雷达机动目标运动模型与跟踪算法研究
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摘要
目标跟踪问题是一个随着跟踪对象的变化、发展而不断发展、深入研究的问题。通过目标跟踪，实现对目标状态的精确估计，从而为后续的很多信息处理，如目标威胁估计、指挥决策等提供稳定的数据基础。由于新型跟踪目标的出现以及对目标跟踪信息的不断需求，机动目标跟踪越来越成为当前研究热点。论文结合863课题:“空天多源信息×××研究”，主要开展雷达机动目标的运动建模与滤波跟踪算法方面的研究。论文的主要内容包括：
首先介绍了论文的研究背景，并对机动目标跟踪中的两大问题：目标运动模型、跟踪算法的研究现状进行了详细论述，并介绍了本文的研究内容。
以参数“α”和“η”为特征参量，建立了基于α-η参数的强机动目标运动模型。通过详细分析Singer模型和Jerk模型的特征，分析了二者在表征目标运动特征方面的不足。基于此，以参数α和η为参数特征，建立了强机动目标的α-η参数运动模型。通过对α-η参数运动模型的离散化处理，推导出α-η参数运动模型的状态-测量模型，并详细分析了α-η参数运动模型的特征。实验表明该运动模型具有较强的目标机动模式表征能力。
提出了一种基于修正不敏卡尔曼滤波的目标跟踪算法。在UKF算法中，滤波增益的计算主要由两个协方差决定：状态协方差、状态与测量的协方差，当目标作机动时，滤波增益将滞后于目标的机动状态，从而使跟踪误差变大。因而，在跟踪过程中，通过实时估计噪声协方差的修正因子，然后利用修正因子实时修正预测状态协方差，利用修正后的预测协方差更新状态协方差，进而修正滤波增益。采用自适应因子修正后的协方差来计算滤波增益，使得修正后的滤波增益与目标的运动相匹配，从而获得较好的滤波跟踪精度。实验表明该算法具有比UKF更好的跟踪性能。
融合UT变换和EKF各自优点，在提高算法的跟踪性能和较少运算时间方面，提出了两种目标跟踪算法。（1）不敏扩展卡尔曼滤波跟踪算法。UKF在非线性跟踪系统中具有比EKF更好的跟踪性能，但是所需的计算时间大于EKF的计算时间。基于此原因，提出了一种融合不敏变换（UT）和扩展卡尔曼滤波的目标跟踪方法，该方法主要通过把UKF中状态协方差以及状态和测量值的互协方差的多项矢量相乘转换成多个相加的计算，从而有效减少算法的运算时间。该算法融合UT变换的多样性Sigma粒子的特点以及EKF的运算时间快的特点，既保留了较好的滤波跟踪精度，又具有较少的运算时间。（2）自适应不敏扩展卡尔曼滤波跟踪算法。在不敏扩展卡尔曼滤波过程中，利用残差信息，采用指数衰减和遗忘因子的方式实时估计和修正两个噪声协方差，实现噪声协方差的自适应估计。实验表明这两种算法具有比UKF较好的跟踪精度，又具有较少的运算时间。
在提高模型概率估计准确性方面，提出了一种基于模型概率修正的交互多模型算法。交互多模算法在计算滤波后的状态信息时，加权因子（即模型概率）的计算主要利用两类信息：新息和模型概率预测值，该方法没有利用当前时刻状态协方差的有效信息，造成对模型概率估计的不准确。基于这个特性，把状态协方差的信息融合得到另一个加权因子，利用该加权因子修正IMM算法中的模型概率估计值，即：加权因子的模型概率修正。该算法既利用了预测模型概率因子，又利用了当前状态方差加权因子，因而，具有较为准确的模型选择概率估计。通过实验验证了该算法具有比IMM较准确的模型概率估计能力。
最后对论文的工作进行了总结，并指出论文的不足和今后的研究方向。
With the change and development of tracking target, the study of target tracking iscontinuously and deeply developed. Through target tracking, accurate estimation oftarget state is gotten, and then a large amount of subsequent information processing canbe realized, such as target threat estimation, command decisions, and so on, which arebased on stable tracking data of the target. For the emergence of new tracking targetsand the increasing information requirement of target tracking, maneuvering targettracking is more and more becoming the current research hotspot. Combined with the863project:“the research of xxx aerospace multi-source information”, this dissertationmainly studies the motion model and tracking algorithms of radar maneuvering target.The main contents of the dissertation include:
Firstly, research background of this dissertation is introduced, then two keyproblems in maneuvering target tracking are discussed detailly, which include targetmotion model and tracking algorithms, and the research contents of this dissertation areintroduced.
The motion model of strong maneuvering target is studied, which is based on “α”and “η” parameters. Based on detail analysis of Singer model and Jerk model, someshortages of Singer model and Jerk model in the characterization of target motioncharacteristics are pointed out. Based on this, α-η parameter motion model of strongmaneuvering target is built, which is using maneuvering frequency α and jerkingfrequency η as parameter characteristics. Through discretization processing for α-ηparameter motion model, the state-measurement model of α-η parameter motion modelis deduced, and the characteristics of α-η parameter motion model are analyzed in detail.The experimental results show that the proposed motion model is effective for the targetmaneuvering model representation.
