CN117353705A - One-step delay tracking filtering method and system with unknown delay probability - Google Patents
One-step delay tracking filtering method and system with unknown delay probability Download PDFInfo
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- H—ELECTRICITY
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- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
- G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
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- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/35—Details of non-pulse systems
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- H03H17/00—Networks using digital techniques
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Abstract
The invention discloses a one-step delay tracking filtering method and a system with unknown delay probability, wherein the method comprises the steps of constructing a nonlinear target tracking model and receiving a data equation based on a tracked target, and the nonlinear target tracking model comprises the following steps: state equations and measurement equations; and performing operation processing of state dimension expansion, state time update, delay probability time update and parameter joint measurement iteration update on the state equation, the measurement equation and the received data equation by adopting one-step random time delay target tracking of a variable decibel leaf method. The method adopts a variable decibel leaf method to estimate the unknown delay probability, and a volume Kalman filtering method is fused to track and position the target. The method solves the problems of reduced tracking precision and even divergence caused by one-step random measurement delay with unknown delay probability in target tracking. Not only is the target tracking of one-step time delay processed, but also the delay probability of unknown time variation can be estimated.
Description
Technical Field
The invention relates to the technical field of target tracking, in particular to a one-step delay tracking filtering method and system with unknown delay probability.
Background
At present, the Kalman filtering method is the most engineering application target tracking method in target tracking, namely, the target tracking utilizes an active or passive sensor to acquire various information between the target and the target, estimates the relative position, the speed and the acceleration of the target, and has wide application in military, automatic driving and traffic control.
However, one of the basic assumptions of the conventional kalman filtering method is that the measurement data is received in real time, however, as shown in fig. 1, when the data communication network is blocked or the signal transmission is interfered by a complex environment, the measurement data may be randomly delayed, and in this case, if the Extended Kalman (EKF) method is adopted to deal with the object tracking problem, there is a problem that the estimation accuracy is reduced or even diverged. Furthermore, the delay probability of the measurement data may also be unknown and time-varying.
In order to ensure continuous and stable tracking of a maneuvering target, namely, delay of measurement data of the maneuvering target caused by maneuvering in the moving process of the target, how to ensure that a tracking result cannot diverge is a problem to be solved by a person skilled in the art.
Disclosure of Invention
In view of the above, the invention provides a one-step delay tracking filtering method and system with unknown delay probability, which solve the problems of tracking accuracy reduction and even divergence caused by one-step random measurement delay with unknown delay probability in target tracking.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
in a first aspect, an embodiment of the present invention provides a one-step delay tracking filtering method with unknown delay probability, including the steps of:
s1, constructing a nonlinear target tracking model and receiving a data equation based on a tracked target, wherein the nonlinear target tracking model comprises: state equations and measurement equations;
s2, performing operation processing of state expansion, state time updating, delay probability time updating and parameter joint measurement iteration updating on the state equation, the measurement equation and the received data equation by adopting one-step random time delay target tracking of a variable dB leaf method.
Further, in the step S1:
the state equation is:
x k ＝f(x k-1 )+w k-1 (1.1)
the measurement equation is:
z k ＝h(x k )+v k (1.2)
the received data equation is:
in the method, in the process of the invention,n-dimensional state vectors of the tracked target at the moment k are the position, the speed and the acceleration of the target in each direction respectively; />The m-dimensional measurement vector of the radar sensor to the target at the moment k; f (·) and h (·) are known nonlinear target motion equations and radar measurement equations, respectively; />For variance of Q k Is a random noise of the n-dimensional process of (c),for variance R k The m-dimensional Gaussian measurement noise of (1) is characterized in that subscripts k and k-1 are discrete time sequence numbers;
y k data actually received for the tracking filter; z k Is true measurement data;is a binary random variable representing whether the measured data is delayed, one element is 1 at the same time, and the rest is 0; assume that the delay probability of occurrence of measurement of one-step delay is μ k I.e. +.> Thus there is
In the formula (1.4), lambda k In order to introduce the binary reach variable,representing that no delay has occurred in the data,/-> A one-step delay occurs in the representative data.
Further, the state extension in step S2 includes:
augmenting the state vector:
X k ＝F(X k-1 )+Bw k-1 (1.5)
wherein X is k ＝[x k x k-1 ] T ，F(X k-1 )＝[f(x k-1 ) x k-1 ] T ，X k Including the state at the current time and at the previous time, b= [ I ] n 0] T ，I n Is an n-dimensional identity matrix.
