CN115238454A - Method and device for correcting data - Google Patents
Method and device for correcting data Download PDFInfo
- Publication number
- CN115238454A CN115238454A CN202210654243.1A CN202210654243A CN115238454A CN 115238454 A CN115238454 A CN 115238454A CN 202210654243 A CN202210654243 A CN 202210654243A CN 115238454 A CN115238454 A CN 115238454A
- Authority
- CN
- China
- Prior art keywords
- algorithm
- parameter
- value
- error model
- sensor error
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Indication And Recording Devices For Special Purposes And Tariff Metering Devices (AREA)
Abstract
The embodiment of the invention discloses a method and a device for correcting data. The data correction method comprises the following steps: acquiring a pre-established sensor error model; performing parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result; correcting the measurement data according to the parameter identification result; the preset joint algorithm is an improved joint estimation algorithm based on an expectation maximization algorithm and a cubature Kalman smoother. According to the invention, the problem that the estimation accuracy of the unknown parameters in the sensor error model in the high-sensor noise environment is obviously reduced due to the fact that the prior art is not consistent with an actual system when the system noise is processed in the related art is solved, and the technical effect of improving the estimation accuracy of the unknown parameters in the sensor error model in the high-sensor noise environment is achieved.
Description
Technical Field
The invention relates to the field of aerospace technology application, in particular to a method and a device for data correction.
Background
When the measured data of a certain sensor in the flight data can be indirectly calculated by the measured data of other sensors and the motion equation of the aircraft, redundant information exists in the flight data at the moment, and in the flight data containing the redundant information, if the data fitting degree of the directly measured data and the indirectly calculated data from two sources is poor, the group of data is called as uncoordinated. The reason for causing data incompatibility is that systematic measurement errors exist in the sensors, the core of the coordination analysis is to identify the systematic errors of the sensors in the flight data, and the measured data of the sensors are corrected through the identified errors, so that more accurate flight data are provided for follow-up work.
In the process of estimating the sensor error, in order to avoid coupling with the identification problem of the pneumatic parameters, the number of unknown parameters and the dimensionality of a state equation are increased, and generally only an aircraft motion equation is considered. By replacing the acceleration generated by thrust and aerodynamic forces in the aircraft's equations of motion with the measurements from the accelerometers, the unknown aerodynamic forces in the line motion will be completely isolated. After such processing, the angular velocity and the acceleration in the recognition model exist in the system equation in the form of "input quantity", and random measurement noise in the input quantity is also introduced.
With the continuous development of the optimal estimation theory, the combination of the Expectation-maximization (Expectation-maximization) algorithm and the filtering/smoothing algorithm gradually matures, the numerical stability of the EM algorithm is good, and an integrated processing scheme for realizing estimation and identification by using the EM iterative optimization idea has made an important research progress recently. However, the EM-smoother joint estimation methods proposed in the related art all assume that the system noise is additive noise. However, in a series of problems represented by data harmony analysis, the system is an affine nonlinear system. Since the source of the system noise is the noise present in the input quantity, this results in the system also being "affine" to the noise:
the system noise v coefficient is not 1 at this time but a function of the time-varying state, belonging to non-additive noise. The existing EM-CKS (joint estimation algorithm based on Expectation Maximization (EM) algorithm and Cubature Kalman Smoother (CKS)) algorithm can only ignore the characteristics of such systems when processing the systems, and as additive noise processing, the existing EM-CKS are not consistent with the actual systems, and certainly cannot achieve the optimal estimation effect.
Aiming at the problem that the estimation accuracy of unknown parameters in a sensor error model is obviously reduced under the environment of high sensor noise because the prior art is not consistent with an actual system when the system noise is processed in the prior art, the problem is not effectively solved at present.
Disclosure of Invention
The embodiment of the invention provides a method and a device for correcting data, which at least solve the problem that the estimation accuracy of unknown parameters in a sensor error model is obviously reduced in a high-sensor-noise environment because the prior art is not consistent with an actual system when processing system noise in the related art.
According to an aspect of an embodiment of the present invention, there is provided a method of data correction, including: acquiring a pre-established sensor error model; performing parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result; correcting the measurement data according to the parameter identification result; the preset joint algorithm is an improved joint estimation algorithm based on an expectation maximization algorithm and a cubature Kalman smoother.