A kind of target tracking algorithm based on improvedly unscented kalmanfilter(MUKF) is proposed. In the UKF algorithm, filtering gain calculation is mainlydecided by two variances: state covariance and measurement covariance, filter gain willlag behind the target maneuvering state when the target maneuvers, so that the trackingerror is bigger. Therefore, in the process of tracking, the scale factor of state noisecovariance is estimated in every tracking step of UKF, which is used to modify theforecast state covariance, the state covariance is updated by forecast state covariance,then filter gain is modified. The filter gain is got by modified state covariance using adaptive scale factor, which causes the filter gain matches maneuvering state of thetarget, then the better tracking accuracy is got. The experimental results show that thetracking performance of the proposed method is more accurary than that of UKF.
Based on the advantage of unscented transform(UT) and extended kalmanfilter(EKF), two algorithms of target tracking are proposed, which aims to improvetracking performance and decrease operation time of algorithm.(1) A new targettracking algorithm based on unscented extended kalman filter(UEKF) is studied. Innonlinear tracking system, UKF has better tracking performance than EKF, but thecomputational time of UKF is greater than that of the EKF. For these reasons, a newmethod for tracking maneuvering target is put forward, which is to combine the UT withthe EKF. The key idea is to transform multi-vector multiplying into the addition ofmulti-vector, which causes the operation time of new algorithm is much less than that ofthe UKF. The UEKF is to combine the diversity of sigma particle with the lessoperation time of EKF, which causes that not only the better tracking presion but alsothe less operation time is kept.(2) An adaptivly unscented extended Kalmanfilter(AUEKF) algorithm is studied. In course of UEKF, the two covariances of noisebased on the exponential attenuation and forgetting factor are estimated, which is basedon the residual information of filter, so the covariance of noise is adaptively estimated.The experimental results show that the tracking presion of the two kinds of algorithmsis better than that of UKF, but also has less operation time.
Based on modified model probability, a kind of interacting multiple modelalgorithm is brought forward, which aims to improve model probability estimationaccuracy. In calculating course of the interacting multiple model algorithm, the sateweighting factor(or model probability) is calculated by covariance of residualinformation and predicted value of model probability, but information of current statecovariance isn’t effectivly used in IMM algorithm, which causes that the modelprobability estimation isn’t accurate. For these reasons, the new scale factor based onthe current state covariance is studied, then the state weighting factor is modified by thenew scale factor. Both the predicted model probability factor and the scale factor of thecurrent state covariance are used, as a result, the relatively precise model probabilityestimation is got. The experimental results show that the model probability estimationof the proposed method is more accurate than that of IMM.
At last, this paper’s work is concluded, and the shortage of paper is pointed out,research directions in the future are discussed.
首先介绍了论文的研究背景，并对机动目标跟踪中的两大问题：目标运动模型、跟踪算法的研究现状进行了详细论述，并介绍了本文的研究内容。
以参数“α”和“η”为特征参量，建立了基于α-η参数的强机动目标运动模型。通过详细分析Singer模型和Jerk模型的特征，分析了二者在表征目标运动特征方面的不足。基于此，以参数α和η为参数特征，建立了强机动目标的α-η参数运动模型。通过对α-η参数运动模型的离散化处理，推导出α-η参数运动模型的状态-测量模型，并详细分析了α-η参数运动模型的特征。实验表明该运动模型具有较强的目标机动模式表征能力。
提出了一种基于修正不敏卡尔曼滤波的目标跟踪算法。在UKF算法中，滤波增益的计算主要由两个协方差决定：状态协方差、状态与测量的协方差，当目标作机动时，滤波增益将滞后于目标的机动状态，从而使跟踪误差变大。因而，在跟踪过程中，通过实时估计噪声协方差的修正因子，然后利用修正因子实时修正预测状态协方差，利用修正后的预测协方差更新状态协方差，进而修正滤波增益。采用自适应因子修正后的协方差来计算滤波增益，使得修正后的滤波增益与目标的运动相匹配，从而获得较好的滤波跟踪精度。实验表明该算法具有比UKF更好的跟踪性能。
融合UT变换和EKF各自优点，在提高算法的跟踪性能和较少运算时间方面，提出了两种目标跟踪算法。（1）不敏扩展卡尔曼滤波跟踪算法。UKF在非线性跟踪系统中具有比EKF更好的跟踪性能，但是所需的计算时间大于EKF的计算时间。基于此原因，提出了一种融合不敏变换（UT）和扩展卡尔曼滤波的目标跟踪方法，该方法主要通过把UKF中状态协方差以及状态和测量值的互协方差的多项矢量相乘转换成多个相加的计算，从而有效减少算法的运算时间。该算法融合UT变换的多样性Sigma粒子的特点以及EKF的运算时间快的特点，既保留了较好的滤波跟踪精度，又具有较少的运算时间。（2）自适应不敏扩展卡尔曼滤波跟踪算法。在不敏扩展卡尔曼滤波过程中，利用残差信息，采用指数衰减和遗忘因子的方式实时估计和修正两个噪声协方差，实现噪声协方差的自适应估计。实验表明这两种算法具有比UKF较好的跟踪精度，又具有较少的运算时间。
在提高模型概率估计准确性方面，提出了一种基于模型概率修正的交互多模型算法。交互多模算法在计算滤波后的状态信息时，加权因子（即模型概率）的计算主要利用两类信息：新息和模型概率预测值，该方法没有利用当前时刻状态协方差的有效信息，造成对模型概率估计的不准确。基于这个特性，把状态协方差的信息融合得到另一个加权因子，利用该加权因子修正IMM算法中的模型概率估计值，即：加权因子的模型概率修正。该算法既利用了预测模型概率因子，又利用了当前状态方差加权因子，因而，具有较为准确的模型选择概率估计。通过实验验证了该算法具有比IMM较准确的模型概率估计能力。
最后对论文的工作进行了总结，并指出论文的不足和今后的研究方向。
