CN108228535A - A kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion - Google Patents
A kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion Download PDFInfo
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Abstract
The invention discloses a kind of optimal weighting parameter evaluation methods of unequal precision measurement data fusion, including obtaining first kind observation data and the second kind observation data, determine parameter to be estimated；Obtain first kind observation function；Obtain the second kind observation function；Structure first kind observation data merge majorized function with the second kind observation data；The fusion majorized function is solved, calculates optimal weighting value and to be estimated parameter of the first kind observation data with the second kind observation data.The calculating that the present invention passes through estimated bias and mean square error, the computational methods of optimum fusion weights when giving the processing of multiclass measurement data fusion, corresponding parameter estimation algorithm is established simultaneously, the Parameter fusion estimated value that can be further accurately calculated when realizing Data Fusion under unequal precision measurement data optimal weighting.The invention is used to merge the measurement data of unequal accuracy.
Description
Technical field
The present invention relates to Data fusion technique field, more specifically to a kind of unequal precision measurement data fusion most
Excellent weighting parameters evaluation method.
Background technology
In measurement data fusion treatment, the most typically fusion of different type, unequal accuracy data.When number will be observed
After parameter model is expressed as, measurement data fusion problem can be converted to the Parameter Estimation Problem of regression model.Measurement data
Fusion treatment be conducive to improve parameter Estimation precision.Wherein, different types of data or heterogeneous data refer to that observing data closes
It is different in the functional relation of parameter to be estimated, so as to which its all-order derivative is also different.If to a variety of essences such as not involved in fusion treatment
The observation data of degree, the different weighting scheme of these data, have a great impact to parameter estimation result, therefore for the essences such as not
The weighting of degrees of data fusion is treated as improving the key technology of Parameter Estimation Precision.
For the parameter Estimation of linear regression model (LRM), Gauss-Markov theorems (Gauss-Markov theorem) give
Unique optimal weighting principle of unequal precision measurement data, i.e. blending weight are only related with the precision of measurement data.
And for there are during the processing of the multiclass measurement data fusion of nonlinear model, optimum fusion weights are no longer by measurement number
According to precision uniquely determine that but related with the structure of observation model simultaneously, i.e. the Gauss-Markov of linear model classics determines
Reason is no longer set up.
But at present about the measurement data fusion there are nonlinear model during, always assume that it is all observation data for etc.
Precision, that is, the random error for observing data is independent same distribution, so as to not consider to weight or directly use linear model
The conclusion of Gauss-Markov theorems is weighted the multiclass measurement data for including linear and nonlinear model, so as to reduce
The precision of data fusion.During for multiclass measurement data fusion parameter Estimation including nonlinear model, due to being all false
If all observation data for equally accurate or directly merged using the precision for observing data to be weighted, therefore, for depositing
In the multiclass unequal accuracy measurement data fusion of non-linear observation model, there are certain mistakes for Parameter fusion estimated result value
Difference.
Invention content
The technical problem to be solved by the present invention is to：A kind of optimal weighting parameter of unequal precision measurement data fusion is provided to estimate
Calculation method.
The present invention solve its technical problem solution be：
A kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion, including：
First kind observation data and the second kind observation data are obtained, determine parameter to be estimated；
It determines the nonlinear function between the first kind observation data and parameter to be estimated, obtains first kind observation letter
Number；
It determines the linear functional relation between the second kind observation data and parameter to be estimated, obtains the second kind observation letter
Number；
Based on the first kind observation function and the second kind observation function, structure first kind observation data are seen with the second class
The fusion majorized function of measured data；
Based on root mean squared error for channel estimation minimum criteria, the fusion majorized function is solved, and according to solving result, calculate
Optimal weighting value and to be estimated parameter of the first kind observation data with the second kind observation data.
