技术领域technical field
本发明涉及雷达技术领域，尤其涉及一种基于粒子平滑的快速TBD检测方法，适用于微弱目标的检测与跟踪。The invention relates to the field of radar technology, in particular to a fast TBD detection method based on particle smoothing, which is suitable for detection and tracking of weak targets.
背景技术Background technique
目标检测是各种信号处理应用领域面临的共同问题。复杂环境下的机动微弱目标检测是现代雷达面临的严峻挑战之一。如近年出现的无人机、掠海飞行导弹、隐身飞行器等现代武器，采用常规的目标检测方法往往难以有效探测。这些目标的雷达散射截面(RCS)小，目标反射回波的能量非常少，且常常淹没于强杂波或噪声之中，以致雷达的探测能力严重下降。Object detection is a common problem faced by various signal processing application domains. The detection of maneuvering faint targets in complex environments is one of the severe challenges faced by modern radars. For example, modern weapons such as unmanned aerial vehicles, sea-skimming missiles, and stealth aircraft that have appeared in recent years are often difficult to effectively detect using conventional target detection methods. The radar cross-section (RCS) of these targets is small, and the energy reflected by the target is very small, and is often submerged in strong clutter or noise, so that the detection ability of the radar is seriously reduced.
低信噪比情况下如果采用传统的DBT(Detect-Before-Track)方法，可能会丢失目标信息。TBD(Track-Before-Detect)这种同时进行检测与跟踪的方法，能有效克服DBT方法的缺点，提高目标检测概率。If the traditional DBT (Detect-Before-Track) method is used in the case of low SNR, the target information may be lost. TBD (Track-Before-Detect), a method of simultaneous detection and tracking, can effectively overcome the shortcomings of the DBT method and improve the target detection probability.
实现TBD的方法有Hough变换法、动态规划算法及粒子滤波等。Hough变换法只适用于目标航迹为直线的情况，而且它将目标状态空间离散化，跟踪精度不高。动态规划算法虽然克服了速度失配的问题，但它需要同时存储和处理多帧数据，消耗巨大的计算资源，检测性能也会随着回波SNR的降低而迅速下降。粒子滤波算法(PF)是贝叶斯框架下的一种次优算法，它利用大量带有权值的随机样本近似目标状态的后验概率密度函数。此类算法适合处理非线性非高斯动态系统下的状态估计和跟踪问题，是实现低信噪比目标长时间积累检测的有效方法。但是基于贝叶斯滤波模型的粒子滤波算法也仅仅利用了初始时刻到测量时刻的观测信息，没有对后续时刻的观测信息加以利用。The methods to realize TBD include Hough transform method, dynamic programming algorithm and particle filter. The Hough transform method is only suitable for the case where the target track is a straight line, and it discretizes the target state space, and the tracking accuracy is not high. Although the dynamic programming algorithm overcomes the problem of speed mismatch, it needs to store and process multiple frames of data at the same time, consumes huge computing resources, and the detection performance will drop rapidly with the decrease of echo SNR. Particle Filter (PF) is a suboptimal algorithm under the Bayesian framework, which uses a large number of random samples with weights to approximate the posterior probability density function of the target state. This kind of algorithm is suitable for dealing with state estimation and tracking problems in nonlinear non-Gaussian dynamic systems, and is an effective method to realize long-term accumulation detection of low signal-to-noise ratio targets. However, the particle filter algorithm based on the Bayesian filter model only uses the observation information from the initial time to the measurement time, and does not use the observation information at the subsequent time.
发明内容Contents of the invention
针对上述问题，本发明的目的在于提供一种基于粒子平滑PS(ParticleSmoothing)的快速TBD检测方法(称为PS-TBD)，以充分利用传感器的观测信息，提高目标状态估计的精度。In view of the above problems, the object of the present invention is to provide a fast TBD detection method (called PS-TBD) based on particle smoothing PS (ParticleSmoothing), so as to make full use of the observation information of the sensor and improve the accuracy of target state estimation.
