A Computationally Efficient Approach for Distributed Sensor Localization and Multitarget Tracking Publisher: IEEE Kai Da ; Tiancheng Li (corresponding author) ; Yongfeng Zhu ; Qiang Fu Abstract: In the context of distributed target tracking based on a mobile peer-to-peer sensor network, the relative locations between the sensors are critical for their internode information exchange and fusion. For accurate coordinate calibration between the neighboring sensors, namely sensor localization, we propose a computationally efficient approach that minimizes the mismatch error between position estimates of the common targets yielded at neighbor sensors. This mismatch error is given by a Wasserstein-like distance that is a mean square error between two sets of position estimates which are associated efficiently via Hungarian assignment. Simulations have demonstrated that our approach, on the testbed of an arithmetic average fusion based probability hypothesis density filter, performs similar to the cutting-edge approach based on loopy belief propagation, but computes much faster and has much lower communication cost. Published in: IEEE Communications Letters ( Early Access ) Page(s): 1- 1 Date of Publication: 21 November 2019 为实现基于分布式传感器网络的目标跟踪，传感器之间的相对位置是节点间信息交换和融合的关键。为了精确标定相邻传感器之间的坐标，本文提出了一种计算效率很高的传感器自定位方法，该方法通过最小化相邻传感器产生目标位置点估计之间的失配误差而实现。这种失配误差类似于Wasserstein距离，其通过匈牙利算法关联的两组位置估计值之间的均方误差而得到。该方法物理概念清晰，计算简便而有稳定，通信需求低。仿真结果表明，在基于算术平均融合的PHD滤波器的实验平台上，该方法的性能与现有基于后验分布匹配的方法相似，但计算速度快，通信成本低。 此文是在笔者在算术均值一致性信息融合方向上系列文章更进一步，首次考虑动态传感网中传感器位置不确定性问题。所采用的滤波器仍然是最基础的PHD滤波器，因此本文方法可以扩展到后需要的其他滤波器。 前面系列论文请见： 基于算术均值一致性的分布式伯努利滤波目标联合探测与跟踪 多目标信息融合问题 并行一致性：网络通讯与节点滤波计算同步进行！ 基于受限测距传感网的分布式多目标跟踪 分布式网络信息共享：Many Could Be Better Than All 通讯量最小的分布式多目标跟踪器 基于多传感器观测聚类的鲁棒多传感器PHD滤波
Distributed Bernoulli Filtering for Target Detection and Tracking Based on Arithmetic Average Fusion Publisher: IEEE Author(s) Tiancheng Li ; Zhunga Liu ; Quan Pan Abstract: We present a distributed Bernoulli filter for tracking a target that may be present or absent in the cluttered surveillance area in unknown time intervals by using a decentralized sensor network. As a key feature of the Bernoulli filter, a parameter referring to the target existence probability is online updated jointly with the target state probability density function. We propose to fuse them in parallel, both in an arithmetic average fusion manner via the existing consensus or flooding scheme. Alternatively, one may communicate and fuse merely target existence probabilities, leading to a communication-inexpensive protocol. We experimentally compare the proposed approaches, based on the Gaussian mixture implementation, with the cutting-edge geometric average fusion approach based on a Doppler shift sensor network, demonstrating advantages in computing efficiency and in dealing with local missed detection. Published in: IEEE Signal Processing Letters DOI: 10.1109/LSP.2019.2950588 本文推广笔者之前的算术均值-随机有限集融合 AA-RFS fusion 工作，首次将算术均值AA融合推广和应用于分布式伯努利滤波器设计，获得一种 可 完全解析实现 的分布式随机集滤波器。 另外可完全解析实现的分布式随机集滤波器是 AA-PHD （基于GM或SMC实现）滤波器，是笔者前期工作。 而目前主流的几何均值GA融合，虽然对PHD/Bernoulli可闭合求解，但是对于GM和SMC并不能严格解析计算，更不用说更复杂的MB、(G)LMB等（对于其，AA和GA都不能闭合求解），也就是目前的分布式随机有限集滤波器多数都是基于近似均值融合的。只有AA-PHD/Bernoulli-GM/SMC 才是严格的可完全解析实现的。 AA融合相比于GA至少三个方面的明确优势： 计算快而稳，算法实现简单 可有效应对漏检 和近邻目标 更加适合大规模传感网（Clustering 就是一种AA fusion）
或大或小 因为，总不至于总是教导一心想做科研的弟子如此说： （像为师当年一样）紧跟热门话题/大牛脚步，或改进或炒冷饭就好了，代代都给别人做嫁妆（自己养的学生给别人免费当了博士后）。。。这是培养厨子吗？ 原创的价值，抛去科学价值不谈，在于至少能给学生立个样。光见过猪走（别人原创）不行，必须真得吃过两口，才知道啥滋味。否则，讲科研讲原创就是纸上谈兵了！一个合格的“好厨子”应该是吃过猪肉的..... --------------------------------------- --------------------------------------- https://ieeexplore.ieee.org/document/8573875 T. Li, H. Chen, S. Sun and J. M. Corchado, Joint Smoothing and Tracking Based on Continuous-Time Target Trajectory Function Fitting, in IEEE Transactions on Automation Science and Engineering . doi: 10.1109/TASE.2018.2882641 状态估计的新框架？！ 2018-12-14
