CN110209998B - Optimal sequential fusion estimation method under non-ideal channel - Google Patents

Optimal sequential fusion estimation method under non-ideal channel Download PDF

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CN110209998B
CN110209998B CN201910553267.6A CN201910553267A CN110209998B CN 110209998 B CN110209998 B CN 110209998B CN 201910553267 A CN201910553267 A CN 201910553267A CN 110209998 B CN110209998 B CN 110209998B
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朱翠
张善凯
王雅妮
赵圣健
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Beijing Information Science and Technology University
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Abstract

The application discloses an optimal sequential fusion estimation method under a non-ideal channel, which is suitable for fusion calculation of estimated values of sensors in a discrete linear stochastic system, and comprises the following steps: step 1, determining fusion initial update time according to the marked sensor measurement value stored in the adjacent moment buffer; step 2, generating a decorrelation coefficient matrix according to the measurement value, and performing decorrelation on the measurement value, the measurement noise and the measurement transfer matrix according to the decorrelation coefficient matrix; and 3, calculating the estimation value of the sensor according to the fusion initial update time, the decorrelated measurement value, the measurement noise and the measurement transfer matrix by using a preset sequential fusion equation. Through the technical scheme in the application, the problems of noise correlation and communication delay in multi-sensor data fusion are solved, and the generated estimated value has higher filtering precision and stronger reliability.

Description

Optimal sequential fusion estimation method under non-ideal channel
Technical Field
The application relates to the technical field of communication, in particular to an optimal sequential fusion estimation method under a non-ideal channel and a sensor data calculation device.
Background
In recent years, the networking multi-sensor data fusion technology is widely applied to both military and non-military fields. Compared with a single-channel system, the multi-sensor system has the advantages of high estimation precision, strong fault-tolerant capability, wide information space-time coverage range and the like, and can effectively improve the system performance. However, with the development of networks, the conventional convergence method is not suitable due to the problems of packet loss, delay, noise correlation and the like in the networks. Academic research aimed at networked data fusion is now a hotspot.
In the prior art, when data fusion is performed, only how to remove noise correlation or how to solve network delay is generally considered separately, but in practical application, the system may have both noise correlation and communication delay, and in this case, the system cannot accurately obtain a data fusion estimation result.
Disclosure of Invention
The purpose of this application lies in: in the data fusion estimation process, common noise correlation and communication delay problems in the networked multi-sensor data fusion problem are considered, and on the basis of the problems, a noise decorrelation and data caching method is provided to optimize the data fusion process, so that the generated estimation value has higher filtering precision and higher reliability.
The technical scheme of the first aspect of the application is as follows: an optimal sequential fusion estimation method under a non-ideal channel is provided, the method is suitable for fusion calculation of estimated values of sensors in a discrete linear stochastic system, and the method comprises the following steps: step 1, determining fusion initial update time according to marked measurement values stored in a buffer at adjacent moments; step 2, generating a decorrelation coefficient matrix according to the measurement value, and performing decorrelation on the measurement value, the measurement noise and the measurement transfer matrix according to the decorrelation coefficient matrix; and 3, calculating the estimation value of the sensor according to the fusion initial update time, the decorrelated measurement value, the measurement noise and the measurement transfer matrix by using a preset sequential fusion equation.
In any of the above technical solutions, further, the calculation formula for determining the fusion start update time τ is:
Figure BDA0002106118480000021
Figure BDA0002106118480000022
where τ is the fusion initiation update time, t is the time stamp of the measurement value, i is the sensor number, i is 1,2, …, N,
Figure BDA0002106118480000023
for the measured value of the ith sensor at time stamp t stored in the buffer at the current time k
Figure BDA0002106118480000024
L is the storage length of the buffer.
