CN111291312A - Maneuvering target tracking method based on fuzzy adaptive algorithm of current statistical model - Google Patents

Maneuvering target tracking method based on fuzzy adaptive algorithm of current statistical model Download PDF

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CN111291312A
CN111291312A CN202010129395.0A CN202010129395A CN111291312A CN 111291312 A CN111291312 A CN 111291312A CN 202010129395 A CN202010129395 A CN 202010129395A CN 111291312 A CN111291312 A CN 111291312A
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maneuvering target
maneuvering
target
fuzzy
tracking
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索继东
孙博
李雪
邢浩
柳晓鸣
陈晓楠
任硕良
李昱琛
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Dalian Maritime University
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    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis

Abstract

The invention discloses a method for realizing maneuvering target tracking by a fuzzy adaptive algorithm based on a current statistical model, belonging to the technical field of target tracking and comprising the following steps: establishing a state equation and an observation equation of the maneuvering target, predicting the motion state of the maneuvering target by adopting a standard Kalman filtering algorithm, adjusting the acceleration limit value of the maneuvering target by adopting a fuzzy membership function, adaptively adjusting the acceleration limit value through the maneuvering value, and tracking the weak maneuvering target; when the maneuvering target keeps the previous state, the maneuvering target is tracked, and when the maneuvering target changes suddenly, the movement state of the sudden-change maneuvering target is tracked by using a strong tracking filter; the method updates the motion state of the maneuvering target on line to adapt the fuzzy rule of the maneuvering value of the fuzzy output quantity, increases the threshold value for judging the filtering divergence by using the adaptive weakening factor, reduces the probability of misjudging the filtering divergence and enhances the tracking performance of the strong maneuvering target.

Description

Maneuvering target tracking method based on fuzzy adaptive algorithm of current statistical model
Technical Field
The invention relates to a target tracking technology, in particular to a maneuvering target tracking method based on a fuzzy self-adaptive algorithm of a current statistical model.
Background
The target tracking technology is widely applied to navigation, traffic and military related fields. The current statistical model algorithm is a common method for tracking targets, and adopts a non-zero mean value and a modified Rayleigh distribution to represent the statistical characteristics of maneuvering acceleration, and the limit value of the acceleration is fixed when the current statistical model algorithm is used, so that the prediction error of the targets with weak maneuvering is larger. The fuzzy adaptive algorithm is a method for realizing the adaptive adjustment of system parameters. Cai et al adopt a fuzzy reasoning method to adaptively adjust the acceleration limit value and improve the convergence accuracy, but unsmooth trigonometric membership functions can cause abrupt noise estimation of the system, and the prediction error is large; yang et al designs a nonlinear fuzzy membership function to adaptively adjust the limit value of the acceleration and enhance the tracking performance of the weak maneuvering target, but the designed membership function assumes that the maneuvering target is in a certain movement range; wang et al designs an adaptive data smoothing method based on fuzzy theory, which describes the actual motion state of a maneuvering target by using a fuzzy rule, wherein if the mean value of the error in the fuzzy rule is large, the smoothing parameter is increased, if the variance of the error is large, the smoothing parameter is reduced, the maneuvering value of the fuzzy output quantity cannot be adaptively changed, the tracking error of the current statistical model is large, and a strong tracking filter is a filter for a nonlinear system reconstructed from EKF, so that the defect of poor robustness of an extended kalman filter is overcome, and a fuzzy adaptive algorithm and the strong tracking filter can be comprehensively utilized. Hu et al propose a strong tracking Kalman filtering algorithm of self-adaptation based on fuzzy logic, carry on the adaptive adjustment to the suboptimum fading factor in the strong tracking filter, to realize the influence brought by restraining the carrier mutation, but the weakening factor that its selection is fixed, cause the target tracking error to be greater; liu et al use the strong tracking algorithm when dealing with the sudden change of the system state, the threshold of the filtering divergence state is small, resulting in the prediction residual error not being accurately estimated, thereby generating a tracking error.
Disclosure of Invention
According to the problems existing in the prior art, the invention discloses a method for realizing maneuvering target tracking by a fuzzy adaptive algorithm based on a current statistical model, which comprises the following steps:
s1, establishing a state equation and an observation equation of the maneuvering target;
s2, predicting the motion state of the maneuvering target by adopting a standard Kalman filtering algorithm, and judging the mean square error of the predicted motion state and the actual motion state of the maneuvering target;
s3, adjusting the maneuvering target acceleration limit value by adopting a fuzzy membership function;
s4, the motion state of the maneuvering target is re-predicted by using a fuzzy system, and a maneuvering value is obtained;
s5, calculating the maximum acceleration value of the current maneuvering target, adaptively adjusting the limit value of the acceleration through the maneuvering value, and then tracking the weak maneuvering target;
s6, when the maneuvering target is kept in the previous state, the maneuvering target is tracked, and when the maneuvering target is suddenly changed, the movement state of the suddenly changed maneuvering target is tracked by using a strong tracking filter; returning to S3.
Further, the fuzzy membership function is obtained by the following formula:
Figure BDA0002395382210000021
wherein: q is a regulatory factor, amaxThe maximum acceleration of the movement of the maneuvering target is shown, and the positive and negative respectively show the direction of the movement of the maneuvering target.
Further: the fuzzy rule adopted by the fuzzy system is as follows:
when the acceleration of the maneuvering target is increased, the maneuverability is enhanced, and when the acceleration of the maneuvering target is decreased, the maneuverability is weakened.
Due to the adoption of the technical scheme, the maneuvering target tracking method based on the fuzzy adaptive algorithm of the current statistical model strengthens the tracking performance of the weak maneuvering target by using the mutation-free fuzzy membership function, the maneuver value of the fuzzy output quantity can be self-adaptively changed by designing a fuzzy rule, so that the tracking is more accurate when the fuzzy rule deals with different maneuvers, a Gaussian function is adopted as an input membership function of the fuzzy system, it has no mutation phenomenon of trigonometric function, and greatly improves the tracking precision of the weak maneuvering target, the method comprises the steps of updating a fuzzy rule of a maneuvering target motion state on line to adaptively adjust a maneuvering value of a fuzzy output quantity, designing an improved strong tracking filter, increasing a threshold value for judging filtering divergence by using a self-adaptive weakening factor, reducing misjudgment filtering divergence probability, and enhancing the tracking performance of the strong maneuvering target.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of a motorized target motion trajectory;
FIG. 3 is a plot of X-axis distance root mean square error;
FIG. 4 is a plot of the Y-axis distance root mean square error;
FIG. 5 is a plot of X-axis velocity root mean square error;
FIG. 6 is a Y-axis velocity root mean square error plot;
FIG. 7 is a plot of root mean square error of acceleration in the X-axis;
FIG. 8 is a Y-axis acceleration root mean square error plot.
Detailed Description
In order to make the technical solutions and advantages of the present invention clearer, the following describes the technical solutions in the embodiments of the present invention clearly and completely with reference to the drawings in the embodiments of the present invention:
FIG. 1 is a flow chart of the method of the present invention, which provides a method for tracking a maneuvering target based on a fuzzy adaptive algorithm of a current statistical model, and the detailed steps are as follows:
s1, establishing a state equation and an observation equation of the target;
s1.1, establishing a state equation of a target:
Xk＝Fk|k-1Xk-1+Γk-1Wk-1(1)
in the formula, XkIs a system state vector, Fk|k-1Being a state transition matrix, Γk-1Is a system noise matrix, Wk-1Is a system noise vector;
s1.2, establishing an observation equation of a target:
Zk＝HkKk+Vk(2)
in the formula, ZkAs a target observation vector, HkIs an observation function of the system, KkIs a system control vector, VkNoise representing a gaussian state;
s2, predicting the motion state of the maneuvering target by adopting a standard Kalman filtering algorithm, and judging the mean square error of the predicted motion state and the actual motion state of the maneuvering target, wherein the filtering process of the standard Kalman filtering is as follows:
the one-step prediction equation is shown in equation (3):
Figure BDA0002395382210000041
the predicted mean square error formula is as follows:
Pk|k-1＝Fk·Pk-1|k-1·Fk T+Qk-1(4)
the gain matrix is as follows:
Figure BDA0002395382210000042
the filter equation is as follows:
Figure BDA0002395382210000043
the filtered mean square error is as follows:
Pk|k＝[I-Kk·Hk]·Pk|k-1(7)
wherein the content of the first and second substances,
Figure BDA0002395382210000044
as the current acceleration, the acceleration is set to be,
Figure BDA0002395382210000045
for the state vector X in the filtering processkThe estimated amount of (a) is,
Figure BDA0002395382210000046
for one-step prediction of state, KkFor filter gain, PkBeing a covariance matrix of the filtering errors, Pk|k-1For prediction error covariance matrix, I is identity matrix, YkIs a filter covariance matrix, Qk-1Is a predictive covariance matrix, RkIs a gain covariance matrix, Pk-1Is a filtered mean square error covariance matrix;
s3: adjusting the maneuvering target acceleration limit value by adopting a fuzzy membership function;
assuming that the adjusted acceleration limit satisfies:
(4-π)anewmax/4≤a≤anewmax(8)
the (4-pi)/4 is not more than a/anewmaxA is less than or equal to 1, making a/anewmaxP is then in the range of [ 1-pi/4, 1]Let p be qa/amaxThe obtained mixture is substituted into the raw materials for arrangement,
then, a new expression of the fuzzy membership function is obtained as follows:
Figure BDA0002395382210000047
wherein, amaxThe maximum acceleration representing the movement of the maneuvering target, the positive and negative respectively representing the movement direction of the maneuvering target, the limit value of the improved acceleration can be automatically updated, the expression of p is substituted for arrangement, and the range of the limit value of the acceleration is
Figure BDA0002395382210000048
And
Figure BDA0002395382210000049
the range contains an adjusting factor q, the limit value of the acceleration can be adjusted, when the tracked maneuvering target is maneuvered, self-adaptive adjustment can be performed, better tracking performance is achieved, and the prediction performance of the weak maneuvering target is improved.
S4: the motion state of the maneuvering target is re-predicted by using a fuzzy system, and a maneuvering value is obtained;
s4.1, determining the input quantity of the fuzzy system and fuzzifying;
the acceleration plays a crucial role in the accuracy of maneuvering target tracking, and the tracking performance of the maneuvering target is greatly improved if the acceleration can be adaptively adjusted on line, so the current acceleration a and the acceleration change rate △ a are adopted as fuzzy input variables in the text, the output quantity is a maneuvering value U corresponding to the acceleration, and since the domain of discourse adopted in the MATLAB experiment is between [0 and 1], a normalization method is required to be utilized for sorting, namely:
Figure BDA0002395382210000051
the fuzzy sets of the input variables a and △ a are assumed to be NB (negative large), NM (negative medium), NS (negative small), ZO (zero), PS (positive small), PM (positive medium) and PB (positive large), the input membership functions use Gaussian functions, the fuzzy sets respectively represent a certain range of domains of discourse, the central value of each domain of discourse describes the probability of language as 1, the probability of describing other languages as 0, and the probabilities corresponding to other points are described by using triangular membership functions.
S4.2, according to actual conditions, when the maneuvering target moves, the maneuverability may change, when the maneuvering acceleration is increased, the maneuverability is enhanced, when the maneuvering acceleration of the target is reduced, the maneuverability is weakened, and under the two conditions, the maneuvering value required to be output can change in real time according to the actual movement of the maneuvering target, so that the accuracy of target tracking is achieved; therefore, the logic relation is adopted, the specific fuzzy rule is shown in the table I, the fuzzy reasoning adopts a Mamdani method, the target maneuverability is judged in a self-adaptive mode by utilizing the fuzzy rule, the corresponding rule is automatically corresponded according to different fuzzy input quantities, and the fuzzy reasoning is carried out to obtain the output fuzzy quantity.
S4.3, defuzzifying to determine an accurate value of acceleration prediction, defuzzifying the fuzzy quantity obtained at S4.2, converting the output obtained by the fuzzy inference engine into an exact quantity acceptable for subsequent conversation, and deblurring by using an area gravity center method, namely, taking the area enclosed by a membership function curve and a horizontal axis, and then taking the gravity center of the area as an output quantity, wherein the following fuzzy inference form is considered;
rule 1: NB and NB ═ b>PB, rule 2: NB and NM ═ b>PM … rule 49: PB and PB ═>ZO, herein the degree of membership of the output maneuver value U is μci(Ui). The calculation formula of the area barycenter method adopted in the text is as follows:
Figure BDA0002395382210000052
as can be seen from the above expression (11), the weighting factor is μc(Ui)。
S5: calculating the current maximum acceleration amaxThe maneuver value obtained in the previous step is the output accurate value U, and the maximum acceleration value is calculated as follows
Figure BDA0002395382210000053
Therefore, the acceleration limit value can be adjusted in a self-adaptive manner through the maneuvering value, and then the weak maneuvering target is tracked,
step 6: and tracking the maneuvering target with sudden change of the motion state by using a strong tracking filter. Although fuzzy reasoning is adopted to carry out self-adaptive adjustment on the motion state of the target, when the maneuvering target changes suddenly, a strong tracking filter is utilized to track the motion state of the sudden-change maneuvering target; returning to S3, when the maneuvering target is suddenly changed, divergence usually occurs to increase the tracking error and the dynamic time delay, and a strong tracking filtering algorithm is added, wherein the principle is that N is usedKAnd MKThe attenuation factor is determined to achieve the self-adaptive effect, the fading factor is introduced, the influence of data on filtering is weakened, the threshold value for judging filtering divergence is increased, the probability of misjudging filtering divergence is reduced, the robustness of the model is improved, and the tracking of the maneuvering target is more stable.
Assuming the formula of covariance matrix calculation as:
Figure BDA0002395382210000061
λ in the above formula (13)k+1That is, the algorithm for approximating the fading factor and the sub-optimal fading factor is
Figure BDA0002395382210000062
Figure BDA0002395382210000063
Figure BDA0002395382210000064
In the above formulakThe improved strong tracking filter algorithm can adjust N for attenuation factorKAnd MKThe values of the attenuation factors are determined, strong maneuvering and weak maneuvering are tracked adaptively through the changed attenuation factors in the target tracking process, the robustness of the system is improved, and the performance of target state mutation is improved.
Example 1:
(1) simulation conditions are as follows: the simulation is carried out in a rectangular coordinate system two-dimensional plane, the radar sampling period T is 1s, the initial position of the target is assumed to be (100m,200m), and the simulation times on MATLAB are 100 times.
(2) Simulation content:
(2.1) non-motorized: the initial speed of the target is 10m/s, and the target does uniform motion in 0-30 scanning intervals.
(2.2) weak maneuvering: making uniform acceleration motion in 30-50 scanning intervals, the axial acceleration being 1m/s2The acceleration of the Y axis becomes-0.5 m/s2And (3) starting the target to perform weak maneuvering motion, and performing uniform motion on the target in 50-100 scanning intervals.
(2.3) strong maneuvering: the target continues to do uniform acceleration motion in 100-120 scanning intervals, and the X-axis acceleration is-2.5 m/s2The Y axis is 1m/s2The process represents strong maneuvering motion of the target, and the target performs uniform motion in 120-150 scanning intervals until the target motion is finished.
(3) Simulation results and analysis:
FIG. 2 is a diagram of a motorized target motion trajectory; FIG. 3 is a plot of X-axis distance root mean square error; FIG. 4 is a plot of the Y-axis distance root mean square error; FIG. 5 is a plot of X-axis velocity root mean square error; as can be seen from the Y-axis speed root mean square error graph, the improved algorithm can track the target quickly when the moving target moves to 30s, whereas the conventional algorithm and the comparative algorithm both generate large errors, and the improved algorithm generates strong maneuvering when the moving target moves to 100s, as can be seen from simulation experiments, the improved algorithm has higher stability and smaller error, and when the moving target moves to 120s, the target is converted from strong maneuvering to non-maneuvering, and the improved algorithm has higher convergence, higher stability for tracking the target, and smaller error.
FIG. 7 is a plot of root mean square error of acceleration in the X-axis; fig. 8 is a Y-axis acceleration root mean square error graph, it can be seen that when a moving target moves to 30s, weak maneuvering occurs, the improved algorithm can track the target quickly, and from the simulation result, the improved algorithm has a similar tracking effect to the existing algorithm, but has a much smaller error than the conventional statistical model algorithm.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (3)

1. A method for realizing maneuvering target tracking based on fuzzy adaptive algorithm of current statistical model is characterized in that: the method comprises the following steps:
s1, establishing a state equation and an observation equation of the maneuvering target;
s2, predicting the motion state of the maneuvering target by adopting a standard Kalman filtering algorithm, and judging the mean square error of the predicted motion state and the actual motion state of the maneuvering target;
s3, adjusting the maneuvering target acceleration limit value by adopting a fuzzy membership function;
s4, the motion state of the maneuvering target is re-predicted by using a fuzzy system, and a maneuvering value is obtained;
s5, calculating the maximum acceleration value of the current maneuvering target, adaptively adjusting the limit value of the acceleration through the maneuvering value, and then tracking the weak maneuvering target;
s6, when the maneuvering target is kept in the previous state, the maneuvering target is tracked, and when the maneuvering target is suddenly changed, the movement state of the suddenly changed maneuvering target is tracked by using a strong tracking filter; returning to S3.
2. The method of claim 1 for tracking a maneuvering target based on a fuzzy adaptive algorithm of a current statistical model, further characterized by: the fuzzy membership function adopts the following formula:
Figure FDA0002395382200000011
wherein: q is a regulatory factor, amaxThe maximum acceleration of the movement of the maneuvering target is shown, and the positive and negative respectively show the direction of the movement of the maneuvering target.
3. The method of claim 1 for tracking a maneuvering target based on a fuzzy adaptive algorithm of a current statistical model, further characterized by: the fuzzy rule adopted by the fuzzy system is as follows:
when the acceleration of the maneuvering target is increased, the maneuverability is enhanced, and when the acceleration of the maneuvering target is decreased, the maneuverability is weakened.
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