WO2018049602A1 - 一种适用于杂波环境的多目标跟踪方法及跟踪系统 - Google Patents
一种适用于杂波环境的多目标跟踪方法及跟踪系统 Download PDFInfo
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- WO2018049602A1 WO2018049602A1 PCT/CN2016/099036 CN2016099036W WO2018049602A1 WO 2018049602 A1 WO2018049602 A1 WO 2018049602A1 CN 2016099036 W CN2016099036 W CN 2016099036W WO 2018049602 A1 WO2018049602 A1 WO 2018049602A1
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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
- 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
- G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
- G01S13/726—Multiple target tracking
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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
- 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
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/52—Discriminating between fixed and moving objects or between objects moving at different speeds
- G01S13/538—Discriminating between fixed and moving objects or between objects moving at different speeds eliminating objects that have not moved between successive antenna scans, e.g. area MTi
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- the invention relates to the field of multi-sensor information fusion technology, in particular to a multi-target tracking method and a tracking system suitable for a clutter environment.
- an effective multi-target tracking method for a clutter environment mainly includes: a target tracking method based on a Gaussian mixture probability hypothesis density filter and a measurement-driven target tracking method based on an edge distribution.
- the main problem of these two target tracking methods is that the amount of calculation is large, and the state estimation cannot be provided in the first few time steps after the new target appears. How to effectively provide the new target in the first few time steps after its appearance State estimation and reduction of computation are a key technical problem that needs to be explored and solved in the multi-objective Bayesian filtering method.
- an object of the present invention is to provide a multi-target tracking method and system thereof suitable for a clutter environment, which aims to solve the problem that the state estimation cannot be provided in the first few time steps after the emergence of a new target in the prior art. And the problem of large calculations.
- the invention provides a multi-target tracking method suitable for a clutter environment, which mainly comprises:
- the prediction step according to the edge distribution and the existence probability of each target at the previous moment, and the time difference between the current moment and the previous moment, predicting the edge distribution and the existence probability of the existing targets existing at the previous moment at the current moment;
- N represents a Gaussian distribution
- i 1,2,...N k-1
- x i, k-1 is the state vector of the target i at time k-1
- m i, k-1 and P i, k-1 respectively represent the state mean and covariance of the target i at time k-1
- N k-1 is the former The total number of goals at a time;
- the edge distribution and existence probabilities of i at time k are N(x i,k ;m i,k
- k-1 F i,k
- k-1 Q i,k-1 +F i,k
- k-1 p S,k ( ⁇ t k ) ⁇ i,k-1 ,F i,k
- the categorization step determines whether each measurement in the measurement set originates from an existing target at a previous moment according to the predicted edge distribution and the predicted existence probability of the current target at the current moment and the current set of measurement points. And classify them separately;
- the updating step the predicted edge distribution and the predicted existence probability at the current time according to the existing targets existing at the previous moment, and the measurement of the current target from the existing target, using the Bayes rule to determine the existing targets existing at the previous moment Update edge distribution and update existence probability at the current time;
- the clipping and extracting steps according to the updated edge distribution and the existing existence probability of the existing targets existing at the previous moment, the target having the existence probability less than the first threshold is cut off, and the edge of the target having the existence probability greater than the second threshold is extracted Distribution as the output of the current time;
- the supplementary step the extraction of the new target at the current time edge distribution complements the output of the current time, and extracts the state estimation of the new target at the first two moments to supplement the output of the first two moments respectively;
- a merging step combining an edge distribution and an existence probability of the remaining target after the clipping and the extracting step, respectively, and combining the edge distribution and the existence probability of the new target generated at the current time in the generating step to form a current moment
- the classifying step specifically includes: predicting an edge distribution N(x i,k ;m i,k
- the jth measure y j,k in the middle determines whether the measurement y j,k originates from the existing target, and classifies separately;
- the step of determining whether the measurement y j,k originates from an existing target and separately classifying comprises:
- Substep A seeking probability
- H k is the observation matrix
- R k is the observed noise variance matrix
- p D,k is the detection probability of the target
- ⁇ c,k is the clutter density
- Substep B if The measurement y j,k is classified into other measurement classes;
- the measurement y j,k is classified into the measurement originating from the existing target, in the measurement set
- the updating step specifically includes: predicting edge distribution N(x i,k ;m i,k
- the step of determining the updated edge distribution and the existence probability of each existing target at the current moment by using the Bayes rule includes:
- the generating step specifically includes: using other measurements at time k Other measurements at time k-1 And other measurements at time k-2 Generate new targets and use the least squares method to estimate the state mean, covariance and edge distribution of the new target at the current time;
- the other measurement using the k time Other measurements at time k-1 And other measurements at time k-2 The steps to generate new goals include:
- Sub-step E from Take measurement From Take measurement From Take measurement Calculated
- 2 represents the 2 norm of the vector
- Substep F judgment condition v min ⁇ v f, e ⁇ v max , v min ⁇ v g, f ⁇ v max , a g, f, e ⁇ a max and c g, f, e ⁇ c min is satisfied,
- v min , v max , a max and c min are four given parameters representing the minimum speed, the maximum speed, the maximum acceleration and the minimum value of the cosine of the included angle; if the four conditions are satisfied at the same time, the measurement is used And measurement The state average of the new target at time k by least squares Covariance And edge distribution among them
- ⁇ w is the standard deviation of the measured noise; meanwhile, the probability of existence of the specified new target is taken as The state of the new target at k-1 is estimated to be among them The state of the new target at time k-2 is estimated as among them
- the present invention also provides a multi-target tracking system suitable for use in a clutter environment, the system comprising:
- a prediction module configured to predict an edge distribution and an existence probability of each target existing at a previous moment according to an edge distribution and an existence probability of each target at a previous moment, and a time difference between the current moment and a previous moment;
- N represents a Gaussian distribution
- i 1,2,...N k-1
- x i, k-1 is the state vector of the target i at time k-1
- m i, k-1 and P i, k-1 respectively represent the state mean and covariance of the target i at time k-1
- N k-1 is the former The total number of goals at a time;
- the edge distribution and existence probabilities of i at time k are N(x i,k ;m i,k
- k-1 F i,k
- k-1 Q i,k-1 +F i,k
- k-1 p S,k ( ⁇ t k ) ⁇ i,k-1 ,F i,k
- a classification module configured to determine, according to a predicted edge distribution and a predicted existence probability of each target existing at a previous moment, and a current set of measurements, whether each measurement in the measurement set originates from a previous moment Goals and categorize separately;
- An update module configured to determine, according to the predicted edge distribution and the predicted existence probability of the current target at the current moment, and the current moment from the measurement of the existing target, and use the Bayes rule to determine each existing existing moment The updated edge distribution and update existence probability of the target at the current time;
- the clipping and extracting module is configured to: according to the updated edge distribution and the update existence probability of each target existing at the previous moment, reduce the target whose existence probability is less than the first threshold, and extract the target whose existence probability is greater than the second threshold
- the edge distribution is the output of the current moment
- a supplemental module for extracting the edge distribution of the new target at the current time to supplement the output of the current time, and extracting the state estimates of the new target at the first two moments to supplement the outputs of the first two moments respectively;
- a merging module configured to combine the edge distribution and the existence probability of the remaining target after the clipping and the extracting step, respectively, with the edge distribution and the existence probability of the new target generated at the current time in the generating step, to form The edge distribution and existence probability of each target at the current moment, and as the input of the next recursion.