Optionally, before acquiring the pre-created sensor error model, the method further includes: creating a sensor error model, wherein the sensor error model comprises:
z(i)＝(1+λ)y(i)+b+v(i),i＝1,2,…,N；
where z (i) is the sensor ith measurement output, y (i) is the true value, v (i) is the random measurement noise, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
Optionally, performing parameter estimation on the sensor error model according to a preset joint algorithm, and obtaining a parameter identification result includes: setting initial values of parameters in a sensor error model; calculating an initial value according to a cubature Kalman filtering algorithm to obtain a filtered parameter; calculating the filtered parameters according to a volume Kalman smoothing algorithm to obtain smoothing parameters; updating the initial value according to the smooth parameter and the improved expectation-maximization algorithm to obtain an updated initial value; judging whether the iterative computation times of parameter estimation of the sensor error model reach a first preset value or not; if the judgment result is yes, outputting a parameter identification result; and under the condition that the judgment result is negative, sequentially executing a volume Kalman filtering algorithm, a volume Kalman smoothing algorithm and an improved expectation maximization algorithm until the times of iterative computation reach a first preset value.
Further, optionally, calculating the initial value according to a volume kalman filter algorithm, and obtaining the filtered parameter includes: according to the initial value
Initial value of (A) and
an initial value of (d); according to
Initial value of (A) and
is calculated as the mean of the predicted distribution of the states
Sum covariance
Mean value of distribution according to prediction
Sum covariance
Calculating a mean value of a filter distribution of states
Sum covariance value
Is judged to be rightWhether the iterative computation times of the initial value reach a second preset value or not; outputting the filtered parameters under the condition that the judgment result is yes; under the condition that the judgment result is negative, calculating the prediction distribution mean value of the state in sequence
Sum covariance
And calculating the mean of the filter distribution of the states
Sum covariance value
Until the number of iterative calculations reaches a second preset value.
Optionally, calculating the filtered parameter according to a volume kalman smoothing algorithm, and obtaining the smoothing parameter includes: one-step prediction state mean value of complete time sequence obtained by importing volume Kalman filtering algorithm
State prediction covariance
sigma point
And mean value of filter state
Sum covariance
Calculating a smoothing gain G k-1 And smoothed mean value
Sum covariance
Judging whether the iterative computation times of the filtered parameters reach a third preset value or not; if the judgment result is yes, calculating
And
if the judgment result is negative, adjusting the times and calculating the smooth gain G k-1 And smoothed mean value
Sum covariance
Until the number of iterative calculations reaches a third preset value.
Optionally, the updating the initial value according to the smoothing parameter and the improved expectation-maximization algorithm, and obtaining the updated initial value includes: based on smoothing parameters and improved expectation-maximization algorithm, for unknown Q, measured noise variance R and state initial distribution parameters in system noise variance R
And estimating to obtain an updated initial value.
Optionally, the correcting the measurement data according to the parameter identification result includes: correcting the measurement data according to an error correction formula and a parameter identification result, wherein the error correction formula comprises:
where z (i) is the sensor ith measurement output, y (i) is the true value, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
According to another aspect of the embodiments of the present invention, there is provided an apparatus for data correction, including: the acquisition module is used for acquiring a pre-established sensor error model; the estimation module is used for carrying out parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result; the correction module is used for correcting the measurement data according to the parameter identification result; the preset joint algorithm is an improved joint estimation algorithm based on an expectation maximization algorithm and a cubature Kalman smoother.
Optionally, the apparatus further comprises: a creation module for creating a sensor error model prior to acquiring a pre-created sensor error model, wherein the sensor error model comprises:
z(i)＝(1+λ)y(i)+b+v(i),i＝1,2,…,N；
where z (i) is the sensor ith measurement output, y (i) is the true value, v (i) is the random measurement noise, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
Optionally, the estimation module includes: the setting unit is used for setting initial values of parameters in the sensor error model; the first calculation unit is used for calculating the initial value according to a cubature Kalman filtering algorithm to obtain a filtered parameter; the second calculation unit is used for calculating the filtered parameters according to a volume Kalman smoothing algorithm to obtain smoothing parameters; the updating unit is used for updating the initial value according to the smoothing parameter and the improved expectation-maximization algorithm to obtain an updated initial value; the judging unit is used for judging whether the times of iterative calculation for parameter estimation of the sensor error model reaches a first preset value or not; the output unit is used for outputting a parameter identification result under the condition that the judgment result is yes; and the iteration unit is used for sequentially executing the volume Kalman filtering algorithm, the volume Kalman smoothing algorithm and the improved expectation maximization algorithm under the condition that the judgment result is negative until the iterative calculation times reach a first preset value.
