman gain matrix, P t ' is the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix;
kalman filter expansion unit: the Kalman filtering is essentially the least mean square error estimation, and the method can be obtained by expanding and tracing the formula (5)
tr(P t )＝tr(P t ′)-2tr(K kalman QP t ′)+tr(K kalman (QP t ′Q T +C)K kalman T ) (6)，
Wherein K is kalman Is Kalman gain momentArray, P t ' is the prediction error covariance matrix, Q is the measurement matrix, P t For estimating an error covariance matrix;
and a derivation unit: optimal estimation K kalman Let tr (P) t ) Minimum, deriving both sides of formula (6) to be equal to 0
K kalman ＝P t ′Q T (QP t ′Q T +C) -1 (7)，
Wherein K is kalman Is a Kalman gain matrix, P t ' is a prediction error covariance matrix, Q is a measurement matrix, and the value is debugged according to the system;
by collating the above-mentioned derivation processes
P t ′＝P t -K kalman HP t ＝(I-K kalman H)P t (9)，
Wherein,predicted value being true value, +.>Estimated value for true value, +.>K is the predicted value of the observed value kalman Is Kalman gain matrix, H is process excitation noise covariance matrix, P t To estimate the error covariance matrix, P t ' is a prediction error covariance matrix;
kalman filter definition unit: the calculation process of final definition Kalman filtering is as follows
Wherein A is a state transition matrix, B is an input gain matrix,predicted value, u, being the true value of the previous state t-1 For the input of the last state prediction model, P t ' is the prediction error covariance matrix, P t-1 Estimating an error covariance matrix for the previous state, wherein H is a process excitation noise covariance matrix;
defining the correction process of the Kalman filter as
Wherein z is t In order to observe the value of the value,for the predicted value of the observed value, Q is the measurement matrix,>k is the predicted value of the true value kalman Is a Kalman gain matrix, P t ' is the prediction error covariance matrix,>estimated value for true value, +.>To measure the margin;
and a data fusion unit: data fusion is carried out on the data of various sensors to obtain a data fusion value with minimum mean square error, and the accuracy and reliability of the system are improved;
the specific process of obtaining the data fusion value with the minimum mean square error by carrying out data fusion on the data of various sensors is as follows:
assume thatHaving n sensors independent of each other, wherein the state of the ith sensor is X i (i=1,., n), the error of the i-th sensor is MSE i (i＝1,...,n)，
The data of each sensor is fused by a weighted average fusion method to obtain
Wherein omega i (i=1,., n) is the weight assigned to each sensor, X aver Representing the fused average sensor state;
introducing a total mean square error MSE
Wherein omega i Is the weight on the ith sensor, X aver X is the fused average sensor state i Or X j Status of the ith or jth sensor;
according to the limit theory, the weight corresponding to the time of obtaining the minimum MSE is
Wherein MSE i MSE for mean square error of the ith sensor j Is the mean square error of the jth sensor.
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