CN117195946A - WSN maneuvering target tracking method based on extended Kalman filtering - Google Patents
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Abstract
The invention discloses a WSN maneuvering target tracking method based on extended Kalman filtering, which comprises the following specific steps: s1: acquiring data of a maneuvering target by using a sensor network; s2: initializing a snake population, uniformly distributing the snake population in a search space by utilizing Cubic chaos cube mapping, and setting a maximum iteration number, food and temperature trigger threshold; s3: determining an objective function, determining an adaptability function according to an extended Kalman filtering algorithm process, estimating parameters of a maneuvering target according to an extended Kalman filtering step, taking a noise covariance matrix parameter as a position of an optimization algorithm individual, optimizing to generate random noise with covariance of a Q value and an R value, and adding the random noise into an observed value and an estimated value of an SO-C algorithm; the WSN maneuvering target tracking method based on the extended Kalman filtering has the effects of being capable of quickly converging to global optimum and effectively improving the convergence accuracy of an algorithm.
Description
Technical Field
The invention relates to the field of information science sensor positioning, in particular to a WSN maneuvering target tracking method based on extended Kalman filtering.
Background
Wireless sensor networks (Wireless Sensor Network, WSNs) are one research hotspot today for maneuvering target tracking. For the maneuvering target, firstly, track data of the maneuvering target are collected in real time through a wireless sensor network, and then the position and the motion state of the maneuvering target are predicted in real time according to the collected track data, so that the acquisition and the tracking and positioning of the motion state of the maneuvering target are completed.
Among them, the Kalman filtering prediction-based method is easy to realize and has good tracking effect on linear systems, and is widely studied by domestic and foreign students. The algorithm has the problem that the tracking performance of a nonlinear motion system is obviously reduced. In practice, the maneuvering target usually moves in a nonlinear motion mode, so many scholars improve the kalman filtering and propose an extended kalman filtering algorithm (Extended Kalman Filter). The extended Kalman filtering is a nonlinear filtering mode, which uses a state equation and a measurement equation in a Taylor expansion processing system, and simultaneously uses a Jacobian matrix to replace linear transformation in a Kalman algorithm.
The traditional extended kalman filter parameters are relatively fixed, resulting in reduced performance of the algorithm. The filtering parameter Q refers to a covariance value of a covariance matrix of noise in the maneuvering process, and mainly affects the filtered parameter and the estimation accuracy of the parameter. The filtering parameter R is the covariance value of the covariance matrix of the measured noise, and mainly determines the correction speed of the filtering. Incorrect values of the filtering parameters can lead to filtering divergence, so that tracking accuracy is greatly reduced.
The flow of the extended Kalman filtering algorithm comprises the following steps: firstly, a state transition equation and an observation equation are established according to a motion model and an observation model of a system, and then the state transition equation and the state estimation value of the last moment are utilized to predict the state estimation value and the covariance matrix of the current moment. And correcting the predicted state estimation value and covariance matrix by using the observation equation and the observation value at the current moment to obtain a final state estimation value and covariance matrix.
Therefore, aiming at the main reason analysis for influencing the accuracy of the extended Kalman maneuvering target tracking, a plurality of students carry out mathematical optimization on the extended Kalman maneuvering target tracking, or add variant algorithm force of an intelligent optimization algorithm to improve the tracking accuracy.
The SO algorithm (SnakeOptimizer, SO), proposed by fatma. Hashim and Abdelazim g.humiien in 2022, was mainly derived from the mating behaviour of the snake, the next behaviour of the individual snake being judged by the current ambient temperature level and the number of foods. The inspiration of the snake optimization algorithm is derived from the mating behavior of the snake. If the temperature is low and food is available, mating behavior of the snake occurs; otherwise the snake would only look for food or eat the existing food. Based on this, the search process of the snake optimization algorithm is divided into two phases: exploration and development. Exploration describes environmental factors, i.e. cold places and foods, and this phase does not exist where a snake is looking for food in the environment surrounding it. The snake optimization algorithm is used as a simpler and more robust optimization algorithm; the algorithm not only has the characteristic of easy understanding, but also is easy to write program codes. At the same time, the program code is not too long compared to other algorithms, and is easily used to deal with various optimization problems. The iteration speed is high, and the method has great effect and significance in improving tracking precision of a maneuvering target tracking algorithm of the wireless sensor network.