In any one of the above technical solutions, further, in step 2, generating a decorrelation coefficient matrix according to the measurement value, specifically including:
step 21, calculating a decorrelation coefficient between the measurement values of any two sensors according to a decorrelation coefficient calculation formula, wherein the decorrelation coefficient calculation formula is as follows:
Figure BDA0002106118480000025
Figure BDA0002106118480000026
Figure BDA0002106118480000027
Figure BDA0002106118480000028
Figure BDA0002106118480000029
in the formula (I), the compound is shown in the specification,
Figure BDA00021061184800000210
as a decorrelation coefficient between the current time k, the jth sensor and the ith sensor,
Figure BDA00021061184800000211
measuring the noise figure for the cross-correlation after the decorrelation between the current time k, the jth sensor and the ith sensor,
Figure BDA00021061184800000212
measuring the noise coefficient R for the autocorrelation of the j th sensor at the current time ki，j(k) Cross-correlation measurement noise system among current time k, jth sensor and ith sensorNumber, Rj(k) For the autocorrelation measurement of the noise factor, delta, of the j-th sensor at the current time kkzAs function of kronecker, vi(k) The measured noise of the ith sensor at the current time k,
Figure BDA0002106118480000031
is the transpose of the measurement noise, E {. is the expected operation;
step 22, generating a correlation coefficient matrix G of the ith sensor according to the decorrelation coefficients before the ith sensori(k) The calculation formula of the correlation coefficient matrix is as follows:
Figure BDA0002106118480000032
in the formula, Gi(k) And the correlation coefficient matrix of the ith sensor at the current time k.
In any of the above technical solutions, further, the preset sequential fusion equation is:
Figure BDA0002106118480000033
Figure BDA0002106118480000034
Figure BDA0002106118480000035
Figure BDA0002106118480000036
in the formula (I), the compound is shown in the specification,
Figure BDA00021061184800000316
is the estimated value of the ith sensor at the current moment k,
Figure BDA0002106118480000038
in order to be the value of the tag,
Figure BDA0002106118480000039
in order to filter the gain of the filter,
Figure BDA00021061184800000310
in order to obtain a measured value after the decorrelation,
Figure BDA00021061184800000311
for the measurement transfer matrix after the decorrelation,
Figure BDA00021061184800000312
is an estimated value
Figure BDA00021061184800000313
The variance of the error with the actual state value x (t) is expected,
Figure BDA00021061184800000314
in order to measure the noise figure by auto-correlation,
Figure BDA00021061184800000315
for the decorrelated measurement noise, I is the identity matrix.
The technical scheme of the second aspect of the application is as follows: the sensor data calculation device comprises a data receiving unit, a data processing unit and a data output unit, and is characterized in that the data receiving unit is used for receiving the measurement data of a plurality of sensors; the data processing unit is used for performing fusion calculation on the measurement data according to the optimal sequential fusion estimation method under the non-ideal channel according to any one of the technical schemes in the first aspect of the application; the data output unit is used for outputting the fusion calculation result of the data processing unit.
The beneficial effect of this application is: the problems of noise correlation and communication delay in multi-sensor data fusion are solved, and the generated estimated value has higher filtering precision and stronger reliability.
Compared with the traditional sequential fusion filtering algorithm, the algorithm can solve more problems possibly occurring in practical application, such as the problem of network unreliability in networked wireless transmission and the problem of crosstalk of each channel in a multi-sensor system, improves the accuracy and robustness of the whole fusion filtering process, reduces the possibility of divergence of filtering results, and can provide a more accurate filtering estimation value for data fusion estimation.
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The advantages of the above and/or additional aspects of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic flow diagram of an optimal sequential fusion estimation method under non-ideal channels according to one embodiment of the present application;
FIG. 2 is a diagram of a buffer storing data according to one embodiment of the present application.
Detailed Description
In order that the above objects, features and advantages of the present application can be more clearly understood, the present application will be described in further detail with reference to the accompanying drawings and detailed description. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application, however, the present application may be practiced in other ways than those described herein, and therefore the scope of the present application is not limited by the specific embodiments disclosed below.
For a discrete linear stochastic system, the current time k, the measurement value y of the sensori(k) Can be expressed by the following formula:
yi(k)＝Hi(k)x(k)+ｖi(k)
x(k)＝F(k-1)x(k-1)+w(k-1)
where i is the number of the sensor, i1, 2, N, x (k) is the system state, Hi(k) To measure the transfer matrix, vi(k) In order to measure the noise, the noise is measured,f (k-1) is the state transition matrix and w (k-1) is the state noise.