本发明的技术思路是运用后续时刻的观测信息对当前时刻目标状态的后验概率进行修正，建立了以过去和将来所有时刻的观测信息为条件的平滑概率，有效提高了目标状态估计的精度。此外，考虑到工程应用中对计算量的要求，本文对PS-TBD算法做了改进，在粒子平滑权值的计算过程中运用一步平滑思想，并用各个粒子状态间的欧式距离来代替粒子状态的转移概率，大大缩短了平滑时间。计算机仿真结果表明，改进的PS-TBD算法能够在短时间内有效地提高目标状态估计的精度。The technical idea of the present invention is to use the observation information of the subsequent time to correct the posterior probability of the target state at the current time, establish a smooth probability conditional on the observation information of all past and future moments, and effectively improve the accuracy of the target state estimation. In addition, considering the requirements of calculation in engineering applications, this paper improves the PS-TBD algorithm, uses the idea of one-step smoothing in the calculation process of particle smoothing weights, and replaces the particle state with the Euclidean distance between each particle state. Transition probabilities, greatly reducing smoothing time. The computer simulation results show that the improved PS-TBD algorithm can effectively improve the accuracy of target state estimation in a short time.
为达到上述目的，本发明的实施例采用如下技术方案予以实现。In order to achieve the above purpose, the embodiments of the present invention adopt the following technical solutions to achieve.
一种基于粒子平滑的快速TBD检测方法，所述方法包括：A fast TBD detection method based on particle smoothing, said method comprising:
步骤1，设定雷达目标的运动模型；Step 1, setting the motion model of the radar target;
步骤2，设定雷达目标的观测模型；Step 2, setting the observation model of the radar target;
步骤3，设定雷达目标运动过程中的观测周期，设定所述观测周期内的任一时刻为当前时刻；获取雷达目标运动过程中截止到当前时刻的所有历史观测数据；Step 3, setting the observation period during the movement of the radar target, setting any moment in the observation period as the current moment; obtaining all historical observation data up to the current moment during the movement of the radar target;
步骤4，根据所述截止到当前时刻的所有历史观测数据、所述运动模型以及所述观测模型，采用基于粒子滤波的TBD计算雷达目标运动状态的后验概率；Step 4, according to all the historical observation data up to the current moment, the motion model and the observation model, using particle filter-based TBD to calculate the posterior probability of the motion state of the radar target;
步骤5，获取雷达目标运动过程中从当前时刻到整个观测周期最后时刻的所有观测数据，根据从当前时刻到整个观测周期最后时刻的所有观测数据对所述后验概率进行修正，得到平滑概率；Step 5, obtaining all observation data from the current moment to the last moment of the entire observation period during the movement of the radar target, and correcting the posterior probability according to all observation data from the current moment to the last moment of the entire observation period to obtain a smoothed probability;
步骤6，将所述平滑概率作为雷达目标运动状态的后验概率，并根据所述后验概率，对雷达目标进行检测和跟踪。In step 6, the smoothed probability is used as the posterior probability of the motion state of the radar target, and the radar target is detected and tracked according to the posterior probability.
本发明技术方案由于充分利用下一时刻的观测信息对当前时刻目标状态的后验概率进行修正，运用一步平滑思想，建立了以过去和将来时刻的观测信息为条件的平滑概率，并用各个粒子状态间的欧式距离来代替粒子状态的转移概率，所以有效提高了目标状态估计的精度，大大缩短了平滑时间。The technical scheme of the present invention makes full use of the observation information at the next moment to correct the posterior probability of the target state at the current moment, and uses the idea of one-step smoothing to establish a smooth probability conditional on the observation information of the past and future moments, and uses the state of each particle The Euclidean distance between particles is used to replace the transition probability of the particle state, so the accuracy of the target state estimation is effectively improved, and the smoothing time is greatly shortened.
附图说明Description of drawings
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.
图1为本发明实施例提供的基于粒子平滑的快速TBD检测方法的流程示意图；FIG. 1 is a schematic flow diagram of a fast TBD detection method based on particle smoothing provided by an embodiment of the present invention;
图2是PF-TBD算法的实现流程示意图；Figure 2 is a schematic diagram of the implementation flow of the PF-TBD algorithm;
图3是PS-TBD算法的实现流程示意图；Fig. 3 is the realization flow schematic diagram of PS-TBD algorithm;
图4是改进后的PS-TBD算法的实现流程示意图；Fig. 4 is a schematic diagram of the implementation flow of the improved PS-TBD algorithm;
图5是几帧中(2，8，20，29)模态的粒子在空间的分布的情况示意图；Figure 5 is the (2, 8, 20, 29) mode in several frames Schematic diagram of the distribution of particles in space;
图6是500次Monte Carlo仿真中PF-TBD算法认为目标存在的概率情况示意图；Figure 6 is a schematic diagram of the probability that the PF-TBD algorithm believes that the target exists in 500 Monte Carlo simulations;
图7是100次Monte Carlo仿真后三种算法跟踪精度比较示意图，跟踪精度以目标位置的均方根误差(RMSE)来衡量；Figure 7 is a schematic diagram of the tracking accuracy comparison of the three algorithms after 100 Monte Carlo simulations. The tracking accuracy is measured by the root mean square error (RMSE) of the target position;
图8是PS-TBD算法和改进的PS-TBD算法的计算时间随粒子数变化的情况示意图。Fig. 8 is a schematic diagram of the calculation time of the PS-TBD algorithm and the improved PS-TBD algorithm changing with the number of particles.
