WO2020087362A1 - 一种粒子滤波方法、系统和计算机可读存储介质 - Google Patents

一种粒子滤波方法、系统和计算机可读存储介质 Download PDF

Info

Publication number
WO2020087362A1
WO2020087362A1 PCT/CN2018/113079 CN2018113079W WO2020087362A1 WO 2020087362 A1 WO2020087362 A1 WO 2020087362A1 CN 2018113079 W CN2018113079 W CN 2018113079W WO 2020087362 A1 WO2020087362 A1 WO 2020087362A1
Authority
WO
WIPO (PCT)
Prior art keywords
fuzzy
particle
model
function
state
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
PCT/CN2018/113079
Other languages
English (en)
French (fr)
Inventor
李良群
王小梨
谢维信
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shenzhen University
Original Assignee
Shenzhen University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shenzhen University filed Critical Shenzhen University
Priority to PCT/CN2018/113079 priority Critical patent/WO2020087362A1/zh
Publication of WO2020087362A1 publication Critical patent/WO2020087362A1/zh
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/04—Inference or reasoning models

Definitions

  • the invention relates to the technical field of target tracking.
  • the TS (full name Takagi–Sugeno) model is a fuzzy inference model proposed by Takagi and Sugeno. It can introduce fuzzy semantic information that can critically determine the motion model in a simple manner, and this model can approximate a nonlinear system of any shape .
  • Target tracking is to estimate the future movement state of the target based on the estimated state at the previous moment and the effective observation at the current moment, so as to obtain the target's movement trajectory; in order to obtain the state information of the target's movement trajectory, such as the target's position and speed And acceleration, most researchers use the popular Kalman filter algorithm, but the algorithm has many uncertainties in the tracking effect when the target is maneuvering.
  • the multi-model algorithm is mainly used to solve the uncertainty modeling problem.
  • the interactive multi-model algorithm of the model switching mechanism is superior; however, the model switching mechanism makes the algorithm easy to cause large
  • the estimation error makes the tracking effect have a larger error.
  • a first aspect of the present invention provides a basic particle filtering method, including: initializing a timetable and setting the number of TS fuzzy models; extracting particle states from a priori probabilities, and obtaining the TS fuzzy based on the extracted particle states
  • the anterior and posterior parameters of the model The anterior and posterior parameters of the model; the identification of the posterior parameters of the TS fuzzy model; the observation and calculation of the fuzzy membership of each TS fuzzy model; the identification of the antecedent parameters of the TS fuzzy model, and according to the fuzzy
  • the degree of membership calculates the model weights of the TS fuzzy model; fuse the state of each TS fuzzy model and update the model weights; sample the particles; calculate and normalize the particle weights; resample the particles and calculate And standardized re-sampled particle weights; calculate particle state and covariance estimation results based on the identified post-ware parameters, the identified pre-ware parameters, the model weights, and the re-sampled particle weights ; Output particle state and covariance estimation results at non-
  • each TS fuzzy model By calculating the fuzzy membership of each TS fuzzy model and fusing the state of each TS fuzzy model, multiple semantic fuzzy sets can be used to fuzzyly represent the target feature information, and a universal TS fuzzy model semantic framework can be constructed. Therefore, the spatial feature information is introduced into the particle filter to achieve accurate sampling of the particles, so that when the tracked target suddenly changes direction or the target's dynamic a priori information is inaccurate, it can effectively track the target accurately.
  • FIG. 1 is a schematic block diagram of a flow of a particle filtering method according to an embodiment of the invention
  • FIG. 2 is a schematic block diagram of a structure of an electronic device according to an embodiment of the present invention.
  • a first aspect of the present invention provides a basic particle filtering method, including: initializing a timetable and setting the number of TS fuzzy models; extracting particle states from a priori probabilities, and obtaining the TS fuzzy based on the extracted particle states
  • the anterior and posterior parameters of the model The anterior and posterior parameters of the model; the identification of the posterior parameters of the TS fuzzy model; the observation and calculation of the fuzzy membership of each TS fuzzy model; the identification of the antecedent parameters of the TS fuzzy model, and according to the fuzzy
  • the membership degree calculates the model weights of the TS fuzzy model; fuse the state of each TS fuzzy model and update the model weights; sample the particles; calculate and normalize the particle weights; resample the particles and calculate And standardized re-sampled particle weights; calculate particle state and covariance estimation results based on the identified post-ware parameters, the identified pre-ware parameters, the model weights, and the re-sampled particle weights ; Output particle state and covariance estimation results at non-zer
  • the identification of the posterior parameters of the T-S fuzzy model includes: constructing a Kalman filter equation for each T-S fuzzy rule; and identifying posterior parameters according to the Kalman equation.
  • the observing and calculating the fuzzy membership of each TS fuzzy model includes: identifying the similarity function between the estimation result of the TS fuzzy semantic model and the measurement matrix according to the relevant entropy criterion; defining the fuzzy C regression clustering according to the relevant entropy criterion The objective function of the algorithm; maximize the relevant entropy standard, and combine the constraints to optimize the objective function; according to the objective function to derivate the corresponding weight of each particle, get the membership expression between the TS fuzzy model and the data After the membership matrix is calculated by the similarity function, it is applied to the optimized objective function.
  • the identification of the antecedent parameters of the TS fuzzy model includes: setting the fuzzy membership function of the antecedent parameter to a Gaussian function; calculating the mean value and root mean square of the antecedent parameter membership function of the Gaussian function Error; derive the state of the TS fuzzy semantic model and the function of covariance estimation.
  • the calculation of the model weight of the TS fuzzy model according to the fuzzy membership includes: defining the state of the target at non-zero time in the timetable, and defining at least two target features of the non-zero time target Vector; define the fuzzy membership function, which represents the degree to which the vector determines the state; define the posterior probability distribution and the state and weight of the particles at the previous moment; on the basis of the set of particles that existed at the previous moment A sample set is obtained by fusing particles extracted from the posterior probability distribution; the weight of the TS fuzzy model is calculated according to the sample set.
  • the defining the posterior probability distribution includes: establishing a state function of the particle at the time in the timetable according to a known nonlinear function, and establishing a measurement matrix function of the particle at the time in the timetable; according to known The initial value of the probability density of predicts the measured value of the matrix function; the prior value is updated according to the measured value and the Bayesian formula to obtain the posterior probability density distribution.
  • the calculating and normalizing the particle weights include: constructing the importance density function update particle of the particle filter according to the state of the TS fuzzy semantic model and the function of covariance estimation; calculating according to the density function and the weight update formula And standardized particle weights.
  • a second aspect of the present invention provides a target tracking system, including any of the particle filtering methods described above.
  • a third aspect of the present invention provides an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that the processor executes the computer program , Any of the particle filtering methods mentioned above is implemented.
  • a fourth aspect of the present invention provides a computer-readable storage medium on which a computer program is stored.
  • the computer program is executed by a processor, any of the particle filtering methods described above is implemented.
  • FIG. 1 for a particle filtering method, including: S1, initializing the timetable, and setting the number of TS fuzzy models; S2, extracting the particle state from the prior probability, and obtaining the TS fuzzy model according to the extracted particle state Anterior and posterior parameters of S; S3, identify the posterior parameters of the TS fuzzy model; S4, identify the anterior parameters of the TS fuzzy model, and calculate the model weight of the TS fuzzy model; S5, each The state of the TS fuzzy model is fused and the model weights are updated; S6, the particles are sampled; S7, the particle weights are calculated and normalized; S8, the particles are resampled, and the particle weights are calculated and normalized; S9 , Calculate the particle state and covariance estimation results based on the identified afterward parameters, the identified beforehand parameters, model weights and resampled particle weights; S10, output the particle state and covariance at non-zero time in the timetable Estimate the results.
  • the identification of the posterior parameters of the T-S fuzzy model includes: constructing a Kalman filter equation for each T-S fuzzy rule; identifying the posterior parameters according to the Kalman equation.
  • the T-S fuzzy model can use multiple linear systems to represent a nonlinear system of arbitrary precision.
  • each linear model rule is defined as Equation 1, and Equation 1 is expressed as follows:
  • the fuzzy membership function representing the g-th target feature Is the target state equation of the i-th model at time k, Is the observation equation of the i-th model at time k, Are the process noise and observation noise of the i-th model, Is the state estimation result of the i-th model at time k.