In the embodiment of the invention, a pre-established sensor error model is obtained; performing parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result; correcting the measurement data according to the parameter identification result; the preset joint algorithm is an improved joint estimation algorithm based on an expectation maximization algorithm and a cubature Kalman smoother. That is to say, the embodiment of the present invention can solve the problem in the related art that the estimation accuracy of the unknown parameter in the sensor error model in the high sensor noise environment is significantly reduced due to the fact that the prior art is not matched with the actual system when processing the system noise, and achieves the technical effect of improving the estimation accuracy of the unknown parameter in the sensor error model in the high sensor noise environment.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the invention without limiting the invention. In the drawings:
fig. 1 is a schematic flow chart illustrating a data correction method according to an embodiment of the present invention;
FIG. 2 is a flow chart illustrating another method for data correction according to an embodiment of the present invention;
fig. 3 is a schematic flowchart of an improved EM-CKS algorithm in a data correction method according to an embodiment of the present invention;
FIGS. 4 a-4 f are schematic diagrams illustrating the comparison of the real IMU input used by the simulation data with the IMU measurement after adding noise and sensor errors in a data correction method according to an embodiment of the present invention;
fig. 5a to 5f are schematic diagrams illustrating comparison between a data reconstruction result and a measurement result before and after correction of simulated measurement data by an identified sensor error in a data correction method according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a data correction apparatus according to an embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first", "second", and the like in the description and claims of the present invention and the accompanying drawings are used for distinguishing different objects, and are not used for limiting a specific order.
According to an aspect of the embodiment of the present invention, a method for data correction is provided, and fig. 1 is a schematic flow chart of the method for data correction according to the embodiment of the present invention. As shown in fig. 1, a method for providing data correction in an embodiment of the present application includes:
step S102, acquiring a pre-established sensor error model;
optionally, before obtaining the pre-created sensor error model in step S102, the method for providing data correction in the embodiment of the present application further includes: creating a sensor error model, wherein the sensor error model comprises:
z(i)＝(1+λ)y(i)+b+v(i)，i＝1，2，...，N；
where z (i) is the sensor ith measurement output, y (i) is the true value, v (i) is the random measurement noise, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
Specifically, as shown in fig. 2, fig. 2 is a schematic flow chart of another data correction method according to an embodiment of the present invention. Let the sensor error model be of the form:
z(i)＝(1+λ)y(i)+b+v(i)，i＝1，2，...，N (1.1)
where z (i) is the sensor ith measurement output, y (i) is the true value, and v (i) is the random measurement noise. λ is a constant scale factor error parameter and b is a constant error offset parameter.
The state space model for data coordination analysis using the aircraft equations of motion is as follows:
the system equation:
the measurement equation set is as follows:
φ E (i)＝(1+λ φ )φ(i)+v φ (i)
θ E (i)＝(1+λ θ )θ(i)+v θ (i)
ψ E (i)＝(1+λ ψ )ψ(i)+v ψ (i) (1.3)
wherein u, v and w are velocity components of the airspeed under x, y and z axes of an aircraft body coordinate system respectively; p is a radical of E 、q E 、r E Respectively measuring values of angular rate sensors at x, y and z axes of an aircraft body coordinate system;
respectively measuring values of acceleration sensors under x, y and z axes of an aircraft body coordinate system; phi, theta and psi are respectively a rolling angle, a pitch angle and a yaw angle phi E 、θ E 、ψ E Is a sensor measurement; g is the gravitational acceleration of the aircraft at the location. V E Is a measure of airspeed, beta E As a measurement of the slip angle, alpha E Is an angle of attack measurement.
The method for data correction provided by the embodiment of the application has generality, the state space models are slightly different according to different sensors on an aircraft and the existence of sensor error model parameters, but the method can be used for processing the state space models, the model provided herein is only one of the cases, and the method for data correction provided by the embodiment of the application is subject to, and is not limited specifically.
Step S104, performing parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result;
optionally, in step S104, performing parameter estimation on the sensor error model according to a preset joint algorithm, and obtaining a parameter identification result includes: setting initial values of parameters in a sensor error model; calculating an initial value according to a cubature Kalman filtering algorithm to obtain a filtered parameter; calculating the filtered parameters according to a volume Kalman smoothing algorithm to obtain smoothing parameters; updating the initial value according to the smooth parameter and the improved expectation-maximization algorithm to obtain an updated initial value; judging whether the iterative computation times of parameter estimation of the sensor error model reach a first preset value or not; if the judgment result is yes, outputting a parameter identification result; and under the condition that the judgment result is negative, sequentially executing a volume Kalman filtering algorithm, a volume Kalman smoothing algorithm and an improved expectation maximization algorithm until the times of iterative computation reach a first preset value.
