In many autonomy applications, performance of perception algorithms is important for effective planning and control. In this paper, we introduce a framework for computing the probability of satisfaction of formal system specifications given a confusion matrix, a statistical average performance measure for multi-class classification. We define the probability of satisfaction of a linear temporal logic formula given a specific initial state of the agent and true state of the environment. Then, we present an algorithm to construct a Markov chain that represents the system behavior under the composition of the perception and control components such that the probability of the temporal logic formula computed over the Markov chain is consistent with the probability that the temporal logic formula is satisfied by our system. We illustrate this approach on a simple example of a car with pedestrian on the sidewalk environment, and compute the probability of satisfaction of safety requirements for varying parameters of the vehicle. We also illustrate how satisfaction probability changes with varied precision and recall derived from the confusion matrix. Based on our results, we identify several opportunities for future work in developing quantitative system-level analysis that incorporates perception models.

中文翻译：

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利用分类指标进行具有时序逻辑规范的定量系统级分析

在许多自治应用中，感知算法的性能对于有效的计划和控制很重要。在本文中，我们介绍了一个框架，该框架用于在给定混淆矩阵（一种用于多类分类的统计平均性能指标）的情况下，计算满足正式系统规范的概率。给定特定的代理初始状态和环境的真实状态，我们定义了线性时间逻辑公式的满意概率。然后，我们提出一种算法来构造马尔可夫链，该链表示在感知和控制组件的组合下的系统行为，以使在马尔可夫链上计算出的时间逻辑公式的概率与时间逻辑公式为对我们的系统感到满意。我们在人行道环境中行人的汽车的简单示例中说明了这种方法，并计算了满足车辆各种参数的安全要求的概率。我们还说明了满意度概率是如何从混乱矩阵得出的精度和召回率变化的。根据我们的结果，我们在开发结合感知模型的定量系统级分析中发现了一些未来工作的机会。