  • Kalman filtering is used to identify the posterior parameters.
  • least squares or weighted least squares can also be used.
  • the Kalman filter equation is as follows from formula 2 to formula 6, and formula 2 to formula 6 are expressed as follows:
  • Identification of the antecedent parameters of the TS fuzzy model includes: observing and calculating the fuzzy membership of each TS fuzzy model; setting the fuzzy membership function of the antecedent parameter to a Gaussian function; calculating the antecedent parameter membership function of the Gaussian function The mean value and root mean square error of the; the function of the state and covariance estimation of the TS fuzzy semantic model.
  • the fuzzy membership function of the antecedent parameters is defined as a Gaussian function such as Equation 7, which is expressed as follows:
  • Equation 8 Is the mean value of the membership function of the Gaussian model anterior For the root-mean-square error, Equation 8 can be obtained.
  • Observing and calculating the fuzzy membership of each TS fuzzy model includes: identifying the similarity function between the estimation result of the TS fuzzy semantic model and the measurement matrix according to the relevant entropy standard; defining the objective function of the fuzzy C regression clustering algorithm according to the relevant entropy standard; Maximize the relevant entropy standard, and combine the constraints to optimize the objective function; according to the objective function to derivate the corresponding weight of each particle, get the membership expression between the TS fuzzy model and the data; pass the membership matrix through similarity After the degree function is calculated, it is applied to the optimized objective function.
  • Calculating the model weights of the TS fuzzy model includes: defining the state of the target at non-zero time in the timetable, and defining a vector of at least two target features of the target at non-zero time; defining the fuzzy membership function, which represents the vector's Determine the degree; define the posterior probability distribution and the state and weight of the particles at the previous time; fuse the particles extracted from the posterior probability distribution on the basis of the particle set existing at the previous time to obtain the sample set; calculate the TS based on the sample set The weight of the fuzzy model.
  • fuzzy C-regression clustering algorithm set up Is an observation set, Is a set of prediction observations, z k, l means l th observations, and Represents the prediction observation based on fuzzy rule i th at time k.
  • the objective function of fuzzy C-regression clustering algorithm is shown in formula 11, which is as follows:
  • Equation 12 Equation 12
  • Equation 15 is the Lagrangian multiplier vector
  • Equation 16 is the distance measurement function
  • Equation 16 is expressed as follows:
  • Equation 18 the fuzzy membership of the i th fuzzy rule at time k is calculated as Equation 18, which is expressed as follows:
  • Equation 19 is expressed as follows:
  • Defining the posterior probability distribution includes: establishing the state function of the particle at the time in the timetable according to the known nonlinear function, and establishing the measurement matrix function of the particle at the time in the timetable; according to the known initial value of the probability density Predict the measured value of the matrix function; update the prior value according to the measured value and the Bayesian formula to obtain the posterior probability density distribution.
  • Equation 20 Is a set of particles, where x j is a particle, M is the number of particles used in the approximation, ⁇ j is the corresponding weight of each particle, and
  • Equation 20 The ⁇ approximate distribution p (x) is Equation 20, which is expressed as follows:
  • the next important content of particle filtering is importance sampling.
  • the distribution p (x) is approximated by discrete random measures. If particles are extracted from p (x), then each particle will be given an equal weight 1 / M.
  • direct sampling from p (x) is more troublesome, you can extract particles x j from a distribution q (x), set it as an importance density function, and assign according to these distributions
  • the normalized weight of the particles can be expressed by formula 22, which is expressed as follows:
  • the spatial motion feature information is introduced into PF. set up It is a vector composed of g target feature information of the target at time k, and G is the feature number.
  • Discrete stochastic measure Approximating the posterior distribution p (x 0: k-1
  • the sequence importance sampling method achieves this by extracting particles x k, j and appending them to x 0: k-1, j to form x 0: k, j and updating the weight ⁇ k, j .
  • the posterior probability distribution formula is as formula 23, and formula 23 is expressed as follows:
  • formula 24 Based on the trajectories x 0: k 1, j and x k, j , formula 24 can be obtained, which is expressed as follows:
  • weight value update formula is updated according to the weight value update formula, and the weight value update formula is formula 25, which is expressed as follows:
  • x k ) represents the likelihood function
  • x 0: k-1, j , ⁇ k ) is the state transition function
  • the calculation and normalization of particle weights include: building the importance density function of the particle filter according to the state of the T-S fuzzy semantic model and the function of covariance estimation to update the particles; calculating and normalizing the particle weights according to the density function and the weight update formula.
  • Equation 26 The importance density function to update the particles.
  • Equation 26 The importance density function is shown in Equation 26, which is expressed as follows:
  • Equation 28 f k (x k-1 , v k-1 ) 29 means as follows:
  • the posterior probability density function is as shown in Formula 31, and Formula 31 is as follows:
  • Equation 32 p (z k
  • Equation 30 The basic principles of Bayesian filtering in Equation 30 and Equation 31, but the integration of Equation 30 into some dynamic systems can be resolved, and the most important solution is the Kalman filter; set f k and h k is linear, and v k and e k are additive Gaussian noise with known covariance.
  • Monte Carlo based on random sampling operation can convert the integral operation into a summation operation of finite sample points, that is, the formula 30 The operation is transformed into a process of cumulative accumulation of finite sample points.
  • Equation 34 is expressed as follows:
  • the calculation formula of the particle weight value is calculated using the deformation formula of formula 27, that is, the formula 35 is used to calculate the particle weight value, and the normalization of the particle weight value uses the formula 36, and the formula 35 is expressed as follows:
  • Equation 36 is expressed as follows:
  • Equation 35 It is a predictive observation, calculated using Equation 1; then resampling the particles, and estimating the resampled particle state and covariance estimation results according to the above steps; and finally outputting the state and state covariance estimation at time k according to Equation 37 and Equation 38
  • Equation 37 is expressed as follows:
  • Equation 38 is expressed as follows:
  • the present application also provides a target tracking system, including the above particle filtering method, and tracking the target according to the target tracking system.
  • An embodiment of the present application provides an electronic device. Please refer to FIG. 2.
  • the electronic device includes: a memory 601, a processor 602, and a computer program stored on the memory 601 and executable on the processor 602.
  • the processor 602 executes the computer When the program is implemented, the generation method of the incremental kernel density estimator described in the foregoing embodiments of FIGS. 1 to 4 is implemented.
  • the electronic device further includes: at least one input device 603 and at least one output device 604.
  • the aforementioned memory 601, processor 602, input device 603, and output device 604 are connected via a bus 605.
  • the input device 603 may specifically be a camera, a touch panel, a physical button, a mouse, or the like.
  • the output device 604 may specifically be a display screen.
  • the memory 601 may be a high-speed random access memory (RAM, Random Access Memory) memory, or may be a non-volatile memory (non-volatile memory), such as a disk memory.
  • RAM Random Access Memory
  • non-volatile memory non-volatile memory
  • the memory 601 is used to store a set of executable program codes, and the processor 602 is coupled to the memory 601.
  • an embodiment of the present application further provides a computer-readable storage medium.
  • the computer-readable storage medium may be provided in the electronic device in the foregoing embodiments, and the computer-readable storage medium may be as shown in FIG. 6 described above.
  • the memory 601 in the embodiment is shown.
  • a computer program is stored on the computer-readable storage medium, and when the program is executed by the processor 602, the generation method of the incremental kernel density estimator described in the foregoing method embodiment is implemented.
  • the computer storable medium may also be various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory 601 (ROM, Read-Only Memory), RAM, magnetic disk, or optical disk.
  • program codes such as a U disk, a mobile hard disk, a read-only memory 601 (ROM, Read-Only Memory), RAM, magnetic disk, or optical disk.
  • the system is implemented in the form of a software function module and sold or used as an independent product, it may be stored in a computer-readable storage medium.
  • the technical solution of the present invention essentially or part of the contribution to the existing technology or all or part of the technical solution can be embodied in the form of a software product, the computer software product is stored in a storage medium , Including several instructions to enable a computer device (which may be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention.
  • the aforementioned storage media include: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), magnetic disk or optical disk and other media that can store program code .
  • the particle filtering method, system and computer readable storage medium provided by the present invention solve the technical problem that the tracking effect of the target has a large error in the prior art.