话说，搞信息融合有一个很风靡的概念 Covariance Intersection （CI），就是搞出来 UKF -- 这个卡尔曼滤波器最成功的变种（除EKF外） -- 的Uhlmann 和 Julier搞出来的，和 UKF几乎是相近的两年（据最早的刊印都在1995-1996，都在其博士论文中有体现，也可见剑桥的博士学位真有水平）提出来的。。UKF和CI都是解决KF所没能解决或者说没有考虑的更一般性的问题，一个是非线性UKF滤波器，一个是未知关联CI融合方法。 问题扎扎实实存在，两个方法都简单到了极限，但是又那么有说服力和好用 （人家论文引用也说明了，比如有几个滤波器能达到上万的引用呐？） 。 真可谓天才（如果非要在卡尔曼之后搞滤波和估计人中选几个）。。。现在回头看， 两个人出道即巅峰！！ 后来可以说一直吃这两碗饭，但这也足够了，能达到这个光辉层次的工作寥寥无几。 尤其是J.K. Uhlmann，迷一样的存在，至今文章不多(多数是会议)，而且一直都不发什么高档次但篇篇有思想。还是一个专业的电影制作人和录音师！！ 重点：标准CI仅考虑单目标情形的融合，常规的贝叶斯后验，没考虑漏检、虚警等。 能够跟UKF/CI媲美的可能就是 有限集统计学（finite set statistics，FISST）了，大牛Mahler提出的一套解决多目标跟踪的新理论（也是从1993年默默发会议发到2000年，然后开始不断出现爆款）。。相比UKF和CI这类极度简单思想和套路，FISST就显得恢宏大气，甚至早期的工作拖泥带水般让人难理解。。恰显天才的两种定义，各有千秋各有各的美！ PS：Mahler在2000年对CI扩展到多目标随机集框架下，得到 GCI（generalized CI），现在（提出了13年后）也风靡起来了，这得益于FISST和 线传感网的快速发展...... 毕竟是两大宗师接力发展出来的感觉..... 但是我却认为，从单目标贝叶斯后验到含有虚警、漏检的多目标，不能是简单的扩展！不是简单地数学推导从单目标的PDF/density 到 多目标multitarget density这么简单。。还有漏检和虚警，还有不同目标之间的交互呐等这些新问题！ 非常简单的一个问题：一个目标A的信息和另一个目标B的信息融合的结果算是什么呐？ 一个目标的信息和一个杂波进行融合得到什么呐？ 等等 即使 CI 无可挑剔，但是GCI却还有一个物理意义的鸿沟没有填平，被想当然掩盖了。 即使0到1很难，很伟大，但是1到N也可能不是那么简单，甚至可能有更难的问题。 直接完成数学上的推导和扩展，“ 把多目标后验信息当做单目标后验信息来看”，只是在定义域等问题上扩展一下， 从单目标下CI得到多目标的GCI是不靠谱的。会产生很多没有物理意义的东西（比如不同目标之间的信息融合得到什么？）或者说物理上无法解释的现象（近邻的目标会被融合为一个大目标）。。。 理论出发点没有错，数学推导和 计算也没有错 ，但是你得解释计算出来的东西是个什么？ 工程既要有数学的装潢，也要有物理的支撑。 虽然GCI可能也work，甚至在某些场景表现优异 -- 这些不能说没有问题，因为它在有些场景根本不work，融合结果还不如不融合，证实问题确实存在。 然而，这挡不住爱玩数学的人继续这么玩下去，偏就硬生生的忽略这些物理机理/意义问题...... 也许CI提出者会说，我原本没有考虑多目标和漏检、虚警问题，问题不在我；GCI提出者说 我只是一篇小文章为了推广我的FISST，蹭了一下当初的热点扩展了一些CI.. .... 上帝有时候还打盹呐，人类的链条知识传播，也容易走样，变了味（虽然有时候是往更好的方向变了去，众人的力量能够达到超出最初预想的结果）.... 下文通过一些直观性的、具体的案例和一些基础的、针对性统计学分析来研究上述的问题。 Second Order Statistics Analysis and Comparison between Arithmetic and Geometric Average Fusion https://www.sciencedirect.com/science/article/pii/S1566253518308303 Tiancheng Li , Hongqi Fan , Jesús G.García , Juan M Corchado (Submitted on 23 Jan 2019) Two fundamental approaches to information averaging are based on linear and logarithmic combination, yielding the arithmetic average (AA) and geometric average (GA) of the fusing initials, respectively. In the context of multi-sensor target tracking, the two most common formats of data to be fused are random variables and probability density functions, namely v -fusion and f -fusion, respectively. In this work, we analyze and compare the second order statistics (including variance and mean square error) of AA and GA in terms of both v -fusion and f -fusion. The case of weighted Gaussian mixtures representing multitarget densities in the presence of false alarms and missed detections (whose weight sums are not necessarily unit) is also considered, the result of which turns out to be significantly different from that of a single target. In addition to exact derivation, exemplifying analyses and illustrations are also provided. . https://doi.org/10.1016/j.inffus.2019.02.009 Keywords Multisensor fusion, Average consensus, Distributed tracking, Covariance intersection, Arithmetic mean, Geometric mean, Linear pool, Log-linear pool, Aggregation operator, Highlights Arithmetic averaging (AA) and geometric averaging (GA) are compared AA performs better in fusing variables while GA performs better in fusing PDFs Multitarget density fusion in the presence of false alarms and missed detection is studied. A hybrid fusion rule is proposed combining AA and GA for multitarget density fusion GA is comparably more accurate but less robust compared to AA
“一致性”研究如火如荼十余载，源起分布式复杂网络控制，后发展至滤波和跟踪。 现有所有的分布式滤波基本都是“滤波-融合-再滤波-再融合”这种“你方唱罢我登台，轮番上阵”的串行方式，或者说“鸡生蛋，蛋孵鸡”这种相互依赖迭代模式。 下文 提出了 一种 “一边滤波一边融合”并行模式（即网络通讯与节点滤波计算同步进行） ，大家可能会问：没有鸡(滤波)怎么来的蛋(融合)？没有蛋(融合)又怎么来的鸡(滤波)？这就是我们Engineer们需要发挥聪明才智的时候了。。。请看下文（借助了简单而强大的Importance Sampling方法）： 网络通讯与节点滤波计算同步进行的优势自不必说， 甚至有些场景下是唯一选择 ！比如局部节点的滤波计算占据了整个传感器扫描周期，根本没有剩余时间去搞通讯和信息融合 ---- 而这将伴随着传感器扫描周期越来越快变得普遍。。即使有些剩余时间，因为平行通讯可以完成更多周期的信息交换，传播更远，网络收益更大。。 