CN110261859B - Underwater maneuvering static alternating state target tracking method - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
- G01S15/66—Sonar tracking systems
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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
- G06F17/15—Correlation function computation including computation of convolution operations
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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
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
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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
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/20—Analysis of motion
- G06T7/277—Analysis of motion involving stochastic approaches, e.g. using Kalman filters
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20024—Filtering details
Abstract
The invention considers various different motion states including the static tracking performance of a target, and aims to solve the technical problem of providing a tracking method with good applicability and lower error for complex moving targets with alternating underwater motion and static motion. Firstly, establishing a constant speed, variable speed and static three-state model; step two, carrying out filtering initialization; thirdly, performing input interaction; the fourth step is to input interaction of the three models obtained, and filter in parallel respectively; fifthly, obtaining likelihood functions through the measurement error covariance and the measurement prediction errors obtained in the last step, and obtaining the probability of the model at the moment through the likelihood functions; and sixthly, carrying out output interaction. From the simulation test result of adopting the new interaction model, the filtering error is smaller and the tracking performance is better under the condition that the new interaction model is proposed by the patent.
Description
Technical Field
The invention belongs to the field of sonar data simulation, and particularly relates to an underwater maneuvering stationary alternating state target tracking method.
Background
The underwater maneuvering and static state target tracking method is designed for evaluating the tracking performance of the underwater target which is crossed between the moving state and the static state, and under the condition that the underwater target is influenced by the state change factors of unfixed underwater target, the moving state of the underwater target can not be estimated or the estimation is deviated to cause the reduction of the tracking performance; if a part of the underwater targets move at some time and are stationary at some time during approaching or moving away, a tracking method adapted to the moving state of the underwater targets needs to be adopted in the face of similar situations.
At present, when the state of an underwater target is not fixedly changed, by adopting a method of combining a constant-speed non-maneuver model and an acceleration maneuver model, the underwater target can be tracked better under the condition of the actual similar motion state by assuming that the motion state of the target is more in the two motion states. In the original tracking method combining the uniform non-maneuver and accelerating maneuver models, the motion state estimation model of the special underwater target is too single, and the actual motion state is estimated only by using the common target motion model, so that the tracking output result corresponding to the model is obtained, the influence of the motion states such as static, severe maneuver and the like on the tracking performance is not fully considered, and reasonable tracking and positioning cannot be carried out on the actual target, so that the tracking performance is reduced.
Disclosure of Invention
1. Object of the invention
The invention considers various different motion states including the static tracking performance of a target, and aims to solve the technical problem of providing a tracking method with good applicability and lower error for complex moving targets with alternating underwater motion and static motion.
2. Technical proposal
The invention realizes maneuvering and static state target tracking by the following method:
the motion mode of the relatively complex underwater moving target mainly comprises main working states such as non-motorized uniform motion, motorized turning variable speed motion, static and the like, so that a state model related to the target is mainly considered when the target is tracked. Considering a section of target motion track, the target is in a straight line uniform speed and static alternating state at the beginning, is in a turning acceleration and static and uniform speed alternating state at the next, and the tracking performance is observed by comparing the real track with the filtering tracking result through tracking in different forms.
Firstly, establishing a constant speed, variable speed and static three-state model;
secondly, carrying out filtering initialization, initializing a Markov transition probability matrix of three models and the probability of each model, and initializing state estimation and covariance estimation of each model;
thirdly, carrying out input interaction, and obtaining input interaction probability by using model prediction probabilities respectively obtained by the three models; the state estimation obtained by initializing or filtering at the previous moment is calculated with the input interaction probability to obtain the state mixture of each model; on this basis, a state covariance mixture is calculated using the state covariance obtained at the initialization or the previous time.
The fourth step is to carry out input interaction and parallel filtering on the three obtained models, and the three state models are respectively subjected to traditional Kalman filtering to obtain measurement error covariance, measurement prediction error, state estimation value and state variance estimation value;
fifthly, obtaining likelihood functions through the measurement error covariance and the measurement prediction errors obtained in the last step, and obtaining the probability of the model at the moment through the likelihood functions;
and sixthly, performing output interaction, and obtaining state output estimation and state covariance estimation by state estimation, state variance estimation and updated model probability obtained by parallel filtering of each model.
Specifically, the constant motion model is built in this way, and related parameters and variable matrixes are related to the Kalman filtering estimation as follows:
wherein Fm1 is a state transition matrix, G 1 For input matrix, Q 1 Is a state error covariance matrix, H 1 The measurement matrix is R, the measurement error covariance matrix and T, the scanning period.
Initial state estimation:
initial state covariance:
wherein, X (3) and X (2) are respectively estimated at X coordinate time 3 and 2, Y (3) and Y (2) are respectively estimated at Y coordinate time 3 and 2, D is the diagonal element data value in the measurement error covariance matrix.