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Computing Systems (AREA)
  • Data Mining & Analysis (AREA)
  • Evolutionary Computation (AREA)
  • Physics & Mathematics (AREA)
  • Computational Linguistics (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Artificial Intelligence (AREA)
  • Image Analysis (AREA)

Abstract

一种粒子滤波方法，用于目标跟踪，解决了现有技术中对目标的跟踪效果具有较大误差的技术问题，其包括：初始化时刻表，并设定T-S模糊模型的数量(S1)；从先验概率中抽取粒子状态，得出T-S模糊模型的前件参数及后件参数(S2)；对T-S模糊模型的后件参数进行辨识(S3)；对T-S模糊模型的前件参数进行辨识，计算T-S模糊模型的权值(S4)；将每个T-S模糊模型的状态进行融合，更新模型权值(S5)；对粒子进行采样(S6)；计算及标准化粒子权值(S7)；对粒子进行重采样，计算及标准化重采样的粒子权值(S8)；根据辨识后的后件参数、辨识后的前件参数、模型权值及重采样的粒子权值计算粒子状态及协方差估计结果(S9)；输出时刻表内非零时刻的粒子状态及协方差估计结果(S10)，从而能够对目标进行精确跟踪。

Description

一种粒子滤波方法、系统和计算机可读存储介质 技术领域
本发明涉及目标跟踪技术领域。
背景技术
T-S(全称为Takagi–Sugeno)模型是Takagi和Sugeno提出的一种模糊推理模型，它能够以简单的方式引入能够关键性决定运动模型的模糊语义信息，并且这个模型可以逼近任意形状的非线性系统。目标跟踪是在前一时刻的估计状态和当前时刻有效观测的基础上，对目标未来的运动状态进行估计，从而得到目标的运动轨迹；为了得到目标运动轨迹的状态信息，比如目标的位置，速度和加速度，大部分学者采用比较受欢迎的卡尔曼滤波算法，但是该算法在目标机动时，跟踪效果有许多不确定性。
技术问题
目前，多模型算法主要用于解决不确定性建模问题，在此类方法中，模型切换机制的交互多模型算法较为优越；然而，采用模型切换机制使该算法易在模型切换时刻造成较大的估计误差，使跟踪效果存在较大的误差。
技术解决方案
本发明第一方面提供一种基粒子滤波方法，包括：初始化时刻表，并设定T-S模糊模型的数量；从先验概率中抽取粒子状态，根据抽取的所述粒子状态得出所述T-S模糊模型的前件参数及后件参数；对T-S模糊模型的后件参数进行辨识；观测并计算每个T-S模糊模型的模糊隶属度；对T-S模糊模型的前件参数进行辨识，并根据所述模糊隶属 度计算T-S模糊模型的模型权值；将每个T-S模糊模型的状态进行融合，并更新所述模型权值；对粒子进行采样；计算及标准化粒子权值；对粒子进行重采样，并计算及标准化重采样的粒子权值；根据辨识后的所述后件参数、辨识后的所述前件参数、所述模型权值及重采样的所述粒子权值计算粒子状态及协方差估计结果；输出时刻表内非零时刻的粒子状态及协方差估计结果。
有益效果
通过计算观测每个T-S模糊模型的模糊隶属度，并将每个T-S模糊模型的进行状态融合，能够用多个语义模糊集对目标特征信息进行模糊表示，构建一个通用的T-S模糊模型语义框架，从而在粒子滤波中引入空间特征信息，实现对粒子的准确采样，从而在被跟踪目标突然发生方向改变或目标的动态先验信息不精确等复杂情况时，能够有效地对目标进行精确跟踪。
附图说明
图1为本发明实施例粒子滤波方法的流程示意框图；
图2为本发明实施例电子装置的结构示意框图。
本发明的最佳实施方式
本发明第一方面提供一种基粒子滤波方法，包括：初始化时刻表，并设定T-S模糊模型的数量；从先验概率中抽取粒子状态，根据抽取的所述粒子状态得出所述T-S模糊模型的前件参数及后件参数；对T-S模糊模型的后件参数进行辨识；观测并计算每个T-S模糊模型的模糊隶属度；对T-S模糊模型的前件参数进行辨识，并根据所述模糊隶属度计算T-S模糊模型的模型权值；将每个T-S模糊模型的状态进行融合，并更新所述模型权值；对粒子进行采样；计算及标准化粒子权值； 对粒子进行重采样，并计算及标准化重采样的粒子权值；根据辨识后的所述后件参数、辨识后的所述前件参数、所述模型权值及重采样的所述粒子权值计算粒子状态及协方差估计结果；输出时刻表内非零时刻的粒子状态及协方差估计结果。
进一步地，所述对T-S模糊模型的后件参数进行辨识包括：对每条T-S模糊规则，构建卡尔曼滤波方程；根据所述卡尔曼方程对后件参数进行辨识。
进一步地，所述观测并计算每个T-S模糊模型的模糊隶属度包括：根据相关熵标准辨别T-S模糊语义模型估计结果与测量矩阵之间的相似度函数；根据相关熵标准定义模糊C回归聚类算法的目标函数；最大化相关熵标准，并结合约束条件，优化所述目标函数；根据目标函数对各个粒子相对应的权重求偏导，得出T-S模糊模型与数据之间的隶属度表达式；将隶属度矩阵经过所述相似度函数计算后，应用到优化后的所述目标函数内。
进一步地，所述对T-S模糊模型的前件参数进行辨识包括：将前件参数的模糊隶属函数设定为高斯型函数；计算所述高斯型函数的前件参数隶属函数的均值及均方根误差；得出T-S模糊语义模型的状态和协方差估计的函数。
进一步地，所述根据所述模糊隶属度计算T-S模糊模型的模型权值包括：定义目标在时刻表内的非零时刻的状态，并定义所述非零时刻目标的至少两个目标特征组成的向量；定义模糊隶属度函数，表示所述向量对所述状态的决定程度；定义后验概率分布及在前一时刻粒子的状态和权值；在所述前一时刻存在的粒子集合的基础上融合所述后验概率分布中抽取的粒子，获得样本集合；根据样本集合计算T-S 模糊模型的权值。
进一步地，所述定义后验概率分布包括：根据已知的非线性函数建立粒子在时刻表内的时刻时的状态函数，并建立粒子在时刻表内的时刻时的测量矩阵函数；根据已知的概率密度初始值预测所述矩阵函数的测量值；根据所述测量值及贝叶斯公式更新先验值，得到后验概率密度分布。
进一步地，所述计算及标准化粒子权值包括：根据所述T-S模糊语义模型的状态和协方差估计的函数构建粒子滤波的重要性密度函数更新粒子；根据所述密度函数及权值更新公式计算及标准化粒子权值。