Further, optionally, calculating the initial value according to a volume kalman filter algorithm, and obtaining the filtered parameter includes: according to the initial value
Initial value of (A) and
an initial value of (d); according to
Initial value of (A) and
is calculated as the mean of the predicted distribution of the states
Sum covariance
Mean value of distribution according to prediction
Sum covariance
Calculating a mean value of a filter distribution of states
Sum covariance value
Judging whether the iterative computation times of the initial value reach a second preset value or not; if the judgment result is yes, outputting the filtered parameters; under the condition that the judgment result is negative, the prediction distribution average value of the state is calculated in sequence
Sum covariance
And calculating the mean of the filter distribution of the states
Sum covariance value
Until the number of iterative calculations reaches a second preset value.
Optionally, calculating the filtered parameter according to a volume kalman smoothing algorithm, and obtaining the smoothing parameter includes: imported volume kalmanOne-step prediction state mean value of complete time sequence obtained by filtering algorithm
State prediction covariance
sigma point
And mean value of filter state
Sum covariance
Calculating a smoothing gain G k-1 And smoothed mean value
Sum covariance
Judging whether the iterative computation times of the filtered parameters reach a third preset value or not; if the judgment result is yes, calculating
And
if the judgment result is negative, adjusting the times and calculating the smooth gain G k-1 And smoothed mean value
Sum covariance
Until the number of iterative calculations reaches a third preset value.
Optionally, based on the smoothing parameters and the improved expectation-maximization algorithm pairUpdating the initial value, and obtaining the updated initial value comprises the following steps: based on smoothing parameters and improved expectation-maximization algorithm, for unknown Q, measured noise variance matrix R and state initial distribution parameters in system noise variance matrix
And estimating to obtain an updated initial value.
Specifically, as shown in fig. 3, fig. 3 is a schematic flow chart of an improved EM-CKS algorithm in the method for data correction according to the embodiment of the present invention, and the sensor error model parameter estimation using the improved EM-CKS algorithm is as follows:
1) Discretizing a system equation:
let state x = [ uv w φ θ ψ] T Input of
System noise
For the sensor measurement noise at input u, θ is a parameter in the sensor error model. Formula (1.3) is written as follows:
wherein the noise driving matrix gamma (x) is:
if the state quantity x at the moment k-1 k-1 It is known that the state quantity x at the time k can be directly given by means of fixed integration k The calculation formula (c) is as follows:
order to
In the case of a short sampling time interval Δ t, where Γ (x) is considered to be constant within Δ t, then the system equation abstraction form of the discretization is:
x k ＝F(x k-1 ,u k-1 ,θ)+Δt·Γ k-1 ·w k-1 (1.7)
in the formula k-1 Denotes Γ (x) k-1 )，w k-1 ～N(0,Q)。
2) Cubature Kalman Filter (CKF)
And (3) expanding the dimension of the sensor error parameter to be estimated in (1.7) and adding artificial noise to the parameter. The abstract form of the state equation after dimension expansion is
The measurement equation is
In the formula
For an amplification state vector containing an unknown parameter θ at time k, obeying a distribution of
For system noise at time k-1 after dimension expansion, dimension and
identical and obeyed distribution of
Wherein
Q θ In known amounts. z is a radical of k For measurement of k time u k-1 The input quantity at the moment k-1; upsilon is k For measuring noiseAnd upsilon k ～N(0,R)。
The process of the volumetric kalman filter is as follows:
(1) Let k =2 and give
And
an initial value;
(2) Calculating a predicted distribution mean of states
Sum covariance
Amplifying the process noise into a state after amplification
Wherein
Constructing a sigma point matrix:
wherein n' = n + n q N is
Dimension of, n q Is process noise
The dimension(s) of (a) is,
is a matrix
Cholesky decomposition factor of (1), sample point (sigma point of unit)
Is defined as follows:
wherein
Denotes the ith column unit vector, i.e.' i The ith component of (a) is 1 and the other elements are 0.
Calculating a state mean of a prediction distribution
Sum covariance
In the formula
To point sigma
Substituting the predicted k-time state of the state equation.
(3) Calculating a mean value of a filter distribution of states
Sum covariance value
Constructing a sigma point:
wherein
Representing the ith column of unit vectors. Computing
P zz,k|k-1 、P xz,k|k-1 ：
In the formula
To point sigma
And substituting the measured value of k time predicted by the measurement equation.
Calculating a filter gain K k And based on the measured value z k Obtaining state filteringMean value of distribution
Variance (variance)
(4) If k = N (N is the number of data points), a loop is skipped, otherwise, steps (2) and (3) are repeated for k = k + 1.
3) Cubature Kalman Smoothing (CKS)
The volume Kalman smoother comprises the following calculation steps:
(1) Let k = N, introduce the one-step predicted state mean of the complete time series calculated from CKF
State prediction covariance
sigma point
And mean value of filter state
Sum covariance
(2) Calculating a smoothing gain G k-1 And is flatSliding mean value
Sum covariance
Wherein
Is composed of
The first n-dimension of (c).