具体实施方式detailed description
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.
本发明实施例提供一种基于粒子平滑的快速TBD检测方法，如图1所示，所述方法包括：An embodiment of the present invention provides a fast TBD detection method based on particle smoothing, as shown in FIG. 1 , the method includes:
步骤1，设定雷达目标的运动模型。Step 1, set the motion model of the radar target.
设雷达目标在xy平面上作匀速运动，则雷达目标的运动模型方程：Assuming that the radar target moves at a uniform speed on the xy plane, the motion model equation of the radar target is:
xt+1＝f(xt，rt)+utxt+1 = f(xt , rt )+ut
式中t表示离散时间下标，xt表示t时刻的状态向量，定义为：where t represents the discrete time subscript, xt represents the state vector at time t, defined as:
上标T表示矩阵的转置，(xt，yt)和分别表示t时刻目标的位置和速度。rt∈{0，1}为模态变量，rt＝0表示没有目标，rt＝1存在目标。针对不同的rt，f(xt，rt)的定义如下：The superscript T denotes the transpose of the matrix, (xt , yt ) and represent the position and velocity of the target at time t, respectively. rt ∈ {0, 1} is a modal variable, rt =0 means there is no target, rt =1 there is a target. For different rt , the definition of f(xt , rt ) is as follows:
F为状态转移矩阵。过程噪声ut～N(u；0，Q)，N(·)表示高斯分布，Q为噪声协方差阵。F is the state transition matrix. The process noise ut ～N(u; 0, Q), N(·) represents the Gaussian distribution, and Q is the noise covariance matrix.
其中，T0表示传感器的采样周期，q1表示过程噪声的强度。Among them,T0 represents the sampling period of the sensor, andq1 represents the intensity of the process noise.
模态的转移概率可由一个马尔可夫链表示：The transition probability of a mode can be represented by a Markov chain:
其中，Pb表示目标出现的概率，Pd表示目标消失的概率。该马尔可夫模型的状态转移矩阵可以表示为：Among them, Pb represents the probability of the target appearing, and Pd represents the probability of the target disappearing. The state transition matrix of the Markov model can be expressed as:
步骤2，设定雷达目标的观测模型。Step 2, setting the observation model of the radar target.
传感器对R-θ平面某区域进行检测，产生一系列回波数据。将每帧数据划分成n×m个分辨单元，每个单元的大小为ΔR×Δθ，ΔR和Δθ分别表示距离和角度分辨率。假设匹配滤波器输出为sinc(·)函数，则第(i，j)个分辨单元在t时刻接收信号的强度可以表示为：The sensor detects a certain area on the R-θ plane and generates a series of echo data. Divide each frame of data into n×m resolution units, and the size of each unit is ΔR×Δθ, where ΔR and Δθ represent distance and angle resolution, respectively. Assuming that the output of the matched filter is a sinc(·) function, the strength of the signal received by the (i, j)th resolution unit at time t can be expressed as:
表示t时刻目标在第(i，j)个分辨单元贡献的信号强度；表示t时刻第(i，j)个分辨单元的观测噪声强度。为了简化计算，本文中假设A表示回波信号的幅度，回波信噪比SNR＝A2/σ2。Ri＝i·ΔR表示第i个距离分辨单元的距离，θj＝j·Δθ表示第j个角度分辨单元的角度。Rt和θt定义如下： Indicates the signal strength contributed by the target at the (i, j)th resolution unit at time t; Indicates the observation noise intensity of the (i, j)th resolution unit at time t. In order to simplify the calculation, it is assumed in this paper A represents the amplitude of the echo signal, and the echo signal-to-noise ratio SNR=A2 /σ2 . Ri =i·ΔR represents the distance of the i-th distance resolution unit, and θj =j·Δθ represents the angle of the j-th angle resolution unit. Rt and θt are defined as follows:
(xt，yt)表示t时刻目标的位置。(xt , yt ) represents the position of the target at time t.