本发明第二方面提供一种目标跟踪系统，包括上述的任意一项粒子滤波方法。
本发明第三方面提供一种电子装置，包括：存储器、处理器及存储在所述存储器上并可在所述处理器上运行的计算机程序，其特征在于，所述处理器执行所述计算机程序时，实现上述任意一项粒子滤波方法。
本发明第四方面提供一种计算机可读存储介质，其上存储有计算机程序，所述计算机程序被处理器执行时，实现上述任意一项粒子滤波方法。
本发明的实施方式
请参阅图1，为一种粒子滤波方法，包括：S1，初始化时刻表，并设定T-S模糊模型的数量；S2，从先验概率中抽取粒子状态，根据抽取的粒子状态得出T-S模糊模型的前件参数及后件参数；S3，对T-S模糊模型的后件参数进行辨识；S4，对T-S模糊模型的前件参数进行 辨识，并计算T-S模糊模型的模型权值；S5，将每个T-S模糊模型的状态进行融合，并更新模型权值；S6，对粒子进行采样；S7，计算及标准化粒子权值；S8，对粒子进行重采样，并计算及标准化重采样的粒子权值；S9，根据辨识后的后件参数、辨识后的前件参数、模型权值及重采样的粒子权值计算粒子状态及协方差估计结果；S10，输出时刻表内非零时刻的粒子状态及协方差估计结果。
对T-S模糊模型的后件参数进行辨识包括：对每条T-S模糊规则，构建卡尔曼滤波方程；根据卡尔曼方程对后件参数进行辨识。
T-S模糊模型可以利用多个线性系统来表示任意精度的非线性系统，对于加入目标特征信息的T-S模糊模型，每条线性模型规则定义如公式1，公式1表示如下：
Figure PCTCN2018113079-appb-000001
其中，
Figure PCTCN2018113079-appb-000002
表示k时刻目标的g个特征，
Figure PCTCN2018113079-appb-000003
表示第g个目标特征的模糊隶属度函数，
Figure PCTCN2018113079-appb-000004
为k时刻第i个模型的目标状态方程，
Figure PCTCN2018113079-appb-000005
为k时刻第i个模型的观测方程，
Figure PCTCN2018113079-appb-000006
分别为第i个模型过程噪声和观测噪声，
Figure PCTCN2018113079-appb-000007
为k时刻第i个模型的状态估计结果。
在T-S模糊模型建模当中，对于后件参数的辨识，在本实施例中，使用卡尔曼滤波来实现后件参数的辨识，在其他实施例中，也可使用最小二乘或加权最小二乘方法，对于每条T-S模糊规则，卡尔曼滤波方程如下的公式2至公式6，公式2至公式6表示如下：
公式2：
Figure PCTCN2018113079-appb-000008
公式3：
Figure PCTCN2018113079-appb-000009
公式4：
Figure PCTCN2018113079-appb-000010
公式5：
Figure PCTCN2018113079-appb-000011
公式6：
Figure PCTCN2018113079-appb-000012
对T-S模糊模型的前件参数进行辨识包括：观测并计算每个T-S模糊模型的模糊隶属度；将前件参数的模糊隶属函数设定为高斯型函数；计算高斯型函数的前件参数隶属函数的均值及均方根误差；得出T-S模糊语义模型的状态和协方差估计的函数。
为了实现对前件参数的自适应辨识，前件参数的模糊隶属度函数定义为高斯函数如公式7，公式7表示如下：
Figure PCTCN2018113079-appb-000013
其中，
Figure PCTCN2018113079-appb-000014
是高斯模型前件参数隶属函数的均值，
Figure PCTCN2018113079-appb-000015
为均方根误差，则可得到公式8，公式8表示如下：
Figure PCTCN2018113079-appb-000016
最后基于T-S模糊语义模型的状态和协方差估计公式9及公式10，公式9及公式10表示如下：公式9：
Figure PCTCN2018113079-appb-000017
公式10：
Figure PCTCN2018113079-appb-000018
其中，
Figure PCTCN2018113079-appb-000019
表示k时刻第i条线性模型规则卡尔曼滤波后的状态。
观测并计算每个T-S模糊模型的模糊隶属度包括：根据相关熵标准辨别T-S模糊语义模型估计结果与测量矩阵之间的相似度函数；根据相关熵标准定义模糊C回归聚类算法的目标函数；最大化相关熵标 准，并结合约束条件，优化目标函数；根据目标函数对各个粒子相对应的权重求偏导，得出T-S模糊模型与数据之间的隶属度表达式；将隶属度矩阵经过相似度函数计算后，应用到优化后的目标函数内。
计算T-S模糊模型的模型权值包括：定义目标在时刻表内的非零时刻的状态，并定义非零时刻目标的至少两个目标特征组成的向量；定义模糊隶属度函数，表示向量对状态的决定程度；定义后验概率分布及在前一时刻粒子的状态和权值；在前一时刻存在的粒子集合的基础上融合后验概率分布中抽取的粒子，获得样本集合；根据样本集合计算T-S模糊模型的权值。
设定
Figure PCTCN2018113079-appb-000020
是一个观测集，
Figure PCTCN2018113079-appb-000021
是一个预测观测集，z k,l表示l th观测，同时
Figure PCTCN2018113079-appb-000022
表示k时刻基于模糊规则i th的预测观测，模糊C-回归聚类算法的目标函数如公式11，公式11如下：
Figure PCTCN2018113079-appb-000023
其中m是权重指数，一般情况下为
Figure PCTCN2018113079-appb-000024
表示模糊规则l th的观测与输出之间的度量函数，隶属度函数满足公式12，公式12如下：
Figure PCTCN2018113079-appb-000025
同时，为了判别T-S模糊语义模型估计结果与观测z k,l之间的相似度，引入相关熵标准如公式13，公式13表示如下：
Figure PCTCN2018113079-appb-000026
其中，
Figure PCTCN2018113079-appb-000027
是高斯核函数，
Figure PCTCN2018113079-appb-000028