(3) If k =2, then calculate
And
and (4) jumping out of the loop, otherwise, enabling k = k-1 to repeat the step (2).
4) Improved expectation maximization algorithm (EM)
The improved EM algorithm can measure unknown Q, measurement noise variance matrix R and state initial distribution parameters in the system noise variance matrix
And (6) estimating.
Status of state
For unobservable data, measure Z N ＝{z 1 ,z 2 ,…,z N Is the data that can be observed,
is an unknown statistic. As can be seen from the principle of the EM algorithm, the cost function is:
wherein the content of the first and second substances,
by optimizing L 1 Can be initially distributed to the states
Carry out an estimation of L 2 、L 3 The cost functions of the noise variance matrix Q in the estimation process and the measured noise variance matrix R are respectively.
Calculation of L by spherical volume integration 1 Obtaining:
get
Is optimized to estimate
Is composed of
After application of the spherical volume integral (1.21) becomes:
finding the optimal statistics by analytic method using the following theorem:
theorem 1: if the equation is of the form:
φ(D)＝Tr(D -1 A)+logdetD (1.23)
wherein D and A are both symmetric positive definite matrices, when the above equation takes the minimum value, there are:
D＝A (1.24)
to L 1 The optimal estimate of the initial distribution of states that can be obtained by applying theorem 1 is:
L 2 joint distribution of presence states
Definition of
By multi-dimensional Gaussian distribution propertyTo
Distribution of (a):
markov pairs of L from Bayesian theorem and states 2 And simplifying, and taking out the parameter part of the dimension expansion from the optimization process:
the second half part on the right side of the equal sign of the above equation does not contain unknown parameters, so that the unknown parameters can not be considered in the optimization process, and the function to be optimized at this time is:
applying spherical volume integral to the formula (1.30), the number of sampling sigma points is 4n, and the ith sigma point
The expression is as follows:
wherein
Representing the ith column of unit vectors. When gamma is k Reversible time (pitch angle theta is not equal to +/-90 DEG), L 2 Comprises the following steps:
in the formula
By theorem 1, let L be known 2 The maximum system noise variance matrix Q is:
constructing sigma point pairs L 3 And (3) calculating:
wherein N is the total number of samples, N is the dimension of the parameter dimension-expanded state vector, m is the dimension of the measurement,
applying theorem 1 to (1.36) let L 3 The maximum measured noise variance matrix R is:
summarizing the above, it can be seen that the optimal estimate of the unknown statistics is as follows:
the steps of finishing the process to obtain an improved EM algorithm are as follows:
calculated by the formulae (1.38), (1.39), (1.40), (1.41)
And an optimal estimate of R.
5) Improved EM-CKS algorithm summary
According to the derivation process of the algorithm, the improved EM-CKS algorithm proposed by the method can be summarized into the following steps:
step 1: give a
And initial value of R
Step 2: performing a volumetric Kalman filtering algorithm
And step 3: performing a volumetric Kalman smoothing algorithm
And 4, step 4: implementing an improved version of an expectation-maximization algorithm
And 5: if the end condition is reached (the iteration times reach the set upper limit, or the change between the estimation result of the unknown parameters of the current iteration and the last iteration result is less than the set value), the calculation is ended, otherwise, the step 2 is returned.
Step 6: and taking the estimation result of the unknown parameters in the last iteration as a final estimation value.
As a dimension-expanded state vector
The dimension corresponding to the unknown parameter:
step S106, correcting the measurement data according to the parameter identification result;
the preset joint algorithm is an improved joint estimation algorithm based on an expectation maximization algorithm and a cubature Kalman smoother.
Optionally, the correcting the measurement data according to the parameter identification result includes: correcting the measurement data according to an error correction formula and a parameter identification result, wherein the error correction formula comprises:
where z (i) is the sensor ith measurement output, y (i) is the true value, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
Specifically, the sensor measurement value is corrected by using unknown parameters in a sensor error model identified by an improved EM-CKS algorithm, so that a more accurate sensor measurement value can be obtained. As can be seen from equation (1.1), the error correction equation is:
in summary, with reference to steps S102 to S106, fig. 4a to fig. 4f are schematic diagrams illustrating comparison between the real IMU input used by the simulation data in the data correction method according to the embodiment of the present invention and the IMU measurement value added with the noise and the sensor error. Fig. 5 a-5 f are schematic diagrams illustrating comparison between a data reconstruction result and a measurement result before and after correction of simulated measurement data by an identified sensor error in a data correction method according to an embodiment of the present invention.