As a further improvement of the above technical scheme, the first kind observation function is as shown in expression formula 1, y1(ti)=f
(ti,β)+ε1(ti), i=1 ..., m, wherein y1(ti) it is tiThe first kind observation data at moment, f (ti, β) and it is corresponding non-
Systems with Linear Observation function, β are unitary parameter to be estimated, and β ∈ R, R are real number field, ε1(ti) (i=1 ..., m) it is that the first kind observes data
Measurement random noise, independent same distribution is zero in mean value, and variance isNormal distribution,Data are observed for the first kind
Measurement accuracy, m are the observation sample number that the first kind observes data.
As a further improvement of the above technical scheme, the second kind observation function is as shown in expression formula 2, y2(ti)=x
(ti)β+ε2(ti), i=1 ..., k, wherein, y2(ti) it is tiThe second kind observation data at moment, x (ti) observed to be corresponding
Matrix, ε2(ti) (i=1 ..., k) the second kind observation data measurement random noise, independent same distribution is zero in mean value, and variance isNormal distribution,For the measurement accuracy of the second kind observation data, k is the sample number of the second kind observation data.
As a further improvement of the above technical scheme, it is described fusion majorized function as shown in expression formula 3,WhereinData and institute are observed for the first kind
The blending weight of the second kind observation data is stated,
As a further improvement of the above technical scheme, the fusion majorized function is solved, and according to solving result, is calculated
Optimal weighting value and to be estimated parameter of the first kind observation data with the second kind observation data, this process specifically includes following
Step：
Step A. setting weighting initial valuesMinimum is solved by the expression formula 3, is solved
The estimation mean square error that step B. calculates parameter beta to be estimated by expression formula 4 existsThe value at place
Wherein
Step C. solves minimumIt is right by expression formula 4Derivation simultaneously makes expression formula 4
Equal to 0, obtain
Step D. sets convergence criterion, described in judgementWhether set convergence criterion is met, if satisfied, then iteration
Terminate, determineFor optimum fusion weights,Optimal estimation for parameter.
As a further improvement of the above technical scheme, convergence criterion described in step D is as shown in expression formula 5,Wherein τ is convergence threshold, takes τ=0.01.
As a further improvement of the above technical scheme, in step D, if describedSet convergence criterion is unsatisfactory for,
It willIt is assigned toAnd return to step A, until iteration convergence, wherein,It is seen for the first kind
The blending weight of measured data and the second kind observation data.
The beneficial effects of the invention are as follows：The present invention gives multiclass observation by the calculating of estimated bias and mean square error
The computational methods of optimum fusion weights during Data Fusion, while corresponding parameter estimation algorithm is established, realize data
The Parameter fusion estimated value that can be further accurately calculated during fusion treatment under unequal precision measurement data optimal weighting.
The invention is used to merge the measurement data of unequal accuracy.
Description of the drawings
To describe the technical solutions in the embodiments of the present invention more clearly, make required in being described below to embodiment
Attached drawing is briefly described.Obviously, described attached drawing is the part of the embodiment of the present invention rather than all implements
Example, those skilled in the art without creative efforts, can also be obtained according to these attached drawings other designs
Scheme and attached drawing.
Fig. 1 is the evaluation method flow chart of the present invention.
Specific embodiment
The technique effect of the design of the present invention, concrete structure and generation is carried out below with reference to embodiment and attached drawing clear
Chu, complete description, to be completely understood by the purpose of the present invention, feature and effect.Obviously, described embodiment is this hair
Bright part of the embodiment rather than whole embodiments, based on the embodiment of the present invention, those skilled in the art is not paying
The other embodiment obtained under the premise of creative work, belongs to the scope of protection of the invention.
With reference to Fig. 1, the invention discloses a kind of optimal weighting parameter estimation side of unequal precision measurement data fusion
Method, including：
First kind observation data and the second kind observation data are obtained, determine parameter to be estimated；
It determines the nonlinear function between the first kind observation data and parameter to be estimated, obtains first kind observation letter
Number；
It determines the linear functional relation between the second kind observation data and parameter to be estimated, obtains the second kind observation letter
Number；
Based on the first kind observation function and the second kind observation function, structure first kind observation data are seen with the second class
The fusion majorized function of measured data；
Based on root mean squared error for channel estimation minimum criteria, the fusion majorized function is solved, and according to solving result, calculate
Optimal weighting value and to be estimated parameter of the first kind observation data with the second kind observation data.