这样就得到了t时刻(n×m)维的观测信息矩阵zt：In this way, the (n×m)-dimensional observation information matrix zt at time t is obtained:
以及截止到t时刻所有的观测信息Z1∶t＝{zi：i＝1，...，t}。And all observation information Z 1 :t ={zi : i=1, . . . , t} up to time t.
步骤3，设定雷达目标运动过程中的观测周期，设定所述观测周期内的任一时刻为当前时刻；获取雷达目标运动过程中截止到当前时刻的所有历史观测数据。Step 3, setting the observation period during the movement of the radar target, and setting any moment in the observation period as the current moment; obtaining all historical observation data up to the current moment during the movement of the radar target.
当前时刻t，(n×m)维的观测信息矩阵zt为：At the current moment t, the (n×m)-dimensional observation information matrix zt is:
截止到当前时刻t，所有的历史观测数据Z1∶t为：Z1∶t＝{zi：i＝1，...，t}。As of the current moment t, all historical observation data Z 1:t is: Z 1:t = {zi : i=1, . . . , t}.
步骤4，根据所述截止到当前时刻的所有历史观测数据、所述运动模型以及所述观测模型，采用基于粒子滤波的TBD计算雷达目标运动状态的后验概率。Step 4, according to all the historical observation data up to the current moment, the motion model and the observation model, the posterior probability of the motion state of the radar target is calculated by using TBD based on particle filter.
(4a)预测：在获得截止到t-1时刻所有历史观测信息Z1∶t-1的条件下，计算在t时刻目标存在且状态为xt的概率，即计算先验概率p(xt，rt＝1|Z1∶t-1)：(4a) Prediction: Under the condition of obtaining all historical observation information Z1 :t-1 up to time t-1, calculate the probability that the target exists and the state is xt at time t, that is, calculate the prior probability p(xt , rt =1|Z 1:t-1 ):
p(xt，rt＝1|Z1∶t-1)＝∫p(xt，rt＝1|xt-1，rt-1＝1)·p(xt-1，rt-1＝1|Z1∶t-1)dxt-1+∫p(xt，rt＝1|xt-1，rt-1＝0)·p(xt-1，rt-1＝0|Z1∶t-1)dxt-1p(xt , rt =1|Z 1:t-1 )=∫p(xt , rt =1|xt-1 , rt-1 =1) p(xt-1 , rt-1 ＝1|Z 1: t-1 )dxt-1 +∫p(xt , rt ＝1|xt-1 , rt-1 ＝0)·p(xt-1 , rt-1 ＝0|Z 1: t-1 )dxt-1
(4b)更新：在获得截止到t时刻所有历史观测信息Z1∶t后，计算在t时刻目标存在且状态为xt的概率，即计算后验概率p(xt，rt＝1|Z1∶t)：(4b) Update: After obtaining all historical observation information Z1 :t up to time t, calculate the probability that the target exists and the state is xt at time t, that is, calculate the posterior probability p(xt , rt =1| Z 1:t ):
通过PF算法来完成后验概率p(xt，rt＝1|Z1∶t)的近似计算：The approximate calculation of the posterior probability p(xt , rt =1|Z 1:t ) is completed by the PF algorithm:
其中为归一化重要性权值，δ(·)为狄拉克函数。in is the normalized importance weight, and δ(·) is the Dirac function.
在得到p(xt，rt＝1|Z1∶t)后，可得到目标存在的概率p(rt＝1|Z1∶t)：After obtaining p(xt , rt =1|Z 1:t ), the probability p(rt =1|Z 1:t ) of target existence can be obtained:
p(rt＝1|Z1∶t)＝∫p(xt，rt＝1|Z1∶t)dxtp(rt =1|Z 1:t )=∫p (xt , rt =1|Z 1:t )dxt
常见的检测形式可表示为：当p(rt＝1|Z1∶t)≥VT时，判定为H1，否则当p(rt＝1|Z1∶t)≤VT，判定为H0The common detection form can be expressed as: when p(rt =1|Z 1:t )≥VT , judge as H1 , otherwise when p(rt =1|Z1∶t )≤VT , judge for H0
其中VT为检测阈值，通常设定为固定值。H1表示有目标的情况，H0表示没有目标。Among them, VT is the detection threshold, which is usually set as a fixed value. H1 means there is a target, and H0 means there is no target.