Table 1 simulation data noise settings
TABLE 2 simulation data identification improved edition EM-CKS algorithm initial parameter setting
TABLE 3 comparison of the improved EM-CKS algorithm provided by the method with the identification result of the error model of the sensor by the output error method
It should be noted that, when the existing identification algorithm is applied to the problem of coordination analysis, almost additive assumptions are made on system noise, which is not in accordance with the actual situation, and the estimation accuracy of unknown parameters in the sensor error model can be significantly reduced in the high-sensor-noise environment. In order to improve the parameter identification precision in the problem of coordination analysis, the data correction method provided by the embodiment of the application improves the existing EM algorithm, expands the application range from estimation of an additive system noise variance array to estimation of a system noise variance array when a reversible noise driving array exists, combines the system noise variance array with a volume Kalman smoother (CKS) and applies the system noise variance array to the problem of coordination analysis, can effectively reduce the influence of noise on an identification result, and improves the estimation precision of unknown parameters of a sensor error model compared with a common output error method in engineering.
In the embodiment of the invention, a pre-established sensor error model is obtained; performing parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result; correcting the measurement data according to the parameter identification result; the preset joint algorithm is an improved joint estimation algorithm based on an expectation maximization algorithm and a cubature Kalman smoother. That is to say, the embodiment of the present invention can solve the problem in the related art that the estimation accuracy of the unknown parameter in the sensor error model in the high sensor noise environment is significantly reduced due to the fact that the prior art is not matched with the actual system when processing the system noise, and achieves the technical effect of improving the estimation accuracy of the unknown parameter in the sensor error model in the high sensor noise environment.
According to another aspect of the embodiments of the present invention, there is provided an apparatus for data correction, and fig. 6 is a schematic diagram of an apparatus for data correction according to an embodiment of the present invention, as shown in fig. 6, the apparatus for data correction according to the embodiment of the present invention includes: an obtaining module 62, configured to obtain a pre-created sensor error model; the estimation module 64 is configured to perform parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result; a calibration module 66 for calibrating the measurement data according to the parameter identification result; the preset joint algorithm is an improved joint estimation algorithm based on an expectation maximization algorithm and a cubature Kalman smoother.
Optionally, the apparatus for data correction provided in this embodiment of the present application further includes: a creation module for creating a sensor error model prior to acquiring a pre-created sensor error model, wherein the sensor error model comprises:
z(i)＝(1+λ)y(i)+b+v(i)，i＝1，2，…，N；
where z (i) is the sensor ith measurement output, y (i) is the true value, v (i) is the random measurement noise, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
Optionally, the estimation module 64 includes: the setting unit is used for setting initial values of parameters in the sensor error model; the first calculation unit is used for calculating the initial value according to a volume Kalman filtering algorithm to obtain a filtered parameter; the second calculation unit is used for calculating the filtered parameters according to a cubature Kalman smoothing algorithm to obtain smoothing parameters; the updating unit is used for updating the initial value according to the smooth parameter and the improved expectation-maximization algorithm to obtain an updated initial value; the judging unit is used for judging whether the times of iterative calculation for parameter estimation of the sensor error model reaches a first preset value or not; the output unit is used for outputting a parameter identification result under the condition that the judgment result is yes; and the iteration unit is used for sequentially executing the volume Kalman filtering algorithm, the volume Kalman smoothing algorithm and the improved expectation maximization algorithm under the condition that the judgment result is negative until the iterative calculation times reach a first preset value.
Further, optionally, calculating the initial value according to a volume kalman filter algorithm, and obtaining the filtered parameter includes: according to the initial value
Initial value of (A) and
an initial value of (d); according to
Initial value of (A) and
is calculated as the mean of the predicted distribution of the states
Sum covariance
Mean value of distribution according to prediction
Sum covariance
Calculating a mean value of a filter distribution of states
Sum covariance value
Judging whether the iterative computation times of the initial value reach a second preset value or not; outputting the filtered parameters under the condition that the judgment result is yes; under the condition that the judgment result is negative, calculating the prediction distribution mean value of the state in sequence
Sum covariance
And calculating the mean of the filter distribution of the states
Sum covariance value
Until the number of iterative calculations reaches a second preset value.
Optionally, calculating the filtered parameter according to a volume kalman smoothing algorithm, and obtaining the smoothing parameter includes: one step of importing a complete time sequence obtained by a cubature Kalman filter algorithmPredicted mean of states
State prediction covariance
sigma point
And mean value of filter state
Sum covariance
Calculating a smoothing gain G k-1 And smoothed mean value
Sum covariance
Judging whether the iterative computation times of the filtered parameters reach a third preset value or not; in the case that the judgment result is yes, calculating
And
if the judgment result is negative, adjusting the times and calculating the smooth gain G k-1 And smoothed mean value
Sum covariance
Until the number of iterative calculations reaches a third preset value.