A Distributed Particle-PHD Filter with Arithmetic-Average PHD Fusion Tiancheng Li , Franz Hlawatsch (Submitted on 17 Dec 2017 ( v1 ), last revised 20 Dec 2018 (this version, v2)) We propose a particle-based distributed PHD filter for tracking an unknown, time-varying number of targets. To reduce communication, the local PHD filters at neighboring sensors communicate Gaussian mixture (GM) parameters. In contrast to most existing distributed PHD filters, our filter employs an `arithmetic average' fusion. For particles--GM conversion, we use a method that avoids particle clustering and enables a significance-based pruning of the GM components. For GM--particles conversion, we develop an importance sampling based method that enables a parallelization of filtering and dissemination/fusion operations . The proposed distributed particle-PHD filter is able to integrate GM-based local PHD filters. Simulations demonstrate the excellent performance and small communication and computation requirements of our filter. Comments: 13 pages, codes available upon e-mail request Subjects: Systems and Control (cs.SY) ; Distributed, Parallel, and Cluster Computing (cs.DC) Cite as: arXiv:1712.06128 (or arXiv:1712.06128v2 for this version)
Local-Diffusion-based Distributed SMC-PHD Filtering Using Sensors with Limited Sensing Range Tiancheng Li ; Víctor Elvira ; Hongqi Fan ; Juan M. Corchado IEEE Sensors Journal Abstract: We investigate the problem of distributed multitarget tracking by using a set of spatially dispersed, collaborative sensors with limited sensing range (LSR), where each sensor runs a sequential Monte Carlo-probability hypothesis density filter and exchanges relevant posterior information with its neighbors. The key challenge stems from the LSR of neighbor sensors whose fields of view (FoVs) are partially/non-overlapped and therefore they may observe different targets at the same time. With regard to the local common FoVs among neighbor sensors, the proposed distributed fusion scheme, called local diffusion, performs one iteration of neighbor communication per filtering step in either of two means. One is given by immediate particle exchange, in which a reject-control operation is devised to reduce the number of communicating particles. The other is done by converting the particle distribution to Gaussian functions for parametric information exchange and fusion. The performance of both approaches has been experimentally investigated via simulation for different LSR situations and compared with cutting-edge approaches. T. Li, V. Elvira, H. Fan and J. M. Corchado, Local-Diffusion-Based Distributed SMC-PHD Filtering Using Sensors With Limited Sensing Range, in IEEE Sensors Journal , vol. 19, no. 4, pp. 1580-1589, 15 Feb.15, 2019. doi: 10.1109/JSEN.2018.2882084 @ARTICLE{Li2019local, author={T. Li and V. Elvira and H. Fan and J. M. Corchado}, journal={IEEE Sensors Journal}, title={Local-Diffusion-Based Distributed \\cal{SMC-PHD} Filtering Using Sensors With Limited Sensing Range}, year={2019}, volume={19}, number={4}, pages={1580-1589}, doi={10.1109/JSEN.2018.2882084}, ISSN={1530-437X}, month={Feb.},}
( 复杂 ) 网络涉及到一个基础的信息分享问题，即网络节点之间通过信息分享与融合，最终达成“一致” /Consensus ，及网络一致性。特别是相比于基于含有一个网络中间节点的中心式 /Centralized 网络，分布式网络中只通过节点与节点连接（相互称为邻居节点）进行通信，而没有中心节点，所以网络结构更为稳定（不会因为某一节点的破坏等而造成网络瘫痪），易于扩展（网络节点的性质一致，所以任何节点都可以再增加邻居节点）等，也实际上是很多物理网络（如监控传感网、社交网络等）的本质特征。 然而，在多目标跟踪多传感器信息融合里面却存在一个有趣的发现：传感器邻居节点相互之间分享的信息并不一定越多对于大家越有利，这里的“利”特指提高传感器节点估计的精度。这一点初感违背我们的直觉，因为一般的来讲：信息越多（应该）越有利。 那么为什么呐？ 物理传感器往往都遭受两类问题：一类是漏检，一类是虚警。前者是传感器没能获得目标的观测数据所造成，即 missingdata 问题。而后者是传感器遭遇干扰，获得观测数据不属于任何目标，是假信号，即 falsedata 问题。如此情况下，一个直观的逻辑是：因为有些信号可能是 falsedata 相关，其对于邻居节点没有益处，反而可能造成误导。因此， 信息的分享就不见得越多越好， 这一现象可称之为： Many Could Be Better Than All ，或者 Less-is-More 。实际这一现象并不罕见，如在认知科学/cognitive science （Gigerenzer, G., Brighton, H., 2009. Homo heuristicus: Why biased minds make better inferences. Topics in Cognitive Science, 1(1):107–143.） 和神经网络/neural networks（ Zhi-Hua Zhou, Jianxin Wu, Wei Tang, Ensembling neural networks: Many could be better than all, In Artificial Intelligence, Vol. 137, Issues 1–2, 2002, Pages 239-263。 ） 都有所表现。 因此适当的控制信息分享量（更宽泛的是，只分享有利的信息，而尽量减少误导性或者干扰性的信息），不但显然有利于降低通讯开支（这一点在现实中往往很重要，甚至是网络的重要限制。特别是分布式传感器网络往往都是 low-powered/ 低耗的传感器构成，以减少通讯和造价开支等） , 反而还可能更利于获得更高估计精度。 下文基于高斯混合 实现 PHD 滤波进行 杂波环境下的多目标探测与估计 揭示这一发现，提出了“部分一致性” Partial Consensus 的概念： （达成）部分一致要优于(达成)完全一致 。同时在随机集 PHD 一致性信息融合方式上给出了一些探索性思考，特别明确和比较了（简单却被忽视的）算术平均 Arithmetic Average 和（当前主流）几何平均 Geometric Average 的区别和相对优势 。 