CN107426748B - Method for estimating performance of multiple sensors in wireless network control system - Google Patents
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Abstract
The invention relates to the technical field of network control, and discloses a method for estimating performance of multiple sensors in a wireless network control system, which comprises the following steps: (1) acquiring sensor parameters of a wireless network control system, and establishing dynamic characteristics and a sensor measurement equation of the process; (2) connecting a plurality of sensors, and arranging two channels between every two sensors; carrying out data transmission by utilizing one of the communicated channels, and switching the channels if the channel starts to lose packets; respectively calculating estimated values and estimation error covariance matrixes of sensors at the centers of the single channel and the multiple channels; (3) and (3) comparing the transmission performance of two channels between the two sensors, calculating the estimated value and the error covariance matrix in the circulation according to the step (2), generating a comparison graph of the transmission performance of the single channel and the transmission performance of the double channel, and generating a comparison graph of a plurality of channels. The invention utilizes the Kalman filtering algorithm to ensure that the sensor is effectively scheduled in the multi-channel transmission system so as to reduce the estimation error.
Description
Technical Field
The invention relates to the technical field of network control, in particular to a method for estimating performance of multiple sensors in a wireless network control system.
Background
With the development of modern communication science and technology, wireless networked control systems (WirelessNCSs, WNCSs) are gradually replacing traditional wired networked control systems, and compared with wired networks, wireless networks transmit data through wireless media, so that a complex installation and wiring process is omitted, maintenance and upgrade of systems in the future are more convenient, and use cost is effectively saved. This increases the mobility and scalability of the system because there are nodes in the WNCSs that can move within the network and the communication range of the system is only affected by the number of nodes and the power transmitted and received and is not controlled by the wiring. More importantly, WNCSs can still work well in places where people cannot reach or where the environment is very harsh.
Although there are many advantages to the wireless networked control system, there are still many challenges to the practical use of the system. On the one hand, WNCSs have problems that remain to be solved in Networked Control Systems (NCSs), such as packet transmission delay, packet loss, clock synchronization, and packet timing confusion. On the other hand, WNCSs have problems of fading and interference of wireless channels, energy saving requirements of wireless nodes (such as wireless sensors), limited communication channels, bandwidths, and spectrum resources, and the like, which are obstacles for research and application of WNCSs. In addition, for the problem of packet loss of a wireless channel, the existing research is mainly focused on the problem of single-sensor estimation, and the estimation mode is difficult to obtain comprehensive and stable information and has limited transmission distance, so that the continuously improved performance requirement of a control system cannot be met.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a multi-sensor performance estimation method in a wireless network control system, which considers the problem of multi-sensor channel switching in the wireless network control system, can ensure that a sensor is effectively scheduled in a multi-channel transmission system to reduce estimation errors, and completes the optimization of the multi-sensor performance estimation in the wireless network control system.
In order to solve the above technical problems, the present invention is solved by the following technical solutions.
A method for estimating performance of multiple sensors in a wireless network control system comprises the following steps:
(1) acquiring sensor parameters of a wireless network control system, and establishing a dynamic characteristic and a sensor measurement equation of the process:
wherein, A ∈ Rn*nRepresenting a system matrix, C ∈ Rm*nAn observation matrix, x, representing the full rank of the rowsk∈RnAnd yk∈RmIs a real number vector, respectivelyIndicating the state and measurement of the sensor, wk∈RnAnd vk∈RmIs a zero mean Gaussian process, Q is wkR is vkSatisfies Q > 0 and R > 0, m, n is a positive integer, k denotes the time at which (A, C) is detectable,
is stable;
(2) connecting a plurality of sensors, setting two channels between every two sensors, and simultaneously setting parameters of each channel; carrying out data transmission by utilizing one of the communicated channels, and switching the channels if the channel starts to lose packets; setting the number of cycles, initializing x0，P0Respectively calculating estimated values and estimated error covariance matrixes of the sensors at the centers of the single channel and the multiple channels by using a Kalman filtering algorithm, wherein the calculation equation is as follows:
wherein
As an estimate of the sensor at the center, Pκ|κTo estimate the error covariance matrix, P is calculatedk|kUntil the cycle is complete;
(3) and (3) comparing the transmission performance of the two sensors through two channels, and generating a comparison drawing of a plurality of channels according to the data conditions of the estimation value and the estimation error covariance matrix in the channel completion cycle in the step (2).
Preferably, in step (1), the initial state x of the system0Is a mean of 0 and a covariance matrix of P0Gaussian random vector of > 0, wk，vkAnd x0Are independent of each other.