However, as known from the extended kalman filtering algorithm, when the filtering parameters are not properly selected, the filtering diverges, and the tracking accuracy is greatly reduced.
Disclosure of Invention
The invention discloses a WSN maneuvering target tracking method based on extended Kalman filtering, and aims to solve the technical problem that under the condition that filtering parameters are improperly selected, filtering divergence is caused, so that tracking precision is greatly reduced.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a WSN maneuvering target tracking method based on extended Kalman filtering comprises the following specific steps:
s1: acquiring data of a maneuvering target by using a sensor network;
s2: initializing a snake population, uniformly distributing the snake population in a search space by utilizing Cubic chaos cube mapping, and setting a maximum iteration number, food and temperature trigger threshold;
s3: determining an objective function, determining an adaptability function according to an extended Kalman filtering algorithm process, estimating parameters of a maneuvering target according to an extended Kalman filtering step, taking a noise covariance matrix parameter as a position of an optimization algorithm individual, optimizing to generate random noise with covariance of a Q value and an R value, and adding the random noise into an observed value and an estimated value of an SO-C algorithm;
s4: and the SO-C algorithm module iteratively outputs the optimal position.
According to the extended Kalman filtering algorithm, under the condition that the filtering parameters are selected improperly, filtering divergence is caused, so that tracking accuracy is greatly reduced, the occurrence of errors caused by improper selection of the filtering parameters is avoided by utilizing a strategy of dynamically adjusting the filtering parameters by using a snake optimization algorithm, the positioning accuracy of the algorithm is further improved by converting the tracking problem of the extended Kalman filtering algorithm into the problem of searching optimal solutions of the population, the algorithm can be quickly converged to global optimum, the convergence accuracy of the algorithm is improved, the extended Kalman filtering algorithm using the snake optimization algorithm can be applied to optimization of the WSN maneuvering target tracking algorithm, and the extended Kalman filtering algorithm and the extended Kalman algorithm are compared to obtain a position and speed mean square error curve; the comparison shows that the root mean square error of the proposed algorithm is reduced by 51% and 34% respectively compared with the two algorithms.
In a preferred embodiment, in S1, the specific operation of collecting data by using the sensor is as follows: aiming at the tracking problem in the WSN area, assuming that the sensors in the sensor network are all of the same type, the sensors acquire the distance and noise information from the sensor to the target track at the current sampling moment through a distance measuring function, wherein an observation model adopted by the sensors is as follows:
z i ＝(1+γ i )r i +n i ＝r i +u i
(1)
the system firstly acquires data of a maneuvering target by using a sensor network, and dynamically searches optimal parameters by using an SO-C algorithm according to the acquired data SO as to reduce filtering errors and improve tracking accuracy.
In a preferred embodiment, in S2, the initialization of the snake population is based on the formulaAn initial population of each individual snake is generated, where ρ=2.595, n 0 ＝0.3。
By utilizing Cubic chaotic cube mapping to generate an initialization population with more uniform distribution, a chaotic sequence generated by the chaotic mapping can be mapped into a solution space to obtain an initial snake population with better diversity, so that the optimizing search range of an algorithm is enlarged, and the precision and performance of the optimizing algorithm are improved.