T. Li, J.M. Corchado and S. Sun, Partial Consensus and Conservative Fusion of Gaussian Mixtures for Distributed PHD Fusion, IEEE Trans. Aeros. Electr. Syst., 2018, DOI: 10.1109/TAES.2018.2882960. IEEE Xplore 连接： Partial Consensus and Conservative Fusion of Gaussian Mixtures for Distributed PHD Fusion Tiancheng Li ; Juan M. Corchado ; Shudong Sun IEEE Transactions on Aerospace and Electronic Systems Abstract: We propose a novel consensus notion, called partial consensus, for distributed Gaussian mixture probability hypothesis density fusion based on a decentralized sensor network, in which only highly-weighted Gaussian components (GCs) are exchanged and fused across neighbor sensors. It is shown that this does not only gain high efficiency in both network communication and fusion computation but also significantly compensates the effects of clutter and missed detections. Two conservative mixture reduction schemes are devised for refining the combined GCs. One is given by pairwise averaging GCs between sensors based on Hungarian assignment and the other merges close GCs for trace-minimal yet conservative covariance. The close connection of the result to the two approaches, known as covariance union and arithmetic averaging, is unveiled. Simulations based on a sensor network consisting of both linear and nonlinear sensors have demonstrated the advantage of our approaches over the generalized covariance intersection approach. 相关连接： 研究进一步扩展到采用随机样本（粒子滤波器）实现后验分布下的分布式“部分一致性”PHD滤波。 A Distributed Particle-PHD Filter with Arithmetic-Average PHD Fusion Tiancheng Li , Franz Hlawatsch (Submitted on 17 Dec 2017 ( v1 ), last revised 20 Dec 2018 (this version, v2)) We propose a particle-based distributed PHD filter for tracking an unknown, time-varying number of targets. To reduce communication, the local PHD filters at neighboring sensors communicate Gaussian mixture (GM) parameters. In contrast to most existing distributed PHD filters, our filter employs an `arithmetic average' fusion. For particles--GM conversion, we use a method that avoids particle clustering and enables a significance-based pruning of the GM components. For GM--particles conversion, we develop an importance sampling based method that enables a parallelization of filtering and dissemination/fusion operations. The proposed distributed particle-PHD filter is able to integrate GM-based local PHD filters. Simulations demonstrate the excellent performance and small communication and computation requirements of our filter. Comments: 13 pages, codes available upon e-mail request Subjects: Systems and Control (cs.SY) ; Distributed, Parallel, and Cluster Computing (cs.DC) Cite as: arXiv:1712.06128 (or arXiv:1712.06128v2 for this version) 研究进一步扩展到测距受限传感网下的多目标跟踪： Local-Diffusion-based Distributed SMC-PHD Filtering Using Sensors with Limited Sensing Range Tiancheng Li ; Víctor Elvira ; Hongqi Fan ; Juan M. Corchado IEEE Sensors Journal Abstract: We investigate the problem of distributed multitarget tracking by using a set of spatially dispersed, collaborative sensors with limited sensing range (LSR), where each sensor runs a sequential Monte Carlo-probability hypothesis density filter and exchanges relevant posterior information with its neighbors. The key challenge stems from the LSR of neighbor sensors whose fields of view (FoVs) are partially/non-overlapped and therefore they may observe different targets at the same time. With regard to the local common FoVs among neighbor sensors, the proposed distributed fusion scheme, called local diffusion, performs one iteration of neighbor communication per filtering step in either of two means. One is given by immediate particle exchange, in which a reject-control operation is devised to reduce the number of communicating particles. The other is done by converting the particle distribution to Gaussian functions for parametric information exchange and fusion. The performance of both approaches has been experimentally investigated via simulation for different LSR situations and compared with cutting-edge approaches.
