Continuous Estimation Using Context-Dependent Discrete Measurements

Abstract

This paper considers the problem of continuous state estimation from discrete context-based measurements. Context measurements provide binary information as obtained from the system's environment, e.g., a medical alarm indicating that a vital sign is above a certain threshold. Since they provide state information, these measurements can be used for estimation purposes, similar to standard continuous measurements, especially when standard sensors are biased or attacked. Context measurements are assumed to have a known probability of occurring given the state; in particular, we focus on the probit function to model threshold-based measurements, such as the medical-alarm scenario. We develop a recursive context-aware filter by approximating the posterior distribution with a Gaussian distribution with the same first two moments as the true posterior. We show that the filter's expected uncertainty is bounded when the probability of receiving context measurements is lower bounded by some positive number for all system states. Furthermore, we provide an observability-like result-all eigenvalues of the filter's covariance matrix converge to 0 after repeated updates if and only if a persistence of excitation condition holds for the context measurements. Finally, in addition to simulation evaluations, we applied the filter to the problem of estimating a patient's blood oxygen content during surgery using real-patient data.

Distributed fusion Kalman filtering under binary sensors

“…Consider O 2 content estimation in arteries using only the noninvasive binary pulmonary measurements, where the framework of blood dynamic in the lung is shown in Figure . According to the diffusion process described in this figure, the dynamic physiological model for the arterial O 2 content can be derived from the oxygen content equation and the alveolar gas equation as: where , and c 2 ( t )=[1− u ( t )(1− RQ )]/ RQ .…”

“…Remark The estimation problems addressed in the work of Koutsoukos et al and Ivanov et al assumed that the probability of outputs at a given state is known for binary sensors. However, this assumption is not reasonable in practical applications.…”

“…For example, the estimation of hybrid systems was addressed under binary sensors in the work of Koutsoukos . Ivanov et al studied the context‐aware filter for systems with binary sensors to improve estimation accuracy. Apparently, the Gaussian distribution approximation of posterior distribution need to be satisfied for Bayesian approach, which is a strict condition for estimators.…”

“…Ivanov et al studied the context‐aware filter for systems with binary sensors to improve estimation accuracy. Apparently, the Gaussian distribution approximation of posterior distribution need to be satisfied for Bayesian approach, which is a strict condition for estimators. In most of the above‐mentioned research works, the raw measurements from multiple sensors are augmented to design estimators in a centralized fusion structure.…”

Robust Estimation Framework with Semantic Measurements

“…Semantic data, or object detection events, can be modeled as binary measurements that have state-dependent probabilistic likelihood functions [1], [2], [3]. The probability of a positive detection measurement is modeled as an inverseexponential function of the distance to the detected object in [1], meaning positive object detections occur with higher probability when the vehicle is close to the detected object.…”