Further, in the step S2, the state time is updated:
one-step prediction state for target acquisitionAnd corresponding error covariance P k|k-1 Processing nonlinear systems and improving approximation to nonlinearities by volumetric Kalman, i.e
In which Q k Is the process noise covariance;is a volume point, is generated by the following formula
Wherein,for posterior estimation of the last time state, S k-1 Satisfy P k-1|k-1 ＝S k-1 (S k-1 ) T ，P k-1|k-1 Zeta is the error covariance of the state at the last moment j Is the j th column
Where n represents the tracked object state vector dimension.
Further, the updating the delay probability time in the step S2 includes:
will delay the probability mu k Is a priori distributed p (mu) k-1 |y 1:k-1 ) Selected as dilichlet distributionIs a parameter of the delay probability at the previous moment, i.e
Consider the time delay probability to be time-varying, thus will mu k Is modeled as a one-step prediction of
Where τ is a forgetting factor, representing a trade-off between current state and history information,is a one-step prediction parameter of the delay probability.
Further, the step S2 of iterative updating of the parameter joint measurement includes:
1) For state updating, volume Kalman filtering is utilized;
2) For super-parameter updating, updating the delay probability mu by using a variable decibel leaf method k Related parameters of (2)
Further, for state updating, using a volume kalman filter, comprising:
calculating covariance P xy Cross covariance P yy ：
In the method, in the process of the invention,is volume point, S k Satisfy P k|k-1 ＝S k (S k ) T ，/> For the state posterior estimate of the nth iteration, the first initial value is selected as The noise covariance matrix is measured for the correction augmentation of the nth iteration, and is determined by the subsequent super-parameter updating;
calculating a gain matrix K k ：
Calculating the posterior probability of the n+1st iteration stateError covariance +.>
The upper corner mark n+1 represents the iteration number, and T represents the transposition;is an enhanced measurement vector.
Further, for super-parameter updating, the delay probability mu is updated by using a variable decibel-leaf method k Related parameters of (2)The concrete steps are as follows:
wherein E is the desired operation, there are
Wherein,is a vector comprising two elements, i.e. +.>Wherein the method comprises the steps ofRelated to undelayed measurement-> Related to the occurrence of delay measurement, oc represents proportional to tr [. Cndot.]Representing a trace operation, ++>Representing a normalization operation; /> Psi (·) is a double gamma function;
in the method, in the process of the invention,
update delay probability of
In the formula (1.17), the amino acid sequence,representing the calculation of intermediate parameters for calculating the expectation of whether a data delay has occurred at the current moment.
In a second aspect, an embodiment of the present invention further provides a one-step delay tracking filtering system with unknown delay probability, including: the construction module is used for constructing a nonlinear target tracking model and receiving a data equation based on the tracked target, wherein the nonlinear target tracking model comprises the following components: state equations and measurement equations;
and the tracking filtering module is used for carrying out operation processing of state dimension expansion, state time update, delay probability time update and parameter joint measurement iteration update on the state equation, the measurement equation and the received data equation by adopting one-step random time delay target tracking of a variable decibel leaf method.
Compared with the prior art, the invention discloses a one-step delay tracking filtering method with unknown delay probability, which adopts a variable decibel leaf method to estimate the unknown delay probability and fuses a volume Kalman filtering method to track and position a target. The method solves the problems of reduced tracking precision and even divergence caused by one-step random measurement delay with unknown delay probability in target tracking. Not only is the target tracking of one-step time delay processed, but also the delay probability of unknown time variation can be estimated.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a prior art random delay of measurement data;
FIG. 2 is a flow chart of a one-step delay tracking filtering method with unknown delay probability provided by the invention;
FIG. 3 is a schematic diagram of the calculation of the one-step delay tracking filtering method with unknown delay probability provided by the invention;
FIG. 4 is a schematic diagram of the position estimation error of the method of the present invention compared to an EKF;
FIG. 5 is a schematic representation of the velocity error of the method of the present invention compared to an EKF;
fig. 6 is a schematic diagram of the actual value of the delay probability compared to the estimated value.
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. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention discloses a one-step delay tracking filtering method with unknown delay probability, which is shown in fig. 1 and comprises the following steps:
s1, constructing a nonlinear target tracking model and receiving a data equation based on a tracked target, wherein the nonlinear target tracking model comprises: state equations and measurement equations;
s2, performing operation processing of state expansion, state time updating, delay probability time updating and parameter joint measurement iteration updating on the state equation, the measurement equation and the received data equation by adopting one-step random time delay target tracking of a variable dB leaf method.