是i th观测与i th规则在k时刻的模糊隶属度，为了最大化相关熵标准公式11，结合公式10的约束条件，目标函数则定义为公式14，公式14表示如下：
Figure PCTCN2018113079-appb-000029
其中β,λ k为拉格朗日乘子向量，(D ik) 2为距离测量函数，则可以得出公式15及公式16，公式15表示如下：
Figure PCTCN2018113079-appb-000030
公式16表示如下：
Figure PCTCN2018113079-appb-000031
其中，
Figure PCTCN2018113079-appb-000032
为给定目标状态
Figure PCTCN2018113079-appb-000033
的观测z k,l似然函数。
Figure PCTCN2018113079-appb-000034
是由公式2得到的新息协方差矩阵；根据目标函数对
Figure PCTCN2018113079-appb-000035
求偏导，得到隶属度
Figure PCTCN2018113079-appb-000036
更新表达公式17，公式17表示如下：
Figure PCTCN2018113079-appb-000037
因此，对i th模糊规则在时间k上的模糊隶属度进行如公式18的计算，公式18表示如下：
Figure PCTCN2018113079-appb-000038
当隶属度矩阵U由公式16计算后，即可用到T-S模糊模型的前件参数识别的公式19中，公式19表示如下：
Figure PCTCN2018113079-appb-000039
定义后验概率分布包括：根据已知的非线性函数建立粒子在时刻表内的时刻时的状态函数，并建立粒子在时刻表内的时刻时的测量矩阵函数；根据已知的概率密度初始值预测矩阵函数的测量值；根据测量值及贝叶斯公式更新先验值，得到后验概率密度分布。
定义
Figure PCTCN2018113079-appb-000040
是一组粒子，这里x j是粒子，M是在近似中使用的粒子数目，μ j是每个粒子的对应重量，并且
Figure PCTCN2018113079-appb-000041
χ近似分布p(x)为公式20，公式20表示如下：
Figure PCTCN2018113079-appb-000042
其中，δ(x-x j)是狄利克雷函数。
粒子滤波的下一个重要内容是重要性抽样。假设分布p(x)用离散随机测度逼近。如果从p(x)中抽取粒子，那么每个粒子都会被赋予一个相等的重量1/M。当直接采样从p(x)较为麻烦时，可以从一个分布q(x)中提取粒子x j，设定为重要性密度函数，并根据这些分布来分配
权重，则有公式21，公式21表示如下：
Figure PCTCN2018113079-appb-000043
其中，粒子的归一化重量可用公式22表示，公式22表示如下：
Figure PCTCN2018113079-appb-000044
并且考虑到粒子退化和粒子多样性等问题，将空间运动特征信息引入PF中。设定
Figure PCTCN2018113079-appb-000045
是k时刻目标的g个目标特征信息组成的向量，G是特征数。用离散随机测度
Figure PCTCN2018113079-appb-000046
逼近后验分布p(x 0:k-1|z 1:k-1,θ 1:k-)。给定离散的随机测量χ k  1和观测z k，目的是利用χ k  1得到χ k。序列重要性抽样方法通过抽取粒子x k,j并将它们附加到x 0:k-1,j，从而形成x 0:k,j来实现这一点，并更新权重μ k,j。
根据贝叶斯估计的序贯重要性采样滤波思想，为了计算一个后验概率密度函数的序贯估计，设定后验概率分布公式，后验概率分布公式如公式23，公式23表示如下：
q(x 0:k|z 1:k,θ 1:k)＝q(x k|x 0:k-1,z 1:k,θ 1:k)q(x 0:k-1|z 1:k  1,θ 1:k-1)；
基于轨迹x 0:k  1,j和x k,j，可以得到公式24，公式24表示如下：
x k,j～q(x k|x 0:k-1,j,z 1:k,θ 1:k)；
从而根据权值更新公式更新权值，权值更新公式为公式25，公式25表示如下：
Figure PCTCN2018113079-appb-000047
其中，p(z k|x k)表示似然函数，p(x k,j|x 0:k-1,j,θ k)为状态转移函数，
Figure PCTCN2018113079-appb-000048
为重要密度函数。
计算及标准化粒子权值包括：根据T-S模糊语义模型的状态和协方差估计的函数构建粒子滤波的重要性密度函数更新粒子；根据密度函数及权值更新公式计算及标准化粒子权值。
根据公式9及公式10获得T-S模糊模型状态估计
Figure PCTCN2018113079-appb-000049
以及协方差估计
Figure PCTCN2018113079-appb-000050
构建粒子滤波的重要性密度函数来更新粒子，重要性密度函数如公式26，公式26表示如下：
Figure PCTCN2018113079-appb-000051
根据公式24及公式23得到粒子权值计算公式27，公式27表示如下：
Figure PCTCN2018113079-appb-000052
另外，还需考虑非线性离散动态系统，非线性离散动态系统的函数如公式28及公式29所示，公式28表示如下：x k＝f k(x k-1,v k-1)；公式29表示如下：
z k＝h k(x k,e k)；
Figure PCTCN2018113079-appb-000053
和
Figure PCTCN2018113079-appb-000054
是一些已知的非线性函数，
Figure PCTCN2018113079-appb-000055
是系统在k时刻的状态，
Figure PCTCN2018113079-appb-000056
是k时刻的测量矩阵，
Figure PCTCN2018113079-appb-000057
和
Figure PCTCN2018113079-appb-000058
表示过程噪声和测量噪声。贝叶斯滤波原理的实质是用所有已知信息来获得系统状态变量的后验概率密度函数，其中包括预测和更新两个步骤，概率密度初始值p(x 0|z 0)＝p(x 0)已知，则通过公式30进行预测，公式30表示如下：
