Research on data fusion of power wireless sensor networks based on Kalman filter

2.1. Composition of power wireless sensor

At present, in order to achieve the purpose of prediction and prevention, monitoring has been everywhere and has been widely used in many industries and fields. The positioning of wireless sensor networks in the monitoring field is unshakable, so this monitoring method collects more complete information and faster efficiency. However, this method also has a big disadvantage, that is, the node location needs to be determined through a large number of calculations, which is the biggest problem in wireless sensor network monitoring. Wireless sensor network, as its name implies, is a network system composed of several sensors, as shown in Fig. 1 (Seneviratne et al. [9]).

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Fig. 1.

Schematic diagram of wireless sensor network.

There are three types of nodes in the composition of wireless sensor networks, and each type of node plays a different role (Liu et al. [6]). The details are as follows:

According to the composition diagram of power sensors, the multi-source data acquisition function of power grid is designed to obtain the data of power wireless sensor network, and the collected data are normalized to ensure the consistency of data length. On this basis, the data of power wireless sensor network is preprocessed, which lays a solid foundation for the subsequent data fusion of power wireless sensor network. The data acquisition mean square error equation and feature extraction equation of the power system are respectively: (1) x k = A k − 1 , k x k − 1 + B k − 1 , k μ k − 1 + W k − 1 (2) z k = H k x k + v k

In formula (1), x k said power wireless sensor network in k moment of data collection and the mean square error function, expressed in A k − 1 , k said k − 1 time of electricity wireless sensor network data state transition matrix, x k − 1 said k − 1 moment of data collection and the mean square error function, B k − 1 , k said k − 1 times of electricity data area residual matrix wireless sensor network, μ k − 1 represents the network delay at time k − 1 , and W k − 1 represents the data sampling frequency at time k − 1 . In formula (2), z k represents the data feature extraction function extracted by the power wireless sensor network at time k, H k represents the strain function of the power wireless sensor network, and v k represents the network load amount of the power wireless sensor network. Generally, they obey the distribution of N ( 0 , 1 ) .

Assuming that the power wireless sensor network data estimation noise and network load satisfy formula (1), at this time, the Kalman filter algorithm can be used to calculate the mean square error of power wireless sensor network data acquisition. The specific process of Kalman filter algorithm is as follows:

The acquisition error of power wireless sensor network is transformed into the estimated value of data acquisition mean square error x k ′ , and the data acquisition mean square error x k is calculated by inverse recursion. At this time, the pre estimation function is: (3) x k ‾ ′ = A k − 1 , k x k − 1 + B k − 1 , k μ k − 1 (4) P k ‾ = A k − 1 , k P k − 1 A k − 1 , k T + Q

In the above formula, A k − 1 , k T represents the data state transition matrix of power wireless sensor network at k − 1 when the transpose is T, and Q represents the transition function.

Calculate Kalman gain matrix (Anees et al. [1]) (5) K k = P k ‾ H k T [ H k · P k ‾ · H k T + R ] − 1 (6) Q = B k − 1 , k [ u k · u k T ] B k − 1 , k T , R = v k · v k T

In the above formula, R represents the state transition matrix

Update estimate: (7) x k ′ = x k ‾ ′ + K k [ z k − H k · x k ‾ ′ ]

In the above formula, K k represents the observation matrix.

Calculate the updated estimated covariance matrix: (8) P k = [ I − K k · H k ] P k ‾

Recursive loop calculation: (9) x k + 1 = x k ′ P k + 1 = P k ‾

The above formula is the solution process of Kalman filter algorithm. Under the given step coefficient x 0 , P 0 is used to represent the communication range of power wireless sensor communication data, and the real-time state estimation result x k ′ = ( k = 1 , 2 , … , N ) of power wireless sensor communication data is obtained according to the reverse recursive method. For Kalman filter algorithm (Li et al. [4]), an ideal filtering initial value can make the mean estimation error of data acquisition smaller, and the calculation time of error is very short.

When the step coefficient is certain, the initial parameters of the filter are not affected by noise interference, so the selection of the initial value of the filter has a direct impact on the filtering result.

It can be seen from formula (7) of the positioning equations that the TDOA and position acquisition equations are independent of the target speed and will not introduce errors due to the communication target position. Therefore, when studying the communication target of power wireless sensor network, it is necessary to fuse DOA positioning information to obtain the initial filtering value (Li and Liu [5]; Markiewicz et al. [7]).