In the embodiment, a variable decibel leaf method is adopted to estimate the unknown delay probability, and a volume Kalman filtering method is fused to track and position the target. The method solves the problems of reduced tracking precision and even divergence caused by one-step random measurement delay with unknown delay probability in target tracking. Not only is the target tracking of one-step time delay processed, but also the delay probability of unknown time variation can be estimated.
The above steps are described in detail below.
Referring to fig. 3, a calculation schematic diagram of a one-step delay tracking filtering method with unknown delay probability provided by the present invention is shown, which involves two steps:
step S1, constructing a nonlinear tracking model and a received data equation:
consider the following nonlinear target tracking model with one-step random time delay:
the state equation is:
x k ＝f(x k-1 )+w k-1 (1.1)
the measurement equation is:
z k ＝h(x k )+v k (1.2)
the received data equation is:
in the method, in the process of the invention,n-dimensional state vectors of the tracked target at the moment k are the position, the speed and the acceleration of the target in each direction respectively; />The m-dimensional measurement vector of the radar sensor to the target at the moment k; f (·) and h (·) are known nonlinear target motion equations and radar measurement equations, respectively; />For variance of Q k Is a random noise of the n-dimensional process of (c),for variance R k The m-dimensional Gaussian measurement noise of (1) is characterized in that subscripts k and k-1 are discrete time sequence numbers;
due to the unreliability of the communication link, the tracking filter actually receives the data y k And true measurement data z k Different. y is k Data actually received for the tracking filter; z k Is true measurement data;is a binary random variable representing whether the measured data is delayed, and at the same time, only one element is 1, and the rest are 0, namelyMeasurement data representing the moment k are received +.> Indicating that the system receives the measurement data at the moment of one-step delay k-1; assume that the delay probability of occurrence of measurement of one-step delay is μ k I.e.Thus there is
In the formula (1.4), lambda k In order to introduce the binary reach variable,representing that no delay has occurred in the data,/-> Representing data with one-step delay
Step S2, a one-step random time delay target tracking method based on a variable decibel leaf method:
step1: state expansion:
the measurement data y received by the system is caused by the existence of one-step random delay k Not only the state x at the current moment k In connection with the state x at the last moment k-1 In relation, it is therefore necessary to augment the state vector, i.e
X k ＝F(X k-1 )+Bw k-1 (1.5)
Wherein X is k ＝[x k x k-1 ] T ，F(X k-1 )＝[f(x k-1 ) x k-1 ] T ，X k Including the state at the current time and at the previous time, b= [ I ] n 0] T ，I n Is an n-dimensional identity matrix.
Step2: state time update:
one-step prediction state for target acquisitionAnd corresponding error covariance P k|k-1 The nonlinear system can be processed by utilizing the volume Kalman, namely, the approximation degree of the nonlinearity is improved
In which Q k Is the process noise covariance;is a volume point, which can be generated by the following formula
Wherein,for posterior estimation of the last time state, S k-1 Satisfy P k-1|k-1 ＝S k-1 (S k-1 ) T ，P k-1|k-1 Zeta is the error covariance of the state at the last moment j Is the j th column
Where n represents the tracked object state vector dimension.
Step3: delay probability time update:
will delay presumablyRate mu k Is a priori distributed p (mu) k-1 |y 1:k-1 ) Selected as dilichlet distributionIs a parameter of the delay probability at the previous moment, i.e
Consider the time delay probability to be time-varying, thus will mu k Can be modeled as a one-step prediction of
Where τ is a forgetting factor, representing a trade-off between current state and history information,is a one-step prediction parameter of the delay probability.
Step4: and (5) parameter joint measurement iteration update:
in order to realize the estimation of the unknown delay probability, the method adopts a variable decibel leaf method to carry out joint estimation on the state and the delay probability.
Step4.1: for state update, there are by volume Kalman filtering
Calculating covariance P xy Cross covariance P yy
In the method, in the process of the invention,is volume point, S k Satisfy P k|k-1 ＝S k (S k ) T ，/> For the state posterior estimate of the nth iteration, the first initial value may be selected asThe noise covariance matrix is measured for the correction augmentation of the nth iteration, and is determined by subsequent super-parameter updating.
Calculating a gain matrix K k
K k ＝P xy (P yy ) -1 (1.12)
Calculating the posterior probability of the n+1st iteration stateError covariance +.>
The upper corner mark n+1 represents the number of iterations and T represents the transpose.Is an enhanced measurement vector.