p(x k|z 1:k-1)＝∫p(x k|x k-1)p(x k-1|z 1:k-1)dx k-1；
在获得测量值z k后，通过贝叶斯公式更新先验值，得到后验概率密度，后验概率密度函数如公式31，公式31如下所示：
p(x k|z 1:k)＝p(z k|x k)p(x k|z 1:k-1)/p(z k|z 1:k-1)，
其中，p(z k|z 1:k-1)是标准化的常量，p(z k|z 1:k  1)的求解公式如公式32，公式32如下所示：
p(z k|z 1:k-1)＝∫p(z k|x k)p(x k|z 1:k-1)dx k；
公式30及公式31位贝叶斯滤波的基本原理，但是公式30中的积分进队某些动态系统能够获得解析，并且最为重要的一种解决方案是卡尔曼滤波器；设定f k和h k是线性的，而且v k和e k是协方差已知的加性高斯噪声，基于随机采样运算的蒙特卡洛可将积分运算转化为有限样本点的求和运算，即可将式30的运算转化为有限样本点的概率转移累加过程。
本发明提供的粒子滤波方法，其工作过程或原理如下：初始化时刻表，使k＝0，并设定模型数为Nf，从先验概率p(x 0)中抽取粒子状态
Figure PCTCN2018113079-appb-000059
M为粒子数；对于时刻表内的每个时刻，即k分别代表不同时刻时，使j＝1,2…，M，随后使用T-是模糊模型更新粒子，期间使用公式2至公式6估计后件参数
Figure PCTCN2018113079-appb-000060
并使用公式19识别前件参数
Figure PCTCN2018113079-appb-000061
且通过公式8计算模型权值
Figure PCTCN2018113079-appb-000062
并且使用公式9及公式10的变形公式，即公式33及公式34更新粒子j的状态
Figure PCTCN2018113079-appb-000063
和状态 协方差
Figure PCTCN2018113079-appb-000064
公式33表示如下：
Figure PCTCN2018113079-appb-000065
公式34表示如下：
Figure PCTCN2018113079-appb-000066
随后对使用公式23的变形公式，即使用公式35对粒子进行采样，公式35表示如下：
Figure PCTCN2018113079-appb-000067
粒子权值的计算公式使用公式27的变形公式计算，即使用公式35计算粒子权值，粒子权值的标准化使用公式36，公式35表示如下：
Figure PCTCN2018113079-appb-000068
公式36表示如下：
Figure PCTCN2018113079-appb-000069
在公式35及公式36中，
Figure PCTCN2018113079-appb-000070
是预测观测，使用公式1计算；然后对粒子进行重采样，并根据上述步骤估计重采样的粒子状态及协方差估计结果；最后根据公式37以及由公式38输出k时刻的状态及状态协方差估计结果，公式37表示如下：
Figure PCTCN2018113079-appb-000071
公式38表示如下：
Figure PCTCN2018113079-appb-000072
本申请还提供一种目标跟踪系统，包括上述的粒子滤波方法，并根据目标跟踪系统实现对目标的跟踪。
本申请实施例提供一种电子装置，请参阅图2，该电子装置包括： 存储器601、处理器602及存储在存储器601上并可在处理器602上运行的计算机程序，处理器602执行该计算机程序时，实现前述附图1至附图4的实施例中描述的增量核密度估计器的生成方法。
进一步的，该电子装置还包括：至少一个输入设备603以及至少一个输出设备604。
上述存储器601、处理器602、输入设备603以及输出设备604，通过总线605连接。
其中，输入设备603具体可为摄像头、触控面板、物理按键或者鼠标等等。输出设备604具体可为显示屏。
存储器601可以是高速随机存取记忆体(RAM，Random Access Memory)存储器，也可为非不稳定的存储器(non-volatile memory)，例如磁盘存储器。存储器601用于存储一组可执行程序代码，处理器602与存储器601耦合。
进一步的，本申请实施例还提供了一种计算机可读存储介质，该计算机可读存储介质可以是设置于上述各实施例中的电子装置中，该计算机可读存储介质可以是前述图6所示实施例中的存储器601。该计算机可读存储介质上存储有计算机程序，该程序被处理器602执行时实现前述方法实施例中描述的增量核密度估计器的生成方法。
进一步的，该计算机可存储介质还可以是U盘、移动硬盘、只读存储器601(ROM，Read-Only Memory)、RAM、磁碟或者光盘等各种可以存储程序代码的介质。
在本申请所提供的几个实施例中，应该理解到，系统如果以软件功能模块的形式实现并作为独立的产品销售或使用时，可以存储在一个计算机可读取存储介质中。基于这样的理解，本发明的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的全部或部 分可以以软件产品的形式体现出来，该计算机软件产品存储在一个存储介质中，包括若干指令用以使得一台计算机设备(可以是个人计算机，服务器，或者网络设备等)执行本发明各个实施例所述方法的全部或部分步骤。而前述的存储介质包括：U盘、移动硬盘、只读存储器(ROM，Read-Only Memory)、随机存取存储器(RAM，Random Access Memory)、磁碟或者光盘等各种可以存储程序代码的介质。
需要说明的是，对于前述的方法实施例，为了简便描述，故将其都表述为一系列的动作组合，但是本领域技术人员应该知悉，本发明并不受所描述的动作顺序的限制，因为依据本发明，某些步骤可以采用其它顺序或者同时进行。其次，本领域技术人员也应该知悉，说明书中所描述的实施例均属于优选实施例，所涉及的动作和模块并不一定都是本发明所必须的。
以上为对本发明所提供的一种粒子滤波方法、系统和计算机可读存储介质的描述，对于本领域的技术人员，依据本发明实施例的思想，在具体实施方式及应用范围上均会有改变之处，综上，本说明书内容不应理解为对本发明的限制。
工业实用性
本发明提供的一种粒子滤波方法、系统和计算机可读存储介质，解决了现有技术中对目标的跟踪效果具有较大误差的技术问题。