In the present embodiment, the initial value x (0) of the system state is set independently of the measurement noise and the state noise, and satisfies the gaussian distribution, i.e., E { x (0) } μ0，μ0Is a desired initial value, and E { [ x (0) - μ0][x(0)-μ0]T}＝P0Simultaneous w-state noise and measurement noise vi(k) The following statistical properties are satisfied:
E{w(k)}＝0
E{vi(k)}＝0
Figure BDA0002106118480000051
E{w(k)wT(z)}＝Q(k)δkz
Figure BDA0002106118480000052
by introducing a kronecker function deltakzTaking the measurement noise as an example, if the current time k and z are the same time, δ is δ, it is determined whether the state noise or the measurement noise between the ith sensor and the jth sensor has correlation or notkzConsider the measurement noise between the ith and jth sensors to have a cross-correlation measurement noise figure R, 1ij(k) Otherwise, δkz＝0。
Where i and j are the numbers of the sensors, i1, 2kzFor kronecker function, Q (k) is a correlation matrix of state noise at the current moment k, and when i is not equal to j, R isij(k) Measuring a noise figure for a cross-correlation between an ith sensor and a jth sensor, R when i equals jij(k)＝Ri(k)，Ri(k) The noise figure is measured for the autocorrelation of the ith sensor.
In this embodiment, the measurement values of the sensors are time-stamped. Due to the unreliable communication channel, the measurement values may suffer from delays or losses during transmission,then the metrology values may be reordered by time stamping. Setting each measurement delay
Figure BDA0002106118480000053
And step (2), random distribution is satisfied:
Figure BDA0002106118480000054
wherein m is 1,2, 1
Figure BDA0002106118480000055
Independent of state noise w and measurement noise vi(k) And when i1 ≠ i2, k1 ≠ k2,
Figure BDA0002106118480000056
and
Figure BDA0002106118480000057
are independent of each other.
In this embodiment, the set measurement value is stored in a buffer of length L, and if the measurement value does not arrive between times k-L + h (where h is the number of the time slot in the buffer, and h is 1,2i(k-L + h) loss, introducing a marker function
Figure BDA0002106118480000058
For measured value
Figure BDA0002106118480000059
Making a mark, a function of the mark
Figure BDA00021061184800000510
The expression of (a) is:
Figure BDA0002106118480000061
thus, the measurement values in the buffer can be expressed as:
Figure BDA0002106118480000062
the first embodiment is as follows:
as shown in fig. 1, the present embodiment provides an optimal sequential fusion estimation method under a non-ideal channel, which is suitable for fusion calculation of an estimated value of a sensor in a discrete linear stochastic system, and includes:
step 1, determining fusion initial update time tau according to a measurement value of a marked sensor stored in a buffer at an adjacent moment;
further, the calculation formula for determining the fusion initiation update time τ is:
Figure BDA0002106118480000063
Figure BDA0002106118480000064
wherein τ is the fusion initiation update time, and t is the measured value
Figure BDA0002106118480000065
I is the sensor number, i is 1,2, …, N,
Figure BDA0002106118480000066
for the measured value of the ith sensor at the time stamp t stored in the buffer at the time k
Figure BDA0002106118480000067
L is the storage length of the buffer.
Specifically, the length of the register is set to L, and the marked measurement values are:
Figure BDA0002106118480000068
where t is k-L +1, …, k.
The marked measurement value
Figure BDA0002106118480000069
At the current time k, the measurement value is stored in the t + L-k time slot of the buffer, and if the current time k is reached, the marked measurement value
Figure BDA00021061184800000610
If not, storing the virtual variable 0 in the corresponding time slot.
The buffer is a buffer of "sliding window" nature, and due to the limited buffer length, only the measurement value at a limited time can be received, for example, the buffer length L is 3, then at the fourth time k is 4, the measurement values at the 2 nd, 3 rd and 4 th times are stored in the buffer, where the measurement value at the 2 nd time is placed in the first time slot, the measurement value at the 3 rd time is placed in the 2 nd time slot, and the measurement value at the 4 th time is placed in the 3 rd time slot.