- the classification module is specifically configured to: according to the predicted edge distribution N of the target i existing at time k-1 at time k (x i, k ; m i, k
- the jth measure y j,k in the middle determines whether the measurement y j,k originates from the existing target, and classifies separately;
- the classification module includes:
- H k is the observation matrix
- R k is the observed noise variance matrix
- p D,k is the detection probability of the target
- ⁇ c,k is the clutter density
- Second submodule for The measurement y j,k is classified into other measurement classes;
- the measurement y j,k is classified into the measurement originating from the existing target, in the measurement set
- the updating module is specifically configured to: according to the predicted edge distribution N(x i,k ;m i,k
- the update module includes:
- the generating module is specifically configured to: use other measurements at time k Other measurements at time k-1 And other measurements at time k-2 Generate new targets and use the least squares method to estimate the state mean, covariance and edge distribution of the new target at the current time;
- the generating module includes:
- the fifth submodule for Take measurement From Take measurement From Take measurement Calculated
- 2 represents the 2 norm of the vector ,
- v min ⁇ v f, e ⁇ v max , v min ⁇ v g, f ⁇ v max , a g, f, e ⁇ a max and c g, f, e ⁇ c min Satisfied where v min , v max , a max and c min are four given parameters representing the minimum speed, maximum speed, maximum acceleration and the minimum value of the cosine of the included angle; if the four conditions are satisfied at the same time, the measurement is used And measurement
- the state average of the new target at time k by least squares Covariance And edge distribution among them ⁇ w is the standard deviation of the measured noise; meanwhile, the probability of existence of the specified new target is taken as The state of the new target at k-1 is estimated to be among them The state of the new target at time k-2 is estimated as among them
- the technical solution provided by the invention effectively estimates the state estimation of the first three time steps after the occurrence of the new target by using the least square method by predicting, classifying, updating, reducing and extracting, generating, supplementing and merging the steps.
- the existing method can not provide the new target state estimation problem in the first few time steps after the emergence of the new target, and has the characteristics of fast processing speed, and its calculation amount is obviously smaller than the existing method, and has strong practicability.
- FIG. 1 is a flowchart of a multi-target tracking method applicable to a clutter environment according to an embodiment of the present invention
- FIG. 2 is a schematic diagram showing the internal structure of a multi-target tracking system suitable for use in a clutter environment according to an embodiment of the present invention
- FIG. 3 is a measurement data diagram of a sensor provided by an embodiment of the present invention in 50 scanning cycles according to an embodiment of the present invention
- FIG. 4 is a schematic diagram of an OSPA distance obtained by an experiment in a multi-target tracking method and a Gaussian mixture probability hypothesis density filtering method according to the present invention, which is applicable to a clutter environment according to an embodiment of the present invention;
- FIG. 5 is a schematic diagram of an average SPAC distance obtained by 100 experiments in a multi-target tracking method and a Gaussian mixture probability hypothesis density filtering method according to the present invention, which is suitable for use in a clutter environment according to an embodiment of the present invention.
- a multi-target tracking method suitable for a clutter environment provided by the present invention will be described in detail below.
- FIG. 1 is a flowchart of a multi-target tracking method suitable for a clutter environment according to an embodiment of the present invention.
- step S1 the prediction step, based on the edge distribution and the existence probability of each target at the previous moment, and the time difference between the current time and the previous time, predict the edge distribution and the existence probability of each target existing at the previous moment at the current time.
- the predicting step S1 specifically includes:
- N represents a Gaussian distribution
- i 1,2,...N k-1
- x i, K-1 is the state vector of the target i at time k-1
- m i,k-1 and P i,k-1 respectively represent the state mean and covari
- the edge distribution and existence probability of i at time k are N(x i,k ;m i,k
- k-1 F i,k
- k-1 Q i,k-1 +F i,k
- k-1 p S,k ( ⁇ t k ) ⁇ i,k-1 ,F i,k
- step S2 the classification step determines whether each measurement in the measurement set originates from the previous moment according to the predicted edge distribution and the predicted existence probability of the current target at the current time and the current existence measurement set. Existing goals are categorized separately.
- the classifying step S2 specifically includes: predicting an edge distribution N(x i,k ;m i,k
- the jth measure y j,k in the middle determines whether the measurement y j,k originates from the existing target, and classifies separately;
- the step of determining whether the measurement y j,k originates from an existing target and separately classifying comprises:
- Substep A seeking probability
- H k is the observation matrix
- R k is the observed noise variance matrix
- p D,k is the detection probability of the target
- ⁇ c,k is the clutter density
- Substep B if The measurement y j,k is classified into other measurement classes;
- the measurement y j,k is classified into the measurement originating from the existing target, in the measurement set
- step S3 the updating step, the predicted edge distribution and the predicted existence probability of the respective targets existing at the previous moment according to the previous moment, and the current moment originating from the existing target are measured, and the Bayes rule is used to determine the previous moment.
- Each existing target has an updated edge distribution at the current time and an update existence probability.
- the updating step S3 specifically includes: predicting an edge distribution N(x i,k ;m i,k
- the step of determining the updated edge distribution and the existence probability of each existing target at the current moment by using the Bayes rule includes:
- step S4 the clipping and extracting steps, the updated edge distribution and the existing existence probability of the respective targets existing at the previous moment at the current moment, the target having the existence probability less than the first threshold is cut off, and the extraction probability is greater than the second
- the edge distribution of the target of the threshold is taken as the output of the current time.
- step S5 the generating step generates new targets using other measurements of the current time and other measurements of the first two moments, and estimates the state mean, covariance, and edge distribution of the new target at the current time using a least squares method.
- the generating step S5 specifically includes: using other measurements at time k Other measurements at time k-1 And other measurements at time k-2 Generate new targets and use the least squares method to estimate the state mean, covariance and edge distribution of the new target at the current time;
- the other measurement using the k time Other measurements at time k-1 And other measurements at time k-2 The steps to generate new goals include:
- Sub-step E from Take measurement From Take measurement From Take measurement Calculated
- 2 represents the 2 norm of the vector
- step S6 the supplemental step extracts the edge distribution of the new target at the current time to supplement the output of the current time, and extracts the state estimates of the new target at the first two moments to supplement the outputs of the first two moments respectively.
- step S7 the merging step, the edge distribution and the existence probability of the remaining target after the clipping in the clipping and extracting steps are respectively performed with the edge distribution and the existence probability of the new target generated at the current time in the generating step Merging, forming the edge distribution and existence probability of each target at the current moment, and as the input of the next recursion.