Claims (10)

  1. 一种粒子滤波方法，其特征在于，包括：
    初始化时刻表，并设定T-S模糊模型的数量；
    从先验概率中抽取粒子状态，根据抽取的所述粒子状态得出所述T-S模糊模型的前件参数及后件参数；
    对T-S模糊模型的后件参数进行辨识；
    对T-S模糊模型的前件参数进行辨识，并计算T-S模糊模型的模型权值；
    将每个T-S模糊模型的状态进行融合，并更新所述模型权值；
    对粒子进行采样；
    计算及标准化粒子权值；
    对粒子进行重采样，并计算及标准化重采样的粒子权值；
    根据辨识后的所述后件参数、辨识后的所述前件参数、所述模型权值及重采样的所述粒子权值计算粒子状态及协方差估计结果；
    输出时刻表内非零时刻的粒子状态及协方差估计结果。
  2. 根据权利要求1所述的粒子滤波方法，其特征在于，
    所述对T-S模糊模型的后件参数进行辨识包括：
    对每条T-S模糊规则，构建卡尔曼滤波方程；
    根据所述卡尔曼方程对后件参数进行辨识。
  3. 根据权利要求1所述的粒子滤波方法，其特征在于，
    所述对T-S模糊模型的前件参数进行辨识包括：
    观测并计算每个T-S模糊模型的模糊隶属度；
    将前件参数的模糊隶属函数设定为高斯型函数；
    计算所述高斯型函数的前件参数隶属函数的均值及均方根误差；
    得出T-S模糊语义模型的状态和协方差估计的函数。
  4. 根据权利要求3所述的粒子滤波方法，其特征在于，
    所述观测并计算每个T-S模糊模型的模糊隶属度包括：
    根据相关熵标准辨别T-S模糊语义模型估计结果与测量矩阵之间的相似度函数；
    根据相关熵标准定义模糊C回归聚类算法的目标函数；
    最大化相关熵标准，并结合约束条件，优化所述目标函数；
    根据目标函数对各个粒子相对应的权重求偏导，得出T-S模糊模型与数据之间的隶属度表达式；
    将隶属度矩阵经过所述相似度函数计算后，应用到优化后的所述目标函数内。
  5. 根据权利要求1所述的粒子滤波方法，其特征在于，
    所述计算T-S模糊模型的模型权值包括：
    定义目标在时刻表内的非零时刻的状态，并定义所述非零时刻目标的至少两个目标特征组成的向量；
    定义模糊隶属度函数，表示所述向量对所述状态的决定程度；
    定义后验概率分布及在前一时刻粒子的状态和权值；
    在所述前一时刻存在的粒子集合的基础上融合所述后验概率分布中抽取的粒子，获得样本集合；
    根据样本集合计算T-S模糊模型的权值。
  6. 根据权利要求5所述的粒子滤波方法，其特征在于，
    所述定义后验概率分布包括：
    根据已知的非线性函数建立粒子在时刻表内的时刻时的状态函数，并建立粒子在时刻表内的时刻时的测量矩阵函数；
    根据已知的概率密度初始值预测所述矩阵函数的测量值；
    根据所述测量值及贝叶斯公式更新先验值，得到后验概率密度分 布。
  7. 根据权利要求3所述的粒子滤波方法，其特征在于，所述计算及标准化粒子权值包括：
    根据所述T-S模糊语义模型的状态和协方差估计的函数构建粒子滤波的重要性密度函数更新粒子；
    根据所述密度函数及权值更新公式计算及标准化粒子权值。
  8. 一种目标跟踪系统，其特征在于，包括如权利要求1至7中的任意一项所述方法。
  9. 一种电子装置，包括：存储器、处理器及存储在所述存储器上并可在所述处理器上运行的计算机程序，其特征在于，所述处理器执行所述计算机程序时，实现权利要求1至7中的任意一项所述方法。
  10. 一种计算机可读存储介质，其上存储有计算机程序，其特征在于，所述计算机程序被处理器执行时，实现权利要求1至7中的任意一项所述方法。
PCT/CN2018/113079 2018-10-31 2018-10-31 一种粒子滤波方法、系统和计算机可读存储介质 Ceased WO2020087362A1 (zh)