The calculation of the initial filtering value needs to be carried out in the power wireless sensor communication coordinate system. Firstly, it is assumed that the initial position of the radiation source of the power communication target is μ b , t = [ x b , t , y b , t , z b , t ] and the initial positions of different communication targets are represented by s b , t = [ x b , n , y b , n , z b , n ] , where n = 0 represents the initial position of a power communication target, its coordinates in the coordinate system are ( 0 , 0 , 0 ) , and n = 1 , 2 represents the soft and hard thresholds of power communication respectively. r 0 is used to represent the distance between the data transmitting and receiving points of the power communication network, r n is used to represent the regional residual displacement after wavelet decomposition, and n = 1 , 2 is: (10) r 0 = ( x b , t − x b , 0 ) 2 + ( y b , t − y b , 0 ) 2 + ( z b , t − z b , 0 ) 2 = x b , t 2 + y b , t 2 + z b , t 2

In the communication range, the data transmission location estimation equation of power wireless sensor network is: (11) t n , 0 = ‖ S b , 0 − μ b , t ‖ − ‖ S b , n − μ b , t ‖ c + d t 0 θ 0 = arctan ( μ b , t T · e Y μ b , t T · e X ) + d θ 0

Where, t n , 0 represents the time difference between the initial time and the data acquisition characteristics of the power sensor n respectively; θ 0 is the arrival angle measurement at the initial time measured by the one dimension interferometer of the power sensor, d t 0 and d θ 0 represents the power data acquisition error of the initial time difference and angle respectively. It can be obtained from the first equation in equation (2): ( x b , 0 − x b , t ) 2 + ( y b , 0 − y b , t ) 2 + ( z b , 0 − z b , t ) 2 (12) = ( x b , n − x b , t ) 2 + ( y b , n − y b , t ) 2 + ( z b , n − z b , t ) 2 − c 2 t n , 0 2 + 2 c t n , 0 r 0

In the above formula, c represents the error probability.

The second equation and formula (10) of simultaneous positioning formula (11) can be obtained (13) ( x b , n + y b , n · tan θ 0 ) x b , t + z b , n · z b , t = ( x b , n 2 + y b , n 2 + z b , n 2 − c 2 t n , 0 2 ) 2 + c t n , 0 r 0

Where, n = 1 or 2, and then there is (14) x b , t z b , t = x b , 1 + y b , 1 tan θ 0 z b , 1 x b , 2 + y b , 2 tan θ 0 z b , 2 − 1 · ( x b , 1 2 + y b , 1 2 + z b , 1 2 − c 2 t 1 , 0 2 ) 2 + c t 1 , 0 r 0 ( x b , 2 2 + y b , 2 2 + z b , 2 2 − c 2 t 2 , 0 2 ) 2 + c t 2 , 0 r 0

Replace the power data acquisition error function formula (14) and the second equation of data transmission function formula (11) into formula (10), and simplify the formula (15): (15) a · r 0 2 + b · r 0 + d = 0

The two roots of r 0 are solved by formula (15). After removing the image blur value, the obtained solution is substituted into formula (10) and equation (2) of the positioning equation group (11), the initial positioning coordinate of the target in the power communication system is solved, and the position coordinate is converted from equation (2) coordinate to ECEF coordinate system, that is, the filtered initial value u 0 is obtained. For the covariance matrix, the covariance matrix of the initial position estimation can be obtained by solving the total differential of formula (10) and formula (11) of the positioning equations respectively: (16) P ˜ = ( M R 2 R 1 ) − 1 · diag ( c 2 · σ t 2 , c 2 · σ t 2 , sec 4 ( θ 0 ) σ θ 2 ) · [ ( M R 2 R 1 ) − 1 ] − 1

Where, diag is the diagonal matrix with corresponding elements as diagonal elements, σ t represents the measurement accuracy of TDOA, σ θ represents the measurement accuracy of azimuth, and matrix M is (17) M = x b , t − x b , 1 r 1 − x b , t r 0 y b , t − y b , 1 r 1 − y b , t r 0 z b , t − y b , 1 r 1 − z b , t r 0 x b , t − x b , 2 r 2 − x b , t r 0 y b , t − y b , 2 r 2 − y b , t r 0 z b , t − z b , 2 r 2 − z b , t r 0 − y b , t x b , t 2 1 x b , t 0

The state of power communication data is unknown at this time, so set the initial data transmission amount to 0, and the initial filter value is ( u 0 T , 0, 0, 0) and the initial covariance matrix is: (18) P ˜ 0 = b l k | diag ( P ˜ , v max 2 , v max 2 , v max 2 )

Where, v max is the result of no redundant data after power communication data processing. Therefore, the data of power wireless sensor network without redundancy is obtained, which lays a foundation for the next data fusion.

2.3. Data fusion of power wireless sensor networks based on Kalman filter

Kalman filter is an optimal linear state estimation method, which is equivalent to the optimal linear filter under the minimum mean square error criterion. The so-called state estimation is to find the state vector that best fits the observed data through mathematical methods. It only needs the current measured value and the estimated value of the previous sampling period to estimate the state, does not need a large amount of storage space, has a small amount of calculation at each step, has clear calculation steps, and is very suitable for computer processing. Therefore, this paper applies it to the design of data fusion method for power wireless sensor networks, so that this method has the characteristics of low data fusion error and time-consuming, Ensure the data fusion effect of power wireless sensor network.

On the basis of Section 2, the processed power wireless sensor network data is introduced into the Kalman filter model for variable multi cluster data processing. The specific power network data fusion process is shown in Fig. 3.

