Filters

In signal processing, a filter is defined as a device or process that removes from a signal unwanted features [17]. In this sense, the process of extracting shadows from $\tilde{q}_t$ and $\tilde{y}_t$ is exactly a filter. Moreover, $\mathcal I_{hist}$ and $\mathcal I_{ss}$ are connected through this filter. From this perspective, solving a task becomes finding the correct I-space, applying the associated filter, and performing additional computation as events happen. To illustrate the application of this framework, we study two flavors of the problem of tracking hidden targets: 1) a nondeterministic setting in which targets move nondeterministically but have perfect observation of critical events, and 2) a probabilistic setting in which the targets' movement has a probabilistic model and there are imperfect sensors.