50 年代末到60 年代初, 航天技术的发展涉及到大量的多输入多输出系统的最优控制问题, 用经典 控制理论已难以解决. 数字计算机的出现使得亨利￠ 庞加莱(1875-1906) 的状态空间表述方法可以作 为被控对象的数学模型和控制器设计与分析的工具.于是产生了以极大值原理、动态规划和 状态空间法 为核心的现代控制理论。 1. 经典状态空间法： State Space Model 状态空间模型包括两个模型： 一是状态方程模型，反映动态系统在输入变量作用下在某时刻所转移到的状态； 二是输出或量测方程模型，它将系统在某时刻的输出和系统的状态及输入变量联系起来。 如下 : 离散状态空间模型. 其中， k 为离散时间， x k 为状态变量， y k 为观测， u k ,v k 为噪声。 f k (.)为状态模型， h k (.) 为观测模型。 状态空间模型 提供一种方便、有效的时序递归的贝叶斯最优估计框架，因此有了坚实的理论基础。开山之作就是卡尔曼滤波，见下文的回顾： Approximate Gaussian Conjugacy: Parametric Recursive Filtering under Nonlinearity, Multimodality, Uncertainty, and Constraint, and Beyond, Frontiers of Information Technology Electronic Engineering, 2017, 18(12):1913-1939, ＬＩＮＫ 其中特别值得一提的是，哈佛终身教授何毓琦院士1964年发表于TAC的经典文章最早（之一）阐释了卡尔曼滤波和贝叶斯最优估计的关系。这极大助力了后来卡尔曼滤波的蓬勃发展 ，至今已有近六十年（因为一个方法关联一个伟大的理论，将如虎添翼！）： Ho, Y., Lee, R., 1964. A Bayesian approach to problems in stochastic estimation and control. IEEE Trans. Autom. Contr., 9(4):333-339. 状态空间模型的假设条件是动态系统符合马尔科夫Hidden Markov Model (HMM)特性，即上面的 x k = f k ( x k- 1 , u k ) ，即给定系统的现在状态，则系统的将来与其过去独立；这给建模和递归计算带来了极大方便。然而，HMM受限很多，对真实世界的刻画并不一定准确甚至有效，特别是，随着传感大数据时代的到来，其一些弊端日益突出. 毕竟我们今天的传感器和外界条件和卡尔曼、何院士的60年代完全不可同日而语: 目标变得越来越狡猾，难以用简单的HMM建模。特别是系统统计信息缺失(如不知道目标的运动模型，不知道系统噪声、甚至观测噪声模型，以及各种的复杂系统关联、时滞和耦合等等)，根本无法构建较为准确甚至有效的的状态空间模型， 2. 抛弃HMM： 对于传感器数据越来越多，传感器精度越来越高的情况，是否可以有新的解决方案（HMM弃之不用）呐？见 ： 如果我有成百上千个传感器，是否还需要动态模型？ 以及 轻松多传感器多目标探测与跟踪！ 这类方案主要应对完全未知系统背景，但数据量很大的情况 Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful. -- Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 74 3. 数据驱动的新框架： 既然经典方法成也萧何（HMM）败也萧何（HMM），除了弃之不用（太过消极了点）之外，更恰当的解决方法是寻找一个更符合自然规律和更能够准确描述真实世界的替代模型。 下文提出了一种取代HMM的新框架： Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting, IEEE Trans. Automation Science and Engineering, Oct. 2018. DOI:10.1109/TASE.2018.2882641. @ IEEE Xplore Pre-print @ arXiv:1708.02196 Joint Smoothing and Tracking Based on Continuous-Time Target Trajectory Function Fitting 论文中提供了程序源代码(链接) Abstract: This paper presents a joint trajectory smoothing and tracking framework for a specific class of targets with smooth motion. We model the target trajectory by a continuous function of time (FoT), which leads to a curve fitting approach that finds a trajectory FoT fitting the sensor data in a sliding time-window. A simulation study is conducted to demonstrate the effectiveness of our approach in tracking a maneuvering target, in comparison with the conventional filters and smoothers. 基于数据驱动的估计新框架（与基于HMM的经典状态空间法的思路相比）的核心在于将HMM替换为一个连续时间上的目标轨迹曲线函数 FoT (Function of Time) x k = f ( t ) , 从而将传统的滤波、平滑与预报等估计问题转化为一个连续时间窗内的 曲线拟合和参数学习 问题，即可用一个参数化的函数近似曲线轨迹函数： F ( t ; C k ) ≈ f ( t ) , 其中 C k 为待求参数。从而可以采用聚类、拟合与机器学习等数据驱动的工具与方法解决复杂场景下的（多）目标探测、跟踪与预报问题，这样就有望克服传统方法严重依赖目标模型假设、机动探测时滞、对错序数据敏感等难题。如下图所示： 上图中，左侧为 经典的滤波估计方法： KF : Kalman Filter, AGC : Approximate Gaussian Conjugacy, PF : Particle Filter, MHT :Multiple hypothesis tracking, FISST :Finite-Set Statistics. 等等.....近六十年的发展，出现了非常多的理论和方法。 右侧为数据驱动的新范式： O2 : Observation-only ， C4F : Clustering for Filtering ， F4S ：Fitting for Smoothing ， FTC ： Flooding-then-Clustering -， T-FoT : Trajectory Function of Time。 两者均采用相同的观测模型 y k = h k ( x k , v k ) , 但是不同的状态模型: 经典状态空间法采用HMM，新范式采用轨迹FoT。 一提到曲线拟合或者回归分析，可能会觉得计算效率低，不如递归迭代计算所以不能满足实时性？事实上： 对于线性观测系统，那么只需要线性拟合，并一般定义量测误差为范数2的马氏距离，曲线拟合退化为加权最小二乘直接给出，计算效率胜过线性卡尔曼滤波。 对于非线性观测系统进行线性拟合如多项式拟合，拟合需要往往需要迭代近似。对于非线性观测系统下的曲线拟合计算效率至关重要的是 参数的初始化， C k = C k -1 + ρ k 可大大加速计算效率（甚至一两步的梯度下降法就可以搜索到收敛的参数估计），从而可能使得拟合的计算效率扩展卡尔曼滤波（需要计算雅可比阵）还快 --- 这可能超出我们直觉想象 -- 不试不知道！ 更进一步，如果系统含有约束条件呐？仍然可以有效解决，请参考下文： 4. 约束下的SSM和轨迹曲线拟合： Single-Road-Constrained Positioning Based on Deterministic Trajectory Geometry Tiancheng Li， IEEE Communications Letters (Volume: 23, Issue: 1 , Jan. 2019) pp.。 80-83 论文中提供了程序源代码(链接) Abstract: We consider the single-road-constrained estimation problem for positioning a target that moves on a single, deterministic and exactly known trajectory. Based on the geometry of the trajectory curve, we cast the constrained estimation problem as an unconstrained problem with reduced state dimension. Two approaches are devised based on a Markov transition model for unscented Kalman filtering and a continuous function of time for (weighted) least square fitting, respectively. A popular simulation model has been used for demonstrating the performance of the proposed approaches in comparison to existing approaches. 请参考论文。下面给出该短文关键部分的一些截图。