In a preferred embodiment, in S3, the algorithm formula of the extended kalman filter is as follows:
P i | i-1 ＝AP i-1 A T +Q (4)
P i ＝(I-K i H i )P i | i-1 (5)
in the step S3, the specific steps of the extended kalman filter algorithm are as follows:
s31: establishing a state transition equation and an observation equation according to a motion model and an observation model of the system;
s32: based on an extended Kalman filtering algorithm formula, predicting a state estimation value and a covariance matrix at the current moment by using a state transition equation and a state estimation value at the last moment in a prediction formula from step (3) to step (6);
s33: correcting the predicted state estimation value and covariance matrix by updating the steps (7) to (9) in the formula and utilizing the observation equation and the observation value at the current moment to obtain a final state estimation value and covariance matrix;
in the step S4, the specific steps of the SO-C algorithm module are as follows:
s41: dividing a population into two groups, namely male and female, setting fitness functions, calculating corresponding fitness, finding out the current optimal male and female individuals, taking an observed value and an estimated value at the current moment as the fitness functions of an SO-C algorithm, obtaining new filtering parameters after each repetition, and judging the accuracy of the filtering parameters generated in the iteration according to the fitness values calculated by the fitness functions;
s42: defining an ambient temperature temp and a food quantity D according to a formula;
s43: determining that the individual is in the condition of searching for food only or fight and mating according to the food quantity D, if D is less than 0.25, searching for food only, and defining and updating the individual position of the snake according to an optimization algorithm; if the food is sufficient and temp is more than 0.6, only searching the food and eating the existing food, and updating the position according to the definition of the optimization algorithm;
s44: judging to enter a combat mode and a mating mode according to the mode random number, updating the position of the combat mode, respectively replacing Am in the combat mode, replacing the optimal individual with the current individual, updating the position, and if eggs hatch, selecting the worst individual for replacement;
s45: processing the updated position, updating the individual history optimal value, judging whether the individual history optimal value reaches the iteration times, entering the next iteration if the iteration times are not met, and ending the iteration to output the optimal position if the iteration times are met;
in S41, the fitness function is as follows:
in S42, the following formula is defined for the ambient temperature and the food amount:
by optimizing a convergence factor in the SO algorithm, the development capacity during global searching and the mining capacity during local searching can be balanced more effectively, SO that the optimized SO algorithm can be better adapted to a more complex searching process.
From the above, the WSN maneuvering target tracking method based on the extended Kalman filtering comprises the following specific steps: s1: acquiring data of a maneuvering target by using a sensor network; s2: initializing a snake population, uniformly distributing the snake population in a search space by utilizing Cubic chaos cube mapping, and setting a maximum iteration number, food and temperature trigger threshold; s3: determining an objective function, determining an adaptability function according to an extended Kalman filtering algorithm process, estimating parameters of a maneuvering target according to an extended Kalman filtering step, taking a noise covariance matrix parameter as a position of an optimization algorithm individual, optimizing to generate random noise with covariance of a Q value and an R value, and adding the random noise into an observed value and an estimated value of an SO-C algorithm; s4: and the SO-C algorithm module iteratively outputs the optimal position. The WSN maneuvering target tracking method based on the extended Kalman filtering has the technical effects of being capable of quickly converging to global optimum and effectively improving the convergence accuracy of an algorithm.
Drawings
Fig. 1 is a logic flow diagram of a WSN maneuvering target tracking system of the WSN maneuvering target tracking method based on the extended kalman filter.
Fig. 2 is a tracking effect diagram of a WSN maneuvering target tracking method based on extended Kalman filtering.
Fig. 3 is a comparison chart of position errors of three algorithms according to the present invention.
Fig. 4 is a graph showing the root mean square error of the X-direction position of three algorithms according to the present invention.
Fig. 5 is a graph showing the root mean square error of the y-direction position of three algorithms according to the present invention.
Fig. 6 is a graph showing the root mean square error of the X-direction velocity over time for three algorithms according to the present invention.
Fig. 7 is a graph showing the root mean square error of the y-direction velocity over time for three algorithms according to the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments.
The invention discloses a WSN maneuvering target tracking method based on extended Kalman filtering, which is mainly applied to scenes of information science sensor positioning.
Referring to fig. 1 and 2, a WSN maneuvering target tracking method based on extended kalman filtering includes the following specific steps:
s1: acquiring data of a maneuvering target by using a sensor network;
s2: initializing a snake population, uniformly distributing the snake population in a search space by utilizing Cubic chaos cube mapping, and setting a maximum iteration number, food and temperature trigger threshold;
s3: determining an objective function, determining an adaptability function according to an extended Kalman filtering algorithm process, estimating parameters of a maneuvering target according to an extended Kalman filtering step, taking a noise covariance matrix parameter as a position of an optimization algorithm individual, optimizing to generate random noise with covariance of a Q value and an R value, and adding the random noise into an observed value and an estimated value of an SO-C algorithm;
s4: and the SO-C algorithm module iteratively outputs the optimal position.