With the change and development of tracking target, the study of target tracking iscontinuously and deeply developed. Through target tracking, accurate estimation oftarget state is gotten, and then a large amount of subsequent information processing canbe realized, such as target threat estimation, command decisions, and so on, which arebased on stable tracking data of the target. For the emergence of new tracking targetsand the increasing information requirement of target tracking, maneuvering targettracking is more and more becoming the current research hotspot. Combined with the863project:“the research of xxx aerospace multi-source information”, this dissertationmainly studies the motion model and tracking algorithms of radar maneuvering target.The main contents of the dissertation include:
Firstly, research background of this dissertation is introduced, then two keyproblems in maneuvering target tracking are discussed detailly, which include targetmotion model and tracking algorithms, and the research contents of this dissertation areintroduced.
The motion model of strong maneuvering target is studied, which is based on “α”and “η” parameters. Based on detail analysis of Singer model and Jerk model, someshortages of Singer model and Jerk model in the characterization of target motioncharacteristics are pointed out. Based on this, α-η parameter motion model of strongmaneuvering target is built, which is using maneuvering frequency α and jerkingfrequency η as parameter characteristics. Through discretization processing for α-ηparameter motion model, the state-measurement model of α-η parameter motion modelis deduced, and the characteristics of α-η parameter motion model are analyzed in detail.The experimental results show that the proposed motion model is effective for the targetmaneuvering model representation.
A kind of target tracking algorithm based on improvedly unscented kalmanfilter(MUKF) is proposed. In the UKF algorithm, filtering gain calculation is mainlydecided by two variances: state covariance and measurement covariance, filter gain willlag behind the target maneuvering state when the target maneuvers, so that the trackingerror is bigger. Therefore, in the process of tracking, the scale factor of state noisecovariance is estimated in every tracking step of UKF, which is used to modify theforecast state covariance, the state covariance is updated by forecast state covariance,then filter gain is modified. The filter gain is got by modified state covariance using adaptive scale factor, which causes the filter gain matches maneuvering state of thetarget, then the better tracking accuracy is got. The experimental results show that thetracking performance of the proposed method is more accurary than that of UKF.
Based on the advantage of unscented transform(UT) and extended kalmanfilter(EKF), two algorithms of target tracking are proposed, which aims to improvetracking performance and decrease operation time of algorithm.(1) A new targettracking algorithm based on unscented extended kalman filter(UEKF) is studied. Innonlinear tracking system, UKF has better tracking performance than EKF, but thecomputational time of UKF is greater than that of the EKF. For these reasons, a newmethod for tracking maneuvering target is put forward, which is to combine the UT withthe EKF. The key idea is to transform multi-vector multiplying into the addition ofmulti-vector, which causes the operation time of new algorithm is much less than that ofthe UKF. The UEKF is to combine the diversity of sigma particle with the lessoperation time of EKF, which causes that not only the better tracking presion but alsothe less operation time is kept.(2) An adaptivly unscented extended Kalmanfilter(AUEKF) algorithm is studied. In course of UEKF, the two covariances of noisebased on the exponential attenuation and forgetting factor are estimated, which is basedon the residual information of filter, so the covariance of noise is adaptively estimated.The experimental results show that the tracking presion of the two kinds of algorithmsis better than that of UKF, but also has less operation time.
Based on modified model probability, a kind of interacting multiple modelalgorithm is brought forward, which aims to improve model probability estimationaccuracy. In calculating course of the interacting multiple model algorithm, the sateweighting factor(or model probability) is calculated by covariance of residualinformation and predicted value of model probability, but information of current statecovariance isn’t effectivly used in IMM algorithm, which causes that the modelprobability estimation isn’t accurate. For these reasons, the new scale factor based onthe current state covariance is studied, then the state weighting factor is modified by thenew scale factor. Both the predicted model probability factor and the scale factor of thecurrent state covariance are used, as a result, the relatively precise model probabilityestimation is got. The experimental results show that the model probability estimationof the proposed method is more accurate than that of IMM.
At last, this paper’s work is concluded, and the shortage of paper is pointed out,research directions in the future are discussed.
引文
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