参照图2，PF-TBD算法的具体实现步骤如下：Referring to Figure 2, the specific implementation steps of the PF-TBD algorithm are as follows:
(1)初始化：根据先验信息，建立初始状态样本初始化t＝1，其中为0时刻相关权值为的粒子集合；(1) Initialization: According to the prior information, the initial state sample is established Initialize t=1, where When it is 0, the relevant weight is collection of particles;
(2)模态变化：各个时刻各个粒子的模态根据转移矩阵Π来变化；(2) Mode change: the mode of each particle at each moment changes according to the transfer matrix Π;
(3)如果则即将状态值根据观测信息来初始化(此时该粒子认为目标刚出现)：粒子的位置(xt，yt)服从监视区域内的均匀分布，对于目标在x方向上的速度有其中vmax为目标的最大速度(同理y方向相同)；(3) if but That is, the state value is initialized according to the observation information (at this time, the particle thinks that the target has just appeared): the position (xt , yt ) of the particle obeys the uniform distribution in the monitoring area, and for the speed of the target in the x direction Have Where vmax is the maximum speed of the target (similarly the y direction is the same);
如果则状态值根据目标运动模型变化(该粒子认为目标持续存在)：if but The state value changes according to the target motion model (the particle thinks the target persists):
(4)计算权值：(4) Calculate the weight:
是目标强度有贡献的区域。 is the region where the target intensity contributes.
(5)重复(3)-(4)直到每个粒子都运算完毕(5) Repeat (3)-(4) until each particle is calculated
(6)归一化滤波权值：(6) Normalized filtering weights:
(7)重采样(重采样后)；(7) Resampling (after resampling );
(8)通过判断是否有目标存在；(8) pass Determine whether there is a target;
(9)通过得出后验概率密度p(xt，rt＝1|Z1∶t)，在H1的条件下，由MMSE准则得出t时刻目标状态估计：(9) pass The posterior probability density p(xt , rt ＝1|Z1∶t ) is obtained. Under the condition of H1 , the target state estimation at time t is obtained by the MMSE criterion:
(10)t＝t+1；(10)t=t+1;
(11)重复(2)-(10)直到t＞T，T为观测的总时间。(11) Repeat (2)-(10) until t>T, where T is the total observation time.
步骤5，获取雷达目标运动过程中从当前时刻到整个观测周期最后时刻的所有观测数据，根据从当前时刻到整个观测周期最后时刻的所有观测数据对所述后验概率进行修正，得到平滑概率。Step 5: Obtain all observation data from the current moment to the last moment of the entire observation period during the movement of the radar target, and correct the posterior probability according to all observation data from the current moment to the last moment of the entire observation period to obtain a smoothed probability.
运用贝叶斯平滑理论，提出了PS-TBD算法，并根据下一时刻目标的观测数据，在粒子平滑权值的计算过程中运用一步平滑思想，对所述后验概率进行修正；再利用各个粒子状态间的欧式距离来代替它们之间的状态转移概率，进而快速获取一步平滑概率。Using Bayesian smoothing theory, the PS-TBD algorithm is proposed, and according to the observation data of the target at the next moment, the one-step smoothing idea is used in the calculation process of particle smoothing weights to correct the posterior probability; The Euclidean distance between particle states is used to replace the state transition probability between them, so as to quickly obtain one-step smoothing probability.
步骤5具体为：Step 5 is specifically:
(5a)获取截止到时刻T的所有观测数据Z1∶T：Z1∶T＝{zi：i＝1，...，T}，T为观测的总时间；(5a) Obtain all observation data Z1 : T up to time T: Z 1 :T ={zi :i=1,...,T}, T is the total time of observation;
(5b)根据所述截止到时刻T的所有观测数据Z1∶T对所述后验概率进行修正，得到平滑概率p(xt，rt＝1|Z1∶T)为：(5b)Correct the posterior probability according to all the observation data Z 1:T up to the time T, and obtain the smooth probability p(xt , rt =1|Z 1:T ) as:
(5c)通过基于粒子滤波算法的TBD计算平滑概率表示粒子平滑权值。(5c) Calculation of smoothing probability by TBD based on particle filter algorithm Indicates particle smoothing weights.
