Modeling uncertainties for real linear systems are unavoidable. These uncertainties can significantly degrade the performance of optimal state estimators designed for nominal system models. The challenge is quantifying such uncertainties and devising robust estimators that are insensitive to them. This paper is therefore concerned with distributionally robust state estimation for linear Markov systems. We propose a new modeling framework that describes uncertainties using a family of distributions so that the worst-case robust estimate in the state space is made over the least-favorable distribution. This framework uses only one or two scalars to express the uncertainty set and does not require the structural information of model uncertainties. Furthermore, the moment-based ambiguity set is suggested to embody the distributional uncertainty family. As a result, the estimation problem transforms into a nonlinear semidefinite program with linear constraints, which can be analytically and efficiently solved. Intensive experiments illustrate the advantages of the proposed framework over existing methods.

Range-based target localization combines the range measurements and appropriate algorithms [such as time of arrival (TOA)] to determine the real-time position of a moving target not only in a satellite-denied environment but also for high-precision applications in an open (i.e., satellite-available) environment. However, the measurements from sensors always suffer from uncertainties, such as noises, outliers, dropouts, and biases, which make measurements not reliable enough to directly utilize in positioning. This article is, therefore, concerned with two kinds of sensor correction problems: 1) attenuating the noises, removing the outliers, and completing the dropouts and 2) identifying the discredited sensors and forbidding them from use. Specifically, we model a range measurement time series from a ranging sensor as a nonstationary stochastic process and then use a local polynomial to regress the mean function in an online manner. The derivatives of the mean function are identified as the state variables in the state space, and the Kalman filter is used to estimate the states. We will show that: 1) the proposed method is simple yet effective in denoising the measurements and correcting the outliers/dropouts with very high accuracy and precision and 2) the defined and estimated states can clearly reflect the pattern of one type of nonspecific anomaly contained in the range time series, which enables the recognition of the dysfunctional sensors.