Specifically, the present invention gives the processing of multiclass measurement data fusion by the calculating of estimated bias and mean square error
When optimum fusion weights computational methods, while establish corresponding parameter estimation algorithm, energy when realizing Data Fusion
Enough Parameter fusion estimated values being further accurately calculated under unequal precision measurement data optimal weighting.
It is further used as preferred embodiment, in the invention specific embodiment, the first kind observation function
As shown in expression formula 1, y1(ti)=f (ti,β)+ε1(ti), i=1 ..., m, wherein y1(ti) it is tiThe first kind observation at moment
Data, f (ti, β) and for corresponding non-linear observation function, β is unitary parameter to be estimated, and β ∈ R, R are real number field, ε1(ti) (i=
1 ..., m) it is the measurement random noise that the first kind observes data, independent same distribution is zero in mean value, and variance isNormal state point
Cloth,The measurement accuracy of data is observed for the first kind, m is the observation sample number that the first kind observes data.
It is further used as preferred embodiment, in the invention specific embodiment, the second kind observation function
As shown in expression formula 2, y2(ti)=x (ti)β+ε2(ti), i=1 ..., k, wherein, y2(ti) it is tiThe second kind observation at moment
Data, x (ti) for corresponding observing matrix, ε2(ti) (i=1 ..., k) the second kind observation data measurement random noise, it is independent
It is zero with mean value is distributed in, variance isNormal distribution,For the measurement accuracy of the second kind observation data, k is the second class
Observe the sample number of data.
It is further used as preferred embodiment, in the invention specific embodiment, the fusion majorized function is such as
Shown in expression formula 3,WhereinFor the first kind
The blending weight of data and the second kind observation data is observed,
It is further used as preferred embodiment, in the invention specific embodiment, solves the fusion optimization letter
Number, and according to solving result, calculate the optimal weighting value of the first kind observation data and the second kind observation data and wait to estimate ginseng
Number, this process specifically include the following steps：
Step A. setting weighting initial valuesMinimum is solved by the expression formula 3, is solved
The estimation mean square error that step B. calculates parameter beta to be estimated by expression formula 4 existsThe value at place
Wherein
Step C. solves minimumIt is right by expression formula 4Derivation simultaneously makes expression formula 4
Equal to 0, obtain
Step D. sets convergence criterion, described in judgementWhether set convergence criterion is met, if satisfied, then iteration
Terminate, determineFor optimum fusion weights,Optimal estimation for parameter.
It is further used as preferred embodiment, in the invention specific embodiment, convergence criterion described in step D
As shown in expression formula 5,Wherein τ is convergence threshold, takes τ=0.01.
Preferred embodiment is further used as, in the invention specific embodiment, in step D, if describedNo
Meet set convergence criterion, it willIt is assigned toAnd return to step A, until iteration convergence, wherein,The blending weight of data and the second kind observation data is observed for the first kind.
A specific embodiment is lifted herein the invention is described in detail.
The present embodiment considers the measurement and estimation of parameter beta to be estimated to unitary, is illustrated using two classes observation data, a kind of
It is non-Systems with Linear Observation function, another kind of is Systems with Linear Observation function.
First kind observation function is y1(ti)=f1(t1,β)+ε1(ti), wherein f1(ti, β) and=1+ (5+tiβ)0.1For about
The nonlinear function of parameter beta to be estimated, ε1(ti) be mean value it is zero, variance 0.052Measurement random noise, wherein observation sample
Number is：ti=0.05 × (i-1), i=1 ..., 300, i.e. observation sample m=300.
The second kind observation function is y2(tk)=f2(tk,β)+ε2(tk), whereinFor about waiting to estimate ginseng
The linear function of number β, ε2(tk) be mean value it is zero, variance 0.012Measurement random noise, wherein observation sample number is：tk=
2+0.1 × (k-1), k=1 ..., 100, i.e. observation sample k=100.
