Li T, Da K, 2020. Best fit of mixture for distributed Poissonmulti-Bernoulli mixture filtering, https://doi.org/10.36227/techrxiv.12351710 讨论了一种 普适性的多源信息融合Best Fit of Mixture原则 ：将多源后验分布posterior信息混合为一个mixture（包含了全部的信息），然后寻找一种与该mixture信息差异最小，且跟融合源posterior分布同构的新分布。 特别讨论了近年来随机集框架下的一种存在闭合递归解的 泊松多伯努利混合（Poisson Multi-Bernoulli Mixture，PMBM） 分布式融合实现。PMBM是标准多目标跟踪模型下的Conjugate Prior，这一点对于递归贝叶斯滤波很重要。 研究发现： 对多个MBM组成的加权mixture进行KLD最小逼近得到的MBM恰就是这些MBM的算术均值（Arithmetic Average，AA） ！因此采用分布式Flooding点对点通信算法，以及 AA 融合方法就可以实现 MBM的精确闭合融合，简而美的组合。 论文基于PMBM框架证明和验证了该MBM-AA闭合融合的“数学美”和在克服漏检方面的显著性能。（当然还有不足，需要在融合子元上进一步merging for fusion...这个留在正式发表版本报道） 详细请见： https://www.techrxiv.org/articles/Best_Fit_of_Mixture_For_Distributed_Poisson_Multi-Bernoulli_Mixture_Filtering/12351710 预印版DOI：10.36227/techrxiv.12351710 +++++++++++++++++++++++++++更多阅读+++++++++++++++++++++++++++++++ 线性AA融合在 大规模传感网 分布式Multi-Bernoulli 滤波方面的优越性能 T. Li, X. Wang, Y. Liang and Q. Pan, On Arithmetic Average Fusion and Its Application for Distributed Multi-Bernoulli Multitarget Tracking , in IEEE Transactions on Signal Processing , vol. 68, pp. 2883-2896, 2020, doi: 10.1109/TSP.2020.2985643. 证明了 PDF-AA/GA融合的Frechet Mean 数学特性，从而将AA与GA两种均值融合归一到统一框架 提出了一种 target-wise fusion rule （ 目标敏感融合规则 ） 提出对mixture中的元素进行聚类与2D匹配两种归类方法，从而可以采用 target-wise fusion rule进行MB-AA融合，显著改善子元素的定位精度 ，获得了非常显著的融合精度、效率和稳健性！ 提出了两种通讯量极小/最小的 势一致性分布式MB滤波方案 Link： https://ieeexplore.ieee.org/document/9057730 近年来很热的神经网络中神经元节点之间的运算是不是也更多是加法融合/线性加和运算？ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 相关博文链接： 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！ 分布式网络信息共享：Many Could Be Better Than All 轻松多传感器多目标探测与跟踪！ 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邦多传感器PHD滤波 基于受限测距传感网的分布式多目标跟踪 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 基于算术均值一致性的高效、分布式、联合传感定位与多目标跟踪
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
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
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.
标签: 随机集