Optionally, the initial value is updated according to the smoothing parameter and the improved expectation-maximization algorithm to obtain an updated initial valueThe values include: based on smoothing parameters and improved expectation-maximization algorithm, for unknown Q, measured noise variance matrix R and state initial distribution parameters in system noise variance matrix
And estimating to obtain an updated initial value.
Optionally, the correcting the measurement data according to the parameter identification result includes: correcting the measurement data according to an error correction formula and a parameter identification result, wherein the error correction formula comprises:
where z (i) is the sensor ith measurement output, y (i) is the true value, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.
Claims (10)
1. A method of data correction, comprising:
acquiring a pre-established sensor error model;
performing parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result;
correcting the measurement data according to the parameter identification result;
the preset joint algorithm is an improved joint estimation algorithm based on an expectation maximization algorithm and a cubature Kalman smoother.
2. The method of claim 1, wherein prior to said obtaining a pre-created sensor error model, the method further comprises:
creating the sensor error model, wherein the sensor error model comprises:
z(i)＝(1+λ)y(i)+b+v(i),i＝1,2,…,N；
where z (i) is the sensor ith measurement output, y (i) is the true value, v (i) is the random measurement noise, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
3. The method according to claim 1 or 2, wherein the performing parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result comprises:
setting initial values of parameters in the sensor error model;
calculating the initial value according to a cubature Kalman filtering algorithm to obtain a filtered parameter;
calculating the filtered parameters according to a volume Kalman smoothing algorithm to obtain smoothing parameters;
updating the initial value according to the smoothing parameter and the improved expectation-maximization algorithm to obtain the updated initial value;
judging whether the iterative calculation times of parameter estimation of the sensor error model reach a first preset value or not;
if the judgment result is yes, outputting the parameter identification result;
and under the condition that the judgment result is negative, sequentially executing the volume Kalman filtering algorithm, the volume Kalman smoothing algorithm and the improved expectation maximization algorithm until the times of iterative computation reach the first preset value.
4. The method of claim 3, wherein the calculating the initial values according to a volume Kalman Filter algorithm, and wherein obtaining filtered parameters comprises:
according to the initial value
Initial value of (A) and
an initial value of (d);
according to the above
Initial value of (A) and
the mean of the predicted distribution of the initial calculation state of (2)
Sum covariance
According to the mean value of the predicted distribution
And the covariance
Calculating a mean value of a filter distribution of states
Sum covariance value
Judging whether the iterative computation times of the initial value reach a second preset value or not;
outputting the filtered parameters under the condition that the judgment result is yes;
under the condition that the judgment result is negative, calculating the prediction distribution mean value of the state in sequence
Sum covariance
And calculating the mean of the filter distribution of the states
Sum covariance value
Until the number of times of iterative computation reaches the second preset value.
5. The method of claim 3, wherein the calculating the filtered parameters according to a volume Kalman smoothing algorithm to obtain smoothing parameters comprises:
importing a one-step prediction state mean value of a complete time sequence obtained by the cubature Kalman filtering algorithm
State prediction covariance
Dot
And mean value of filter state
Sum covariance
Calculating a smoothing gain G k-1 And smoothed mean value
Sum covariance
Judging whether the iterative computation times of the filtered parameters reach a third preset value or not;
if the judgment result is yes, calculating
And
if the judgment result is negative, adjusting the times and calculating a smooth gain G k-1 And smoothed mean value
Sum covariance
Until the iterative computation times reach the third preset value.
6. The method of claim 3, wherein the updating the initial values according to the smoothing parameters and the improved expectation-maximization algorithm comprises:
based on the smoothing parameters and the improved expectation-maximization algorithm, the unknown Q, the measured noise variance matrix R and the state initial distribution parameters in the system noise variance matrix are obtained
And estimating to obtain the updated initial value.
7. The method of claim 1, wherein the calibrating the measurement data according to the parameter identification comprises:
correcting the measurement data according to an error correction formula and the parameter identification result, wherein the error correction formula comprises:
where z (i) is the sensor ith measurement output, y (i) is the true value, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
8. An apparatus for data correction, comprising:
the acquisition module is used for acquiring a pre-established sensor error model;
the estimation module is used for carrying out parameter estimation on the sensor error model according to a preset joint algorithm to obtain a parameter identification result;
the correction module is used for correcting the measurement data according to the parameter identification result;
the preset joint algorithm is an improved joint estimation algorithm based on an expectation maximization algorithm and a cubature Kalman smoother.