- the invention provides a multi-target tracking method suitable for a clutter environment, which uses the steps of predicting, classifying, updating, reducing and extracting, generating, supplementing and merging, and using the least squares method to estimate the initial target of the new target after its appearance 3
- the state estimation of time steps effectively solves the problem that the existing method can not provide new target state estimation in the first few time steps after the emergence of the new target, and has the characteristics of fast processing speed, and the calculation amount is obviously smaller than the existing method. , has a strong practicality.
- FIG. 2 a schematic structural diagram of a multi-target tracking system 10 suitable for use in a clutter environment according to an embodiment of the present invention is shown.
- the multi-target tracking system 10 suitable for the clutter environment mainly includes a prediction module 11, a classification module 12, an update module 13, a reduction and extraction module 14, a generation module 15, a supplementation module 16, and a merge module 17.
- the prediction module 11 is configured to predict the edge distribution and the existence probability of each target existing at the previous moment according to the edge distribution and the existence probability of each target at the previous moment, and the time difference between the current moment and the previous moment.
- the prediction module 11 is specifically configured to:
- N represents a Gaussian distribution
- i 1,2,...N k-1
- x i, K-1 is the state vector of the target i at time k-1
- m i,k-1 and P i,k-1 respectively represent the state mean and covari
- the edge distribution and existence probabilities of i at time k are N(x i,k ;m i,k
- k-1 F i,k
- k-1 Q i,k-1 +F i,k
- k-1 p S,k ( ⁇ t k ) ⁇ i,k-1 ,F i,k
- the classification module 12 is configured to determine, according to the predicted edge distribution and the predicted existence probability of the current target at the current moment, and the measurement set of the current time, whether each measurement in the measurement set originates from the previous moment. of Goals and categorize separately.
- the classification module 12 is specifically configured to: according to the predicted edge distribution N of the target i existing at time k-1 at time k (x i, k ; m i, k
- the jth measure y j,k in the middle determines whether the measurement y j,k originates from the existing target, and classifies separately;
- the classification module 12 includes: a first sub-module and a second sub-module.
- H k is the observation matrix
- R k is the observed noise variance matrix
- p D,k is the detection probability of the target
- ⁇ c,k is the clutter density.
- Second submodule for The measurement y j,k is classified into other measurement classes;
- the measurement y j,k is classified into the measurement originating from the existing target, in the measurement set
- the updating module 13 is configured to determine, according to the predicted edge distribution and the predicted existence probability of the current target at the current moment, and the current moment from the measurement of the existing target, and use the Bayes rule to determine that the previous moment exists.
- the update edge distribution and update existence probability of each target at the current time are configured to determine, according to the predicted edge distribution and the predicted existence probability of the current target at the current moment, and the current moment from the measurement of the existing target, and use the Bayes rule to determine that the previous moment exists.
- the updating module 13 is specifically configured to: according to the predicted edge distribution N (x i, k ; m i, k
- the update module 13 includes: a third submodule and a fourth submodule.
- the third submodule for measuring with Bayesian rules Processing obtaining the target i corresponding to the measurement Probability of existence Mean vector And covariance matrix among them
- the clipping and extraction module 14 is configured to: according to the updated edge distribution and the update existence probability of the current target existing at the previous moment, the target having the existence probability less than the first threshold is cut off, and the existence probability is greater than the second threshold.
- the edge distribution of the target is used as the output of the current moment.
- the generating module 15 is configured to generate a new target by using other measurements of the current time and other measurements of the first two moments thereof, and estimate a state mean, a covariance, and an edge distribution of the new target at the current time by using a least squares method.
- the generating module 15 is specifically configured to: use other measurements at time k Other measurements at time k-1 And other measurements at time k-2 Generate new targets and use the least squares method to estimate the state mean, covariance and edge distribution of the new target at the current time;
- the generating module 15 includes: a fifth sub-module and a sixth sub-module.
- the fifth submodule for Take measurement From Take measurement From Take measurement Calculated
- 2 represents the 2 norm of the vector
- indicates an absolute value
- ( ⁇ , ⁇ ) indicates the inner product of the two vectors.
- v min ⁇ v f, e ⁇ v max , v min ⁇ v g, f ⁇ v max , a g, f, e ⁇ a max and c g, f, e ⁇ c min Satisfied where v min , v max , a max and c min are four given parameters representing the minimum speed, maximum speed, maximum acceleration and the minimum value of the cosine of the included angle; if the four conditions are satisfied at the same time, the measurement is used And measurement
- the state average of the new target at time k by least squares Covariance And edge distribution among them ⁇ w is the standard deviation of the measured noise; meanwhile, the probability of existence of the specified new target is taken as The state of the new target at k-1 is estimated to be among them The state of the new target at time k-2 is estimated as among them
- the supplementing module 16 is configured to extract the edge distribution of the new target at the current time to supplement the output of the current time, and extract the state estimation of the new target at the first two moments to supplement the output of the first two moments respectively.
- a merging module 17 for dividing the edge distribution and the existence probability of the remaining target after the clipping and extracting steps are performed, The edge distribution and the existence probability of the new target generated at the current time are respectively combined with the new target generated in the generating step, and the edge distribution and the existence probability of each target at the current time are formed, and are used as the input of the next recursion.
- the present invention provides a multi-target tracking system 10 suitable for use in a clutter environment, through the prediction module 11, the classification module 12, the update module 13, the reduction and extraction module 14, the generation module 15, the supplementation module 16, and the merge module 17.
- Estimating the state of the first three time steps of the new target after the occurrence of the new target by using the least squares method effectively solving the problem that the existing method cannot provide the new target state estimation in the first few time steps after the new target appears,
- the processing speed is fast, and the calculation amount is obviously smaller than the existing method, and has strong practicability.
- the state of the target is composed of position and velocity, expressed as Where x and y represent positional components, respectively.
- the superscript T represents the transpose of the vector
- the simulated observation data of the sensor in 50 scan cycles in one experiment is shown in Fig. 3.
- Figure 5 is the average OFPA distance obtained by performing 50 Monte Carlo experiments with the existing Gaussian mixture probability hypothesis density filter and the present invention.
- Table 1 shows the average execution time of the existing Gaussian mixture probability hypothesis density filter and one experiment obtained in 50 experiments of the present invention, and the results show that the average execution time of the present invention is significantly smaller than the existing Gaussian mixture probability hypothesis density filter. Device.
- the technical solution provided by the invention effectively estimates the state estimation of the first three time steps after the occurrence of the new target by using the least square method by predicting, classifying, updating, reducing and extracting, generating, supplementing and merging the steps.
- the existing method can not provide the new target state estimation problem in the first few time steps after the emergence of the new target, and has the characteristics of fast processing speed, and its calculation amount is obviously smaller than the existing method, and has strong practicability.
- each unit included is only divided according to functional logic, but is not limited to the above division, as long as the corresponding function can be implemented; in addition, the specific name of each functional unit is also They are only used to facilitate mutual differentiation and are not intended to limit the scope of the present invention.
