Bounded-Error Estimator Design with Missing Data Patterns via State Augmentation

Simultaneous mode, input and state estimation for switched linear stochastic systems

“…In addition, we also plan to explore other models of the hidden mode transitions, for example, with bounds on time allowed between consecutive switches 32,33 or with specifications of the set of allowable temporal patterns using a formal language. 34,35 ORCID Sze Zheng Yong https://orcid.org/0000-0002-2104-3128…”

“…For future work, we aim to investigate how prior knowledge about the range of possible values of the unknown inputs can be incorporated, similar to Reference 31, along with a rigorous theoretical analysis of the resulting dynamic MM algorithm. In addition, we also plan to explore other models of the hidden mode transitions, for example, with bounds on time allowed between consecutive switches 32,33 or with specifications of the set of allowable temporal patterns using a formal language 34,35 …”

Equalized Recovery State Estimators for Linear Systems with Delayed and Missing Observations

“…Note that i + τ (i)≥T means that the i-th data is delayed beyond the horizon T , which is similar to the situation where that data is missing. In other words, the case considered in [14], [15], [16] is a special case of the delayed data language in this paper. Example 1.…”

“…The authors in [13] introduced the property of equalized performance, which implies that the estimation error always remains equal/invariant. For systems with missing observations, [14] and [15] modeled the feasible missing data patterns with a finite-length language and proposed finite-horizon affine estimators with an extended property called equalized recovery, which implies that within a finite time horizon, especially for times when observations may go missing, the estimation error can have a more relaxed upper bound, but by the end of the horizon should return to the initial upper bound. In more recent work, [16], [17] developed a prefix-based method to predict the possible pattern of missing data to improve the estimation performance.…”

“…Instead of assuming probabilistic missing or delay events, we model them using a fixed-length language that represents the set of all possible temporal patterns of the missing or delayed data and further construct a reduced eventbased language with unique event sequences. In contrast to the worst-case language method in [14], [15], our proposed design monitors the history of available data at run time and adapts the estimator gain matrices. Furthermore, we extend existing equalized recovery estimators to allow time-varying intermediate levels and consider the equalized recovery level as a decision variable, enabling us to directly find the global minimum of the intermediate levels.…”