CN110032711B - Online detection method of rapid Kalman filtering based on dynamic parameter adjustment - Google Patents
Online detection method of rapid Kalman filtering based on dynamic parameter adjustment Download PDFInfo
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Abstract
The invention discloses an online detection method of rapid Kalman filtering based on dynamic parameter adjustment, which comprises the following steps: placing an object to be detected in the same detection environment for pre-sampling to obtain a plurality of groups of noise-containing data, and calculating a filtering data target value, a measurement variance of the filtering data and a Kalman gain lower limit threshold value based on the noise-containing data; calculating an initial estimation value of filtering data and an initial estimation variance value of the filtering data in the online detection process of the detection object; the initial estimation variance is determined according to the interval to which the error between the initial estimation value and the target value belongs; and performing Kalman filtering correction recursive operation based on the initial estimation value and the initial estimation variance value until the filtering data is converged to obtain filtering data of the online detection of the detection object. The method solves the problems of high iteration times and low convergence speed caused by the fact that the initial estimation value cannot be adjusted in the traditional Kalman filtering method, and improves the timeliness of filtering detection.
Description
Technical Field
The invention belongs to the technical field of signal filtering processing, and particularly relates to a rapid Kalman filtering on-line detection method based on dynamic parameter adjustment.
Background
Kalman filtering is a method for optimally estimating the state of a system by using a linear system state equation and observing input and output data of the system. At present, the kalman filtering theory is widely applied to communication systems, industrial control, radar signal processing and the like, wherein the kalman filtering theory is widely applied to time sequence analysis in the field of automatic detection. Nowadays, the computer programming realization of the Kalman filtering theory is quite mature, but the traditional realization method mainly emphasizes the operation logic of revising recursion in the Kalman filtering theory, and neglects the direct influence of parameter setting on the result.
At present, some adaptive Kalman filtering methods (AKF) also perform relevant improvements on parameter setting, and although the defect of uncertainty of convergence duration caused by measurement random errors can be restrained to a certain degree, an optimization space still exists in the aspect of timeliness, and the timeliness requirement of online detection is difficult to meet.
Disclosure of Invention
The invention aims to provide a rapid Kalman filtering on-line detection method based on parameter dynamic adjustment, wherein an initial estimation variance value is dynamically adjusted according to an error between an initial estimation value and a target value, so that the problems of high iteration times and low convergence speed caused by the fact that the initial estimation value cannot be adjusted in the traditional Kalman filtering method are solved, the timeliness of filtering detection is improved, and the method can meet the requirement of on-line detection.
The invention provides an online detection method of rapid Kalman filtering based on dynamic parameter adjustment, which comprises the following steps:
s1: placing an object to be detected in the same detection environment for pre-sampling to obtain a plurality of groups of noise-containing data, and calculating a filtering data target value, a measurement variance of the filtering data and a Kalman gain lower limit threshold value based on the noise-containing data;
the data to be filtered is a target characteristic value of each group of noisy data;
respectively calculating a target characteristic value of each group based on a plurality of groups of noise-containing data obtained by pre-sampling, and further calculating a filtering data target value, a measurement variance of filtering data and a Kalman gain lower limit threshold, wherein the Kalman gain lower limit threshold is related to the filtering data target value and the measurement variance of the filtering data;
s2: calculating an initial estimation value of filtering data and an initial estimation variance value of the filtering data in the online detection process of the detection object;
the initial estimation value is determined according to a target characteristic value of a group of noisy data collected in the online detection process, and the error value range of the initial estimation value and the target value is divided into three intervals: the method comprises the steps of (1), (0, R), (R, 2R) and (2R, 3R), wherein R represents the measurement variance of filtering data, each interval corresponds to an initial estimation variance value, the initial estimation variance values corresponding to the three intervals of (0, R), (R, 2R) and (2R, 3R) are sequentially increased, and the initial estimation variance value is determined according to the interval to which an error belongs;
s3: performing Kalman filtering correction recursive operation based on the initial estimation value and the initial estimation variance value until filtering data are converged to obtain filtering data of online detection of the detection object;
the method comprises the steps of taking an initial estimation value and an initial estimation variance value as a posterior estimation value and a posterior estimation variance value of an initial moment, and sequentially calculating the posterior estimation value, the posterior estimation variance value and Kalman gain of filtering data at a subsequent sampling moment in the on-line detection process by utilizing Kalman filtering correction recursive operation until a convergence condition is reached;
the kalman gain at the current sampling time is positively correlated with the a posteriori estimated variance value at the previous time,
the rule for identifying whether the current time reaches the convergence condition is as follows:
a: if the posterior estimated value of the current sampling moment falls into a preset steady-state error range, continuously iterating from the current sampling moment backwards for N times, and if the posterior estimated value after each iteration falls into the preset steady-state error range, achieving a convergence condition;
b: whether the Kalman gain at the current sampling moment is less than or equal to a Kalman gain lower limit threshold value or not is judged, and if yes, a convergence condition is achieved; if none of the A, B rules are satisfied, the convergence condition is not reached at the current time.