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Abstract
一种适用于杂波环境的多目标跟踪方法,其中,所述方法包括:预测步骤(S1)、分类步骤(S2)、更新步骤(S3)、裁减与提取步骤(S4)、生成步骤(S5)、补充步骤(S6)、合并步骤(S7)。还提供一种适用于杂波环境的多目标跟踪系统(10)。具有处理速度快的特点,同时有效地解决了现有方法在新目标出现后的前几个时间步不能提供新目标状态估计的问题。
Description
本发明涉及多传感器信息融合技术领域,尤其涉及一种适用于杂波环境的多目标跟踪方法及跟踪系统。
贝叶斯滤波技术能够提供一种强大的统计方法工具,用于协助解决杂波环境下以及测量数据具有不确定性情况下的多传感器信息的融合与处理。在现有技术中,用于杂波环境的多目标跟踪有效方法主要有:基于高斯混合概率假设密度滤波器的目标跟踪方法和传递边缘分布的测量驱动目标跟踪方法。这两种目标跟踪方法的主要问题是计算量较大,并且在新目标出现后的最初几个时间步中不能提供其状态估计,如何有效提供新目标在其出现后的最初几个时间步的状态估计,同时减少计算量是多目标贝叶斯滤波方法中需要探索和解决的一个关键技术问题。
发明内容
有鉴于此,本发明的目的在于提供一种适用于杂波环境的多目标跟踪方法及其系统,旨在解决现有技术中在新目标出现后的最初几个时间步中不能提供其状态估计以及计算量大的问题。
本发明提出一种适用于杂波环境的多目标跟踪方法,主要包括:
预测步骤、根据前一时刻各个目标的边缘分布和存在概率,以及当前时刻与前一时刻的时间差,预测前一时刻已存在的各个目标在当前时刻的边缘分布和存在概率;
其中,以k-1表示前一时刻,k表示当前时刻,tk-1表示前一时刻的时间,tk表示当前时刻的时间,k-1时刻目标i的边缘分布和存在概率分别表示为N(xi,k-1;mi,k-1,Pi,k-1)和ρi,k-1,其中N表示高斯分布,i=1,2,…Nk-1,xi,k-1为k-1时刻目标i的状态向量,mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差,Nk-1为前一时刻目标的总数;
由k-1时刻目标i的边缘分布N(xi,k-1;mi,k-1,Pi,k-1)和存在概率ρi,k-1,预测k-1时刻的目标i在k时刻的边缘分布和存在概率分别为N(xi,k;mi,k|k-1,Pi,k|k-1)和ρi,k|k-1,其中mi,k|k-1=Fi,k|k-1mi,k-1,Pi,k|k-1=Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T,ρi,k|k-1=pS,k(Δtk)ρi,k-1,Fi,k|k-1为状态转移矩阵,上标T表示矩阵或向量的转置,Δtk=tk-tk-1为k时刻与k-1时刻的时间差,Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵,pS,k(Δtk)为目标的幸存概率,且T为采样周期,δ为给定的常数,i=1,2,…Nk-1;
分类步骤、根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻的测量集,确定出测量集中的每个测量是否源于前一时刻已存在的目标,并分别进行归类;
更新步骤、根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻源于已存在目标的测量,利用贝叶斯规则确定前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率;
裁减与提取步骤、根据前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率,将存在概率小于第一阈值的目标裁减掉,同时提取存在概率大于第二阈值的目标的边缘分布作为当前时刻的输出;
生成步骤、利用当前时刻的其它测量和其前两时刻的其它测量产生新目标,并利用最小二乘法估计新目标在当前时刻的状态均值、协方差和边缘分布;
补充步骤、提取新目标在当前时刻的边缘分布对当前时刻的输出进行补充,并提取新目标在前两个时刻的状态估计分别对前两个时刻的输出进行补充;
合并步骤、将在所述裁减与提取步骤中裁减后余下目标的边缘分布和存在概率,分别与在所述生成步骤中生成的新目标在当前时刻的边缘分布和存在概率进行合并,形成当前时刻各个目标的边缘分布和存在概率,并作为下一次递归的输入。
优选的,所述分类步骤具体包括:根据k-1时刻已存在的目标i在k时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及k时刻的测量集合中的第j个测量yj,k,确定测量yj,k是否源于已存在目标,并分别进行归类;
其中,所述确定测量yj,k是否源于已存在目标,并分别进行归类的步骤包括:
子步骤B、若将测量yj,k归入其它测量类;若将测量yj,k归入源于已存在目标的测量,在测量集合中的每个测量处理后,测量集合中yk的测量被分为两类,一类是源于已存在目标的测量,表示为另一类是其它测量,表示为其中M1,k和M2,k分别源于已存在目标测量的数目和其它测量的数目,且M1,k+M2,k=Mk。
优选的,所述更新步骤具体包括:根据前一时刻已存在的各个目标在当前时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及当前时刻源于已存在目标的测量集合利用贝叶斯规则确定当前时刻各个已存在目标的更新边缘分布和存在概率;
其中,所述利用贝叶斯规则确定当前时刻各个已存在目标的更新边缘分布和存在概率的步骤包括:
子步骤C、利用贝叶斯规则对测量处理,得到目标i对应于测量的存在概率均值向量和协方差矩阵其中在所有的M1,k个测量处理后,各个目标对应于各测量的更新边缘分布和存在概率分别为和其中i=1,…,Nk-1,j=1,…,M1,k;
子步骤E、从中取测量从中取测量从中取测量计算得到
其中e=1,…,M2,k-2,f=1,…,M2,k-1,g=1,…,M2,k,||·||2表示向量的2范数,|·|表示取绝对值,(·,·)表示两向量的内积;
子步骤F、判断条件vmin≤vf,e≤vmax、vmin≤vg,f≤vmax、ag,f,e≤amax和cg,f,e≥cmin是否满足,其中vmin、vmax、amax和cmin为4个给定的参数,分别表示最小速度、最大速度、最大加速度和夹角余弦的最小值;若4个条件同时满足,利用测量和测量由最小二乘法得到一个新目标的在k时刻的状态均值协方差和边缘分布其中
另一方面,本发明还提供一种适用于杂波环境的多目标跟踪系统,所述系统包括:
预测模块,用于根据前一时刻各个目标的边缘分布和存在概率,以及当前时刻与前一时刻的时间差,预测前一时刻已存在的各个目标在当前时刻的边缘分布和存在概率;
其中,以k-1表示前一时刻,k表示当前时刻,tk-1表示前一时刻的时间,tk表示当前
时刻的时间,k-1时刻目标i的边缘分布和存在概率分别表示为N(xi,k-1;mi,k-1,Pi,k-1)和ρi,k-1,其中N表示高斯分布,i=1,2,…Nk-1,xi,k-1为k-1时刻目标i的状态向量,mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差,Nk-1为前一时刻目标的总数;