As shown in fig. 2, the number N of sensors is set to 3, corresponding to the number of rows of the buffer, and the length L of the buffer is set to 4, corresponding to the number of columns of the buffer. At time 8, i.e., k is 8, the labeled sensor measurement values stored in the buffer time slot are:
Figure BDA0002106118480000071
and
Figure BDA0002106118480000072
and the marked measurement value
Figure BDA0002106118480000073
And
Figure BDA0002106118480000074
when the buffer arrives at the 9 th time (i.e., k is 9), the calculation formula of the fusion start update time τ determines that the timestamp t in the first sensor is 6, which is the fusion start update time τ corresponding to the 9 th time.
Since the buffer is a buffer with a certain length (L ═ 4), that is, one buffer stores the measured values at a plurality of time instants, the measured values must be updated sequentially, that is, the measured values at the previous time instants are updated, and the next time instants can be updated. In the buffer, the computation load can be reduced by comparing the time stamps of the measurement values stored in the adjacent time buffers, determining the earliest time stamp of the measurement values received at that time, and updating the fusion estimation value from this time.
Step 2, generating a decorrelation coefficient matrix according to the marked measuring value, and carrying out decorrelation on the marked measuring value according to the decorrelation coefficient matrix
Figure BDA0002106118480000075
Performing decorrelation on the measurement noise and the measurement transfer matrix;
further, in this embodiment, a method for calculating a decorrelation coefficient matrix at the current time k is provided, and in step 2, a decorrelation coefficient matrix is generated according to the measurement value, which specifically includes:
step 21, calculating a decorrelation coefficient between the measurement values of any two sensors according to a decorrelation coefficient calculation formula, wherein the decorrelation coefficient calculation formula is as follows:
Figure BDA0002106118480000076
Figure BDA0002106118480000077
Figure BDA0002106118480000078
Figure BDA0002106118480000079
Figure BDA0002106118480000081
in the formula (I), the compound is shown in the specification,
Figure BDA0002106118480000082
as a decorrelation coefficient between the current time k, the jth sensor and the ith sensor,
Figure BDA0002106118480000083
measuring the noise figure for the cross-correlation after the decorrelation between the current time k, the jth sensor and the ith sensor,
Figure BDA0002106118480000084
measuring the noise coefficient R for the autocorrelation of the j th sensor at the current time ki，j(k) The cross-correlation between the current time k, the jth sensor and the ith sensor measures the noise figure, Rj(k) For the autocorrelation measurement of the noise factor, delta, of the j-th sensor at the current time kkzAs function of kronecker, vi(k) The measured noise of the ith sensor at the current time k,
Figure BDA0002106118480000085
is the transpose of the measurement noise, E {. is the expected operation;
specifically, in the case of decorrelation, the measurement values of the sensors before the self number are decorrelated, that is, after the measurement value of the second sensor is decorrelated from the measurement value of the first sensor, the correlation between the measurement values of the third sensor is decorrelated using the measurement values in which the correlations are decorrelated by the first and second sensors. Therefore, i is less than j.
Step 22, generating a correlation coefficient matrix G of the ith sensor according to the decorrelation coefficients before the ith sensori(k) The calculation formula of the correlation coefficient matrix is:
Figure BDA0002106118480000086
in the formula, Gi(k) And the correlation coefficient matrix of the ith sensor at the current time k.
Specifically, the measurement noise of the ith sensor after decorrelation at the time k is set
Figure BDA0002106118480000087
Comprises the following steps:
Figure BDA0002106118480000088
in the formula, vi(k) Corresponding un-decorrelated measurement noise.