Step4.2: for super-parameter updating, updating the delay probability mu by using a variable decibel leaf method k Related parameters of (2)Which is specifically expressed as
Wherein E is the desired operation, there are
Wherein,is a vector comprising two elements, i.e. +.>Wherein the method comprises the steps ofRelated to undelayed measurement-> Related to the occurrence of delay measurement, oc represents proportional to tr [. Cndot.]Representing a trace operation, ++>Representing the normalization operation. /> ψ (·) is the double gamma function.
In the method, in the process of the invention,representing the calculation of an intermediate parameter for calculating the expectation of whether a data delay has occurred at the current moment, +.>
Update delay probability of
Wherein steps 4.1 and 4.2 require iterative updating. The proposed algorithm flow is now sorted as shown in fig. 3.
In order to verify the effectiveness of the method, firstly, constructing a following tracking scene for simulation, wherein a ground target does uniform linear motion, and a target motion model can be described as a constant velocity model
Simulation step length is t=1s, x t ＝[x y v x v y ]Representing a vector containing the position and velocity of the object in the x and y directions, I 2 Representing a two-dimensional identity matrix, the tracking filter can obtain the position information of the target, and then the measurement equation can be expressed as
z t ＝[I 2 0]x t +v t (1.20)
With one step of random delay, i.e
The delay probability varies with time as
The target state being the position and velocity in two directionsIts initial value is x 0 ＝[0 0 30 40] T ，P 0 ＝diag[10000 10000 100 100]，P 0 Error covariance indicating the initial time (time 0); diag represents the construction of a diagonal array operation. System process noise is-> The measured noise is r=δ×i 2 Wherein δ=25m 2 。
100 Monte Carlo tests are performed, and the result is shown in FIG. 4 and is a schematic diagram of the position estimation error; as shown in fig. 5, a velocity error is schematically illustrated. As shown in fig. 6, a schematic diagram of the actual value of the delay probability compared with the estimated value is shown. It can be seen that the method provided by the invention can solve the problem of measuring one-step random time delay in the tracking system, and can estimate the unknown and time-varying delay probability in real time.
In the embodiment, a variable decibel leaf method is adopted to estimate the unknown delay probability, and a volume Kalman filtering method is fused to track and position the target; not only is the target tracking of one-step time delay processed, but also the delay probability of unknown time variation can be estimated. Finally, the method is favorable for realizing accurate tracking of maneuvering targets, and can be widely applied to military, automatic driving and traffic control.
Based on the same inventive concept, the embodiment of the invention also provides a one-step delay tracking filtering system with unknown delay probability, and because the principle of the problem solved by the system is similar to that of the one-step delay tracking filtering method with unknown delay probability, the implementation of the system can be referred to the implementation of the method, and the repetition is omitted.
The system comprises:
the construction module constructs a nonlinear target tracking model and a received data equation based on the tracked target, a target tracking model and a received data equation
The nonlinear target tracking model includes: state equations and measurement equations;
and the tracking filtering module is used for carrying out operation processing of state dimension expansion, state time update, delay probability time update and parameter joint measurement iteration update on the state equation, the measurement equation and the received data equation by adopting one-step random time delay target tracking of a variable decibel leaf method.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (9)
1. A one-step delay tracking filtering method with unknown delay probability, comprising the steps of:
s1, constructing a nonlinear target tracking model and receiving a data equation based on a tracked target, wherein the nonlinear target tracking model comprises: state equations and measurement equations;
s2, performing operation processing of state expansion, state time updating, delay probability time updating and parameter joint measurement iteration updating on the state equation, the measurement equation and the received data equation by adopting one-step random time delay target tracking of a variable dB leaf method.
2. The method of one-step delay tracking filtering with unknown delay probability of claim 1, wherein in step S1:
the state equation is:
x k ＝f(x k-1 )+w k-1 (1.1)
the measurement equation is:
z k ＝h(x k )+v k (1.2)
the received data equation is:
in the method, in the process of the invention,n-dimensional state vectors of the tracked target at the moment k are the position, the speed and the acceleration of the target in each direction respectively; />The m-dimensional measurement vector of the radar sensor to the target at the moment k; f (·) and h (·) are known nonlinear target motion equations and radar measurement equations, respectively; />For variance of Q k Is a random noise of the n-dimensional process of (c),for variance R k The m-dimensional Gaussian measurement noise of (1) is characterized in that subscripts k and k-1 are discrete time sequence numbers;
y k data actually received for the tracking filter; z k Is true measurement data;is a binary random variable representing whether the measured data is delayed, one element is 1 at the same time, and the rest is 0; assume that the delay probability of occurrence of measurement of one-step delay is μ k I.e. +.> Thus there is
In the formula (1.4), lambda k In order to introduce the binary reach variable,representing that no delay has occurred in the data,/-> A one-step delay occurs in the representative data.