由k-1时刻目标i的边缘分布N(xi,k-1;mi,k-1,Pi,k-1)和存在概率ρi,k-1,预测k-1时刻的目标i在k时刻的边缘分布和存在概率分别为N(xi,k;mi,k|k-1,Pi,k|k-1)和ρi,k|k-1,其中mi,k|k-1=Fi,k|k-1mi,k-1,Pi,k|k-1=Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T,ρi,k|k-1=pS,k(Δtk)ρi,k-1,Fi,k|k-1为状态转移矩阵,上标T表示矩阵或向量的转置,Δtk=tk-tk-1为k时刻与k-1时刻的时间差,Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵,pS,k(Δtk)为目标的幸存概率,且T为采样周期,δ为给定的常数,i=1,2,…Nk-1;
分类模块,用于根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻的测量集,确定出测量集中的每个测量是否源于前一时刻已存在的目标,并分别进行归类;
更新模块,用于根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻源于已存在目标的测量,利用贝叶斯规则确定前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率;
裁减与提取模块,用于根据前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率,将存在概率小于第一阈值的目标裁减掉,同时提取存在概率大于第二阈值的目标的边缘分布作为当前时刻的输出;
生成模块,用于利用当前时刻的其它测量和其前两时刻的其它测量产生新目标,并利用最小二乘法估计新目标在当前时刻的状态均值、协方差和边缘分布;
补充模块,用于提取新目标在当前时刻的边缘分布对当前时刻的输出进行补充,并提取新目标在前两个时刻的状态估计分别对前两个时刻的输出进行补充;
合并模块,用于将在所述裁减与提取步骤中裁减后余下目标的边缘分布和存在概率,分别与在所述生成步骤中生成的新目标在当前时刻的边缘分布和存在概率进行合并,形成当前时刻各个目标的边缘分布和存在概率,并作为下一次递归的输入。
优选的,所述分类模块具体用于:根据k-1时刻已存在的目标i在k时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及k时刻的测量集合中的第j个测量yj,k,确定测量yj,k是否源于已存在目标,并分别进行归类;
其中,所述分类模块包括:
第二子模块,用于若将测量yj,k归入其它测量类;若将测量yj,k归入源于已存在目标的测量,在测量集合中的每个测量处理后,测量集合中yk的测量被分为两类,一类是源于已存在目标的测量,表示为另一类是其它测量,表示为其中M1,k和M2,k分别源于已存在目标测量的数目和其它测量的数目,且M1,k+M2,k=Mk。
优选的,所述更新模块具体用于:根据前一时刻已存在的各个目标在当前时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及当前时刻源于已存在目标的测量
集合利用贝叶斯规则确定当前时刻各个已存在目标的更新边缘分布和存在概率;
其中,所述更新模块包括:
第三子模块,用于利用贝叶斯规则对测量处理,得到目标i对应于测量的存在概率均值向量和协方差矩阵其中在所有的M1,k个测量处理后,各个目标对应于各测量的更新边缘分布和存在概率分别为和其中i=1,…,Nk-1,j=1,…,M1,k;
其中,所述生成模块包括:
第五子模块,用于从中取测量从中取测量从中取测量计算得到
其中e=1,…,M2,k-2,f=1,…,M2,k-1,g=1,…,M2,k,||·||2表示向量的2范数,|·|表示取绝对值,(·,·)表示两向量的内积;
第六子模块,用于判断条件vmin≤vf,e≤vmax、vmin≤vg,f≤vmax、ag,f,e≤amax和cg,f,e≥cmin是否满足,其中vmin、vmax、amax和cmin为4个给定的参数,分别表示最小速度、最大速度、最大加速度和夹角余弦的最小值;若4个条件同时满足,利用测量和测量由最小二乘法得到一个新目标的在k时刻的状态均值协方差和边缘分布其中
σw为测量噪声的标准差;同时,指定新目标的存在概率取为新目标在k-1时刻的
状态估计为其中新目标在k-2时刻的状态估计为其中
本发明提供的技术方案,通过预测、分类、更新、裁减与提取、生成、补充、合并这些步骤,利用最小二乘法估计新目标在其出现后的最初3个时间步的状态估计,有效地解决了现有方法在新目标出现后的前几个时间步不能提供新目标状态估计的问题,具有处理速度快的特点,且其计算量明显小于现有方法,具有很强的实用性。
图1为本发明一实施方式中适用于杂波环境的多目标跟踪方法流程图;
图2为本发明一实施方式中适用于杂波环境的多目标跟踪系统的内部结构示意图;
图3为本发明一实施方式中利用本发明实施例提供的传感器在50个扫描周期的测量数据图;
图4为本发明一实施方式中根据本发明适用于杂波环境下的多目标跟踪方法与高斯混合概率假设密度滤波方法经过一次实验得到的OSPA距离示意图;
图5为本发明一实施方式中根据本发明用于适用于杂波环境下的多目标跟踪方法与高斯混合概率假设密度滤波方法在经过100次实验得到的平均OSPA距离示意图。
为了使本发明的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本发明进行进一步详细说明。应当理解,此处所描述的具体实施例仅仅用以解释本发明,并不用于限定本发明。
以下将对本发明所提供的一种适用于杂波环境的多目标跟踪方法进行详细说明。
请参阅图1,为本发明一实施方式中适用于杂波环境的多目标跟踪方法流程图。
在步骤S1中,预测步骤、根据前一时刻各个目标的边缘分布和存在概率,以及当前时刻与前一时刻的时间差,预测前一时刻已存在的各个目标在当前时刻的边缘分布和存在概率。
在本实施方式中,所述预测步骤S1具体包括:
以k-1表示前一时刻,k表示当前时刻,tk-1表示前一时刻的时间,tk表示当前时刻的时间,k-1时刻目标i的边缘分布和存在概率分别表示为N(xi,k-1;mi,k-1,Pi,k-1)和ρi,k-1,其中N表示高斯分布,i=1,2,…Nk-1,xi,k-1为k-1时刻目标i的状态向量,mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差,Nk-1为前一时刻目标的总数;
由k-1时刻目标i的边缘分布N(xi,k-1;mi,k-1,Pi,k-1)和存在概率ρi,k-1,预测k-1时刻的目标i在k时刻的边缘分布和存在概率分别为N(xi,k;mi,k|k-1,Pi,k|k-1)和ρi,k|k-1,其中
mi,k|k-1=Fi,k|k-1mi,k-1,Pi,k|k-1=Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T,ρi,k|k-1=pS,k(Δtk)ρi,k-1,Fi,k|k-1为状态转移矩阵,上标T表示矩阵或向量的转置,Δtk=tk-tk-1为k时刻与k-1时刻的时间差,Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵,pS,k(Δtk)为目标的幸存概率,且T为采样周期,δ为给定的常数,i=1,2,…Nk-1。
在步骤S2中,分类步骤、根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻的测量集,确定出测量集中的每个测量是否源于前一时刻已存在的目标,并分别进行归类。
