CN110516193B - Maneuvering target tracking method based on transformation Rayleigh filter under Cartesian coordinate system - Google Patents
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Abstract
The invention relates to a maneuvering target tracking method based on a conversion Rayleigh filter under a Cartesian coordinate system. The invention relates specifically to the problem of maneuvering target tracking with angular measurement information only. The method comprises two parts, namely determination of a measurement equation under a Cartesian coordinate based on the idea of converting Rayleigh filtering and tracking of a maneuvering target by adopting an interactive multi-model centralized conversion Rayleigh filtering (MAIMMCSRF) algorithm with corrected acceleration provided by the invention according to the measurement equation of a Cartesian coordinate system. The core of the invention is the generation of a measurement equation under a Cartesian coordinate based on the idea of converting Rayleigh filtering and the tracking of a maneuvering target by an MAIMMCSRF algorithm provided under a Cartesian coordinate system. The invention can realize more accurate tracking and positioning for the high maneuvering target, adopts median filtering in the maneuvering target tracking algorithm to reduce the acceleration error in the interactive multi-model algorithm, and has smaller target tracking error and more accurate tracking and positioning.
Description
Technical Field
The invention belongs to the technical field of sensors, and particularly relates to a target tracking problem only with angle measurement.
Background
Radar is the most effective remote electronic detection device at present, and irradiates a target by transmitting electromagnetic waves and receives echoes, so that the position and attribute information of the target is obtained to achieve the purposes of positioning, tracking and identifying the target. When a target echo is collected to detect and locate a target, a radar needs to radiate high-power electromagnetic waves to the air, so that a transmitting signal of the radar is easy to discover and intercept by an enemy, and the radar is easy to attack by electronic interference and anti-radiation missiles. Passive localization techniques have become the mainstream of localization method development today with increasing emphasis on covert attacks and hard kills. Unlike active positioning techniques, passive positioning techniques do not actively transmit electromagnetic signals, but rather determine the location of the radiation source by receiving the radiated transmit signals. The method has the advantages of long action distance, good concealment and strong anti-interference capability, and provides an important means for concealed detection and accurate striking. In modern real battlefield environments, the feature data available about the target is very limited, and the azimuth of the target becomes almost the only reliable measurement information.
Generally, a passive tracking system can only acquire azimuth/pitch angle information of a target, and belongs to incomplete observation. Target tracking is not easy to realize by a single-station ESM sensor only with angle information, and the problem of weak observability exists. Currently, research on the target tracking problem of the ESM sensor mainly focuses on two aspects of a filtering algorithm and selection of a coordinate system. Since the target tracking problem with only angle measurement is essentially a non-linear estimation problem, only recursive tracking can be performed by using a non-linear filtering algorithm. The traditional nonlinear filtering method is Extended Kalman Filtering (EKF), which carries out first-order linear truncation through a Taylor expansion of a nonlinear function, so that the nonlinear problem is converted into linearity, the positioning and tracking effect of the EKF depends on the estimation of an initial state, and the corresponding filtering covariance is very easy to generate ill-condition, thereby causing the divergence phenomenon of a filter. Although there are many improved methods for EKF, such as high-order truncated EKF, iterative EKF, etc., to make up for this deficiency, the above problem is still difficult to completely solve. Since the probability density distribution of a nonlinear function is easier than approximating a nonlinear function, it is considered to approximate a nonlinear distribution using a sampling method to solve the nonlinear problem, and sampling-based nonlinear filter algorithms, typically a Particle Filter (PF) algorithm and an Unscented Kalman Filter (UKF) algorithm, have a large amount of calculation although these two algorithms achieve good results. In 2005, clark et al proposed a converted rayleigh filtering (SRF), which uses a nonlinear structure of a measurement equation, i.e., a projection of an n-dimensional vector on a unit circle or a unit sphere, and accurately calculates a conditional probability density of a target azimuth using observation information at a current time under a condition that a state at a previous time obeys gaussian distribution, thereby avoiding an approximation error of other filtering.