Due to the adoption of the technical scheme, the invention has the remarkable technical effects that:
firstly, establishing dynamic characteristics of a process and a sensor measurement equation to obtain system parameters; then, calculating the critical packet receiving probability, namely the error is dispersed along with the time when the packet receiving rate is smaller than the critical value; then, respectively solving the estimated values and estimation error covariance matrixes of the sensors at the centers of the single channel and the multiple channels in an iterative manner; and finally, according to the estimated value and the estimation error obtained by calculation, determining that the multi-channel switching transmission is superior to the single-channel transmission and providing a switching method to complete the optimization of the multi-sensor estimation performance in the wireless network control system. The method for designing the multi-sensor estimation performance in the wireless network control system by using the Kalman filtering algorithm can ensure that the sensors are effectively scheduled in a multi-channel transmission system to reduce the estimation error.
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FIG. 1 is a schematic diagram of a model structure in a method for estimating performance of multiple sensors in a wireless network control system according to the present invention;
FIG. 2 is a schematic diagram of a workflow of a method for estimating performance of multiple sensors in a wireless network control system according to the present invention;
FIG. 3 is a comparison graph of the true value and the estimated value of a single channel in the method for estimating performance of multiple sensors in a wireless network control system according to the present invention;
FIG. 4 is a diagram of comparison of estimation errors of a single channel sensor 1 and a sensor 2 in a method for estimating performance of multiple sensors in a wireless network control system according to the present invention;
FIG. 5 is a graph of the average estimation error of the single channel sensor 2 in the method for estimating performance in the multi-sensor method for estimating performance in the wireless network control system according to the present invention;
FIG. 6 is a comparison graph of the real values and estimated values of the dual channels in the method for estimating performance of the multi-sensor in the wireless network control system according to the present invention;
FIG. 7 is a diagram illustrating the comparison of the estimation errors of the dual-channel sensor 1 and the sensor 2 in the method for estimating performance of multiple sensors in the wireless network control system according to the present invention;
fig. 8 is a diagram of the average estimation error of the dual-channel sensor 2 in the method for estimating performance of multiple sensors in the radio network control system according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1 to 8, a method for estimating performance of multiple sensors in a wireless network control system includes the following steps:
(1) acquiring sensor parameters of a wireless network control system, and establishing a dynamic characteristic and a sensor measurement equation of the process:
wherein, A ∈ Rn*nRepresenting a system matrix, C ∈ Rm*nAn observation matrix, x, representing the full rank of the rowsk∈RnAnd yk∈RmIs a real number vector representing the state and measurement of the sensor, wk∈RnAnd vk∈RmIs a zero mean Gaussian process, Q is wkR is upsilonkThe covariance matrix of (1) satisfies Q > O and R > 0; initial state x of the system0Is a mean of 0 and a covariance matrix of P0Gaussian random vector of > 0, wk，vkAnd x0Are independent of each other, m, n are positive integers, k denotes the time of day, (A, C) is detectable,
is stable;
(2) connecting a plurality of sensors, setting two channels between every two sensors, and simultaneously setting parameters of each channel; carrying out data transmission by utilizing one of the communicated channels, and switching the channels if the channel starts to lose packets; setting the number of cycles, initializing x0，P0Respectively calculating estimated values and estimated error covariance matrixes of the sensors at the centers of the single channel and the multiple channels by using a Kalman filtering algorithm, wherein the calculation equation is as follows:
wherein
As an estimate of the sensor at the center, Pk|kTo estimate the error covariance matrix, P is calculatedk|kUntil the cycle is complete;
(3) and (3) comparing the transmission performance of the two sensors through two channels, and generating a comparison drawing of a plurality of channels according to the data conditions of the estimation value and the estimation error covariance matrix in the channel completion cycle in the step (2).
For multiple sensors in a single-channel wireless network control system, due to channel attenuation or congestion, data packets may be lost during the propagation of the channel. Similarly, γkIndicating whether the estimator received the measurement ykThe estimator also knows ykThe information of (1) is obtained according to the optimality of the Kalman filter without considering other uncertain factors such as time delay and the like:
wherein, Kalman gain Kk＝Pk|k-1C′(CPk|k-1C′+R)-1And the update of the kalman filter over time is also optimal, i.e.
Pk+1|k＝APk|kA' + Q and
P0|-1＝P0。
due to random data packet loss of the network, the covariance matrix of the estimation error is also random, unlike the standard kalman filter, which is deterministic. Let Pk＝Pk|k-1Then P iskThe update equation of (1) is:
Pk+1＝APkA′+Q-γkAPkC′(CPkC′+R)-1CPkA′
now, a value is output from the system, and after the value reaches the sensor 1, the value reaches the sensor 2, wherein the packet loss rate and the time delay exist, assuming that from the 9 th time, the sensor 1 receives the signal and successfully transmits the signal to the sensor 2 at the 9 th time, the transmission is unsuccessful at the 10 th time, the transmission is unsuccessful at the 11 th time, the transmission is successful at the 12 th time, the following relationship can be obtained, that is,
as can be seen from the figure, when the success between the sensors 1 and 2 is achieved, the value obtained by the sensor 2 is 1, the output value is multiplied by the system coefficient A, and the success probability is
If not, a calculation is made from the value that the sensor 2 has obtained at the last moment. It can be seen that the estimation error covariance of multiple sensors in a single channel wireless network control system will grow exponentially with a high probability.