In the Kalman filtering algorithm, under the condition that the measurement variance is constant, the iteration times of filtering a value with a large difference with a target value are more than one value with a small difference, which is the uncertainty of the iteration times and also causes the increase of convergence time. Because the Kalman gain at the current sampling moment is in positive correlation with the posterior estimation variance value at the previous moment, when a value with a large difference from a target value is filtered, the error is larger, the initial estimation variance value is increased, the Kalman gain at the subsequent sampling moment is also increased, the iteration times are reduced based on the convergence condition, and the convergence speed is further improved. Therefore, the method changes the Kalman gain at the subsequent sampling moment by adjusting the initial estimation variance value, further greatly converges the time length, and simultaneously greatly reduces the difference under the action of different random error values.
The invention determines the target value of the filtering data, the measurement variance of the filtering data and the Kalman gain lower limit threshold value through pre-sampling, namely, more matched parameters are set according to different measurement environments, so that the filtering effect is better.
It should be understood that the set of noisy data for calculating the initial estimation value and the initial estimation variance in step S2 is necessarily noisy data at the sampling time in the front row during the online detection, because the present invention performs the filtering process on the online detection, i.e., the subsequent step S3 is performed based on the data at the subsequent sampling time of the set of noisy data in step S2. In addition, in the filtered data of the present invention, if the current time satisfies the convergence condition a or B, the posterior estimated value of each sampling time before convergence is obtained, and the value of each sampling time after convergence is regarded as a steady state. From the process of identifying whether convergence occurs, the present invention needs backward iteration data to identify whether convergence occurs at the current time, and it should be understood that N times are effective and the time is short, and thus it is still considered as a real-time filtering process.
Further preferably, the initial estimation value in step S2 is equal to the target characteristic value of the collected set of noisy data; the initial estimated variance values are as follows:
in the formula, P(1|1)Representing the initial estimated variance value, Z(1)Representing a target characteristic value of a set of noisy data collected, X representing a target value of the filtered data, R representing a measured variance of the filtered data, and d representing an adjustment parameter.
As can be seen from the above equation, the larger the error value, the larger the initial estimated variance value corresponding to the section. Compared with the situation that the initial estimation variance value in the traditional Kalman filtering is not adjustable, the method can obviously improve the convergence speed when the initial estimation variance value is filtered with a large difference with a target value. Based on the 3 delta principle, the random noise intensity in the environment has a certain probability distribution, so that the invention uses R,2R and 3R as interval division basis.
Further preferably, the acquisition process of the set of noisy data for calculating the initial estimation value and the initial estimation variance value in step S2 is as follows:
firstly, acquiring noise-containing data of a detection object at a first sampling moment in an online detection process in the same detection environment, and judging whether the noise-containing data at the first sampling moment is reserved or not based on the noise-containing data; delta is more than 3R and is not reserved; otherwise, reserving;
if the difference value is reserved, calculating an initial estimation value of filtering data based on the noisy data, and determining an initial estimation variance value based on the initial estimation value and a target value;
and if not, acquiring the noise-containing data at the next sampling moment and judging whether to retain, and if not, repeating the step until a group of noise-containing data which can be retained is obtained.