The median filtering is a special nonlinear filtering algorithm, has the characteristics of noise suppression and edge protection, and is greatly emphasized in the signal field. It has two main advantages: (1) The spike pulse (the pulse length is less than the width of the filter) can be completely filtered, and the high-frequency noise in the acceleration signal can be eliminated. (2) The median filtering may not cause phase distortion for symmetric wavelets by steps and ramps. It also has some disadvantages, mainly represented by signal distortion (the longer the filtering, the more severe the signal distortion), which introduces spurious high frequencies.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a maneuvering target tracking method based on a conversion Rayleigh filter under a Cartesian coordinate system.
The transformed rayleigh filtering (SRF) proposed by j.m.c.clark is a new time-matched filtering algorithm for 2/3 dimensional tracking problem with only angle measurement.
The state equation and the measurement equation of the system are respectively set as follows:
X(k)＝FX(k-1)+U s (k-1)+W(k-1) (1)
B(k)＝Π[HX(k)+U m (k)+V(k)] (2)
in the formula: f is a system transfer matrix; u shape s (k-1) a system-known input signal; h is an expansion measurement matrix; u shape m (k) To measure the input signal; w (k-1) and V (k) areThe independent zero median and covariance are respectively Q s (k-1)、Q m (k) White gaussian noise; Π denotes the projection of the n-dimensional vector on a unit circle (n = 2) or unit sphere (n = 3). When n =2, the measurement obtained is only the azimuth angle θ (k), then B (k) = [ sin (θ (k)), cos (θ (k))] T (ii) a When n =3, measurements are obtained with an azimuth angle θ (k) and a pitch angle η (k), then
B(k)＝[cos(θ(k))cos(η(k)),sin(θ(k))cos(η(k)),sin(η(k))] T 。
In the invention, the state equation and the measurement equation of the system are still the formulas (1) and (2), but pi in the formula (2) represents that an n-dimensional vector is projected on a two-dimensional or three-dimensional Cartesian coordinate system. When n =2, the only measurement obtained is the azimuth angle θ (k), then B (k) = [ sin (θ (k)), cos (θ (k))] T (ii) a When n =3, the obtained measurement has an azimuth angle θ (k) and a pitch angle η (k), and B (k) = [ sin (θ (k)) cos (η (k)), sin (θ (k)) cos (η (k)), sin (η (k))] T 。
In the tracking of the moving target, the motion of the target is not enough to be described by only one model, and the motion of the target can be better described only by adopting different motion models in different motion states. The method adopts a plurality of parallel model filters to track the target, and can realize self-adaptive soft switching among the models when the target is in a maneuvering mode, and the final state estimation of the target is the weighted mixture of estimation results obtained by different models at each moment. The interactive multi-model algorithm is a target tracking algorithm suitable for the situation of high maneuvering of the target, and has the best tracking effect from the global perspective. However, even if the interactive multi-model filtering is used when the target maneuvers, the acceleration still has a large error. The invention provides an interactive multi-model centralized conversion Rayleigh filtering (MAIMMCSRF) with corrected acceleration formed by combining an interactive multi-model, centralized Rayleigh filtering and median filtering. The algorithm reduces the error of acceleration estimation in the interactive multi-model algorithm and improves the tracking precision. The invention provides an MAIMMCSRF target tracking algorithm, which is deduced to the expression of a likelihood function and a median filtering acceleration estimation process, thereby giving a complete cycle process.