通讯量无疑是很多分布式传感网一个重要的考量指标。网络协作算法的设计常常受限于此。 本文提出了一种最小节点间通讯量（邻居节点每次只需要相互传递一个实数的信息量）的分布式PHD滤波器实现分布式多目标跟踪。除了通讯量小之外，不同节点可以采用不同的PHD滤波器实现方式，比如高斯混合和粒子滤波。虽然通讯消耗小，但算法的精度收益显著。 详见： T. Li, F. Hlawatsch and P. M. Djurić, Cardinality-Consensus-Based PHD Filtering for Distributed Multitarget Tracking, in IEEE Signal Processing Letters , vol. 26, no. 1, pp. 49-53, Jan. 2019. doi: 10.1109/LSP.2018.2878064 基于模一致性的PHD滤波实现分布式多目标跟踪。 连接 Cardinality-Consensus-Based PHD Filtering for Distributed Multitarget Tracking Tiancheng Li ; Franz Hlawatsch ; Petar M. Djurić Abstract: We present a distributed probability hypothesis density (PHD) filter for multitarget tracking in decentralized sensor networks with severely constrained communication. The proposed “cardinality consensus” (CC) scheme uses communication only to estimate the number of targets (or, the cardinality of the target set) in a distributed way. The CC scheme allows for different implementations—e.g., using Gaussian mixtures or particles—of the local PHD filters. Although the CC scheme requires only a small amount of communication and of fusion computation, our simulation results demonstrate large performance gains compared with noncooperative local PHD filters. Published in: IEEE Signal Processing Letters (Volume: 26, Issue: 1 , Jan. 2019) Page(s): 49- 53 DOI: 10.1109/LSP.2018.2878064
欢迎投稿，信息融合大会2018专题-智能信号处理与数据挖掘应用于目标跟踪”。大会2018年7月10-13号在美丽的英国剑桥举办！ information fusion - data mining - signal processing 交叉前沿！ SS11 - Intelligent Information Fusion and Data Mining for Tracking Research on Intelligent Systems for information fusion data mining has matured during the past years and many effective applications of this technology are now deployed such as Wearable Computing, Intelligent Surveillance, Smart City/Home-Care, Smart Grid, Web Tracking, Network Management. The rapid development of modern sensors and their application to distributed networks provide a foundation for new paradigms to combat the challenges that arise in target detection, tracking, trajectory forecasting and sensor fusion in harsh environments with poor prior information. For example, the advent of large-scale/massive sensor systems provides very informative observation, which facilitates novel perspectives based on data clustering and model learning to deal with false alarms and misdetection, given little knowledge about the objects, sensors and the background. Sensor data fitting and regression analysis provide another unlimited means to utilize the unstructured context information such as “the trajectory is smooth” for continuous-time trajectory estimation and forecasting. As such, the sensor community has the interest in novel information fusion data mining methods coupling traditional statistical techniques for substantial performance enhancement, especially for challenging problems that make traditional approaches inappropriate. This special session aims to assemble and disseminate information on recent, novel advances in intelligent systems, information fusion sensor data mining techniques and approaches, and promote a forum for continued discussion on the future development. Both theoretical and practical approaches to address the problems in this area are welcome. IMPORTANT DEADLINES Full paper submission Deadline extended to15 March 2018