And (5) carrying out state estimation on the constant-speed model by adopting a classical Kalman filtering method. Constructing a target track, setting the speed to-15, setting the scanning period to 2, setting the measurement error to 50, and carrying out Monte Carlo calculation 50 times in the filtering process to obtain a simulation result as shown in figure 1.
And respectively obtaining the two-dimensional comparison of the real track and the filter estimation, and the filter error mean value and the error standard value.
As can be seen from the figure 1, the constant speed model is normal in the alternating condition of constant speed and static state, and the filtering is abnormal in the alternating condition of turning speed change, constant speed and static state, and the filtering errors in the X and Y axis directions are larger.
Specifically, the constant-speed and variable-speed motion model is established in such a way that relevant parameters and variable matrixes are involved in Kalman filtering estimation as follows:
the meaning of the parameters in the matrix is the same as that of the uniform velocity model.
An interactive multi-model algorithm is used to control the switching between the two states.
X(k+1)＝Fm j X(k)+G j W j (k) j＝1,2
Wherein W is j (k) Is the k time state error.
The transition between the models can be controlled by a Markov chain whose transition probability matrix is:
the state estimation and the state covariance are obtained through multi-model Kalman filtering:
wherein mu j (k) For the probability that the target is in the j-th state at time k,P j (k/k) is the state estimation and state covariance matrix of the j-th state at the time of filtering, respectively.
And carrying out state estimation on the constant-speed and variable-speed interaction model by adopting a multi-model Kalman filtering method. For the same construction track, the filtering process is calculated by 50 Monte Carlo, and the simulation results are shown in figure 2.
And respectively obtaining the two-dimensional comparison of the real track and the filter estimation, and the filter error mean value and the error standard value.
As can be seen from fig. 2, the X-axis filtering error of the constant speed and variable speed interaction model is very small under the condition of alternation of constant speed and static state, the Y-axis filtering error is certain, and the X, Y-axis filtering error is certain to be large under the condition of alternation of turning speed, constant speed and static state.
Through the experimental simulation, when the X-axis or Y-axis error becomes larger and the motorized or non-motorized motion interacts with the static state, the static model is added in the multi-state interaction to adapt to the change of the static state of the complex underwater target in order to solve the problem of poor tracking performance of the static state transition.
In the static model Kalman filtering estimation, related parameters and variable matrixes are as follows:
specifically, in the second step, the switching markov transition probability matrix between the three models is:
the initial state estimation for the constant speed, variable speed, stationary model is as follows:
the initial state covariance of the constant, variable, stationary model is as follows:
the method comprises the steps of carrying out input interaction through state mixing, and respectively carrying out state mixing of the model according to motion state probabilities updated at the next moment on the basis of three possible models, wherein the updating probability of model switching is determined by parallel filtering, and model prediction probability is obtained by likelihood functions and model probabilities obtained by parallel filtering, so that the input interaction probability is obtained.
The state mix is as follows:
wherein mu j/i (k) I represents constant speed, variable speed and static model identification, j/i represents state probability at the next moment j of the i state, such as probability that the variable speed state is changed to the static state at the moment k of the frogman or probability that the frogman returns to the variable speed state or constant speed state from the static state.
Covariance mix is as follows:
wherein P is j (k/k) is the state variance.
In the fourth step, the traditional Kalman filtering is adopted for parallel filtering, and three model state estimation are carried out:
three model state variances:
P i (k+1/k+1)＝[I-K i (k+1)H i (k+1)]P i (k+1/k)
model likelihood function:
model probability:
the output interaction state estimation and state covariance is:
the meaning of the parameters is the same as above.
And carrying out state estimation on the new interaction model by adopting a multi-model Kalman filtering method. For the same construction track, the filtering process is calculated by 50 Monte Carlo, and the simulation results are shown in figure 3.
And respectively obtaining the two-dimensional comparison of the real track and the filter estimation, and the filter error mean value and the error standard value.
As can be seen from fig. 3, the filtering track of the new interaction model is clear under the condition of uniform speed and static state alternation or turning speed change, uniform speed and static alternation, and the filtering errors in the X-axis direction and the Y-axis direction are smaller than those of the two model methods.
3. Technical effects
Compared with a constant-speed and acceleration interaction model algorithm, according to the simulation test result of the new interaction model, as the target track proceeds, X, Y axis filtering error values are reduced by nearly one time on average, and the fact that the filtering error is smaller and the tracking performance is better under the condition that the new interaction model is provided by the patent can be summarized.
Drawings
FIG. 1 is a graph of a target trajectory, speed is set to-15, scanning period is set to 2, measurement error is set to 50, and the filtering process is subjected to 50 Monte Carlo calculations to obtain a simulation result.
FIG. 2 employs a multi-model Kalman filtering method to perform state estimation on a constant velocity, variable velocity interaction model. And for the same construction track, the filtering process is calculated for 50 times by Monte Carlo, and a result is obtained through simulation.
Fig. 3 uses a multi-model kalman filtering method to perform state estimation on the new interaction model. And for the same construction track, the filtering process is calculated for 50 times by Monte Carlo, and a result is obtained through simulation.