The invention is described from a cyclic process of interactive multiple models. The interactive multi-model recursion cycle consists of 4 steps of input interaction, model filtering, model probability updating, interaction output and acceleration estimation. When model filtering is carried out, the likelihood function of each model needs to be calculated, namely, the new observed quantity b at the current time is estimated by utilizing the target state estimation of the previous time input by each model t Likelihood function of (2), and model
(t represents the time of state estimation, j represents the model corresponding to time t) the likelihood function of the match can be expressed as:
model filtering adopts centralized conversion Rayleigh filtering, and assumes that the target is fused and tracked by M stations, and the observed quantity obtained at each moment is b i,t (i denotes an observation station or platform, i =1,2, 3.., M), then with respect to b i,t The likelihood function of (d) is:
carrying out likelihood function estimation on the observed quantities of all observation stations (M) simultaneously to obtain
The matched likelihood function is:
wherein the content of the first and second substances,
respectively the innovation size and the filtering corresponding to the observation station i in the jth model filterMean square error of the residual. Equation (5) is a likelihood function calculation method. Combining the interactive multi-model, the centralized Rayleigh filtering and the acceleration estimation to form the interactive multi-model centralized conversion Rayleigh filtering (MAIMMCSRF) with the corrected acceleration, and specifically circulating the steps as follows, wherein the number of observation stations is M, the number of models is N, and the measurement noise of an observation station i in a jth model filter is M
The model of the object motion is input as
In the formula
And
representing the acceleration in the x, y and z directions in the model j cartesian coordinate system, respectively. The probability of model jump is P j ＝{p ij } N×N ，(j＝1,2,...,N；i＝1,2,...,M)。
Step 1, input interaction
Estimation of target states from model filters at a previous time, i.e. at time t-1
(j denotes the jth model) with model probability for each filter
Deriving hybrid estimates
Sum covariance
And taking the mixed estimation as the initial state of the cycle at the time t:
step 2, model filtering
Target state based on reinitialization
Sum covariance
After obtaining a new measurement b t Then, the state estimation is updated by a centralized conversion rayleigh filter, and a model likelihood function is calculated according to equation (21):
in the formula (18)
Is represented as follows:
in the formula (19), r represents the dimension of the scene, wherein
To convert the mean of the rayleigh filter transform:
wherein
And
in a simplified form as follows:
wherein the content of the first and second substances,
the cumulative function of the standard normal distribution N (0, 1) can be expressed as:
wherein the model input matrix G and the process noise matrix Q S Respectively, the following steps:
computing sum using residual and covariance
A matching likelihood function.
Step 3, model probability updating
When the model likelihood function calculation is performed by equation (21), the model probability at time t is updated as:
step 4, interactive output and acceleration correction
(a) Interactive output
Model probability based on time t
Weighting and combining the estimation results of each filter to obtain combined estimation
Sum covariance P t|t 。
(b) Acceleration correction
The acceleration is corrected by median filtering. The acceleration information in X, Y and Z directions obtained by the interactive multi-model algorithm is respectively recorded as
And
and with a x (t|t)、a y (t | t) and a z (t | t) represents the median filtered accelerations, respectively. Median filtering is performed by taking the acceleration in the corrected X-axis direction as an example. Suppose that the X-axis acceleration data is expressed by the following equation (28):
{a i }(i＝1,K,N x ) (28)
wherein i represents the acceleration data of the ith number, N x Number of X-axis acceleration data. Assuming that the length of a given median filter is N (sliding window length, typically an odd number), the median filter for the K-th point of the ith data is:
(1) Taking N sampling points, and taking the Kth point as a center;
(2) The N sampling points are sorted from small to large;
(3) And taking the central point numerical value of the sequenced N sampling points as the K-th output value.
Special cases are as follows:
{a i when the number of acceleration data in the data is less than the number of sampling points N, if N =5, then there is
When N is present x If =1, then there is a x (t|t)＝a 1 Wherein
When N is present x When =2, then
When N is present x If =3, then a is 1 、a 2 And
arranging the data according to the sequence from small to large, and taking a middle value;
when N is present x When =4, { a ] is first set i And
the two values are arranged from small to large, and the average value is taken.
When N is present x >If =5, a is obtained by the median filtering method described above x The value of (t | t).
Repeating the above process to obtain a x (t|t)、a y (t | t) and a z (t | t), thereby modifying and updating the model parameters.
The invention has the beneficial effects that:
the invention tracks the maneuvering target by using an interactive multi-model method, optimally estimates the position information of the maneuvering target by adopting the latest conversion Rayleigh filtering algorithm, and corrects and estimates the acceleration by adopting a median filtering method in order to make up the problem that the interactive multi-model cannot estimate the acceleration estimation precision of the maneuvering target.
Detailed Description
The implementation of the invention mainly comprises three parts, namely acquisition of observation information of an observation station, tracking of a non-maneuvering target and tracking of a maneuvering target.