Through the above calculation formula, the correlation coefficient matrix G of the current time k can be obtainedi(k) Using a matrix G of correlation coefficientsi(k) For the marked measurement value
Figure BDA0002106118480000089
Measurement noise vi(k) Measuring the transfer matrix Hi(k) Performing decorrelation, wherein the corresponding calculation formula is as follows:
Figure BDA00021061184800000810
Figure BDA00021061184800000811
Figure BDA00021061184800000812
wherein the content of the first and second substances,
Figure BDA0002106118480000091
Figure BDA0002106118480000092
Figure BDA0002106118480000093
therefore, the current time k, the ith sensor, and the decorrelated measurement value
Figure BDA0002106118480000094
Comprises the following steps:
Figure BDA0002106118480000095
when there is no correlation in the measurement noise, that is, when the variance of the measurement noise is expected to be 0, there is no correlation, and the correlation coefficient matrix G is obtainedi(k)＝0。
Step 3, updating time and decorrelated measurement value according to fusion start by using a preset sequential fusion equation
Figure BDA0002106118480000096
Measuring noise
Figure BDA0002106118480000097
And a measurement transfer matrix
Figure BDA0002106118480000098
Calculating an estimate of a sensor
Figure BDA0002106118480000099
Further, the preset sequential fusion equation is:
Figure BDA00021061184800000910
Figure BDA00021061184800000911
Figure BDA00021061184800000912
Figure BDA00021061184800000913
in the formula (I), the compound is shown in the specification,
Figure BDA00021061184800000923
the estimate for the ith sensor at the current time k,
Figure BDA00021061184800000914
in order to be the value of the tag,
Figure BDA00021061184800000915
in order to filter the gain of the filter,
Figure BDA00021061184800000916
to the measured values after the decorrelation,
Figure BDA00021061184800000917
for the measurement transfer matrix after decorrelation,
Figure BDA00021061184800000918
is an estimated value
Figure BDA00021061184800000919
The variance of the error with the actual state value x (t) is expected,
Figure BDA00021061184800000920
in order to measure the noise figure by auto-correlation,
Figure BDA00021061184800000921
for the decorrelated measurement noise, I is the identity matrix.
In the present embodiment, the filter gain is set
Figure BDA00021061184800000922
Is the kalman filter gain. For the kalman filter, an initial value can be given arbitrarily, but a filter value can be adjusted by continuously inputting a measurement value, and a state value is finally tracked, and the kalman filter gain is a parameter for adjusting the reliability between the measurement value and the filter value at the previous moment, and is a core parameter in the kalman filter.
Specifically, at the previous time k-1, the estimation values of the previous time k-1, the corresponding timestamps, and the measurement values may be calculated, and the transmission of the estimation values between the previous time k-1 and the current time k is performed to implement initialization, where the initialization formula is as follows:
Figure BDA0002106118480000101
Figure BDA0002106118480000102
Figure BDA0002106118480000103
Figure BDA0002106118480000104
substituting the initial values into a preset sequential fusion equation, sequentially selecting timestamps as measurement values from fusion initial update time tau to current time k, and performing k-tau circulation calculation to obtain the current time k and the estimated value of the ith sensor
Figure BDA0002106118480000105
Wherein for the error covariance matrix
Figure BDA0002106118480000106
During the process of loop calculation, the system will self-correct and gradually convergeThe method belongs to a basic process of Kalman filtering, wherein a calculation formula of an error covariance matrix P (t, t) is as follows:
Figure BDA0002106118480000107
wherein x (t) is an actual state value,
Figure BDA0002106118480000108
are estimated values.
Example two:
the present embodiment provides a sensor data calculating apparatus including a data receiving unit, a data processing unit, and a data output unit, wherein,
the data receiving unit is used for receiving the measurement data of the plurality of sensors;
the data processing unit is used for carrying out fusion calculation on the measurement data according to the optimal sequential fusion estimation method under the non-ideal channel disclosed in the first embodiment;
the data output unit is used for outputting the fusion calculation result of the data processing unit.
The technical scheme of the present application is described in detail above with reference to the accompanying drawings, and the present application provides an optimal sequential fusion estimation method under a non-ideal channel, which is suitable for fusion calculation of estimated values of sensors in a discrete linear stochastic system, and includes: step 1, determining fusion initial update time according to marked measurement values stored in a buffer at adjacent moments; step 2, generating a decorrelation coefficient matrix according to the measurement value, and performing decorrelation on the measurement value, the measurement noise and the measurement transfer matrix according to the decorrelation coefficient matrix; and 3, calculating the estimation value of the sensor according to the fusion initial update time, the decorrelated measurement value, the measurement noise and the measurement transfer matrix by using a preset sequential fusion equation. Through the technical scheme in the application, the problems of noise correlation and communication delay in multi-sensor data fusion are solved, and the generated estimated value has higher filtering precision and stronger reliability.
The steps in the present application may be sequentially adjusted, combined, and subtracted according to actual requirements.
The units in the device can be merged, divided and deleted according to actual requirements.
Although the present application has been disclosed in detail with reference to the accompanying drawings, it is to be understood that such description is merely illustrative and not restrictive of the application of the present application. The scope of the present application is defined by the appended claims and may include various modifications, adaptations, and equivalents of the invention without departing from the scope and spirit of the application.