在本实施方式中,所述分类步骤S2具体包括:根据k-1时刻已存在的目标i在k时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及k时刻的测量集合中的第j个测量yj,k,确定测量yj,k是否源于已存在目标,并分别进行归类;
其中,所述确定测量yj,k是否源于已存在目标,并分别进行归类的步骤包括:
子步骤B、若将测量yj,k归入其它测量类;若将测量yj,k归入源于已存在目标的测量,在测量集合中的每个测量处理后,测量集合中yk的测量被分为两类,一类是源于已存在目标的测量,表示为另一类是其它测量,表示为其中M1,k和M2,k分别源于已存在目标测量的数目和其它测量的数目,且M1,k+M2,k=Mk。
在步骤S3中,更新步骤、根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻源于已存在目标的测量,利用贝叶斯规则确定前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率。
在本实施方式中,所述更新步骤S3具体包括:根据前一时刻已存在的各个目标在当前时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及当前时刻源于已存在目标的测量集合利用贝叶斯规则确定当前时刻各个已存在目标的更新边缘分布和存在概率;
其中,所述利用贝叶斯规则确定当前时刻各个已存在目标的更新边缘分布和存在概率的步骤包括:
子步骤C、利用贝叶斯规则对测量处理,得到目标i对应于测量的存在概率均值向量和协方差矩阵其中在所有的M1,k个测量处理后,各个目标对应于各测量的更新边缘分布和存在概率分别为和其中i=1,…,Nk-1,j=1,…,M1,k;
在步骤S4中,裁减与提取步骤、根据前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率,将存在概率小于第一阈值的目标裁减掉,同时提取存在概率大于第二阈值的目标的边缘分布作为当前时刻的输出。
在步骤S5中,生成步骤、利用当前时刻的其它测量和其前两时刻的其它测量产生新目标,并利用最小二乘法估计新目标在当前时刻的状态均值、协方差和边缘分布。
子步骤E、从中取测量从中取测量从中取测量计算得到
其中e=1,…,M2,k-2,f=1,…,M2,k-1,g=1,…,M2,k,||·||2表示向量的2范数,|·|表示取绝对值,(·,·)表示两向量的内积;
子步骤F、判断条件vmin≤vf,e≤vmax、vmin≤vg,f≤vmax、ag,f,e≤amax和cg,f,e≥cmin是否满足,其中vmin、vmax、amax和cmin为4个给定的参数,分别表示最小速度、最大速度、最大加速度和夹角余弦的最小值;若4个条件同时满足,利用测量和测量由最小二乘法得到一个新目标的在k时刻的状态均值协方差和边缘分布其中
σw为测量噪声的标准差;同时,指定新目标的存在概率取为新目标在k-1时刻的
状态估计为其中新目标在k-2时刻的状态估计为其中
在步骤S6中,补充步骤、提取新目标在当前时刻的边缘分布对当前时刻的输出进行补充,并提取新目标在前两个时刻的状态估计分别对前两个时刻的输出进行补充。
在步骤S7中,合并步骤、将在所述裁减与提取步骤中裁减后余下目标的边缘分布和存在概率,分别与在所述生成步骤中生成的新目标在当前时刻的边缘分布和存在概率进行合并,形成当前时刻各个目标的边缘分布和存在概率,并作为下一次递归的输入。
本发明提供的一种适用于杂波环境的多目标跟踪方法,通过预测、分类、更新、裁减与提取、生成、补充、合并这些步骤,利用最小二乘法估计新目标在其出现后的最初3个时间步的状态估计,有效地解决了现有方法在新目标出现后的前几个时间步不能提供新目标状态估计的问题,具有处理速度快的特点,且其计算量明显小于现有方法,具有很强的实用性。
请参阅图2,所示为本发明一实施方式中适用于杂波环境的多目标跟踪系统10的结构示意图。
在本实施方式中,适用于杂波环境的多目标跟踪系统10,主要包括预测模块11、分类模块12、更新模块13、裁减与提取模块14、生成模块15、补充模块16以及合并模块17。
预测模块11,用于根据前一时刻各个目标的边缘分布和存在概率,以及当前时刻与前一时刻的时间差,预测前一时刻已存在的各个目标在当前时刻的边缘分布和存在概率。
在本实施方式中,所述预测模块11具体用于:
以k-1表示前一时刻,k表示当前时刻,tk-1表示前一时刻的时间,tk表示当前时刻的时间,k-1时刻目标i的边缘分布和存在概率分别表示为N(xi,k-1;mi,k-1,Pi,k-1)和ρi,k-1,其中N表示高斯分布,i=1,2,…Nk-1,xi,k-1为k-1时刻目标i的状态向量,mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差,Nk-1为前一时刻目标的总数;
由k-1时刻目标i的边缘分布N(xi,k-1;mi,k-1,Pi,k-1)和存在概率ρi,k-1,预测k-1时刻的目标i在k时刻的边缘分布和存在概率分别为N(xi,k;mi,k|k-1,Pi,k|k-1)和ρi,k|k-1,其中mi,k|k-1=Fi,k|k-1mi,k-1,Pi,k|k-1=Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T,ρi,k|k-1=pS,k(Δtk)ρi,k-1,Fi,k|k-1为状态转移矩阵,上标T表示矩阵或向量的转置,Δtk=tk-tk-1为k时刻与k-1时刻的时间差,Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵,pS,k(Δtk)为目标的幸存概率,且T为采样周期,δ为给定的常数,i=1,2,…Nk-1。
分类模块12,用于根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻的测量集,确定出测量集中的每个测量是否源于前一时刻已存在的
目标,并分别进行归类。
在本实施方式中,所述分类模块12具体用于:根据k-1时刻已存在的目标i在k时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及k时刻的测量集合中的第j个测量yj,k,确定测量yj,k是否源于已存在目标,并分别进行归类;
其中,所述分类模块12包括:第一子模块和第二子模块。
第二子模块,用于若将测量yj,k归入其它测量类;若将测量yj,k归入源于已存在目标的测量,在测量集合中的每个测量处理后,测量集合中yk的测量被分为两类,一类是源于已存在目标的测量,表示为另一类是其它测量,表示为其中M1,k和M2,k分别源于已存在目标测量的数目和其它测量的数目,且M1,k+M2,k=Mk。
更新模块13,用于根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻源于已存在目标的测量,利用贝叶斯规则确定前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率。
在本实施方式中,所述更新模块13具体用于:根据前一时刻已存在的各个目标在当前时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及当前时刻源于已存在目标的测量集合利用贝叶斯规则确定当前时刻各个已存在目标的更新边缘分布和存在概率;
其中,所述更新模块13包括:第三子模块和第四子模块。