1. Acquisition of observation information
Suppose the number of observation stations is M and the measurement dimension is n. When n =2, M measurement information, i.e. the azimuth angle θ (k), measured from the observation station corresponds to the measurement equation B (k) = [ sin (θ (k)), cos (θ (k) ])] T (ii) a When n =3, M pairs of measurement information, i.e. an azimuth angle θ (k) and a pitch angle η (k), are measured from the observation station, and the corresponding measurement equations are B (k) = [ sin (θ (k)) cos (η (k)), sin (θ (k)) cos (η (k)), sin (η (k))] T . In this way, a projection of the vector formed by the observation station and the target in a cartesian coordinate system is obtained. In addition, each observation station has an angle measurement error σ, and a system noise covariance Q s 。
2. Maneuvering target tracking
In the tracking of the moving target, the motion of the target is not enough to be described by only one model, and the motion of the target can be better described only by adopting different motion models in different motion states. The method adopts a plurality of parallel model filters to track the target, and when the target is in a maneuvering mode, self-adaptive 'soft switching' can be realized among the models, and the final state estimation of the target is the weighted mixture of estimation results obtained by different models at each moment. The interactive multi-model algorithm is a target tracking algorithm suitable for the situation of high maneuvering of the target, and has the best tracking effect from the global perspective. However, even if the interactive multi-model filtering is used during target maneuvering, the acceleration still has a large error. The invention combines the interactive multi-model, the centralized Rayleigh filtering and the median filtering to form the interactive multi-model centralized conversion Rayleigh filtering (MAIMMCSRF) with the corrected acceleration. The algorithm reduces the error of acceleration estimation in the interactive multi-model algorithm and improves the tracking precision. The specific implementation of the algorithm is as follows.
The method comprises the following steps: and inputting an interaction.
Estimation of target state from each model filter at the previous time, i.e. t-1
(j denotes the jth model) with model probability for each filter
Deriving hybrid estimates
Sum covariance
And the hybrid estimate is taken as the initial state of the cycle at time t:
at the initial time, firstly, the target state estimation of each initial model is given
And corresponding model probabilities
Assuming that the number of observation stations is M, the number of models is N, and the model input of the object motion is
In the formula
And
representing the acceleration in the x, y and z directions in the model j cartesian coordinate system, respectively. The probability of model jump is P j ＝{p ij } N×N ，(j＝1,2,...,N；i＝1,2,...,M)。
And step two, model filtering.
The measurement noise of observation station i in the jth model filter can be obtained from 1
System noise covariance Q s And obtaining a measurement vector from the measurement equation B (k). Target state based on reinitialization
Covariance
And a system transfer matrix F, which is updated by state estimation using a centralized conversion Rayleigh filter, and calculates a model likelihood function according to the formula (21):
wherein the model input matrix is:
the process noise matrix is:
computing sum using residual and covariance
A matching likelihood function. The concrete implementation is as follows:
calculated according to equation (5) to obtain
A matching likelihood function.
Step three: and updating the model probability.
When the model likelihood function calculation is performed by equation (21), the model probability at time t is updated as:
step four: and (5) interacting output and correcting acceleration.
(a) Interactive output
Model probability based on time t
Weighting and combining the estimation results of each filter to obtain combined estimation
Sum covariance P t|t 。
(b) Acceleration correction
The acceleration is corrected by median filtering. The acceleration information in X, Y and Z directions obtained by the interactive multi-model algorithm is respectively recorded as
And
and with a x (t|t)、a y (t | t) and a z (t | t) represents the median filtered addition, respectivelySpeed. The median filtering is performed by taking the acceleration in the corrected X-axis direction as an example. Suppose that the X-axis acceleration data is expressed by the following equation (28):
{a i }(i＝1,K,N x ) (28)
wherein i represents the acceleration data of the i-th number, N x Number of X-axis acceleration data. Assuming that the length of a given median filter is N (sliding window length, typically an odd number), the median filter for the K-th point of the ith data is:
(1) Taking N sampling points, and taking the Kth point as a center;
(2) The N sampling points are sorted from small to large;
(3) And taking the central point numerical values of the sequenced N sampling points as the K-th output value.