Claims (4)

1. An optimal sequential fusion estimation method under a non-ideal channel is characterized in that the method is suitable for fusion calculation of an estimated value of a sensor in a discrete linear stochastic system, and comprises the following steps:
step 1, determining fusion initial update time according to the marked sensor measurement value stored in the adjacent moment buffer;
step 2, generating a decorrelation coefficient matrix according to the measurement value, and performing decorrelation on the measurement value, the measurement noise and the measurement transfer matrix according to the decorrelation coefficient matrix;
step 3, calculating the estimated value of the sensor according to the fusion initial update time, the decorrelated measurement value, the measurement noise and the measurement transfer matrix by using a preset sequential fusion equation, wherein the preset sequential fusion equation is as follows:
Figure FDA0003499080630000011
Figure FDA0003499080630000012
Figure FDA0003499080630000013
Figure FDA0003499080630000014
where t τ, …, k,
Figure FDA0003499080630000015
the estimate for the ith sensor at the current time k,
Figure FDA0003499080630000016
in order to be the value of the tag,
Figure FDA0003499080630000017
in order to filter the gain of the filter,
Figure FDA0003499080630000018
to the measured values after the decorrelation,
Figure FDA0003499080630000019
for the measurement transfer matrix after decorrelation,
Figure FDA00034990806300000110
is an estimated value
Figure FDA00034990806300000111
The variance of the error with the actual state value x (t) is expected,
Figure FDA00034990806300000112
in order to measure the noise figure by auto-correlation,
Figure FDA00034990806300000113
for the decorrelated measurement noise, I is the identity matrix.
2. The method for optimal sequential fusion estimation under non-ideal channels according to claim 1, wherein the calculation formula for determining the fusion start update time τ is:
Figure FDA00034990806300000114
Figure FDA00034990806300000115
where τ is the fusion initiation update time, t is the time stamp of the measurement value, i is the sensor number, i is 1,2, …, N,
Figure FDA00034990806300000116
the measured value of the ith sensor at the time stamp t stored in the buffer for the current time k
Figure FDA00034990806300000117
L is the storage length of the buffer.
3. The method according to claim 1, wherein the step 2 of generating a decorrelation coefficient matrix according to the measurement values specifically includes:
step 21, calculating a decorrelation coefficient between the measurement values of any two sensors according to a decorrelation coefficient calculation formula, wherein the decorrelation coefficient calculation formula is as follows:
Figure FDA0003499080630000021
Figure FDA0003499080630000022
Figure FDA0003499080630000023
Figure FDA0003499080630000024
Figure FDA0003499080630000025
in the formula (I), the compound is shown in the specification,
Figure FDA0003499080630000026
for the decorrelation coefficients between the current time k, the jth sensor and the ith sensor,
Figure FDA0003499080630000027
measuring the noise figure for the cross-correlation after the decorrelation between the current time k, the jth sensor and the ith sensor,
Figure FDA0003499080630000028
measuring the noise coefficient R for the autocorrelation of the j th sensor at the current time ki,j(k) The cross-correlation between the current time k, the jth sensor and the ith sensor measures the noise figure, Rj(k) For the autocorrelation measurement of the noise factor, delta, of the j-th sensor at the current time kkzAs function of kronecker, vi(k) The measured noise of the ith sensor at the current time k,
Figure FDA0003499080630000029
is the transpose of the measurement noise, E {. is the expected operation;
step 22, generating the decorrelation coefficient matrix G of the ith sensor according to the decorrelation coefficients before the ith sensori(k) What is, what isThe calculation formula of the decorrelation coefficient matrix is as follows:
Figure FDA00034990806300000210
in the formula, Gi(k) The decorrelation coefficient matrix of the ith sensor at the current time k.
4. A sensor data calculation device, the calculation device comprising a data receiving unit, a data processing unit and a data output unit,
the data receiving unit is used for receiving measurement data of a plurality of sensors;
the data processing unit is used for carrying out fusion calculation on the measurement data according to the optimal sequential fusion estimation method under the non-ideal channel as claimed in any one of claims 1 to 3;
the data output unit is used for outputting the fusion calculation result of the data processing unit.
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