Further preferably, in step S3, the process of calculating the posterior estimate value, the posterior estimate variance value, and the kalman gain of the filtered data at any k sampling time by using the kalman filtering correction recursive operation is as follows:
s31: calculating a prior estimation value of the k sampling moment by using the posterior estimation value of the k-1 sampling moment, and calculating a prior estimation variance value of the k sampling moment by using the posterior estimation variance value of the k-1 sampling moment;
X(k|k-1)＝AX(k-1|k-1)+BU(k)
P(k|k-1)＝P(k-1|k-1)+Q
in the formula, X(k|k-1)A priori estimate, X, representing the k sampling instants(k-1|k-1)Expressing the posterior estimated value of k-1 sampling time, A is the target transfer matrix, B is the input conversion matrix, U(k)An external input variable at the sampling moment of k; p(k|k-1)Representing a priori estimated variance values, P, of k sampling instants(k-1|k-1)Expressing the posterior estimation variance value of k-1 sampling time, wherein Q is the covariance of the system process; wherein, A, B, U(k)Q is a conventional parameter in a Kalman filter;
s32: calculating Kalman gain by using a priori estimation variance value at the k sampling moment;
Kf(k)＝P(k|k-1)/(P(k|k-1)+R)
in the formula, Kf(k)Representing the Kalman gain at the sampling moment of k;
s33: calculating a posterior estimation value of the k sampling moment by using the Kalman gain, the target characteristic value of the noisy data and the prior estimation value of the k sampling moment, and calculating a posterior estimation variance value of the k sampling moment by using the Kalman gain and the prior estimation variance value of the k sampling moment;
X(k|k)＝(1-Kf(k))X(k|k-1)+Kf(k)Z(k)
P(k|k)＝(1-Kf(k))P(k|k-1)
in the formula, X(k|k)Representing the posterior estimate of the k sampling instants, Z(k)Target characteristic value, P, representing noisy data at k sampling instants(k|k)Representing the a posteriori estimated variance value for the k sampling instants.
In the Kalman filtering correction recursive operation, a state quantity-measurement quantity conversion matrix H in the traditional Kalman filtering algorithm is eliminated, so that a more simplified iterative manner is obtained, and the calculation complexity of the method is reduced.
Further preferably, the kalman gain lower limit threshold is related to the target value of the filtered data and the measurement variance of the filtered data, and is related as follows:
in the formula, KmRepresenting a kalman gain lower threshold value and X representing a filtered data target value.
On one hand, the Kalman gain lower limit threshold is set according to the detection environment, and a more matched Kalman gain lower limit threshold is set according to different detection environments, and on the other hand, the Kalman gain lower limit threshold is used as one of convergence conditions, so that the time overhead caused by blind iteration of the traditional Kalman filtering is overcome, and the real-time performance of the detection filtering is improved.
Further preferably, in step S1, the target value of the filtered data is equal to the mean of the target characteristic values of the several groups of collected noisy data, and the measured variance of the filtered data is equal to the standard deviation of the target characteristic values of the several groups of collected noisy data;
in the formula (I), the compound is shown in the specification,
δ represents the mean and standard deviation, Z, of the target characteristic value, respectively(i)Representing the target characteristic value of a group of collected noisy data, and n is the number of the collected groups.
Further preferably, in the identification process of step S3, N iterations are 5 iterations.
Advantageous effects
1. The initial estimation variance value is determined according to the interval to which the error of the initial estimation value and the target value belongs, namely different error intervals correspond to different initial estimation variance values, the interval with the larger error value corresponds to the larger initial estimation variance value, the Kalman gain at the current sampling moment is in positive correlation with the posterior estimation variance value at the previous moment, and the Kalman gain at the subsequent sampling moment is changed by changing the initial estimation variance value.
2. According to the invention, the target value of the filtering data, the measurement variance of the filtering data and the Kalman gain lower limit threshold are determined through pre-sampling, namely, more matched parameters are set according to different measurement environments, so that the filtering effect is better, meanwhile, the time overhead caused by blind iteration of the traditional Kalman filtering is overcome to a certain extent by utilizing the Kalman gain lower limit threshold, and the filtering instantaneity is improved.