If the true value of β is 10, observation data are generatedUtilize 100 systems of Monte Carlo simulation
The estimated result of parameter beta to be estimated is counted, the estimated result that table 1 is given under various different blending weights compares.
When the weighting scheme using linear model is weighted fusion to above two class observation data, that is, the blending weight is taken to beWhen, the estimated value of obtained parameter beta is 10.064, and the mean square error of estimation is 0.054；
And use the optimum fusion weights of iteration convergenceWhen, the estimated value of obtained parameter beta is 9.987, is estimated at this time
Mean square error is minimum, is 0.015.
The better embodiment of the present invention is illustrated, but the invention is not limited to the implementation above
Example, those skilled in the art can also make various equivalent modifications under the premise of without prejudice to spirit of the invention or replace
It changes, these equivalent modifications or replacement are all contained in the application claim limited range.
Claims (7)
1. a kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion, which is characterized in that including：
First kind observation data and the second kind observation data are obtained, determine parameter to be estimated；
It determines the nonlinear function between the first kind observation data and parameter to be estimated, obtains first kind observation function；
It determines the linear functional relation between the second kind observation data and parameter to be estimated, obtains the second kind observation function；
Based on the first kind observation function and the second kind observation function, structure first kind observation data and the second kind observation number
According to fusion majorized function；
Based on root mean squared error for channel estimation minimum criteria, the fusion majorized function is solved, and according to solving result, described in calculating
The first kind observes the optimal weighting value of data and the second kind observation data and parameter to be estimated.
2. a kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion according to claim 1, special
Sign is that the first kind observation function is as shown in expression formula 1, y1(ti)=f (ti,β)+ε1(ti), i=1 ..., m, wherein y1
(ti) it is tiThe first kind observation data at moment, f (ti, β) and for corresponding non-linear observation function, β is unitary parameter to be estimated, β
∈ R, R are real number field, ε1(ti) the measurement random noise of (i=1 ..., m) for first kind observation data, independent same distribution is in mean value
It is zero, variance isNormal distribution,The measurement accuracy of data is observed for the first kind, m is the sight that the first kind observes data
Survey sample number.
3. a kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion according to claim 2, special
Sign is that the second kind observation function is as shown in expression formula 2, y2(ti)=x (ti)β+ε2(ti), i=1 ..., k, wherein, y2
(ti) it is tiThe second kind observation data at moment, x (ti) for corresponding observing matrix, ε2(ti) (i=1 ..., k) sight of the second class
The measurement random noise of measured data, independent same distribution are zero in mean value, and variance isNormal distribution,For the second kind observation
The measurement accuracy of data, k are the sample number of the second kind observation data.
4. a kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion according to claim 3, special
Sign is, the fusion majorized function as shown in expression formula 3,
WhereinThe blending weight of data and the second kind observation data is observed for the first kind,
5. a kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion according to claim 4, special
Sign is, solves the fusion majorized function, and according to solving result, calculate the first kind observation data and the second kind observation
The optimal weighting value and parameter to be estimated of data, this process specifically include the following steps：
Step A. setting weighting initial valuesMinimum is solved by the expression formula 3, is solved
The estimation mean square error that step B. calculates parameter beta to be estimated by expression formula 4 existsThe value at place Wherein
Step C. solves minimumIt is right by expression formula 4Derivation is simultaneously equal to expression formula 4
0, it obtains
Step D. sets convergence criterion, described in judgementWhether set convergence criterion is met, if satisfied, then iteration terminates,
It determinesFor optimum fusion weights,Optimal estimation for parameter.
6. a kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion according to claim 5, special
Sign is, convergence criterion described in step D as shown in expression formula 5,Wherein τ be convergence threshold, take τ=
0.01。
7. a kind of optimal weighting parameter evaluation method of unequal precision measurement data fusion according to claim 6, special
Sign is, in step D, if describedSet convergence criterion is unsatisfactory for, it willIt is assigned toAnd return to step A, directly
Until iteration convergence, wherein,Melting for data and the second kind observation data is observed for the first kind
Close weights.
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