3. The method of one-step delay tracking filtering with unknown delay probability of claim 2, wherein the state expansion in step S2 includes:
augmenting the state vector:
X k ＝F(X k-1 )+Bw k-1 (1.5)
wherein X is k ＝[x k x k-1 ] T ，F(X k-1 )＝[f(x k-1 ) x k-1 ] T ，X k Including the state at the current time and at the previous time, b= [ I ] n 0] T ，I n Is an n-dimensional identity matrix.
4. A one-step delay tracking filtering method with unknown delay probability as defined in claim 3, wherein the state time is updated in step S2:
one-step prediction state for target acquisitionAnd corresponding error covariance P k|k-1 Processing nonlinear systems and improving approximation to nonlinearities by volumetric Kalman, i.e
In which Q k Is the process noise covariance;is a volume point, is generated by the following formula
Wherein,for posterior estimation of the last time state, S k-1 Satisfy P k-1|k-1 ＝S k-1 (S k-1 ) T ，P k-1|k-1 Zeta is the error covariance of the state at the last moment j Is the j th column
Where n represents the tracked object state vector dimension.
5. The method of one-step delay tracking filtering with unknown delay probability of claim 4, wherein the updating the delay probability time in step S2 comprises:
will delay the probability mu k Is a priori distributed p (mu) k-1 |y 1:k-1 ) Selected as dilichlet distribution Is a parameter of the delay probability at the previous moment, i.e
Consider the time delay probability to be time-varying, thus will mu k Is modeled as a one-step prediction of
Where τ is a forgetting factor, representing a trade-off between current state and history information,is a one-step prediction parameter of the delay probability.
6. The method of one-step delay tracking filtering with unknown delay probability of claim 5, wherein the iterative updating of the parameter joint measurement in step S2 comprises:
1) For state updating, volume Kalman filtering is utilized;
2) For super-parameter updating, updating the delay probability mu by using a variable decibel leaf method k Related parameters of (2)
7. The one-step delay tracking filtering method with unknown delay probability of claim 6, wherein for the state update, using a volume kalman filter, comprising:
calculating covariance P xy Cross covariance P yy ：
In the method, in the process of the invention,is volume point, S k Satisfy P k|k-1 ＝S k (S k ) T ，/> For the state posterior estimate of the nth iteration, the first initial value is selected as For the nth iterationThe corrected and amplified measurement noise covariance matrix is determined by subsequent super-parameter updating;
calculating a gain matrix K k ：
K k ＝P xy (P yy ) -1 (1.12)
Calculating the posterior probability of the n+1st iteration stateError covariance +.>
The upper corner mark n+1 represents the iteration number, and T represents the transposition;is an enhanced measurement vector.
8. The one-step delay tracking filtering method with unknown delay probability of claim 7 wherein for the super-parametric update, the delay probability μ is updated using a variational Bayesian method k Related parameters of (2)The concrete steps are as follows:
wherein E is the desired operation, there are
Wherein,is a vector comprising two elements, i.e. +.>Wherein the method comprises the steps ofRelated to undelayed measurement-> Related to the occurrence of delay measurement, oc represents proportional to tr [. Cndot.]Representing a trace operation, ++>Representing a normalization operation; /> Psi (·) is a double gamma function;
in the method, in the process of the invention,
update delay probability of
In the formula (1.17), the amino acid sequence,representing the calculation of intermediate parameters for calculating the expectation of whether a data delay has occurred at the current moment.
9. A one-step delay tracking filter system with unknown delay probabilities, comprising:
the construction module is used for constructing a nonlinear target tracking model and receiving a data equation based on the tracked target, wherein the nonlinear target tracking model comprises the following components: state equations and measurement equations;
and the tracking filtering module is used for carrying out operation processing of state dimension expansion, state time update, delay probability time update and parameter joint measurement iteration update on the state equation, the measurement equation and the received data equation by adopting one-step random time delay target tracking of a variable decibel leaf method.
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