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Fig. 3.

Data fusion algorithm of power sensor network based on Kalman filter.

According to Fig. 3, relevant data are collected in the power wireless sensor network, and then multiple sensors are used to process the data collected by each node, and the data filtering is realized through the Kalman filter. Through multiple iterations, the interference of dirty data in the power network can be effectively reduced, the data to be fused is cleaner, and the effect of data fusion is improved. In the figure above, x n [ m ] represents the data output result after the nth Kalman filter processing, that is, the mth cluster head fusion state estimation after wireless sensor processing, and then the cluster head fusion state estimation is processed by principal component analysis, and all these data are gathered. The specific number of uploads is represented by k ( k ⩽ n ), The fused target data of power wireless sensor network is obtained for people to use.

Figure 4 shows the data fusion process of power wireless sensor network based on Kalman filter.

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Fig. 4.

Data fusion flow of power wireless sensor network based on Kalman filter.

In the process of data fusion, Kalman filter algorithm can effectively avoid the truncation error generated in the process of multiple iterations, and effectively avoid the problem that the traditional methods may lead to large filtering result error (Cheng et al. [2]). Therefore, this paper will use the filtering results for data fusion and define the data fusion cost function: (19) C ( X k ) = ( X k − X ˜ k n ) T P ˜ k ( X k − X ˜ k ) + ( Z k − h ( X ˜ k ) ) T R ˜ k ( Z k − h ( X ˜ k ) )

In the above formula, X k represents the initial prediction covariance matrix, X ˜ k n represents the prediction covariance matrix constructed at the nth time, P ˜ k represents the modified covariance matrix, Z k represents the truncation error matrix, and h ( X ˜ k ) represents the filtering matrix.

In this paper, the prediction covariance matrix is adjusted by L-M method to ensure the global convergence of the algorithm. The core of the algorithm is to modify the covariance prediction matrix by using the damping factor in each iteration, and update the observation iteratively with the modified covariance matrix P ˙ k . The specific process is as follows:

Target state prediction: (20) X ˜ k | k − 1 = A X k − 1 + ω k − 1

In the above formula, ω k − 1 represents the damping factor.

Prediction covariance matrix: (21) P ˜ k | k − 1 = A P k − 1 A T + Q k

At the beginning of iteration, L-M method modifies the covariance matrix: (22) P ˜ k | k − 1 = [ I − P ˜ k | k − 1 n ( P ˜ k | k − 1 n + μ − 1 I ) − 1 ] P ˜ k | k − 1 n

Kalman gain matrix calculation: (23) K k n = P ˜ k | k − 1 n + 1 ( H k n ) T ( R k n + H k n P ˜ k | k − 1 n + 1 ( H k n ) T ) − 1

Update target status: (24) X ˜ k | k − 1 n + 1 = X ˜ k | k − 1 n + K k n ( z k − h ( X ˜ k | k − 1 n ) )

Update covariance matrix: (25) P k − 1 = ( I − K k n H k n ) P ˜ k | k − 1 n + 1

At the end of the iteration, let X k = X ˜ k | k − 1 n + 1 , where n is the number of iterations. Define cost function: (26) q k = 1 2 ( Z k − h ( X ˜ k | k − 1 n ) ) T · K k − 1 ( Z k − h ( X ˜ k | k − 1 n ) )

If q k n + 1 ⩾ q k n , it means that the direction of the iteration is wrong, which will increase the cost function. The iteration result of this equation of state is omitted and let μ = μ × 2 . On the contrary, it means that the direction of the iteration is correct, record the iteration result and let μ = μ / 3 . When μ is large, the algorithm is similar to the steepest descent method, and when μ is close to 0, the algorithm is similar to the Gaussian Newton algorithm.

When the contemporary valence function is less than a certain limit with the increase of the number of iterations, it is considered that the convergence has reached near the extreme point, and the iteration termination condition can be written as (27) ‖ q k n + 1 − q k n ‖ < ε ( ‖ q k n ‖ + ε )

Where, q k n and q k n + 1 represent the cost function of n and n + 1 times respectively, and ε represents the preset threshold value. The specific flow chart of the whole process is shown in Fig. 5.

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Fig. 5.

Data fusion result correction flow chart of L-M method.

3.1. Experimental scheme

For the design method in this paper, in order to analyze its practical application performance, it is necessary to carry out application test on the system. The overall experimental scheme is as follows:

As most of the application environments of the methods in this paper are applied to Windows system, and most of them are C/S architecture, the relevant environment parameters required by the test are shown in Table 1.

Experimental data: The power wireless sensor network parameters and test data are taken as experimental sample data, and the collected data are integrated and de-noised, and the processing results are taken as experimental sample data. The experimental sample data is divided into two parts on average, one part for software testing and the other part for experimental testing. The test data is input into the simulation software, and the optimal operating parameters of the software are obtained after several tests. The parameter is taken as the initial parameter to ensure the authenticity and reliability of the simulation results.