Approximate Gaussian conjugacy : parametric recursive filtering under nonlinearity, multimode, uncertainty, and constraint, and beyond Author(s): Tian-cheng Li, Jin-ya Su, Wei Liu, Juan M. Corchado Affiliation(s): School of Sciences, University of Salamanca, Salamanca 37007, Spain; more Corresponding email(s): t.c.li@usal.es , J.Su2@lboro.ac.uk , w.liu@sheffield.ac.uk , corchado@usal.es Key Words: Kalman filter, Gaussian filter, time series estimation, Bayesian filtering, nonlinear filtering; constrained filtering, Gaussian mixture, maneuver, unknown inputs Abstract: Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek exact analytical estimates based on closed-form Markov-Bayes recursion, e.g., recursion from a Gaussian or gaussian mixture (GM) prior to a Gaussian/GM posterior (termed Gaussian conjugacy in this paper), form the backbone for general time series filter design. Due to challenges arising from nonlinearity, multimode (including target maneuver ), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), and so on, new theories, algorithms and technologies are continuously being developed in order to maintain, or approximate to be more precise, such a conjugacy. They have in a large part contributed to the prospective developments of time series parametric filters in the last six decades. This paper reviews the stateof- the-art in distinctive categories and highlights some insights which may otherwise be overlooked . In particular, specific attention is paid to nonlinear systems with very informative observation , multimodal systems including gaussian mixture posterior and maneuver s, intractable unknown inputs and constraints, to fill the voids in existing reviews/surveys. To go beyond a pure review, we also provide some new thoughts on alternatives to the first order Markov transition model and on filter evaluation with regard to computing complexity. 10 Highlights presented in the paper: CRLB (Cramer-Rao Lower Bound) limits only the variance of unbiased estimators and lower MSE (mean squared error) can be obtained by allowing for a bias in the estimation, while ensuring that the overall estimation error is reduced. The KF (Kalman filter) is conditionally biased with a non-zero process noise realization in the given state sequence and is not an efficient estimator in a conditional sense, even in a linear and Gaussian system. Among all possible distributions of the observation noise $\\mathbf{w}$ with a fixed covariance matrix, the CRLB for $\\mathbf{x}$ attains its maximum when $\\mathbf{w}$ is Gaussian, i.e., the Gaussian scenario is the ``worst-case'' for estimating $\\mathbf{x}$. For sufficiently precise measurements, none of the KF variants, including the KF itself, are based on an accurate approximation of the joint density. Conversely, for imprecise measurements all KF variants accurately approximate the joint density, and therefore the posterior density. Differences between the KF variants become evident for moderately precise measurements. While the BCRLB (Bayesian Cramer-Rao Lower Bound) sets a best line (in the sense of MMSE) that any unbiased sequential estimator can at maximum achieve, the O2 inference sets the bottom line that any ``effective'' estimator shall at worst achieve. Many adaptive-model approaches proposed for MTT (manuevering target tracking) may show superiority when the target indeed maneuvers but perform disappointingly or even significantly worse than those without using an adaptive model, when there is actually no maneuver. We call this over-reaction due to adaptability. The theoretically best achievable second order error performance, namely the CRLB, in target state estimation is independent of knowledge (or the lack of it) of the observation noise variance. Robust filtering is much more related to robustness with respect to statistical variations than it is to optimality with respect to a specified statistical model. Typically, the worst case estimation error rather than the MSE needs to be minimized in a robust filter. As a result, robustness is usually achieved by sacrificing the performance in terms of other criteria such as MSE and computing efficiency. The standard structure of recursive filtering is based on infinite impulse response (IIR), namely all the observations prior to the present time have effect on the state estimate at present time and therefore the filter suffers from legacy errors. Computing speed matters! open access page: http://www.jzus.zju.edu.cn/iparticle.php? doi=10.1631/FITEE.1700379