Fig. 1 shows a block diagram of a dual-channel radio network control system.
Fig. 2 is a flow chart of a method for estimating performance of multiple sensors in a wireless network control system. Specifically, the following can be described:
a method for estimating performance of multiple sensors in a wireless network control system comprises the following steps:
step 1: establishing dynamic characteristics of the process and a sensor measurement equation:
wherein, A ∈ Rn*nRepresenting a system matrix, C ∈ Rm*nRepresenting an observation matrix, xk∈RnAnd yk∈RmRespectively representing the state and measurements of the system, wk∈RnAnd vk∈RmIs zero mean valueThe covariance matrices of Q > 0 and R > 0 respectively, require
Controllable, (A, C) is observable, the measurement matrix C is full rank, i.e. rank (C) m ≦ n, the initial state x of the system0Is a mean of 0 and a covariance matrix of P0Gaussian random vector > 0, further, wk，vkAnd x0Are independent of each other.
Step 2: measurement of the System ykTransmitted to the remote estimator via an unreliable communication channel, there may be a loss of data packets during propagation through the channel due to channel fading or congestion. Intuitively, the larger the packet loss probability is, the more serious the information loss is, the more the error covariance matrix P is estimatedk|k-1The greater the likelihood of divergence. For the independent and identically distributed packet loss process, a critical packet receiving probability criterion exists, so that the average boundedness can be achieved by estimating an error covariance matrix as long as the packet receiving probability is larger than the critical packet receiving probability criterion.
Firstly, solving the characteristic value of the matrix A:
eigvalues＝eig(A)
then, the spectrum radius of the matrix A is calculated:
spectrumofA＝max(abs(eigvalues))
and finally obtaining the critical packet receiving probability:
and step 3: respectively calculating estimated values and estimated error covariance matrixes of the sensors at the centers of the single channel and the multiple channels by using a Kalman filtering algorithm:
standard kalman filter equation:
from the above formula, one can obtain:
this can give Pk|kWhich satisfies the equation X ═ g (h (X)). For a multi-sensor in a single-channel wireless network control system, due to channel attenuation or congestion, a data packet may be lost in the propagation process of a channel, and the estimation error covariance of the multi-sensor in the single-channel wireless network control system can be obtained and exponentially increased on the basis of a large probability.
And 4, step 4: now compare the performance comparison between two sensors transmitted over two channels:
suppose that channel 1:
suppose channel 2:
so as to define the transition probability of two channels, i.e. T1(1，1)＞0.5，T1(2，2)＞0.5，T2(1，1)＞0.5，T2(2, 2) > 0.5 is because such channels are called Gilbert-Elliott channels, and the memory that such channels typically exist depends on the transition probability between states. Markov proposes that in the process of transferring some factors of the system, the result of the Nth time only depends on the influence of the result of the (N-1) th time, namely, the result is only related to the current state and is not related to the previous state, so when T is1(1，1)＞0.5，T1When the value is more than (2, 2) > 0.5, the packet receiving rate of two elements of the transition matrix at the next moment is still higher, so that the error is more easily generated.
Taking two channels as an example, suppose that the sensors transmit through channel 1 first, the failure is converted into channel 2 transmission after n1 times of success, and then the failure is converted back to channel 1 after n2 times of success, so the scheduling method is adopted because the system starts generating errors after the first channel transmits errors, if the transmission is continued through the channel, the packet loss rate is more than the packet receiving rate, the error value is easy to start increasing in an exponential manner, and at this time, the system starts transmitting again through a channel, so the exponential increase of the error is avoided. Similarly, it can be generalized to multi-channel systems.
And 5: and determining that multi-channel switching transmission is superior to single-channel transmission according to the estimated value obtained by calculation, and giving a channel switching method to complete optimization of the estimation performance of the multi-sensor in the wireless network control system.
Further, the channel switching method obtained in step 4 can ensure that the sensor is effectively scheduled in the multi-channel transmission system to reduce estimation errors.
