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Estimation and Kalman Filters
Published in S. Sitharama Iyengar, Richard R. Brooks, Distributed Sensor Networks, 2016
An alternative approach to batch estimation is the sequential estimation approach. This approach incrementally updates the estimate of the state vector as each new observation is received. Hence if x(to) is the estimate of a state vector at time to based on n previous observations, then sequential estimation provides the means of obtaining a new estimate for x, (i.e., xn+1(to)), based on n + 1 observations by modifying the estimate xn(to). This new estimate is obtained without revisiting all previous n observations. By contrast in batch estimation, if a value of xn(to) had been obtained utilizing n observations, then to determine xn+1(to), all n + 1 observations would have to be processed. The Kalman filter is a commonly used approach for sequential estimation.
Case study on applying sequential analyses in operational testing
Published in Quality Engineering, 2023
Monica Ahrens, Rebecca Medlin, Keyla Pagán-Rivera, John W. Dennis
Medlin et al. (2021) subdivides the field of Sequential Analysis into three broad functional categories: sequential testing, sequential design, and sequential estimation. These categories are not mutually exclusive in the sense that design procedures often include an objective related to testing or estimation. The problems categorized as sequential testing and estimation only allow the number of observations to depend upon information acquired throughout the investigation. Design problems increase the complexity of the sequential procedure by allowing elements affecting the pattern and composition of the observations to depend upon acquired information as well (Govindarajulu 1975). In this paper, we focus on the methods for sequential testing and sequential design. Even though these methods can be used to benefit a variety of disciplines, we use sequential analysis techniques to demonstrate an efficient and effective way for the DoD to maximize system understanding in test.
Monitoring sparse and attributed networks with online Hurdle models
Published in IISE Transactions, 2021
Samaneh Ebrahimi, Mostafa Reisi-Gahrooei, Kamran Paynabar, Shawn Mankad
The Hurdle model has been used previously to account for network sparsity (Heard et al., 2010); however, previous approaches did not utilize edge and node attributes, instead modeling edge probabilities as a function of time. To take the network dynamics coupled with edges and nodes’ attributes into account, we integrate the state-space model with the Hurdle model, where it is assumed that the parameters of the Hurdle regression follow a Markovian process, and develop a sequential estimation scheme using an Extended Kalman Filter (EKF) to update the state space parameters and predict the value of upcoming networks. The overall framework is illustrated in Figure 1. As shown in the figure, in the offline phase, using a stream of in-control (i.e., training) networks, we build a Hurdle model using nodes and edges attributes, and estimate the initial state-space parameters. In the online (i.e., deployment) phase, as new network observations arrive, the estimated Hurdle model is used to predict the edge values for the incoming network snapshot. Additionally, with the upcoming network observations, the parameters of the state-space Hurdle model are updated using EKF. As time progresses, residuals that compare the newly realized network with the predicted one are used to detect a sudden, structural change in the network through EWMA control charts.