Fig. 4 is a flow chart of an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings. The flow chart of the invention is shown in figure 4.
Firstly, carrying out filtering initialization, and initializing Markov transition probability matrixes P of three models ij And probability μ for each model j (k) Initializing state estimates for each modelCovariance estimation P j (k/k)。
Secondly, input interaction is carried out, and model prediction probability mu obtained by using three models respectively i (k+1/k) obtaining input interaction probability mu j/i (k) The method comprises the steps of carrying out a first treatment on the surface of the The state estimation obtained by initializing or filtering at the previous moment is calculated with the input interaction probability to obtain the state mixture of each modelOn the basis, a state covariance mixture is calculated by using the state covariance obtained at the initial or previous moment>
And obtaining the input interaction of the three models, and respectively filtering in parallel. The three state models respectively adopt the traditional Kalman filtering to obtain the measurement error covariance S i (k+1), measuring the prediction error v i (k+1), state estimation valueState variance estimation value P i (k+1/k+1). Wherein the state estimation value and the state variance estimation value are used in the input interaction process of the next moment.
Obtaining likelihood function lambda through measurement error covariance and measurement prediction error obtained in the last step i (k+1) model probability μ from the likelihood function to the present time i (k+1). Wherein the state modelThe probability will be used in the input interaction process for the next moment.
Finally, performing output interaction, and obtaining state output estimation by state estimation obtained by parallel filtering of all the models, state variance estimation and updated model probabilityAnd a state covariance estimate P (k+1/k+1).
Claims (5)
1. A maneuvering and static state target tracking method specifically comprises the following steps:
firstly, establishing a constant speed, variable speed and static three-state model;
secondly, carrying out filtering initialization, initializing a Markov transition probability matrix of three models and the probability of each model, and initializing state estimation and covariance estimation of each model;
thirdly, carrying out input interaction, and obtaining input interaction probability by using model prediction probabilities respectively obtained by the three models; the state estimation obtained by initializing or filtering at the previous moment is calculated with the input interaction probability to obtain the state mixture of each model; on the basis, using the state covariance obtained at the initial or previous moment to calculate to obtain a state covariance mixture;
the fourth step, the input interaction of the three obtained models is respectively and parallelly filtered, and the three state models are respectively subjected to traditional Kalman filtering to obtain measurement error covariance, measurement prediction error, state estimation and state covariance estimation;
fifthly, obtaining likelihood functions through the measurement error covariance and the measurement prediction errors obtained in the last step, and obtaining the probability of the model at the moment through the likelihood functions;
and sixthly, performing output interaction, and obtaining state output estimation and state covariance estimation by state estimation, state covariance estimation and updated model probability obtained by parallel filtering of each model.
2. The method of claim 1, wherein the constant velocity state model involves a matrix of related parameters and variables as follows:
wherein Fm 1 For state transition matrix, G 1 For input matrix, Q 1 Is a state error covariance matrix, H 1 The measurement matrix is R, the measurement error covariance matrix is R, and the scanning period is T;
the variable speed state model involves the following related parameters and variable matrixes:
the meaning of the parameters in the matrix is the same as that of the constant-speed state model;
the static state model involves the following related parameters and variable matrices:
the meaning of the parameters in the matrix is the same as that of the constant speed state model.
3. A maneuver and stationary state target tracking method as defined in claim 2 wherein in said second step, the switching markov transition probability matrix between the three models is:
the initial state estimation for the constant speed, variable speed, stationary model is as follows:
(X(3)+X(1)-2*X(2))/T*T，(Y(3)+Y(1)-2*Y(2))/T*T
wherein X (3), X (2) and X (1) are respectively corresponding time X coordinate state estimation, and Y (3), Y (2) and Y (1) are respectively corresponding time Y coordinate state estimation;
the initial state covariance of the constant, variable, stationary model is as follows:
wherein D is measurement error covarianceDiagonal element data values in the matrix.
4. A maneuvering and stationary object tracking method as defined in claim 3, wherein in said third step, input interactions are performed, and the probabilities μ are predicted using models derived from the three models respectively i (k+1/k) obtaining input interaction probability mu j/i (k) The method comprises the steps of carrying out a first treatment on the surface of the And calculating the state estimation obtained by initializing or filtering at the previous moment and the input interaction probability to obtain the state mixture of each model:
wherein i represents the identification of the constant speed, variable speed and static state models,estimating the state of a j model at the k moment;
on the basis, the state covariance mixture is obtained by using the state covariance calculation obtained at the initial or previous moment Wherein P is j (k/k) is the state covariance of the jth model at time k.
5. The maneuvering and stationary target tracking method according to claim 4, wherein in the fourth step, the parallel filtering is performed by using conventional kalman filtering, and three model state estimations are:
three model state covariances:
P i (k+1/k+1)＝[I-K i (k+1)H i (k+1)]P i (k+1/k)
model likelihood function:
model probability:
the output interaction state estimation and state covariance is:
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