Special cases are as follows:
{a i the number of acceleration data in is less than the number of sample points N, provided that N =5, there is
When N is present x If =1, then there is a x (t|t)＝a 1 Wherein
When N is present x When =2, then there is
When N is present x If =3, then a is 1 、a 2 And
arranging the data according to the sequence from small to large, and taking a middle value;
when N is present x When =4, { a ] is first set i And
the two values are arranged from small to large, and the average value is taken.
When N is present x >If =5, a is obtained by the median filtering method described above x The value of (t | t).
Repeating the above process to obtain a x (t|t)、a y (t | t) and a z (t | t), thereby modifying and updating the model parameters.
Based on the four steps, the method provided by the invention can track the maneuvering target, and the tracking precision is higher than that of the traditional interactive multi-model.
Claims (1)
1. The maneuvering target tracking method based on the conversion Rayleigh filter under the Cartesian coordinate system is characterized in that:
the state equation and the measurement equation of the system are respectively as follows:
X(k)＝FX(k-1)+U s (k-1)+W(k-1) (1)
B(k)＝Π[HX(k)+U m (k)+V(k)] (2)
in the formula: f is a system transfer matrix; u shape s (k-1) a system-known input signal; h is an expansion measurement matrix; u shape m (k) To measure an input signal; w (k-1) and V (k) are independent zero median, and covariance is Q s (k-1)、Q m (k) Pi is the projection of an n-dimensional vector on a two-dimensional or three-dimensional Cartesian coordinate system; when n =2, the only measurement obtained is the azimuth angle θ (k), then B (k) = [ sin (θ (k)), cos (θ (k))] T (ii) a When n =3, the obtained measurement has an azimuth angle θ (k) and a pitch angle η (k), and B (k) = [ sin (θ (k)) cos (η (k)), sin (θ (k)) cos (η (k)), sin (η (k))] T
The method is described from a cyclic process of interactive multiple models; the interactive multi-model recursion cycle comprises four steps of input interaction, model filtering, model probability updating, interaction output and acceleration estimation; when model filtering is carried out, the likelihood function of each model needs to be calculated, namely, the new observed quantity b at the current time is estimated by utilizing the target state estimation of the previous time input by each model t Likelihood function of (2), and model
The matching likelihood function can be expressed as:
model filtering adopts centralized conversion Rayleigh filtering, and assumes that the target is fused and tracked by M stations, and the observed quantity obtained at each moment is b i,t Then with respect to b i,t The likelihood function of (d) is:
carrying out likelihood function estimation on the observed quantities of all the observation stations at the same time to obtain
The matched likelihood function is:
wherein the content of the first and second substances,
respectively representing the innovation size and the mean square error of a filtering residual error corresponding to an observation station i in the jth model filter; equation (5) is a likelihood function calculation method; combining the interactive multi-model, the centralized Rayleigh filtering and the acceleration estimation to form the interactive multi-model centralized conversion Rayleigh filtering (MAIMMCSRF) with the corrected acceleration, and the specific circulation steps are as follows: wherein the number of observation stations is M, the number of models is N, and the measurement noise of an observation station i in a jth model filter is
The model of the object motion is input as
In the formula
And
respectively representing the acceleration of the model j in the directions of an x axis, a y axis and a z axis in a Cartesian coordinate system; the probability of model jump is P j ＝{p ij } N×N ：
Step 1, input interaction
Estimation of target state from each model filter at the previous time, i.e. t-1
Model probability with each filter
Obtaining hybrid estimates
Sum covariance
And the hybrid estimate is taken as the initial state of the cycle at time t:
step 2, model filtering
Target state based on reinitialization
Sum covariance
After obtaining a new measurement b t Then, the state estimation is updated by a centralized conversion rayleigh filter, and a model likelihood function is calculated according to equation (21):