基于步骤4，使用贝叶斯平滑的理论，不仅保留了PF-TBD算法的优点，还利用了后续时刻的观测信息来修正后验概率p(xt，rt＝1|Z1∶t)，得到平滑概率p(xt，rt＝1|Z1∶T)，使目标的状态估计更为精确。Based on step 4, using Bayesian smoothing theory not only retains the advantages of the PF-TBD algorithm, but also uses the observation information at subsequent moments to correct the posterior probability p(xt , rt =1|Z1∶t ) , to obtain the smooth probability p(xt , rt =1|Z 1:T ), which makes the state estimation of the target more accurate.
通过PF算法来完成平滑概率p(xt，rt＝1|Z1∶T)的近似计算：The approximate calculation of the smoothing probability p(xt , rt =1|Z 1:T ) is completed by the PF algorithm:
参照图3，PS-TBD算法的具体实现步骤如下：Referring to Figure 3, the specific implementation steps of the PS-TBD algorithm are as follows:
(1)首先进行PF-TBD(步骤4)：得到(1) First perform PF-TBD (step 4): get
(2)初始化：对n＝1，2，...N，设置T时刻粒子权值(2) Initialization: For n=1, 2, ... N, set the particle weight at time T
(3)如果则(3) if but
(上式中权值是利用t时刻和t+1时刻认为目标持续存在的粒子计算的，M表示这些粒子的个数)；(The weight in the above formula is calculated by using the particles that the target persists at time t and t+1, and M represents the number of these particles);
否则otherwise
(4)重复(3)直到每个粒子都运算完毕(4) Repeat (3) until each particle is calculated
(5)归一化平滑权值：(5) Normalized smoothing weight:
(6)通过求出平滑概率密度p(xt，rt＝1|Z1∶T)，在H1的条件下，由MMSE准则得出t时刻目标状态估计：(6) pass Find the smooth probability density p(xt , rt =1|Z 1:T ), under the condition of H1 , the target state estimation at time t is obtained by the MMSE criterion:
(7)t＝t-1；(7) t=t-1;
(8)重复(3)-(7)直到t＜1。(8) Repeat (3)-(7) until t<1.
为降低计算复杂度，在PS-TBD算法的基础上作出改进。在粒子平滑权值的计算过程中运用一步平滑思想，只利用下一时刻的观测数据，对所述后验概率密度函数进行修正；再利用各个粒子状态间的欧式距离来代替它们之间的状态转移概率，进而快速获取一步平滑概率根据所述平滑概率。根据所述平滑概率，对雷达目标进行检测和跟踪。In order to reduce the computational complexity, an improvement is made on the basis of PS-TBD algorithm. In the calculation process of particle smoothing weights, the idea of one-step smoothing is used, and only the observation data at the next moment is used to modify the posterior probability density function; and then the Euclidean distance between the states of each particle is used to replace the states between them Transition probabilities, and then quickly obtain one-step smoothed probabilities according to the smoothed probabilities. Based on the smoothed probabilities, radar targets are detected and tracked.
改进1：在粒子平滑过程中运用一步平滑思想，表示一步平滑权值：Improvement 1: Using one-step smoothing idea in the particle smoothing process, Represents one-step smoothing weights:
上式中，表示t+1时刻重采样后的滤波权值，对于不同的粒子下标n，是一个常量，因此上式又可近似为：In the above formula, Indicates the filter weight after resampling at time t+1, for different particle subscript n, is a constant, so the above formula can be approximated as:
符号表示近似正比于。此时平滑过程的计算复杂度被减小为O(M)，但仍需要多次计算粒子间的状态转移概率symbol Indicates approximately proportional to . At this time, the computational complexity of the smoothing process is reduced to O(M), but it is still necessary to calculate the state transition probability between particles multiple times
改进2：用各个粒子状态间的欧式距离来代替它们之间的状态转移概率并采取一定近似，得到改进PS-TBD算法的平滑权值：Improvement 2: Use the Euclidean distance between each particle state to replace the state transition probability between them and take a certain approximation to obtain the smoothing weight of the improved PS-TBD algorithm:
上式中，是改进的PS-TBD算法得到的平滑权值。f(·)表示状态转移函数，表示t+1时刻PF-TBD得出的目标状态估计。由上式可以看出，改进的PS-TBD算法不仅平滑的计算复杂度降为O(M)，也避免了多次计算粒子间的状态转移概率，一步平滑概率可写为：In the above formula, is the smoothing weight obtained by the improved PS-TBD algorithm. f(·) represents the state transition function, Indicates the target state estimate obtained by PF-TBD at time t+1. It can be seen from the above formula that the improved PS-TBD algorithm not only reduces the computational complexity of smoothing to O(M), but also avoids multiple calculations of the state transition probability between particles, and one-step smoothing probability can be written as:
参照图4，改进的PS-TBD算法的具体实现步骤如下：With reference to Fig. 4, the specific implementation steps of the improved PS-TBD algorithm are as follows:
(1)初始化t＝1；(1) Initialize t=1;
(2)如果t＝1，2...，T-1，则进行PF-TBD(步骤3)：得到和(2) If t=1, 2..., T-1, then perform PF-TBD (step 3): get and
跳转到步骤(3)；Jump to step (3);
否则如果t＝T，跳转到步骤(5)；Otherwise, if t=T, jump to step (5);
(3)如果则通过求出(式中，由得到)(3) if then pass find out (where, Depend on get)
否则otherwise
(4)重复步骤(3)直到每个粒子都运算完毕，转到5)；(4) Repeat step (3) until each particle is calculated, go to 5);
(5)对每个粒子执行(5) Execute for each particle
(6)归一化平滑权值：(6) Normalized smoothing weight:
(7)通过求出一步平滑概率密度在H1的条件下，根据MMSE准则得出t时刻目标状态估计：(7) pass find one-step smoothed probability density Under the condition of H1 , the target state estimation at time t is obtained according to the MMSE criterion:
(8)t＝t+1；(8)t=t+1;
(9)重复(2)-(8)直到t＞T。(9) Repeat (2)-(8) until t>T.
步骤6，将所述平滑概率作为雷达目标运动状态的后验概率，并根据所述后验概率，对雷达目标进行检测和跟踪。In step 6, the smoothed probability is used as the posterior probability of the motion state of the radar target, and the radar target is detected and tracked according to the posterior probability.
本发明由于充分利用传感器的观测信息，运用后续时刻的观测信息对当前时刻目标状态的后验概率进行修正，建立了以过去和将来所有时刻的观测信息为条件的平滑概率，而且在粒子平滑权值的计算过程中运用一步平滑思想，并用各个粒子状态间的欧式距离来代替粒子状态的转移概率，所以有效提高了目标状态估计的精度，大大缩短了平滑时间。The present invention makes full use of the observation information of the sensor, uses the observation information of the subsequent time to correct the posterior probability of the target state at the current time, and establishes the smooth probability conditional on the observation information of all past and future moments, and in the particle smoothing weight The one-step smoothing idea is used in the calculation process of the value, and the transition probability of the particle state is replaced by the Euclidean distance between the particle states, so the accuracy of the target state estimation is effectively improved, and the smoothing time is greatly shortened.
本发明的效果通过以下仿真对比试验进一步说明：Effect of the present invention is further illustrated by following simulation comparison test:
1.仿真参数：1. Simulation parameters:
观测空间的距离是从30km～34.5km，方位角为30°～60°，距离分辨率为150m，角度分辨率为1°。回波强度A＝2.512，观测噪声标准差σ＝1，于是信噪比：The distance of the observation space is from 30km to 34.5km, the azimuth angle is 30° to 60°, the distance resolution is 150m, and the angle resolution is 1°. Echo intensity A=2.512, observation noise standard deviation σ=1, so the signal-to-noise ratio:
目标的初始位置在(21.2，21.2)km处，目标的速度大小为150m/s，方向为45°。目标的状态转移矩阵粒子数N＝5000，门限VT＝0.6，过程噪声强度q1＝0.001。初始时刻各粒子均匀分布在[30km，34.5km]和[30°，60°]的空间内，速度均匀分布在[100，200]m/s和[100，200]m/s的范围内。The initial position of the target is at (21.2, 21.2) km, the speed of the target is 150m/s, and the direction is 45°. The state transition matrix of the target The particle number N=5000, the threshold VT =0.6, and the process noise intensity q1 =0.001. At the initial moment, each particle is evenly distributed in the space of [30km, 34.5km] and [30°, 60°], and the velocity Evenly distributed in the range of [100, 200] m/s and [100, 200] m/s.
2.仿真内容：2. Simulation content:
本发明针对一个径向飞行的匀速目标场景，采用PF-TBD、PS-TBD和改进的PS-TBD算法作仿真实验。The present invention uses PF-TBD, PS-TBD and improved PS-TBD algorithms for simulation experiments aiming at a uniform-velocity target scene of radial flight.