Referring to fig. 1, in a preferred embodiment, the specific operation of collecting data using the sensor in S1 is as follows: aiming at the tracking problem in the WSN area, assuming that the sensors in the sensor network are all of the same type, the sensors acquire the distance and noise information from the sensor to the target track at the current sampling moment through a distance measuring function, wherein an observation model adopted by the sensors is as follows:
z i ＝(1+γ i )r i +n i ＝r i +u i
(1)
referring to FIG. 1, in a preferred embodiment, in S2, the initialization of the snake population is based on the formulaAn initial population of each individual snake is generated, where ρ=2.595, n 0 The method comprises the steps of (1) generating an initialization population with more uniform distribution by utilizing Cubic chaotic cube mapping, generating a random number sequence by using chaotic mapping to replace a pseudo-random number sequence used in a traditional optimization algorithm, generating a chaotic initialization population with better diversity by adopting a Cubic chaotic cube initialization population strategy by an SO-C algorithm and utilizing the characteristics of randomness and ergodic property of chaotic variables, selecting the Cubic chaotic cube chaotic mapping initialization population with higher iteration speed and better ergodic property and uniformity, and mapping the chaotic sequence generated by the chaotic mapping into a solution space to obtain an initial snake population with better diversity, thereby expanding the optimization search range of the algorithm and improving the precision and performance of the optimization algorithm.
Referring to fig. 1, in a preferred embodiment, in S3, the algorithm formula of the extended kalman filter is as follows:
P i | i-1 ＝AP i-1 A T +Q (4)
P i ＝(I-K i H i )P i | i-1 (5)
referring to fig. 1, in a preferred embodiment, in S3, the specific steps of the extended kalman filter algorithm are as follows:
s31: establishing a state transition equation and an observation equation according to a motion model and an observation model of the system;
s32: based on an extended Kalman filtering algorithm formula, predicting a state estimation value and a covariance matrix at the current moment by using a state transition equation and a state estimation value at the last moment in a prediction formula from step (3) to step (6);
s33: and (3) correcting the predicted state estimation value and covariance matrix by updating the steps (7) to (9) in the formula and utilizing the observation equation and the observation value at the current moment to obtain the final state estimation value and covariance matrix.
Referring to FIG. 1, in a preferred embodiment, the steps of the SO-C algorithm module in S4 are as follows:
s41: dividing a population into two groups, namely male and female, setting fitness functions, calculating corresponding fitness, finding out the current optimal male and female individuals, taking an observed value and an estimated value at the current moment as the fitness functions of an SO-C algorithm, obtaining new filtering parameters after each repetition, and judging the accuracy of the filtering parameters generated in the iteration according to the fitness values calculated by the fitness functions;
s42: defining an ambient temperature temp and a food quantity D according to a formula;
s43: determining that the individual is in the condition of searching for food only or fight and mating according to the food quantity D, if D is less than 0.25, searching for food only, and defining and updating the individual position of the snake according to an optimization algorithm; if the food is sufficient and temp is more than 0.6, only searching the food and eating the existing food, and updating the position according to the definition of the optimization algorithm;
s44: judging to enter a combat mode and a mating mode according to the mode random number, updating the position of the combat mode, respectively replacing Am in the combat mode, replacing the optimal individual with the current individual, updating the position, and if eggs hatch, selecting the worst individual for replacement;
s45: and processing the updated position, updating the historical optimal value of the individual, judging whether the optimal value reaches the iteration times, entering the next iteration if the optimal value does not meet the iteration times, and ending the iteration to output the optimal position if the optimal value meets the iteration times.
Referring to fig. 1, in a preferred embodiment, in S41, the fitness function is as follows:
referring to fig. 1, in a preferred embodiment, in S42, the ambient temperature and the food amount are defined as follows:
by optimizing a convergence factor in the SO algorithm, the attenuation degree is low in the initial stage, and the snake can move in a larger step, SO that the global optimal solution can be better found. By the later stage, the attenuation degree of the environmental temperature Temp and the food quantity D is improved, the moving steps of the snakes are reduced, and the optimal solution can be found more accurately. Therefore, the development capacity during global searching and the mining capacity during local searching are balanced more effectively, and the optimized SO algorithm can be better adapted to a complex searching process.