The technical solution of the present invention is further illustrated by the following specific examples. In the experiment, single-channel and double-channel wireless network control systems are compared to carry out algorithm verification. Specifically, the following experimental parameters were used:
separately assuming system matrices
Observation matrix C ═ 32]The system covariance matrix
Observing that the covariance matrix R is 0.6, setting the cycle number to be 1000, and taking a random number between 0 and 1 as an estimated value xk|kEstimating an error covariance matrix Pk|kAnd true value xkDefining an initial observation y k0, true value xkThe second column is [ 10.4 ]]Setting channel parameters
Kalman filtering is carried out on a single-channel wireless network control system and a double-channel wireless network control system, a value is output in the single-channel wireless network control system, the value reaches a sensor 2 after reaching a sensor 1, packet loss rate and time delay exist, when the sensors 1 and 2 succeed, the value obtained by the sensor 2 is 1, the output value is multiplied by a system coefficient A, the success probability is
If not, a calculation is made from the value that the sensor 2 has obtained at the last moment. It can be obtained that the estimation error covariance of multiple sensors in a single-channel wireless network control system will grow exponentially; for a dual-channel system, it is assumed that sensors transmit through channel 1 first, a failure is converted into channel 2 transmission after n1 times of success, and then a failure is converted back into channel 1 after n2 times of success, so this scheduling manner is adopted because the system starts generating an error after the first channel has transmitted an error, if the packet loss rate is still greater than the packet reception rate after the channel continues to transmit, the error value is liable to start increasing exponentially, and at this time, the system starts transmitting again by using a channel, so that the exponential increase of the error is avoided.
Fig. 3, 4, 5, 6, 7, and 8 are graphs of simulation verification results of the designed method by the Matlab system.
Fig. 3 shows a comparison of the true values, the estimated values at sensor 1 and the estimated values at sensor 2 in a single channel system, fig. 4 shows a comparison of the estimation errors at sensor 1 and sensor 2 in a single channel system, and fig. 5 shows the average estimation error at sensor 2 in a single channel system. It can be seen from the figure that the estimation error at the sensor 2 and the average estimation error are relatively large.
Fig. 6 shows a comparison of the true values, the estimated values at sensor 1 and the estimated values at sensor 2 in a dual channel system, fig. 7 shows a comparison of the estimation errors at sensor 1 and sensor 2 in a dual channel system, and fig. 8 shows the average estimation errors at sensor 2 in a dual channel system. It can be seen from the figure that the estimation error at the sensor 2 and the average estimation error are relatively small.
Firstly, establishing dynamic characteristics of a process and a sensor measurement equation to obtain system parameters; then, calculating the critical packet receiving probability, namely the error is dispersed along with the time when the packet receiving rate is smaller than the critical value; then, respectively solving the estimated values and estimation error covariance matrixes of the sensors at the centers of the single channel and the multiple channels in an iterative manner; and finally, according to the estimated value and the estimation error obtained by calculation, determining that the multi-channel switching transmission is superior to the single-channel transmission and providing a switching method to complete the optimization of the multi-sensor estimation performance in the wireless network control system. The method for designing the multi-sensor estimation performance in the wireless network control system by using the Kalman filtering algorithm can ensure that the sensors are effectively scheduled in a multi-channel transmission system to reduce the estimation error.
In summary, the above-mentioned embodiments are only preferred embodiments of the present invention, and all equivalent changes and modifications made in the claims of the present invention should be covered by the claims of the present invention.
Claims (2)
1. A method for estimating performance of multiple sensors in a wireless network control system is characterized by comprising the following steps:
(1) acquiring sensor parameters of a wireless network control system, and establishing a dynamic characteristic and a sensor measurement equation of the process:
wherein, A ∈ Rn*nRepresenting a system matrix, C ∈ Rm*nAn observation matrix, x, representing the full rank of the rowsk∈RnAnd yk∈RmIs a real number vector representing the state and measurement of the sensor, wk∈RnAnd vk∈RmIs a zero mean Gaussian process, Q is wkR is upsilonkSatisfies Q > 0 and R > 0, m, n is a positive integer, k denotes the time at which (A, C) is detectable,
is stable;
(2) connecting a plurality of sensors, setting two channels between every two sensors, and simultaneously setting parameters of each channel; carrying out data transmission by utilizing one of the communicated channels, and switching the channels if the channel starts to lose packets; setting cycleNumber of loops, initialization x0，P0Respectively calculating estimated values and estimated error covariance matrixes of the sensors at the centers of the single channel and the multiple channels by using a Kalman filtering algorithm, wherein the calculation equation is as follows:
wherein
As an estimate of the sensor at the center, Pk|kTo estimate the error covariance matrix, P is calculatedk|kUntil the cycle is complete;
(3) and (3) fixing two adjacent sensors, and calculating the estimated value and the error covariance matrix in the circulation according to the step (2) to generate a comparison graph of the transmission performance of the single channel and the transmission performance of the double channels.
2. The method of claim 1, wherein the performance of the multiple sensors is estimated according to the following parameters: in step (1), the initial state x of the system0Is a mean of 0 and a covariance matrix of P0Gaussian random vector of > 0, wk，vkAnd x0Are independent of each other.
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