3.仿真结果分析：3. Simulation result analysis:
共30帧数据，目标在第4帧出现，在第24帧消失，图5给出了几帧中(2，8，20，29)模态的粒子在空间的分布的情况。A total of 30 frames of data, the target appears in the 4th frame and disappears in the 24th frame. Figure 5 shows the (2, 8, 20, 29) mode in several frames The distribution of particles in space.
在目标存在的情况下，将PF-TBD、PS-TBD以及改进后的PS-TBD三种算法进行性能比较。图6给出了500次Monte Carlo仿真中PF-TBD算法认为目标存在的概率情况。图7给出了100次Monte Carlo仿真后三种算法跟踪精度的比较，跟踪精度以目标位置的均方根误差(RMSE)来衡量的。而在目标存在的第4帧至第24帧之间，PS-TBD算法和改进的PS-TBD算法的计算时间随粒子数变化的情况则如图8所示。In the presence of the target, the performance of the three algorithms PF-TBD, PS-TBD and improved PS-TBD is compared. Figure 6 shows the probability that the PF-TBD algorithm believes that the target exists in 500 Monte Carlo simulations. Figure 7 shows the comparison of the tracking accuracy of the three algorithms after 100 Monte Carlo simulations. The tracking accuracy is measured by the root mean square error (RMSE) of the target position. From the 4th frame to the 24th frame when the target exists, the calculation time of the PS-TBD algorithm and the improved PS-TBD algorithm changes with the number of particles, as shown in Figure 8.
由图8可以看出，在目标出现后的前几帧，三种算法的RMSE都很大。因为此时模态为1的粒子所占概率(图5所示，出现了检测延时)，大多数粒子认为没有目标存在，PF-TBD在这种情况下给出的目标位置的估计是相当不精确的。而本发明提出的PS-TBD与改进的PS-TBD算法也只在认为目标持续存在的粒子间进行，因此在图8的前几帧三种算法的RMSE都很大。几帧检测延时后PF-TBD算法跟踪上目标，大多数粒子认为目标持续存在，由图8看出，本文提出的PS-TBD算法和改进的PS-TBD算法都明显的提高了跟踪精度。但结合图8发现，虽然PS-TBD算法虽然跟踪精度很高，但该算法平滑时间很长(计算复杂度为O(M2T))，而改进的PS-TBD算法通过引入一步平滑思想，将平滑过程的计算复杂度降为O(M)，并用各个粒子状态间的欧式距离来代替它们之间的状态转移概率，大大的缩短了平滑时间，具有很强的实用性。It can be seen from Figure 8 that in the first few frames after the target appears, the RMSE of the three algorithms are all very large. Because the probability of particles with mode 1 at this time is (As shown in Figure 5, there is a detection delay), most particles think that there is no target, and the estimation of the target position given by PF-TBD in this case is quite inaccurate. The PS-TBD and improved PS-TBD algorithms proposed by the present invention are only carried out between the particles that the target is considered to persist, so the RMSEs of the three algorithms are all very large in the first few frames of Fig. 8 . After a few frames of detection delay, the PF-TBD algorithm tracks the target, and most particles believe that the target continues to exist. It can be seen from Figure 8 that both the PS-TBD algorithm proposed in this paper and the improved PS-TBD algorithm have significantly improved the tracking accuracy. However, combined with Figure 8, it is found that although the PS-TBD algorithm has high tracking accuracy, the smoothing time of the algorithm is very long (computational complexity is O(M2 T)), and the improved PS-TBD algorithm introduces one-step smoothing idea, The calculation complexity of the smoothing process is reduced to O(M), and the Euclidean distance between each particle state is used to replace the state transition probability between them, which greatly shortens the smoothing time and has strong practicability.
本领域普通技术人员可以理解：实现上述方法实施例的全部或部分步骤可以通过程序指令相关的硬件来完成，前述的程序可以存储于一计算机可读取存储介质中，该程序在执行时，执行包括上述方法实施例的步骤；而前述的存储介质包括：ROM、RAM、磁碟或者光盘等各种可以存储程序代码的介质。Those of ordinary skill in the art can understand that all or part of the steps for realizing the above-mentioned method embodiments can be completed by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, the It includes the steps of the above method embodiments; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other various media that can store program codes.
以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应以所述权利要求的保护范围为准。The above is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Anyone skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present invention. Should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.
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| CN201610160872.3ACN105842686A (en) | 2016-03-21 | 2016-03-21 | Fast TBD detection method based on particle smoothness |
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