SS6: Sensor Data Mining For Tracking Description: The rapid development of advanced sensors and their joint application provide a foundation for new paradigms to combat the challenges that arise in target detection, tracking and forecasting in harsh environments with poor prior information. As a consequence, the sensor community has expressed interest in novel data mining methods coupling traditional statistical techniques for substantial performance enhancement. For example, the advent of multiple/massive sensor systems provides very rich observation at high frequency yet low financial cost, which facilitates novel perspectives based on data clustering and model learning to deal with false alarms and misdetection, given little statistical knowledge about the objects, sensors and the background. Numerical fitting and regression analysis provide another unlimited means to utilize the unstructured context information such as “the trajectory is smooth” for continuous-time target trajectory estimation. Incorporating additional, readily available information to constrain the adaptive response and to combat poor scenario knowledge, has shown promise as a means of restoring sensor capability over a range of challenging operating conditions as well as to deal with a variety of challenging problems that makes traditional approaches awkward. The purpose of this special section is to assemble and disseminate information on recent, novel advances in sensor signal and data mining techniques and approaches, and promote a forum for continued discussion on the future development. Both theoretical and practical approaches in the area are welcomed. Organizers: Tiancheng Li ( t.c.li@usal.es ) Haibin Ling ( hbling@temple.edu ) and Genshe Chen ( gchen@intfusiontech.com ) The topics of interest of this specialsection include but are not limited to: · Adaptive filtering · Learning for state space models · Manoeuvring target detectionand tracking · Object recognition/classificationusing sonar, radar, video, soft data sources, etc. · Clustering approaches fortracking · Regression analysis for trajectoryestimation · Multiple Intelligent dataassociation/fusion · Machine learning technology fortracking Submission链接： http://www.fusion2017.org/submissions.html 欢迎投稿！ The 20th International Conference on Information Fusion (Fusion 2017) will be held in Xi'an, China during July 10–13, 2017. Conference Venue: Wyndham Grand Xian South Video of Xi'an : http://www.fusion2017.org/video/Fusion2017_2.ogv
用计算机视觉追踪苍蝇 2010年3月3日 cvchina 没有评论 Ctrax: The Caltech Multiple Walking Fly Tracker 当生物学家要研究小型生物，比如果蝇的行为时，传统的法布尔式的人为观测变得不可能。加州理工利用计算机视觉，在一个相当长的时间里，跟踪每个果蝇的位置和朝向，从而为生物学家解决了大量观测数据的来源问题。 Ctrax 是基于matlab的开源代码，大伙可以在夏天抓几只苍蝇来试验一下。。。 Ctrax is an open-source, freely available, machine vision program for estimating the positions and orientations of many walking flies, maintaining their individual identities over long periods of time. It was designed to allow high-throughput, quantitative analysis of behavior in freely moving flies. Our primary goal in this project is to provide quantitative behavior analysis tools to the neuroethology community, thus weve endeavored to make the system adaptable to other labs setups. We have assessed the quality of the tracking results for our setup, and found that it can maintain fly identities indefinitely with minimal supervision, and on average for 1.5 fly-hours automatically. To minimize the number of identity errors made during tracking, we provide the FixErrors Matlab GUI that identifies suspicious sequences of frames and allows a user to correct any tracking errors. We also distribute the BehavioralMicroarray Matlab Toolbox for defining and detecting a broad palette of individual and social behaviors. This software inputs the trajectories output by Ctrax and computes descriptive statistics of the behavior of each individual fly. We provide software for three proof-of-concept experiments to show the potential of the Ctrax software and our behavior detectors. This software is described in the article High-Throughput Ethomics in Large Groups of Drosophila .
标签: 目标跟踪