in the formula (18)
Is represented as follows:
in the formula (19), r represents the dimension of the scene, wherein
To convert the mean of the rayleigh filter transform:
wherein
And
in a simplified form as follows:
wherein the content of the first and second substances,
the cumulative function of the standard normal distribution N (0, 1) can be expressed as:
wherein the model input matrix is:
the process noise matrix is:
step 3, model probability updating
When the model likelihood function calculation is performed by equation (21), the model probability at time t is updated as:
step 4, interactive output and acceleration correction
4-1, interactive output
Model probability based on time t
For eachWeighting and combining the estimation results of the filters to obtain combined estimation
Sum covariance P t|t ；
4-2, acceleration correction
The acceleration is corrected by median filtering; the acceleration information in X, Y and Z directions obtained by the interactive multi-model algorithm is respectively recorded as
And
and with a x (t|t)、a y (t | t) and a z (t | t) respectively represent median filtered accelerations; performing median filtering by taking the acceleration in the direction of the corrected X axis as an example; suppose that the X-axis acceleration data is expressed by the following equation (28):
{a i }(i＝1,K,N x ) (28)
wherein i represents the acceleration data of the i-th number, N x A number representing X-axis acceleration data; assuming that the length of the given median filter is N, the median filter for the kth point of data number i is:
(1) Taking N sampling points and taking the Kth point as a center;
(2) The N sampling points are sorted from small to large;
(3) Taking the central point numerical values of the sequenced N sampling points as the K-th output value;
{a i the number of acceleration data in the test is less than that of sampling pointsIf the number N is N =5, the number is
When N is present x If =1, then there is a x (t|t)＝a 1 Wherein
When N is present x When =2, then there is
When N is present x If =3, then a is 1 、a 2 And
arranging the data according to the sequence from small to large, and taking a middle value;
when N is present x When =4, { a ] is first set i And
the two values are arranged from small to large, and the average value is obtained;
when N is present x When the value is more than or equal to 5, a is obtained according to the method of median filtering x The value of (t | t);
repeating the above process to obtain a x (t|t)、a y (t | t) and a z (t | t), thereby modifying and updating the model parameters.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107045125A (en) * | 2017-03-17 | 2017-08-15 | 电子科技大学 | A kind of Interactive Multiple-Model radar target tracking method based on predicted value measurement conversion |
| CN107193009A (en) * | 2017-05-23 | 2017-09-22 | 西北工业大学 | A kind of many UUV cooperative systems underwater target tracking algorithms of many interaction models of fuzzy self-adaption |
| CN108896986A (en) * | 2018-04-23 | 2018-11-27 | 电子科技大学 | A kind of measurement conversion Sequential filter maneuvering target tracking method based on predicted value |
| CN109001699A (en) * | 2018-01-30 | 2018-12-14 | 哈尔滨工业大学 | Based on the tracking constrained with noise destination information |
-
2019
- 2019-07-08 CN CN201910610729.3A patent/CN110516193B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107045125A (en) * | 2017-03-17 | 2017-08-15 | 电子科技大学 | A kind of Interactive Multiple-Model radar target tracking method based on predicted value measurement conversion |
| CN107193009A (en) * | 2017-05-23 | 2017-09-22 | 西北工业大学 | A kind of many UUV cooperative systems underwater target tracking algorithms of many interaction models of fuzzy self-adaption |
| CN109001699A (en) * | 2018-01-30 | 2018-12-14 | 哈尔滨工业大学 | Based on the tracking constrained with noise destination information |
| CN108896986A (en) * | 2018-04-23 | 2018-11-27 | 电子科技大学 | A kind of measurement conversion Sequential filter maneuvering target tracking method based on predicted value |
Non-Patent Citations (3)
| Title |
|---|
| 刘梅 ; 陈锦海 ; 高扬 ; 王骏 ; 林超 ; 张声杰 ; .基于IMM-CSRF的多平台机动目标被动跟踪方法.2011,(01),全文. * |
| 张恒 ; 高敏 ; 徐超 ; .改进的强跟踪容积卡尔曼滤波的机动目标跟踪.2015,(06),全文. * |
| 潘平俊 ; 冯新喜 ; 李锋 ; 石磊 ; 李鸿艳 ; .基于转换瑞利滤波器的红外目标跟踪算法.2008,(06),全文. * |
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