3. According to the Kalman filtering correction recursive operation, a state quantity-measurement quantity conversion matrix H in the traditional Kalman filtering algorithm is eliminated, so that a more simplified iterative mode is obtained, and the calculation complexity of the Kalman filtering correction recursive operation is reduced.
Drawings
FIG. 1 is a flow chart of an on-line detection method of fast Kalman filtering based on dynamic adjustment of parameters;
fig. 2 is a comparison graph of the filtering effects of the conventional kalman filtering method and the fast kalman filtering method.
Detailed Description
The present invention will be further described with reference to the following examples.
As shown in fig. 1, the fast kalman filter online detection method based on dynamic parameter adjustment provided by the present invention mainly includes two parts, where part a represents a target value of filter data dynamically adjusted according to a detection environment, a measurement variance of the filter data, a kalman gain lower limit threshold, an initial estimation value, and an initial estimation variance value. And part B represents an online detection filtering process by utilizing Kalman filtering correction recursive operation. The method provided by the invention can be widely applied to time sequence analysis in the field of automatic detection.
Specifically, the invention relates to an online detection method of rapid Kalman filtering based on dynamic parameter adjustment, which comprises the following steps:
s1: the method comprises the steps of placing an object to be detected in the same detection environment for pre-sampling to obtain a plurality of groups of noisy data, and calculating a filtering data target value, a measurement variance of the filtering data and a Kalman gain lower limit threshold value based on the noisy data.
In this embodiment, under the conditions of a gas pressure of 1atm and a temperature of 296K, nitrogen is used as a balance gas, a sealed glass vial with an oxygen concentration of 0% is selected as a sample, a tunable laser is used to irradiate the gas in the glass vial, and a receiver collects second harmonic sample data demodulated by an oxygen absorption spectrum.
The system is placed in a working environment, pre-sampling is carried out after the system is ensured to run stably, 200 groups of second harmonic sample data are collected, and each group comprises 500 original data points. Next, their maximum values, i.e., second harmonic peak data, are extracted as target feature values from 500 raw data points of each period.
The target value of the filtering data, the measurement variance of the filtering data and the Kalman gain lower limit threshold are calculated as follows:
in the formula, X represents the target value of the filtered data, which is equal to the average of the target characteristic values of several sets of collected noisy data, in this embodiment, 200 sets of second harmonic samplesMean of second harmonic peaks, Z, of this data(i)The second harmonic peak value of a set of second harmonic sample data is represented by a target characteristic value of a set of acquired noisy data, and n is the number of the acquired sets. In this example, n is 200; r represents the measured variance of the filtered data, which is equal to the standard deviation δ of the target feature values of several sets of noisy data acquired, in this example, the standard deviation of the second harmonic peak values of 200 sets of second harmonic sample data. KmRepresenting the kalman lower gain threshold.
S2: and calculating an initial estimation value of the filtering data and an initial estimation variance value of the filtering data in the online detection process of the detection object.
Acquiring noise-containing data of a detection object at a first sampling moment in an online detection process under the same detection environment, and judging whether the noise-containing data at the first sampling moment is reserved or not based on the noise-containing data; delta is more than 3R and is not reserved; otherwise, reserving;
if the difference value is reserved, calculating an initial estimation value of the filtering data based on the noisy data, and determining an initial estimation variance value based on the initial estimation value and a target value;
and if not, acquiring the noise-containing data at the next sampling moment and judging whether to retain, and if not, repeating the step until a group of noise-containing data which can be retained is obtained.
In this embodiment, under the same working environment, a new set of second harmonic data is obtained from the sample bottle to be measured, the second harmonic peak value is extracted as the target characteristic value, and the observation result is recorded as xaThen, the observation result x is calculatedaError Δ, Δ ═ x from the target valuea-X |, i.e. XaAnd (4) the absolute value of the difference value with the target value X, and judging whether the difference value is greater than 3R, if so, the group of data is not reserved, and if not, the group of data is reserved.