Examples:
in order to verify the positioning performance of the algorithm, MATLAB2022a is utilized to carry out simulation experiment analysis on the four aspects of the algorithm, the snake-optimized WSN maneuvering target tracking algorithm and the extended Kalman filtering algorithm, namely, the position root mean square error in the X-axis direction, the position root mean square error in the Y-axis direction, the speed root mean square error in the X-axis direction and the speed root mean square error in the Y-axis direction. Within a 100m x 100m simulation area, a certain number of network nodes are randomly generated.
The parameter settings of the algorithm are shown in table 1.
Table 1 algorithm related parameter settings
The tracking root mean square error calculation formula (13) of the algorithm is as follows:
where RMSE is the normalized average positioning error of the node,and estimating coordinates for the moment t, wherein (x, y) is the actual unknown node coordinates.
We verify the effectiveness of the present invention through a series of experimental simulation analyses.
The total node number is set to be 100, the anchor node number is set to be 50, and the sensor communication radius is set to be 20m.
The tracking effect of the algorithm provided by the invention is shown in figure 3, and the tracking track of the WSN maneuvering target tracking algorithm of the SO-C algorithm almost coincides with the real track, SO that the tracking of the nonlinear model target by using the SO-C algorithm is effective.
50 nodes are randomly deployed in the monitoring area, the communication radius of the sensor is set to be 20m, the sampling period is set to be 0.1s, and the sampling point number is set to be 50. The parameter Q is set to a random value in [0.0001,0.01], and the parameter R is set to a random value in [5,10 ].
In the SO-C optimization algorithm, the population number M is set to 20, and the maximum iteration number of the algorithm is set to 100. The food quantity threshold G is set to 0.25 and the temperature threshold Temp is set to 0.6. The RSME profile for the X, Y orientation position is shown in fig. 4 and 5.
Therefore, compared with SO-EKF and EKF algorithms, the position root mean square error of the extended Kalman filtering and SO-C algorithm in the x direction and the y direction is lower than that of the two algorithms, and the fluctuation of the extended Kalman filtering and SO-C algorithm is smaller, SO that the extended Kalman filtering and SO-C algorithm are less influenced by the position prediction result of the previous step, and the tracking stability and accuracy are good.
As shown in FIG. 6 and FIG. 7, compared with the SO-EKF and EKF algorithms, the RSME variation curves of X, Y direction speed are lower than the root mean square error of the speed of the extended Kalman filtering and SO-C algorithm in the x direction and the y direction, and the extended Kalman filtering and SO-C algorithm has good prediction performance on the speed of the nonlinear motion model due to the fact that the simulation is a uniform turning motion model. Meanwhile, compared with an SO-EKF algorithm and an EKF algorithm, the speed prediction fluctuation is smaller, and the extended Kalman filtering algorithm and the SO-C algorithm are proved to be less influenced by the speed prediction result of the previous step.
Simulation results show that in the aspects of tracking precision and errors, the SO and SO-C algorithms are superior to the traditional EKF algorithms in terms of speed and tracking position errors due to dynamic adjustment of filtering parameters, and the tracking effect is further improved due to the fact that the SO-C is added with a self-adaptive strategy and Cubic chaotic cube mapping compared with the SO. The validity of SO-C and the rationality of the regulatory factor are demonstrated.