第三子模块,用于利用贝叶斯规则对测量处理,得到目标i对应于测量的存在概率均值向量和协方差矩阵其中在所有的M1,k个测量处理后,各个目标对应于各测量的更新边缘分布和存在概率分别为和其中i=1,…,Nk-1,j=1,…,M1,k。
裁减与提取模块14,用于根据前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率,将存在概率小于第一阈值的目标裁减掉,同时提取存在概率大于第二阈值的目标的边缘分布作为当前时刻的输出。
生成模块15,用于利用当前时刻的其它测量和其前两时刻的其它测量产生新目标,并利用最小二乘法估计新目标在当前时刻的状态均值、协方差和边缘分布。
其中,所述生成模块15包括:第五子模块和第六子模块。
第五子模块,用于从中取测量从中取测量从中取测量计算得到
其中e=1,…,M2,k-2,f=1,…,M2,k-1,g=1,…,M2,k,||·||2表示向量的2范数,|·|表示取绝对值,(·,·)表示两向量的内积。
第六子模块,用于判断条件vmin≤vf,e≤vmax、vmin≤vg,f≤vmax、ag,f,e≤amax和cg,f,e≥cmin是否满足,其中vmin、vmax、amax和cmin为4个给定的参数,分别表示最小速度、最大速度、最大加速度和夹角余弦的最小值;若4个条件同时满足,利用测量和测量由最小二乘法得到一个新目标的在k时刻的状态均值协方差和边缘分布其中
σw为测量噪声的标准差;同时,指定新目标的存在概率取为新目标在k-1时刻的状态估计为其中新目标在k-2时刻的状态估计为其中
补充模块16,用于提取新目标在当前时刻的边缘分布对当前时刻的输出进行补充,并提取新目标在前两个时刻的状态估计分别对前两个时刻的输出进行补充。
合并模块17,用于将在所述裁减与提取步骤中裁减后余下目标的边缘分布和存在概率,
分别与在所述生成步骤中生成的新目标在当前时刻的边缘分布和存在概率进行合并,形成当前时刻各个目标的边缘分布和存在概率,并作为下一次递归的输入。
本发明提供的一种适用于杂波环境的多目标跟踪系统10,通过预测模块11、分类模块12、更新模块13、裁减与提取模块14、生成模块15、补充模块16以及合并模块17这些模块,利用最小二乘法估计新目标在其出现后的最初3个时间步的状态估计,有效地解决了现有方法在新目标出现后的前几个时间步不能提供新目标状态估计的问题,具有处理速度快的特点,且其计算量明显小于现有方法,具有很强的实用性。
以下通过将本发明的适用于杂波环境的多目标跟踪系统10与现有的高斯混合概率假设密度滤波器进行对比来说明本发明的有益效果。
作为本发明的一个实例,考虑二维空间[-1000m,1000m]×[-1000m,1000m]中运动的目标,目标的状态由位置和速度构成,表示为其中x和y分别表示位置分量,和分别表示速度分量,上标T表示向量的转置;过程噪声方差矩阵为其中,Δtk=tk-tk-1为当前时刻与前一时刻的时间差,σv为过程噪声标准差;观测噪声方差矩阵σw为观测噪声的标准差;参数δ取为δ=2.5,最小速度vmin、最大速度vmax、最大加速度amax和夹角余弦的最小值cmin分别取为vmin=30ms-1、vmax=80ms-1、amax=10ms-2和cmin=0.94。
为了产生仿真数据,取幸存概率pS,k=1.0、检测概率pD,k=0.95、杂波密度λc,k=2.5×10-6m-2、过程噪声的标准差σv,=1ms-2、观测噪声的标准差σw=2m和传感器的扫描周期T=1s。一次实验中传感器在50个扫描周期的仿真观测数据如图3所示。
为了处理仿真数据,将本发明与高斯混合概率假设密度滤波器的相关参数设置为pS,k=1.0、pD,k=0.95、λc,k=2.5×10-6m-2、σw=2m、σv=1ms-2、第一阈值为10-3、第二阈值为0.5、高斯混合概率假设密度滤波器新目标的权重为wγ=0.1,新目标的协方差为图4为用现有的高斯混合概率假设密度滤波器与本发明对图3中的数据处理得到的最优亚模式分配(Optimal Subpattern Assignment,OSPA)距离。图5为用现有的高斯混合概率假设密度滤波器与本发明分别进行50次Monte Carlo实验得到的平均OSPA距离。
现有的高斯混合概率假设密度滤波器与本发明的实验结果比较表明,本发明的方法可以获得更为精确和可靠的目标状态估计、其OSPA距离比现有的这种方法得到的OSPA距离要小,特别在多目标出现的最初时刻(t=1s至t=16s),OSPA距离减小更为明显。
表1
表1显示了现有的高斯混合概率假设密度滤波器与本发明在50次实验中得到的一次实验的平均执行时间,结果表明本发明的平均执行时间明显小于现有的高斯混合概率假设密度滤波器。
本发明提供的技术方案,通过预测、分类、更新、裁减与提取、生成、补充、合并这些步骤,利用最小二乘法估计新目标在其出现后的最初3个时间步的状态估计,有效地解决了现有方法在新目标出现后的前几个时间步不能提供新目标状态估计的问题,具有处理速度快的特点,且其计算量明显小于现有方法,具有很强的实用性。
值得注意的是,上述实施例中,所包括的各个单元只是按照功能逻辑进行划分的,但并不局限于上述的划分,只要能够实现相应的功能即可;另外,各功能单元的具体名称也只是为了便于相互区分,并不用于限制本发明的保护范围。
另外,本领域普通技术人员可以理解实现上述各实施例方法中的全部或部分步骤是可以通过程序来指令相关的硬件来完成,相应的程序可以存储于一计算机可读取存储介质中,所述的存储介质,如ROM/RAM、磁盘或光盘等。
以上所述仅为本发明的较佳实施例而已,并不用以限制本发明,凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等,均应包含在本发明的保护范围之内。
Claims (8)
- 一种适用于杂波环境的多目标跟踪方法,其特征在于,所述方法包括:预测步骤、根据前一时刻各个目标的边缘分布和存在概率,以及当前时刻与前一时刻的时间差,预测前一时刻已存在的各个目标在当前时刻的边缘分布和存在概率;其中,以k-1表示前一时刻,k表示当前时刻,tk-1表示前一时刻的时间,tk表示当前时刻的时间,k-1时刻目标i的边缘分布和存在概率分别表示为N(xi,k-1;mi,k-1,Pi,k-1)和ρi,k-1,其中N表示高斯分布,i=1,2,…Nk-1,xi,k-1为k-1时刻目标i的状态向量,mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差,Nk-1为前一时刻目标的总数;由k-1时刻目标i的边缘分布N(xi,k-1;mi,k-1,Pi,k-1)和存在概率ρi,k-1,预测k-1时刻的目标i在k时刻的边缘分布和存在概率分别为N(xi,k;mi,k|k-1,Pi,k|k-1)和ρi,k|k-1,其中mi,k|k-1=Fi,k|k-1mi,k-1,Pi,k|k-1=Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T,ρi,k|k-1=pS,k(Δtk)ρi,k-1,Fi,k|k-1为状态转移矩阵,上标T表示矩阵或向量的转置,Δtk=tk-tk-1为k时刻与k-1时刻的时间差,Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵,pS,k(Δtk)为目标的幸存概率,且T为采样周期,δ为给定的常数,i=1,2,…Nk-1;分类步骤、根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻的测量集,确定出测量集中的每个测量是否源于前一时刻已存在的目标,并分别进行归类;更新步骤、根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻源于已存在目标的测量,利用贝叶斯规则确定前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率;裁减与提取步骤、根据前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率,将存在概率小于第一阈值的目标裁减掉,同时提取存在概率大于第二阈值的目标的边缘分布作为当前时刻的输出;生成步骤、利用当前时刻的其它测量和其前两时刻的其它测量产生新目标,并利用最小二乘法估计新目标在当前时刻的状态均值、协方差和边缘分布;补充步骤、提取新目标在当前时刻的边缘分布对当前时刻的输出进行补充,并提取新目标在前两个时刻的状态估计分别对前两个时刻的输出进行补充;合并步骤、将在所述裁减与提取步骤中裁减后余下目标的边缘分布和存在概率,分别与在所述生成步骤中生成的新目标在当前时刻的边缘分布和存在概率进行合并,形成当前时刻各个目标的边缘分布和存在概率,并作为下一次递归的输入。
- 如权利要求1所述的适用于杂波环境的多目标跟踪方法,其特征在于,所述分类步骤具体包括:根据k-1时刻已存在的目标i在k时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及k时刻的测量集合中的第j个测量yj,k,确定测量yj,k是否源于已存在目标,并分别进行归类;其中,所述确定测量yj,k是否源于已存在目标,并分别进行归类的步骤包括:
- 如权利要求2所述的适用于杂波环境的多目标跟踪方法,其特征在于,所述更新步骤具体包括:根据前一时刻已存在的各个目标在当前时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及当前时刻源于已存在目标的测量集合利用贝叶斯规则确定当前时刻各个已存在目标的更新边缘分布和存在概率;其中,所述利用贝叶斯规则确定当前时刻各个已存在目标的更新边缘分布和存在概率的步骤包括:子步骤C、利用贝叶斯规则对测量处理,得到目标i对应于测量的存在概率均值向量和协方差矩阵其中在所有的M1,k个测量处理后,各个目标对应于各测量的更新边缘分布和存在概率分别为和其中i=1,…,Nk-1,j=1,…,M1,k;
- 如权利要求3所述的适用于杂波环境的多目标跟踪方法,其特征在于,所述生成步骤具体包括:利用k时刻的其它测量k-1时刻的其它测量和k-2时刻的其它测量产生新目标,并利用最小二乘法估计新目标在当前时刻的状态均值、协方差和边缘分布;子步骤E、从中取测量从中取测量从中取测量计算得到 其中e=1,…,M2,k-2,f=1,…,M2,k-1,g=1,…,M2,k,||·||2表示向量的2范数,|·|表示取绝对值,(·,·)表示两向量的内积;
- 一种适用于杂波环境的多目标跟踪系统,其特征在于,所述系统包括:预测模块,用于根据前一时刻各个目标的边缘分布和存在概率,以及当前时刻与前一时刻的时间差,预测前一时刻已存在的各个目标在当前时刻的边缘分布和存在概率;其中,以k-1表示前一时刻,k表示当前时刻,tk-1表示前一时刻的时间,tk表示当前时刻的时间,k-1时刻目标i的边缘分布和存在概率分别表示为N(xi,k-1;mi,k-1,Pi,k-1)和ρi,k-1,其中N表示高斯分布,i=1,2,…Nk-1,xi,k-1为k-1时刻目标i的状态向量,mi,k-1和Pi,k-1分别表示k-1时刻目标i的状态均值和协方差,Nk-1为前一时刻目标的总数;由k-1时刻目标i的边缘分布N(xi,k-1;mi,k-1,Pi,k-1)和存在概率ρi,k-1,预测k-1时刻的目标i在k时刻的边缘分布和存在概率分别为N(xi,k;mi,k|k-1,Pi,k|k-1)和ρi,k|k-1,其中mi,k|k-1=Fi,k|k-1mi,k-1,Pi,k|k-1=Qi,k-1+Fi,k|k-1Pi,k-1(Fi,k|k-1)T,ρi,k|k-1=pS,k(Δtk)ρi,k-1,Fi,k|k-1为状态转移矩阵,上标T表示矩阵或向量的转置,Δtk=tk-tk-1为k时刻与k-1时刻的时间差,Qi,k-1为k-1时刻目标i的过程噪声协方差矩阵,pS,k(Δtk)为目标的幸存概率,且T为采样周期,δ为给定的常数,i=1,2,…Nk-1;分类模块,用于根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻的测量集,确定出测量集中的每个测量是否源于前一时刻已存在的目标,并分别进行归类;更新模块,用于根据前一时刻已存在的各个目标在当前时刻的预测边缘分布和预测存在概率,以及当前时刻源于已存在目标的测量,利用贝叶斯规则确定前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率;裁减与提取模块,用于根据前一时刻已存在的各个目标在当前时刻的更新边缘分布和更新存在概率,将存在概率小于第一阈值的目标裁减掉,同时提取存在概率大于第二阈值的目标的边缘分布作为当前时刻的输出;生成模块,用于利用当前时刻的其它测量和其前两时刻的其它测量产生新目标,并利用最小二乘法估计新目标在当前时刻的状态均值、协方差和边缘分布;补充模块,用于提取新目标在当前时刻的边缘分布对当前时刻的输出进行补充,并提取新目标在前两个时刻的状态估计分别对前两个时刻的输出进行补充;合并模块,用于将在所述裁减与提取步骤中裁减后余下目标的边缘分布和存在概率,分别与在所述生成步骤中生成的新目标在当前时刻的边缘分布和存在概率进行合并,形成当前时刻各个目标的边缘分布和存在概率,并作为下一次递归的输入。
- 如权利要求5所述的适用于杂波环境的多目标跟踪系统,其特征在于,所述分类模块具体用于:根据k-1时刻已存在的目标i在k时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及k时刻的测量集合中的第j个测量yj,k,确定测量yj,k是否源于已存在目标,并分别进行归类;其中,所述分类模块包括:
- 如权利要求6所述的适用于杂波环境的多目标跟踪系统,其特征在于,所述更新模块具体用于:根据前一时刻已存在的各个目标在当前时刻的预测边缘分布N(xi,k;mi,k|k-1,Pi,k|k-1)和预测存在概率ρi,k|k-1,以及当前时刻源于已存在目标的测量集合利用贝叶斯规则确定当前时刻各个已存在目标的更新边缘分布和存在概率;其中,所述更新模块包括:第三子模块,用于利用贝叶斯规则对测量处理,得到目标i对应于测量的存在概率均值向量和协方差矩阵其中在所有的M1,k个测量处理后,各个目标对应于各测量的更新边缘分布和存在概率分别为其中i=1,…,Nk-1,j=1,…,M1,k;
- 如权利要求7所述的适用于杂波环境的多目标跟踪系统,其特征在于,所述生成模块具体用于:利用k时刻的其它测量k-1时刻的其它测量和k-2时刻的其它测量产生新目标,并利用最小二乘法估计新目标在当前时刻的状态均值、协方差和边缘分布;其中,所述生成模块包括:第五子模块,用于从中取测量从中取测量从中取测量计算得到 其中e=1,…,M2,k-2,f=1,…,M2,k-1,g=1,…,M2,k,||·||2表示向量的2范数,|·|表示取绝对值,(·,·)表示两向量的内积;
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