Priority Applications (1)

Application Number Priority Date Filing Date Title
PCT/CN2018/113079 WO2020087362A1 (zh) 2018-10-31 2018-10-31 一种粒子滤波方法、系统和计算机可读存储介质

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/CN2018/113079 WO2020087362A1 (zh) 2018-10-31 2018-10-31 一种粒子滤波方法、系统和计算机可读存储介质

Publications (1)

Publication Number Publication Date
WO2020087362A1 true WO2020087362A1 (zh) 2020-05-07

Family

ID=70461986

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2018/113079 Ceased WO2020087362A1 (zh) 2018-10-31 2018-10-31 一种粒子滤波方法、系统和计算机可读存储介质

Country Status (1)

Country Link
WO (1) WO2020087362A1 (zh)

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7526414B2 (en) * 2003-07-25 2009-04-28 Siemens Corporate Research, Inc. Density morphing and mode propagation for Bayesian filtering
CN102082560A (zh) * 2011-02-28 2011-06-01 哈尔滨工程大学 一种基于集合卡尔曼滤波的粒子滤波方法
CN103684350A (zh) * 2013-12-04 2014-03-26 北京理工大学 一种粒子滤波方法
CN106487356A (zh) * 2015-08-26 2017-03-08 南京理工大学 一种导向粒子滤波方法
CN106683122A (zh) * 2016-12-16 2017-05-17 华南理工大学 一种基于高斯混合模型和变分贝叶斯的粒子滤波方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7526414B2 (en) * 2003-07-25 2009-04-28 Siemens Corporate Research, Inc. Density morphing and mode propagation for Bayesian filtering
CN102082560A (zh) * 2011-02-28 2011-06-01 哈尔滨工程大学 一种基于集合卡尔曼滤波的粒子滤波方法
CN103684350A (zh) * 2013-12-04 2014-03-26 北京理工大学 一种粒子滤波方法
CN106487356A (zh) * 2015-08-26 2017-03-08 南京理工大学 一种导向粒子滤波方法
CN106683122A (zh) * 2016-12-16 2017-05-17 华南理工大学 一种基于高斯混合模型和变分贝叶斯的粒子滤波方法

Similar Documents

Publication Publication Date Title
CN110503071B (zh) 基于变分贝叶斯标签多伯努利叠加模型的多目标跟踪方法
CN107765347B (zh) 一种高斯过程回归和粒子滤波的短期风速预测方法
WO2020173105A1 (zh) 机动目标跟踪方法及装置
CN105719312B (zh) 基于序贯贝叶斯滤波的多目标跟踪方法及跟踪系统
CN109325128B (zh) 一种机动目标的跟踪方法及系统
CN101975575B (zh) 基于粒子滤波的被动传感器多目标跟踪方法
WO2017124299A1 (zh) 基于序贯贝叶斯滤波的多目标跟踪方法及跟踪系统
CN109492769A (zh) 一种粒子滤波方法、系统和计算机可读存储介质
CN107462882B (zh) 一种适用于闪烁噪声的多机动目标跟踪方法及系统
Yang et al. Adaptive probability hypothesis density filter based on variational Bayesian approximation for multi‐target tracking
CN110111367B (zh) 用于目标跟踪的模型粒子滤波方法、装置、设备及存储介质
CN106772353B (zh) 一种适用于闪烁噪声的多目标跟踪方法及系统
Fonseca-Delgado et al. An assessment of ten-fold and Monte Carlo cross validations for time series forecasting
WO2018010099A1 (zh) 一种用于跟踪转弯机动目标的方法及其系统
JP2021527289A (ja) 総和確率的勾配推定方法、装置、およびコンピュータプログラム
CN113537302A (zh) 一种多传感器随机化数据关联融合方法
Xu et al. Residual autoencoder-LSTM for city region vehicle emission pollution prediction
CN117607853A (zh) 基于状态回归Transformer架构的多目标高精度连续跟踪方法
Rosato et al. Inference of stochastic disease transmission models using particle-mcmc and a gradient based proposal
Saini et al. Forecasting volatility in indian stock market using state space models
CN105373805A (zh) 一种基于最大熵准则的多传感器机动目标跟踪方法
Yu A novel semiparametric hidden Markov model for process failure mode identification
Turkmen IMM fuzzy probabilistic data association algorithm for tracking maneuvering target
WO2020113353A1 (zh) 一种机动目标的跟踪方法及系统
WO2020087362A1 (zh) 一种粒子滤波方法、系统和计算机可读存储介质

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 18938621

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE

32PN Ep: public notification in the ep bulletin as address of the adressee cannot be established

Free format text: NOTING OF LOSS OF RIGHTS PURSUANT TO RULE 112(1) EPC (EPO FORM 1205 DATED 24/08/2021)

122 Ep: pct application non-entry in european phase

Ref document number: 18938621

Country of ref document: EP

Kind code of ref document: A1