机器人代写|SLAM代写机器人导航代考|Joint Compatibility Branch and Bound

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

机器人代写|SLAM代写机器人导航代考|Joint Compatibility Branch and Bound

If multiple observations are gathered per control, the maximum likelihood approach will treat each data association decision as a independent problem. However, because data association ambiguity is caused in part by robot pose uncertainty, the data associations of simultaneous observations are correlated. Considering the data association of each of the observations separately also ignores the issue of mutual exclusion. Multiple observations cannot be associated with the same landmark during a single time step.

Neira and Tardos [68] showed that both of these problems can be remedied by considering the data associations of all of the observations simultaneously, much like the Local Map Sequencing algorithm does. Their algorithm, called Joint Compatibility Branch and Bound (JCBB), traverses the Interpretation Tree [35], which is the tree of all possible joint correspondences. Different joint data association hypotheses are compared using joint compatibility, a measure of the probability of the set of observations occurring together. In the EKF framework, this can be computed by finding the probability of the joint innovations of the observations. Clearly, considering joint correspondences comes at some computational cost, because an exponential number of different hypotheses must be considered. However, Neira and Tardos showed that many of these hypotheses can be excluded without traversing the entire tree.

机器人代写|SLAM代写机器人导航代考|Combined Constraint Data Association

Bailey [1] presented a data association algorithm similar to JCBB called Combined Constraint Data Association (CCDA). Instead of building a tree of joint correspondences, CCDA constructs a undirected graph of data association constraints, called a “Correspondence Graph”. Each node in the graph. represents a candidate pairing of observed features and landmarks, possibly determined using a nearest neighbor test. Edges between the nodes represent joint compatibility between pairs of data associations. The algorithm picks the set of joint data associations that correspond to the largest clique in the correspondence graph. The results of JCBB and CCDA should be similar, however the CCDA algorithm is able to determine viable data associations when the pose of the robot relative to the map is completely unknown.

Scan matching $[54]$ is a data association method that based on a modified version of the Iterative Closest Point (ICP) algorithm [4]. This algorithm alternates between a step in which correspondences between data are identified, and a step in which a new robot path is recovered from the current correspondences. This iterative optimization is similar in spirit to Expectation Maximization (EM) [17] and RANSAC [27]. First, a locally consistent map is built using scan-matching $[39]$, a maximum likelihood mapping approach. Next, observations are matched between different sensor scans using a distance metric. Based on the putative correspondences, a new set of robot poses is derived. This alternating process is iterated several times until some convergence criterion is reached. This process has shown significant promise for the data association problems encountered in environments with very large loops.

机器人代写|SLAM代写机器人导航代考|Multiple Hypothesis Tracking

Thus far, all of the data association algorithms presented all choose a single data association hypothesis to be fed into an EKF, or approximate EKF algorithm. There are a few algorithms that maintain multiple data association hypotheses over time. This is especially useful if the correct data association of an observation cannot be inferred from a single measurement. One such approach in the target tracking literature is the Multiple Hypothesis Tracking or MHT algorithm [77]. MHT maintains a set of hypothesized tracks of multiple targets. If a particular observation has multiple, valid data association

interpretation s, new hypotheses are created according to each hypothesis. In order to keep the number of hypotheses from expanding without bound, heuristics are used to prune improbable hypotheses from the set over time.
Maintaining multiple EKF hypotheses for SLAM is unwieldy because each EKF maintains a belief over robot pose and the entire map. Nebot et al. [67] have developed a similar technique that “pauses”. map-building when data association becomes ambiguous, and performs multi-hypothesis localization using a particle filter until the ambiguity is resolved. Since map building is not performed when there is data association ambiguity, the multiple hypotheses are over robot pose, which is a low-dimensional quantity. However, this approach only works if data association ambiguity occurs sporadically. This can be useful for resolving occasional data association problems when closing loops, however the algorithm will never spend any time mapping if the ambiguity is persistent.

机器人代写|SLAM代写机器人导航代考|Joint Compatibility Branch and Bound

Neira 和 Tardos [68] 表明，这两个问题都可以通过同时考虑所有观察结果的数据关联来解决，就像局部地图排序算法一样。他们的算法称为联合兼容性分支定界 (JCBB)，它遍历解释树 [35]，它是所有可能的联合对应的树。使用联合兼容性来比较不同的联合数据关联假设，联合兼容性是一组观测值一起发生的概率的度量。在 EKF 框架中，这可以通过找到观察的联合创新的概率来计算。显然，考虑联合对应需要一些计算成本，因为必须考虑指数数量的不同假设。然而，

机器人代写|SLAM代写机器人导航代考|Combined Constraint Data Association

Bailey [1] 提出了一种类似于 JCBB 的数据关联算法，称为组合约束数据关联 (CCDA)。CCDA 不是构建联合对应树，而是构建数据关联约束的无向图，称为“对应图”。图中的每个节点。表示观察到的特征和地标的候选配对，可能使用最近邻测试确定. 节点之间的边表示数据关联对之间的联合兼容性。该算法选择与对应图中最大集团相对应的联合数据关联集。JCBB 和 CCDA 的结果应该相似，但是当机器人相对于地图的位姿完全未知时，CCDA 算法能够确定可行的数据关联。

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