After a group of reserved noisy data is obtained, an initial estimation value X is calculated1And an initial estimated variance value P(1|1)Initial estimated value X1Equal to the target eigenvalue of the retained set of acquired noisy data, the variance value P is initially estimated(1|1)The following were used:
in the formula, P(1|1)Representing the initial estimated variance value, Z(1)A target characteristic value representing a retained set of acquired noisy data, X representing a filtered data target value, R representing a measured variance of the filtered data, and d representing an adjustment parameter. In this embodiment, d is 1.
S3: and performing Kalman filtering correction recursive operation based on the initial estimation value and the initial estimation variance value until the filtering data is converged to obtain filtering data of the online detection of the detection object. The initial estimation value and the initial estimation variance value are used as a posterior estimation value and a posterior estimation variance value of an initial moment, and then a posterior estimation value, a posterior estimation variance value and a Kalman gain of filtering data at a subsequent sampling moment in the online detection process are calculated in sequence by utilizing Kalman filtering correction recursive operation until a convergence condition is reached.
The process of calculating the posterior estimation value, the posterior estimation variance value and the Kalman gain of the filtering data at any k sampling time by utilizing Kalman filtering correction recursive operation is as follows:
s31: calculating a prior estimation value of the k sampling moment by using the posterior estimation value of the k-1 sampling moment, and calculating a prior estimation variance value of the k sampling moment by using the posterior estimation variance value of the k-1 sampling moment;
X(k|k-1)＝AX(k-1|k-1)+BU(k)
P(k|k-1)＝P(k-1|k-1)+Q
in the formula, X(k|k-1)A priori estimate, X, representing the k sampling instants(k-1|k-1)Expressing the posterior estimated value of k-1 sampling time, A is the target transfer matrix, B is the input conversion matrix, U(k)An external input variable at the sampling moment of k; p(k|k-1)Representing a priori estimated variance values, P, of k sampling instants(k-1|k-1)Expressing the posterior estimation variance value of k-1 sampling time, wherein Q is the covariance of the system process; wherein, A, B, U(k)And Q is KarlThe conventional parameters in the manfilter are set as follows in this embodiment:
s32: calculating Kalman gain by using a priori estimation variance value at the k sampling moment;
Kf(k)＝P(k|k-1)/(P(k|k-1)+R)
in the formula, Kf(k)Representing the Kalman gain at the sampling moment of k;
s33: calculating a posterior estimation value of the k sampling moment by using the Kalman gain, the target characteristic value of the noisy data and the prior estimation value of the k sampling moment, and calculating a posterior estimation variance value of the k sampling moment by using the Kalman gain and the prior estimation variance value of the k sampling moment;
X(k|k)＝(1-Kf(k))X(k|k-1)+Kf(k)Z(k)
P(k|k)＝(1-Kf(k))P(k|k-1)
in the formula, X(k|k)Representing the posterior estimate of the k sampling instants, Z(k)Target characteristic value, P, representing noisy data at k sampling instants(k|k)Representing the a posteriori estimated variance values at the k sampling instants.
From the above process, the posterior estimation value, the posterior estimation variance value, and the kalman gain of the filtering data at the subsequent sampling time can be calculated after the initial estimation value and the initial estimation variance value are obtained. The convergence conditions provided by the present invention are as follows:
a: if the posterior estimation value of the current sampling moment falls into a preset steady-state error range, continuously iterating from the current sampling moment backwards for N times, and if the posterior estimation value after each iteration falls into the preset steady-state error range, achieving a convergence condition;
b: whether the Kalman gain at the current sampling moment is less than or equal to a Kalman gain lower limit threshold value or not is judged, and if yes, a convergence condition is achieved;
if none of the A, B rules are satisfied, the convergence condition is not reached at the current time.
As shown in FIG. 1, rule B is determined first, and then rule A is identified; in other feasible embodiments, rule a may be identified first, and then rule B may be identified, if the posterior estimation value of the current sampling time falls within the preset steady-state error range, and N successive iterations are performed backwards from the current sampling time k, and the posterior estimation value after each iteration falls within the preset steady-state error range, then a convergence condition is reached; otherwise, judging the Kalman gain Kf of the current sampling moment(k)Whether or not it is less than or equal to the Kalman gain lower threshold KmIf yes, convergence conditions are reached; otherwise, the current time does not reach the convergence condition.