9. The apparatus of claim 8, further comprising:
a creation module for creating a sensor error model prior to said obtaining a pre-created sensor error model, wherein said sensor error model comprises:
z(i)＝(1+λ)y(i)+b+v(i),i＝1,2,…,N；
where z (i) is the sensor ith measurement output, y (i) is the true value, v (i) is the random measurement noise, λ is the constant scale factor error parameter, and b is the constant error offset parameter.
10. The apparatus of claim 8 or 9, wherein the estimation module comprises:
a setting unit for setting initial values of parameters in the sensor error model;
the first calculation unit is used for calculating the initial value according to a cubature Kalman filtering algorithm to obtain a filtered parameter;
the second calculation unit is used for calculating the filtered parameters according to a volume Kalman smoothing algorithm to obtain smoothing parameters;
the updating unit is used for updating the initial value according to the smoothing parameter and the improved expectation-maximization algorithm to obtain the updated initial value;
the judging unit is used for judging whether the iterative calculation times of parameter estimation of the sensor error model reaches a first preset value or not;
the output unit is used for outputting the parameter identification result under the condition that the judgment result is yes;
and the iteration unit is used for sequentially executing the volume Kalman filtering algorithm, the volume Kalman smoothing algorithm and the improved expectation maximization algorithm under the condition that the judgment result is negative until the iterative calculation times reach the first preset value.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210654243.1A CN115238454A (en) | 2022-06-10 | 2022-06-10 | Method and device for correcting data |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210654243.1A CN115238454A (en) | 2022-06-10 | 2022-06-10 | Method and device for correcting data |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115238454A true CN115238454A (en) | 2022-10-25 |
Family
ID=83669277
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210654243.1A Pending CN115238454A (en) | 2022-06-10 | 2022-06-10 | Method and device for correcting data |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115238454A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116678381A (en) * | 2023-07-31 | 2023-09-01 | 江西飞尚科技有限公司 | Measurement method, system, readable storage medium and computer equipment |
-
2022
- 2022-06-10 CN CN202210654243.1A patent/CN115238454A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116678381A (en) * | 2023-07-31 | 2023-09-01 | 江西飞尚科技有限公司 | Measurement method, system, readable storage medium and computer equipment |
| CN116678381B (en) * | 2023-07-31 | 2023-10-24 | 江西飞尚科技有限公司 | Measurement method, system, readable storage medium and computer equipment |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| US6928341B2 (en) | Computational air data system for angle-of-attack and angle-of-sideslip | |
| CN105136145A (en) | Kalman filtering based quadrotor unmanned aerial vehicle attitude data fusion method | |
| CN112577516B (en) | Method and system for identifying and compensating wheel speed error of vehicle | |
| US20040128096A1 (en) | System and method for kinematic consistency processing | |
| CN108255786B (en) | Method and system for calculating interference compensation of weighing result | |
| CN115238454A (en) | Method and device for correcting data | |
| CN108762072B (en) | Prediction control method based on nuclear norm subspace method and augmentation vector method | |
| CN111623779A (en) | Time-varying system adaptive cascade filtering method suitable for unknown noise characteristics | |
| CN114186189A (en) | Method, device and equipment for calculating coordinate transformation matrix and readable storage medium | |
| CN111553954B (en) | Online luminosity calibration method based on direct method monocular SLAM | |
| Peyada et al. | Aerodynamic characterization of HANSA-3 aircraft using equation error, maximum likelihood and filter error methods | |
| CN113959447A (en) | Relative navigation high-noise measurement identification method, device, equipment and storage medium | |
| CN113932815A (en) | Robustness optimized Kalman filtering method and device, electronic equipment and storage medium | |
| CN114186190A (en) | Method, device and equipment for calculating coordinate transformation matrix and readable storage medium | |
| CN114186477A (en) | Elman neural network-based orbit prediction algorithm | |
| CN110514209B (en) | Interactive multi-model combined navigation method | |
| CN114147713A (en) | Trajectory tracking control method based on adaptive neural network high-order dynamic sliding mode | |
| Saleem et al. | Application and comparison of kernel functions for linear parameter varying model approximation of nonlinear systems | |
| CN112987054A (en) | Method and device for calibrating SINS/DVL combined navigation system error | |
| CN111442786A (en) | Zero drift deviation and attitude estimation method of aircraft gyroscope | |
| CN113063444B (en) | Sub-angle second precision star sensor optical axis measurement reference deviation calibration method and system | |
| Fleischmann et al. | A systematic LPV/LFR modelling approach optimized for linearised gain scheduling control synthesis | |
| CN115186715B (en) | Bayesian identification method of electromechanical positioning system based on state space model | |
| US20220180233A1 (en) | Method for determining simulation data | |
| Canepa | A note on Bartlett correction factor for tests on cointegrating relations |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |