CN109085571B - Hypersonic target tracking method based on triple Bayesian criterion - Google Patents

Hypersonic target tracking method based on triple Bayesian criterion Download PDF

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CN109085571B
CN109085571B CN201810950211.XA CN201810950211A CN109085571B CN 109085571 B CN109085571 B CN 109085571B CN 201810950211 A CN201810950211 A CN 201810950211A CN 109085571 B CN109085571 B CN 109085571B
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CN109085571A (en
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张翔宇
黄婧丽
王国宏
李林
杨林
辛婷婷
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Naval Aeronautical University
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Abstract

The invention belongs to the field of hypersonic target tracking, and provides a hypersonic target tracking method based on a triple Bayesian criterion aiming at the problem of hypersonic target tracking. Firstly, designing a closed tracking channel taking a sinusoidal model as a main body aiming at all possible motion forms of the hypersonic target so as to realize matching tracking processing of the hypersonic target; secondly, designing a first Bayesian criterion, and designing cooperation modes of different tracking channels as functions of model weights and prior model switching weights so as to improve the degree of engagement between the selected model and the target real track; then, designing a second Bayesian criterion, and designing the model weight as a closed loop updated in real time along with the information intercepted by the radar so as to improve the tracking precision of the hypersonic target; and finally, designing a third Bayesian criterion, and resetting the switching weight of the prior model into a closed loop updated in real time along with the information intercepted by the radar so as to further improve the sensitivity of the hypersonic target tracking.

Description

Hypersonic target tracking method based on triple Bayesian criterion
Technical Field
The invention belongs to the field of hypersonic target tracking, and is suitable for solving the tracking problem of targets such as a hypersonic reconnaissance aircraft, a hypersonic unmanned aerial vehicle and a hypersonic cruise missile.
Background
The hypersonic aircraft is an aircraft which can make lasting flight with the Mach number of more than 5 by utilizing the characteristic of rarefied atmosphere in the atmosphere. The aircraft can carry a nuclear warhead in modern war to enhance the strategic deterrence capability of the country, can selectively carry conventional weapons to remotely and accurately attack important enemy targets, and can carry various active and passive detection devices for rapidly detecting and early warning global sensitive targets. In particular, in the united states, under global strategy, hypersonic weapons have become the first weapon to deliver global blows in the united states. Therefore, how to effectively realize the tracking interception of the hypersonic aircraft becomes a key problem which needs to be solved urgently at present.
In the research on the tracking and intercepting of the hypersonic aircraft, the early research mostly considers the target motion as high-speed turning motion or snake-shaped maneuvering motion in a certain plane, but does not pay enough attention to the real characteristics of the target, so that the problem of low tracking precision often exists. For this situation, various target tracking models are widely applied in the field of hypersonic target tracking. For example, the target trajectory approximation is regarded as a CV model and a CA model of linear motion, a CT model focusing on circular motion, a Sine model having the highest degree of matching with the S trajectory of the hypersonic velocity trajectory. However, the disadvantage of these models is that there is a high requirement for a priori information of the target, and especially, when the selected model is greatly different from the real situation of the target, a large model tracking error is inevitably introduced. That is, it is difficult to achieve reliable tracking of a hypersonic target by means of only a single model.
For this case, a multimode tracking method is effectively proposed. The method organically combines different models according to a certain mode, and can solve the problem of tracking mismatch of a single model to a certain extent. However, when the difference between the selected model and the real motion of the target is large or the cooperation mode between different models is not reasonable, the tracking accuracy is often reduced, and in severe cases, the tracking is not as good as single-mode tracking.
Therefore, the invention provides a hypersonic target tracking method based on a triple Bayes criterion aiming at all possible motion forms of the target, through the optimization selection of different target tracking models and the optimization design of cooperation modes among different models, so as to solve the problem of hypersonic target tracking.
Disclosure of Invention
The invention aims to break through the limitation of the traditional multi-mode tracking method, solve the tracking problem under the condition of hypersonic motion of a target, improve the capability of the traditional radar for detecting and tracking the hypersonic target and provide the hypersonic target tracking method based on the triple Bayesian criterion. The problems to be solved include:
1) the existing hypersonic target tracking method has the problem of unreasonable model selection and can not match all possible motion forms of the target;
2) the existing hypersonic target tracking method has the problems that the model cooperation mode is unreasonable, the multimode tracking precision is not high, and the tracking effect is not good as that of a single mode;
3) the existing hypersonic target tracking method has the problems that the model weight is not updated timely, further, the model is mismatched, and the tracking precision is reduced;
4) the existing hypersonic target tracking method has the problem that the model switching weight is not updated, and further has the problem of model mismatch caused by model switching errors.
The invention relates to a novel hypersonic target tracking method based on a triple Bayesian criterion, which is characterized by comprising the following technical measures:
the method comprises the following steps: before tracking a hypersonic target, designing a tracking channel matched with all possible motion forms of the target by using a sine model;
step two: switching weights by using a posterior model, and designing different tracking channels into a closed loop capable of jumping in real time;
step three, building a first Bayes criterion, and resetting posterior model switching weights of different tracking channels as functions of the model weights and the prior model switching weights;
step four, building a second Bayesian rule, and re-setting the model weights of different tracking channels at the current moment as functions of the model weight, the prior model switching weight and the model likelihood at the previous moment;
step five, building a third Bayesian criterion, and resetting prior model switching weights of different tracking channels at the current moment as functions of the model weight, the prior model switching weight and the model likelihood at the previous moment;
and sixthly, designing the model likelihood of different tracking channels as a function of the information intercepted by the radar by using the filtering tracking algorithm of each channel.
Compared with the prior art, the novel hypersonic target tracking method based on the triple Bayesian criterion has the advantages that:
1) the method is an improvement of the existing hypersonic target tracking algorithm, and can optimize the cooperation mode among different models while matching all possible motion modes of the target;
2) according to the invention, the cooperation mode of different models is designed into a closed loop capable of jumping in real time, so that the conformity of the selected model and the target real track can be effectively improved;
3) according to the method, the weights of different models are designed into a closed loop which is time-varying along with information intercepted by a radar, so that the tracking precision of the hypersonic target can be effectively improved;
4) according to the method, the model switching weights of different models are designed into a closed loop which is time-varying along with information intercepted by a radar, so that the sensitivity of tracking the hypersonic speed target can be effectively improved.
Drawings
FIG. 1 is a flow chart of the steps of a hypersonic target tracking method based on a triple Bayesian criterion;
FIG. 2 is a closed channel diagram for hypersonic target tracking with a sinusoidal model as the main body;
FIG. 3 is a close-up update diagram of posterior model switching weights designed using first-weighted Bayesian criteria;
FIG. 4 is a close-up updated graph of model weights designed using a second-fold Bayesian criterion;
FIG. 5 is a close-up updated graph of prior model switching weights designed using a third Bayesian criterion.
Detailed description of the invention
Aiming at the difficulty of hypersonic target tracking, the invention provides a hypersonic target tracking method based on a triple Bayesian criterion. Firstly, designing a target closed tracking channel taking a sinusoidal model as a main body aiming at all possible motion forms of the hypersonic target so as to realize matching tracking processing of the hypersonic target; secondly, designing a first Bayesian criterion, and designing cooperation modes of different tracking channels as functions of model weights and prior model switching weights so as to improve the degree of engagement between the selected model and the target real track; then, designing a second Bayesian criterion, and designing the model weight as a closed loop updated in real time along with the information intercepted by the radar so as to improve the tracking precision of the selected model on the hypersonic speed target; and finally, designing a third Bayesian criterion, and resetting the switching weight of the prior model into a closed loop updated in real time along with the intercepted information of the radar so as to further improve the sensitivity of the selected model to the tracking of the hypersonic target.
The invention is described in further detail below with reference to the drawings. Referring to fig. 1, the process flow of the present invention comprises the following steps:
1) design of tracking channel matched with all possible motion forms of target by using sinusoidal model
⑴ design of matching tracking model sets
In the horizontal plane, the frequency w is selected to have the maximum angular frequency1Sine model M of1And has a minimum angular frequency w2Sine model M of2To match all possible motion patterns of the target in the horizontal plane, the set of tracking models of the target in the horizontal plane can be designed
MLevel of＝{M1,M2} (1)
In the vertical plane, the frequency w is selected to have the maximum angular frequency3Sine model M of3And has a minimum angular frequency w4Sine model M of4To match all possible motion patterns of the target in the vertical plane, the set of tracking models of the target in the vertical plane can be designed as
MIs perpendicular to＝{M3,M4} (2)
In three-dimensional space, using MLevel ofAnd MIs perpendicular toComprehensively designing a matching tracking model set of the target into
M＝{MLevel of,MIs perpendicular to}＝{M1,M2,M3,M4} (3)
Thereby matching all possible motion patterns of the object in three-dimensional space.
⑵ construction and design model M1、M2、M3And M4Matching 4-entry tag trace channel
Channel 1 is composed of a model M1And a filter tracking algorithm, wherein the input function of the filter tracking algorithm at the moment k (1,2, 3.). is X1input(k) The output function is X1output(k)；
Channel 2 is composed of model M2And its filter tracking algorithm, its input function at k time is X2input(k) The output function is X2output(k)；
Channel 3 is composed of model M3And its filter tracking algorithm, its input function at k time is X3input(k) The output function is X3output(k)；
Channel 4 is formed by model M4And its filter tracking algorithm, its input function at k time is X4input(k) The output function is X4output(k)。
2) Different tracking channels are designed into a closed loop capable of jumping in real time by utilizing the switching weight of an input function, an output function and a posterior model
⑴ design for tracking channel 1-4 input function
The input function of the k moment tracking channel 1 is designed to be the combination of the output function of the k-1 moment tracking channels 1-4 and the posterior model switching weight thereof, so that the input function of the k moment tracking channel 1 can be designed to be
Figure BDA0001771295710000041
The input function of the k moment tracking channel 2 is designed to be the combination of the output function of the k-1 moment tracking channels 1-4 and the posterior model switching weight thereof, so that the input function of the k moment tracking channel 2 can be designed to be
Figure BDA0001771295710000042
The input function of the k moment tracking channel 3 is designed to be the combination of the output function of the k-1 moment tracking channels 1-4 and the posterior model switching weight thereof, so that the input function of the k moment tracking channel 3 can be designed to be
Figure BDA0001771295710000043
The input function of the k moment tracking channel 4 is designed to be the combination of the output function of the k-1 moment tracking channels 1-4 and the posterior model switching weight thereof, so that the input function of the k moment tracking channel 4 can be designed to be
Figure BDA0001771295710000044
Wherein, Pr [ M ]1(k-1)|M1(k)]、Pr[M2(k-1)|M1(k)]、Pr[M3(k-1)|M1(k)]、Pr[M4(k-1)|M1(k)]Respectively switching weights for posterior models of a tracking channel 1 designed by utilizing a first Bayesian rule; pr [ M ]1(k-1)|M2(k)]、Pr[M2(k-1)|M2(k)]、Pr[M3(k-1)|M2(k)]、Pr[M4(k-1)|M2(k)]Respectively switching weights for posterior models of the tracking channel 2 designed by utilizing a first Bayesian rule; pr [ M ]1(k-1)|M3(k)]、Pr[M2(k-1)|M3(k)]、Pr[M3(k-1)|M3(k)]、Pr[M4(k-1)|M3(k)]Respectively switching weights for posterior models of the tracking channel 3 designed by utilizing a first Bayesian rule; pr [ M ]1(k-1)|M4(k)]、Pr[M2(k-1)|M4(k)]、Pr[M3(k-1)|M4(k)]、Pr[M4(k-1)|M4(k)]The weights are switched for the posterior models of the tracking channel 4 designed using the first bayesian criterion, respectively.
⑵ acquisition of tracking channel 1-4 output function
In obtaining tracking channel1-4 input function X1input(k)、X2input(k)、X3input(k) And X4input(k) On the basis, the output function X of the tracking channels 1-4 can be further obtained by utilizing a Kalman filtering method1output(k)、X2output(k)、X3output(k) And X4output(k) At this time, the tracking channels 1-4 are respectively constructed to form a channel composed of
X1output(k-1)→X1input(k)→X1output(k) (8)
X2output(k-1)→X2input(k)→X2output(k) (9)
X3output(k-1)→X3input(k)→X3output(k) (10)
X4output(k-1)→X4input(k)→X4output(k) (11)
As shown in particular in fig. 2.
3) Designing a first Bayes criterion, and designing cooperation modes of different tracking channels as functions of model weight and prior model switching weight
⑴ design to track posterior model switching weights in channel 1
Establishing a first Bayesian criterion by using the model weight and the prior model switching weight, and resetting the posterior model switching weight in the tracking channel 1 to be
Figure BDA0001771295710000051
Figure BDA0001771295710000052
Figure BDA0001771295710000053
Figure BDA0001771295710000054
Wherein, Pr [ M ]1(k-1)]、Pr[M2(k-1)]、Pr[M3(k-1)]And Pr [ M ]4(k-1)]Tracking model weights of channels 1-4 at the k-1 moment respectively; pr [ M ]1(k)|M1(k-1)]、Pr[M1(k)|M2(k-1)]、Pr[M1(k)|M3(k-1)]And Pr [ M ]1(k)|M4(k-1)]Respectively tracking the prior model switching weight of the channel 1 at the k-1 moment;
⑵ design to track posterior model switching weights in channel 2
Establishing a first Bayesian criterion by using the model weight and the prior model switching weight, and resetting the posterior model switching weight in the tracking channel 2 to be
Figure BDA0001771295710000061
Figure BDA0001771295710000062
Figure BDA0001771295710000063
Figure BDA0001771295710000064
Wherein, Pr [ M ]2(k)|M1(k-1)]、Pr[M2(k)|M2(k-1)]、Pr[M2(k)|M3(k-1)]And Pr [ M ]2(k)|M4(k-1)]Respectively switching weights of prior models of the tracking channel 2 at the k-1 moment;
⑶ design to track posterior model switching weights in channel 3
Establishing a first Bayesian criterion by using the model weight and the prior model switching weight, and resetting the posterior model switching weight in the tracking channel 3 to be
Figure BDA0001771295710000065
Figure BDA0001771295710000066
Figure BDA0001771295710000067
Figure BDA0001771295710000068
Wherein, Pr [ M ]3(k)|M1(k-1)]、Pr[M3(k)|M2(k-1)]、Pr[M3(k)|M3(k-1)]And Pr [ M ]3(k)|M4(k-1)]Respectively switching weights of prior models of the tracking channel 3 at the k-1 moment;
⑷ design to track posterior model switching weights in channel 4
Establishing a first Bayesian criterion by using the model weight and the prior model switching weight, and resetting the posterior model switching weight in the tracking channel 4 to be
Figure BDA0001771295710000071
Figure BDA0001771295710000072
Figure BDA0001771295710000073
Figure BDA0001771295710000074
Wherein, Pr [ M ]4(k)|M1(k-1)]、Pr[M4(k)|M2(k-1)]、Pr[M4(k)|M3(k-1)]And Pr [ M ]4(k)|M4(k-1)]The prior model switching weights for the tracking channel 4 at time k-1, respectively, are shown in detail in fig. 3.
4) Designing a second Bayesian rule, and designing the model weight as a closed loop updated in real time along with the information intercepted by the radar
⑴ model M1Design of weights
Establishing a second Bayesian criterion by using the model weight at the k-1 moment, the prior model switching weight at the k-1 moment and the model likelihood at the k moment, and enabling the model M at the k moment1Is designed as
Figure BDA0001771295710000075
Wherein, Pr [ Z (k) | M1(k)]、Pr[Z(k)|M2(k)]、Pr[Z(k)|M3(k)]And Pr [ Z (k) | M4(k)]Respectively k time model M1～M4The model likelihood of (2);
⑵ model M2Design of weights
Establishing a second Bayesian criterion by using the model weight at the k-1 moment, the prior model switching weight at the k-1 moment and the model likelihood at the k moment, and enabling the model M at the k moment2Is designed as
Figure BDA0001771295710000081
⑶ model M3Design of weights
Establishing a second Bayesian criterion by using the model weight at the k-1 moment, the prior model switching weight at the k-1 moment and the model likelihood at the k moment, and enabling the model M at the k moment3Is designed as
Figure BDA0001771295710000082
⑷ model M4Design of weights
Establishing a second Bayesian criterion by using the model weight at the k-1 moment, the prior model switching weight at the k-1 moment and the model likelihood at the k moment, and enabling the model M at the k moment4Is designed as
Figure BDA0001771295710000083
As shown in detail in fig. 4.
5) Designing a third Bayesian rule, and designing the switching weight of the prior model as a closed loop updated in real time along with the intercepted information of the radar
⑴ prior model switching weight Pr M1(k)|M1(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]1(k+1)|M1(k)]Is designed as
Figure BDA0001771295710000084
⑵ prior model switching weight Pr M1(k)|M2(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]1(k+1)|M2(k)]Is designed as
Figure BDA0001771295710000091
⑶ prior model switching weight Pr M1(k)|M3(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]1(k+1)|M3(k)]Is designed as
Figure BDA0001771295710000092
⑷ prior model switching weight Pr M1(k)|M4(k-1)]Design (2) of
Model likelihood building by using model weight at k-1 moment, prior model switching weight at k-1 moment and model likelihood at k momentThe third Bayes criterion is to switch the prior model at the moment k to the weight Pr [ M ]1(k+1)|M4(k)]Is designed as
Figure BDA0001771295710000093
⑸ prior model switching weight Pr M2(k)|M1(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]2(k)|M1(k-1)]Is designed as
Figure BDA0001771295710000101
⑹ prior model switching weight Pr M2(k)|M2(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]2(k)|M2(k-1)]Is designed as
Figure BDA0001771295710000102
⑺ prior model switching weight Pr M2(k)|M3(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]2(k)|M3(k-1)]Is designed as
Figure BDA0001771295710000103
⑻ prior model switching weight Pr M2(k)|M4(k-1)]Design (2) of
Using model weights at time k-1, time k-1The third Bayesian rule is built by the prior model switching weight and the model likelihood at the moment k, and the prior model at the moment k is switched to the weight Pr [ M ]2(k)|M4(k-1)]Is designed as
Figure BDA0001771295710000104
⑼ prior model switching weight Pr M3(k)|M1(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]3(k)|M1(k-1)]Is designed as
Figure BDA0001771295710000111
⑽ prior model switching weight Pr M3(k)|M2(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]3(k)|M2(k-1)]Is designed as
Figure BDA0001771295710000112
⑾ prior model switching weight Pr M3(k)|M3(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]3(k)|M3(k-1)]Is designed as
Figure BDA0001771295710000113
⑿ prior model switching weight Pr M3(k)|M4(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]3(k)|M4(k-1)]Is designed as
Figure BDA0001771295710000114
⒀ prior model switching weight Pr M4(k)|M1(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]4(k)|M1(k-1)]Is designed as
Figure BDA0001771295710000121
⒁ prior model switching weight Pr M4(k)|M2(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]4(k)|M2(k-1)]Is designed as
Figure BDA0001771295710000122
⒂ prior model switching weight Pr M4(k)|M3(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]4(k)|M3(k-1)]Is designed as
Figure BDA0001771295710000123
⒃ prior model switching weight Pr M4(k)|M4(k-1)]Design (2) of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]4(k)|M4(k-1)]Is designed as
Figure BDA0001771295710000131
As shown in detail in fig. 5.

Claims (4)

1. The hypersonic target tracking method based on the triple Bayes criterion is characterized by comprising the following steps of:
firstly, before tracking a hypersonic target, constructing a tracking channel matched with all possible motion forms of the target by using a sine model;
step two, establishing different tracking channels as a closed loop which can jump in real time by using an input function, an output function and a posterior model switching weight;
step three, building a first Bayes criterion, and building posterior model switching weights of different tracking channels as a function of the model weight and the prior model switching weight;
step four, building a second Bayesian rule, and building model weights of different tracking channels at the current moment as functions of the model weight, the prior model switching weight and the model likelihood at the previous moment;
step five, building a third Bayesian rule, and building prior model switching weights of different tracking channels at the current moment as functions of the model weight, the prior model switching weight and the model likelihood at the previous moment;
constructing model likelihoods of different tracking channels as functions of radar interception information by using a filtering tracking algorithm of each channel;
the method for constructing the tracking channel in the first step specifically comprises the following steps:
1) construction of a set of matching pursuit models
In the horizontal plane, the frequency w is selected to have the maximum angular frequency1Sine model M of1And has a minimum angular frequency w2Sine model M of2To match all possible motion patterns of the target in the horizontal plane, the set of tracking models of the target in the horizontal plane can be constructed as
MLevel of＝{M1,M2}
In the vertical plane, the frequency w is selected to have the maximum angular frequency3Sine model M of3And has a minimum angular frequency w4Sine model M of4To match all possible motion patterns of the target in the vertical plane, the set of tracking models of the target in the vertical plane can be constructed as
MIs perpendicular to＝{M3,M4}
In three-dimensional space, using MLevel ofAnd MIs perpendicular toComprehensively constructing a matching tracking model set of the target into
M＝{MLevel of,MIs perpendicular to}＝{M1,M2,M3,M4}
Thereby matching all possible motion forms of the target in the three-dimensional space;
2) model M constructed and constructed1、M2、M3And M4Matching 4-entry tag trace channel
Channel 1 is composed of a model M1And a filter tracking algorithm, wherein the input function of the filter tracking algorithm at the moment k (1,2, 3.). is X1input(k) The output function is X1output(k)，
Channel 2 is composed of model M2And its filter tracking algorithm, its input function at k time is X2input(k) The output function is X2output(k)，
Channel 3 is composed of model M3And its filter tracking algorithm, its input function at k time is X3input(k) The output function is X3output(k)，
Channel 4 is formed by model M4And its filter tracking algorithm, its input function at k time is X4input(k)，Output function of X4output(k)；
In the second step, the method for constructing the closed loop capable of jumping in real time by using the input function, the output function and the posterior model switching weight comprises the following steps:
1) construction of 1-4 input functions of tracking channels
Constructing the input function of the k-moment tracking channel 1 as the combination of the output function of the k-1 moment tracking channels 1-4 and the posterior model switching weight thereof, and then constructing the input function of the k-moment tracking channel 1 as
X1input(k)＝X1output(k-1)Pr[M1(k-1)|M1(k)]+X2output(k-1)Pr[M2(k-1)|M1(k)]+X3output(k-1)Pr[M3(k-1)|M1(k)]+X4output(k-1)Pr[M4(k-1)|M1(k)]
Constructing the input function of the k moment tracking channel 2 as the combination of the output function of the k-1 moment tracking channels 1-4 and the posterior model switching weight, and then constructing the input function of the k moment tracking channel 2 as
X2input(k)＝X1output(k-1)Pr[M1(k-1)|M2(k)]+X2output(k-1)Pr[M2(k-1)|M2(k)]+X3output(k-1)Pr[M3(k-1)|M2(k)]+X4output(k-1)Pr[M4(k-1)|M2(k)]
Constructing the input function of the k-moment tracking channel 3 as the combination of the output function of the k-1 moment tracking channels 1-4 and the posterior model switching weight thereof, and then constructing the input function of the k-moment tracking channel 3 as
X3input(k)＝X1output(k-1)Pr[M1(k-1)|M3(k)]+X2output(k-1)Pr[M2(k-1)|M3(k)]+X3output(k-1)Pr[M3(k-1)|M3(k)]+X4output(k-1)Pr[M4(k-1)|M3(k)]
Constructing the input function of the k-moment tracking channel 4 as the combination of the output function of the k-1 moment tracking channels 1-4 and the posterior model switching weight thereof, and then constructing the input function of the k-moment tracking channel 4 as
X4input(k)＝X1output(k-1)Pr[M1(k-1)|M4(k)]+X2output(k-1)Pr[M2(k-1)|M4(k)]+X3output(k-1)Pr[M3(k-1)|M4(k)]+X4output(k-1)Pr[M4(k-1)|M4(k)]
Wherein, Pr [ M ]1(k-1)|M1(k)]、Pr[M2(k-1)|M1(k)]、Pr[M3(k-1)|M1(k)]、Pr[M4(k-1)|M1(k)]Respectively, model M in tracking channel 11～M4The posterior model switching weight of (1); pr [ M ]1(k-1)|M2(k)]、Pr[M2(k-1)|M2(k)]、Pr[M3(k-1)|M2(k)]、Pr[M4(k-1)|M2(k)]Respectively model M in tracking channel 21～M4The posterior model switching weight of (1); pr [ M ]1(k-1)|M3(k)]、Pr[M2(k-1)|M3(k)]、Pr[M3(k-1)|M3(k)]、Pr[M4(k-1)|M3(k)]Respectively model M in tracking channel 31～M4The posterior model switching weight of (1); pr [ M ]1(k-1)|M4(k)]、Pr[M2(k-1)|M4(k)]、Pr[M3(k-1)|M4(k)]、Pr[M4(k-1)|M4(k)]Respectively model M in tracking channel 41～M4The posterior model switching weight of (1);
2) acquisition of tracking channel 1-4 output function
Obtaining an input function X of tracking channels 1-41input(k)、X2input(k)、X3input(k) And X4input(k) On the basis, the output function X of the tracking channels 1-4 can be further obtained by utilizing a Kalman filtering method1output(k)、X2output(k)、X3output(k) And X4output(k) At this time, the tracking channels 1-4 are respectively constructed to form a channel composed of
X1output(k-1)→X1input(k)→X1output(k)
X2output(k-1)→X2input(k)→X2output(k)
X3output(k-1)→X3input(k)→X3output(k)
X4output(k-1)→X4input(k)→X4output(k) Is closed loop.
2. The hypersonic target tracking method based on the triple Bayesian rule as claimed in claim 1, wherein the method for constructing the posterior model switching weight of different tracking channels as a function of the model weight and the prior model switching weight by using the first Bayesian rule in the third step is as follows:
1) construction of posterior model switching weight in tracking channel 1
Establishing a first Bayesian criterion by using the model weight and the prior model switching weight, and constructing the posterior model switching weight in the tracking channel 1 as
Figure FDA0002383928860000031
Figure FDA0002383928860000032
Figure FDA0002383928860000033
Figure FDA0002383928860000034
Wherein, Pr [ M ]1(k-1)]、Pr[M2(k-1)]、Pr[M3(k-1)]And Pr [ M ]4(k-1)]Respectively k-1 moment model M1～M4The weight of (c); pr [ M ]1(k)|M1(k-1)]、Pr[M1(k)|M2(k-1)]、Pr[M1(k)|M3(k-1)]And Pr [ M ]1(k)|M4(k-1)]Are respectively k-Tracking the prior model switching weight of a channel 1 at the moment 1;
2) construction of posterior model switching weight in tracking channel 2
Establishing a first Bayesian criterion by using the model weight and the prior model switching weight, and constructing the posterior model switching weight in the tracking channel 2 as
Figure FDA0002383928860000041
Figure FDA0002383928860000042
Figure FDA0002383928860000043
Figure FDA0002383928860000044
Wherein, Pr [ M ]2(k)|M1(k-1)]、Pr[M2(k)|M2(k-1)]、Pr[M2(k)|M3(k-1)]And Pr [ M ]2(k)|M4(k-1)]Respectively switching weights of prior models of the tracking channel 2 at the k-1 moment;
3) construction of posterior model switching weight in tracking channel 3
Establishing a first Bayesian criterion by using the model weight and the prior model switching weight, and constructing the posterior model switching weight in the tracking channel 3 as
Figure FDA0002383928860000045
Figure FDA0002383928860000046
Figure FDA0002383928860000047
Figure FDA0002383928860000048
Wherein, Pr [ M ]3(k)|M1(k-1)]、Pr[M3(k)|M2(k-1)]、Pr[M3(k)|M3(k-1)]And Pr [ M ]3(k)|M4(k-1)]Respectively switching weights of prior models of the tracking channel 3 at the k-1 moment;
4) construction of posterior model switching weights in tracking channel 4
Establishing a first Bayesian criterion by using the model weight and the prior model switching weight, and constructing the posterior model switching weight in the tracking channel 4 as
Figure FDA0002383928860000051
Figure FDA0002383928860000052
Figure FDA0002383928860000053
Figure FDA0002383928860000054
Wherein, Pr [ M ]4(k)|M1(k-1)]、Pr[M4(k)|M2(k-1)]、Pr[M4(k)|M3(k-1)]And Pr [ M ]4(k)|M4(k-1)]The prior model switching weights of the tracking channel 4 at time k-1, respectively.
3. The hypersonic target tracking method based on the triple Bayesian rule as claimed in claim 2, wherein the method for constructing the model weight as the closed loop updated in real time with the intercepted information of the radar by using the second Bayesian rule in the fourth step is as follows:
1) model M1Construction of weights
Establishing a second Bayesian criterion by using the model weight at the k-1 moment, the prior model switching weight at the k-1 moment and the model likelihood at the k moment, and enabling the model M at the k moment1Is constructed as
Figure FDA0002383928860000055
Wherein, Pr [ Z (k) | M1(k)]、Pr[Z(k)|M2(k)]、Pr[Z(k)|M3(k)]And Pr [ Z (k) | M4(k)]Respectively k time model M1～M4The model likelihood of (2);
2) model M2Construction of weights
Establishing a second Bayesian criterion by using the model weight at the k-1 moment, the prior model switching weight at the k-1 moment and the model likelihood at the k moment, and enabling the model M at the k moment2Is constructed as
Figure FDA0002383928860000061
3) Model M3Construction of weights
Establishing a second Bayesian criterion by using the model weight at the k-1 moment, the prior model switching weight at the k-1 moment and the model likelihood at the k moment, and enabling the model M at the k moment3Is constructed as
Figure FDA0002383928860000062
4) Model M4Construction of weights
Establishing a second Bayesian criterion by using the model weight at the k-1 moment, the prior model switching weight at the k-1 moment and the model likelihood at the k moment, and enabling the model M at the k moment4Is constructed as
Figure FDA0002383928860000063
4. The hypersonic target tracking method based on the triple Bayesian rule as claimed in claim 3, wherein the third Bayesian rule is utilized in the fifth step, and the method for constructing the prior model switching weight comprises the following steps:
1) priori model switching weights Pr [ M1(k)|M1(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]1(k+1)|M1(k)]Is constructed as
Figure FDA0002383928860000064
2) Priori model switching weights Pr [ M1(k)|M2(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]1(k+1)|M2(k)]Is constructed as
Figure FDA0002383928860000071
3) Priori model switching weights Pr [ M1(k)|M3(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]1(k+1)|M3(k)]Is constructed as
Figure FDA0002383928860000072
4) Priori model switching weights Pr [ M1(k)|M4(k-1)]Construction of
Using the modulus of the time instant k-1The type weight, the prior model switching weight at the moment k-1 and the model likelihood at the moment k are used for building a third Bayesian criterion, and the prior model switching weight at the moment k is Pr [ M ]1(k+1)|M4(k)]Is constructed as
Figure FDA0002383928860000073
5) Priori model switching weights Pr [ M2(k)|M1(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]2(k)|M1(k-1)]Is constructed as
Figure FDA0002383928860000081
6) Priori model switching weights Pr [ M2(k)|M2(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]2(k)|M2(k-1)]Is constructed as
Figure FDA0002383928860000082
7) Priori model switching weights Pr [ M2(k)|M3(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]2(k)|M3(k-1)]Is constructed as
Figure FDA0002383928860000083
8) Priori model switching weights Pr [ M2(k)|M4(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]2(k)|M4(k-1)]Is constructed as
Figure FDA0002383928860000084
9) Priori model switching weights Pr [ M3(k)|M1(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]3(k)|M1(k-1)]Is constructed as
Figure FDA0002383928860000091
10) Priori model switching weights Pr [ M3(k)|M2(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]3(k)|M2(k-1)]Is constructed as
Figure FDA0002383928860000092
11) Priori model switching weights Pr [ M3(k)|M3(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]3(k)|M3(k-1)]Is constructed as
Figure FDA0002383928860000093
12) Priori model switching weights Pr [ M3(k)|M4(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]3(k)|M4(k-1)]Is constructed as
Figure FDA0002383928860000101
13) Priori model switching weights Pr [ M4(k)|M1(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]4(k)|M1(k-1)]Is constructed as
Figure FDA0002383928860000102
14) Priori model switching weights Pr [ M4(k)|M2(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]4(k)|M2(k-1)]Is constructed as
Figure FDA0002383928860000103
15) Priori model switching weights Pr [ M4(k)|M3(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]4(k)|M3(k-1)]Is constructed as
Figure FDA0002383928860000111
16) Priori model switching weights Pr [ M4(k)|M4(k-1)]Construction of
Establishing a third Bayesian rule by using the model weight at the moment k-1, the prior model switching weight at the moment k-1 and the model likelihood at the moment k, and switching the prior model switching weight at the moment k to Pr [ M ]4(k)|M4(k-1)]Is constructed as
Figure FDA0002383928860000112
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