In this embodiment, the steady state error threshold essX0.005 and N is 5. Posterior estimated value X of tested object at current moment(k|k)And judging, if the posterior estimation values after five continuous iterations all fall within the steady-state error range, the filtering process is successfully completed, and the posterior estimation value of the last iteration is the convergence estimation value of the detection object. If the above determination is not satisfied all the time, and Kalman gain Kf(k)Reach the lower limit K of the gain valuemIf not, the filtering process is forcibly ended, and the posterior estimated value of the last iteration is still the estimated value of the convergence of the detection object, otherwise, the step S3 is returned to calculate the next moment.
As shown in fig. 2, the effect difference of the conventional kalman filtering method and the fast kalman filtering method using parameter dynamic adjustment is obtained under the same data of the second harmonic measurement value. The fast Kalman filtering method can converge on a target value under a shorter iteration number, has the same stability and precision as the traditional Kalman filtering method, and reflects the inhibition performance of the improved method on the uncertainty of convergence time length caused by a larger measurement random error. Specifically, under the same precision (X0.005), the fast kalman filtering method only needs 82 iterations, whereas the conventional kalman filtering method needs 280 iterations.
The results of the 5 filtering experiments with random decimation are shown in Table 1, where the final estimation value is equal to the lower limit K by Kalman gainmThe current posterior estimate of time is determined and the filtering efficiency is calculated as follows:
it can be found that in Kalman gain Kf(k)Gradually decreasing with iteration to a lower limit value KmThe filtering process is basic and complete, and the subsequent iteration process has very limited benefit to the system. Therefore, a p-Kalman gain Kf is introduced in the method(k)The iteration can be ended in advance, and the signal advancing efficiency is greatly improved
TABLE 1
It should be emphasized that the examples described herein are illustrative and not restrictive, and thus the invention is not to be limited to the examples described herein, but rather to other embodiments that may be devised by those skilled in the art based on the teachings herein, and that various modifications, alterations, and substitutions are possible without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. An on-line detection method of rapid Kalman filtering based on parameter dynamic regulation is characterized in that: the method comprises the following steps:
s1: placing gas in a glass bottle as an object to be detected in the same detection environment, performing laser irradiation pre-sampling to obtain a plurality of groups of second harmonic noisy data demodulated by oxygen absorption spectrum, and calculating a filtering data target value, a measurement variance of the filtering data and a Kalman gain lower limit threshold value based on the noisy data;
the data to be filtered is a target characteristic value of each group of noisy data;
s2: calculating an initial estimation value of filtering data and an initial estimation variance value of the filtering data in the online detection process of the detection object;
the initial estimation value is determined according to a target characteristic value of a group of noisy data collected in the online detection process, and the error value range of the initial estimation value and the target value is divided into three intervals: the method comprises the following steps that [0, R), [ R,2R), [2R,3R ], R represents the measurement variance of filtering data, the initial estimation variance determines an initial estimation variance value according to a section to which an error belongs, each section corresponds to an initial estimation variance value, the initial estimation variance values corresponding to the [0, R), [ R,2R), [2R,3R ] are sequentially increased, and the initial estimation variance value is determined according to the section to which the error belongs;
s3: performing Kalman filtering correction recursive operation based on the initial estimation value and the initial estimation variance value until filtering data are converged to obtain filtering data of the detection object in the online detection process;
the method comprises the steps of taking an initial estimation value and an initial estimation variance value as a posterior estimation value and a posterior estimation variance value of an initial moment, and sequentially calculating the posterior estimation value, the posterior estimation variance value and Kalman gain of filtering data at a subsequent sampling moment in the on-line detection process by utilizing Kalman filtering correction recursive operation until a convergence condition is reached;
the kalman gain at the current sampling time is positively correlated with the a posteriori estimated variance value at the previous time,
the rule for identifying whether the current time reaches the convergence condition is as follows:
a: if the posterior estimation value of the current sampling moment falls into a preset steady-state error range, continuously iterating from the current sampling moment backwards for N times, and if the posterior estimation value after each iteration falls into the preset steady-state error range, achieving a convergence condition;
b: whether the Kalman gain at the current sampling moment is less than or equal to a Kalman gain lower limit threshold value or not is judged, and if yes, a convergence condition is achieved;
if none of the A, B rules are satisfied, the convergence condition is not reached at the current time.