Working principle: in the iterative process, the nonlinear convergence factor is utilized, the development capacity in global search and the mining capacity in local search can be balanced more effectively, SO that an SO-C algorithm can be better adapted to a more complex search process, meanwhile, the characteristics of randomness and ergodic property of chaos variables are utilized to generate a chaos initial population with better diversity, the searching range of algorithm optimization is enlarged, the precision and performance of an optimization algorithm are improved, the tracking problem of the extended Kalman filtering algorithm is converted into the problem of searching an optimal solution of the population, the positioning precision of the algorithm is further improved, the algorithm can be converged to global optimum rapidly, the convergence precision of the algorithm is improved, the extended Kalman filtering algorithm and the extended Kalman algorithm of the snake optimization algorithm are compared with the algorithm, and a position and speed mean square error curve is obtained; the comparison shows that the root mean square error of the proposed algorithm is reduced by 51% and 34% respectively compared with the two algorithms.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (8)
1. The WSN maneuvering target tracking method based on the extended Kalman filtering is characterized by comprising the following specific steps of:
s1: acquiring data of a maneuvering target by using a sensor network;
s2: initializing a snake population, uniformly distributing the snake population in a search space by utilizing Cubic chaos cube mapping, and setting a maximum iteration number, food and temperature trigger threshold;
s3: determining an objective function, determining an adaptability function according to an extended Kalman filtering algorithm process, estimating parameters of a maneuvering target according to an extended Kalman filtering step, taking a noise covariance matrix parameter as a position of an optimization algorithm individual, optimizing to generate random noise with covariance of a Q value and an R value, and adding the random noise into an observed value and an estimated value of an SO-C algorithm;
s4: and the SO-C algorithm module iteratively outputs the optimal position.
2. The extended kalman filter-based WSN maneuvering target tracking method according to claim 1, wherein in S1, the specific operation of collecting data by using the sensor is as follows: aiming at the tracking problem in the WSN area, the sensors in the sensor network are all of the same model, and the sensors acquire the distance from the sensor to the target track at the current sampling time and noise information through a distance measuring function.
3. The extended kalman filter-based WSN maneuvering target tracking method according to claim 1, wherein in S2, the initialization of the snake population is based on a formulaAn initial population of each individual snake is generated, where ρ=2.595, n 0 ＝0.3。
4. The extended kalman filter-based WSN maneuvering target tracking method according to claim 1, wherein in S3, an algorithm formula of the extended kalman filter is as follows:
P i | i-1 ＝AP i-1 A T +Q (4)
P i ＝(I-K i H i )P i | i-1 (5)
5. the extended kalman filter-based WSN maneuvering target tracking method according to claim 1, wherein in the step S3, the specific steps of the extended kalman filter algorithm are as follows:
s31: establishing a state transition equation and an observation equation according to a motion model and an observation model of the system;
s32: based on an extended Kalman filtering algorithm formula, predicting a state estimation value and a covariance matrix at the current moment by using a state transition equation and a state estimation value at the last moment in a prediction formula from step (3) to step (6);
s33: and (3) correcting the predicted state estimation value and covariance matrix by updating the steps (7) to (9) in the formula and utilizing the observation equation and the observation value at the current moment to obtain the final state estimation value and covariance matrix.
6. The extended kalman filter-based WSN maneuvering target tracking method according to claim 1, wherein in the S4, the specific steps of the S0-C module are as follows:
s41: dividing a population into two groups, namely male and female, setting fitness functions, calculating corresponding fitness, finding out the current optimal male and female individuals, taking an observed value and an estimated value at the current moment as the fitness functions of an SO-C algorithm, obtaining new filtering parameters after each repetition, and judging the accuracy of the filtering parameters generated in the iteration according to the fitness values calculated by the fitness functions;
s42: defining an ambient temperature temp and a food quantity D according to a formula;
s43: determining that the individual is in the condition of only searching food or fight and mating according to the food quantity D;
s44: judging to enter a combat mode and a mating mode according to the mode random number, updating the position of the combat mode, respectively replacing Am in the combat mode, replacing the optimal individual with the current individual, updating the position, and if eggs hatch, selecting the worst individual for replacement;
s45: and processing the updated position, updating the historical optimal value of the individual, judging whether the optimal value reaches the iteration times, entering the next iteration if the optimal value does not meet the iteration times, and ending the iteration to output the optimal position if the optimal value meets the iteration times.
7. The extended kalman filter-based WSN maneuvering target tracking method according to claim 6, wherein in S41, the fitness function is as follows:
8. the extended kalman filter-based WSN maneuvering target tracking method according to claim 6, wherein in S42, the defining formulas of the ambient temperature and the number of foods are as follows:
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