2. The method of claim 1, wherein: in step S2, the initial estimation value is equal to the target characteristic value of the collected group of noisy data; the initial estimated variance values are as follows:
in the formula, P(1|1)Representing the initial estimated variance value, Z(1)Representing a target characteristic value of a set of acquired noisy data, X representing a target value of filtered data, R representing a measured variance of the filtered data, and d representing an adjustment parameter.
3. The method of claim 2, wherein: the acquisition process of a group of noisy data for calculating the initial estimation value and the initial estimation variance value in step S2 is as follows:
firstly, acquiring noise-containing data of a detection object at a first sampling moment in an online detection process in the same detection environment, and judging whether the noise-containing data at the first sampling moment is reserved or not based on the noise-containing data; delta is more than 3R and is not reserved; otherwise, reserving;
and if not, acquiring the noise-containing data at the next sampling moment and judging whether to retain, and if not, repeating the step until a group of noise-containing data which can be retained is obtained.
4. The method of claim 1, wherein: in step S3, the process of calculating the posterior estimate value, the posterior estimate variance value, and the kalman gain of the filtered data at any k sampling time by using the kalman filtering correction recursive operation is as follows:
s31: calculating a prior estimation value of the k sampling moment by using the posterior estimation value of the k-1 sampling moment, and calculating a prior estimation variance value of the k sampling moment by using the posterior estimation variance value of the k-1 sampling moment;
X(k|k-1)＝AX(k-1|k-1)+BU(k)
P(k|k-1)＝P(k-1|k-1)+Q
in the formula, X(k|k-1)A priori estimate, X, representing the k sampling instants(k-1|k-1)Represents the posterior estimate of the k-1 sampling instant, A being the eyeA label transfer matrix, B being an input conversion matrix, U(k)An external input variable at the sampling moment of k; p(k|k-1)Representing the a priori estimated variance value, P, of the k sampling instants(k-1|k-1)Expressing the posterior estimation variance value of k-1 sampling time, wherein Q is the covariance of the system process;
s32: calculating Kalman gain by using a priori estimation variance value at the k sampling moment;
Kf(k)＝P(k|k-1)/(P(k|k-1)+R)
in the formula, Kf(k)Representing the Kalman gain at the sampling moment of k;
s33: calculating a posterior estimation value of the k sampling moment by using the Kalman gain, the target characteristic value of the noisy data and the prior estimation value of the k sampling moment, and calculating a posterior estimation variance value of the k sampling moment by using the Kalman gain and the prior estimation variance value of the k sampling moment;
X(k|k)＝(1-Kf(k))X(k|k-1)+Kf(k)Z(k)
P(k|k)＝(1-Kf(k))P(k|k-1)
in the formula, X(k|k)Representing the posterior estimate of the k sampling instants, Z(k)Target characteristic value, P, representing noisy data at k sampling instants(k|k)Representing the a posteriori estimated variance value for the k sampling instants.
5. The method of claim 1, wherein: the Kalman gain lower limit threshold is related to a filtering data target value and the measurement variance of filtering data, and the relationship is as follows:
in the formula, KmRepresenting a kalman gain lower threshold value and X representing a filtered data target value.
6. The method of claim 5, wherein: in step S1, the target value of the filtered data is equal to the mean of the target characteristic values of the several groups of collected noisy data, and the measurement variance of the filtered data is equal to the standard deviation of the target characteristic values of the several groups of collected noisy data;
in the formula (I), the compound is shown in the specification,
δ represents the mean and standard deviation, Z, of the target characteristic value, respectively(i)Representing the target characteristic value of a group of collected noisy data, and n is the number of the collected groups.
7. The method of claim 1, wherein: in step S3, the number of iterations N in the identification process is 5.
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