Abstract
Sequential detection is a methodology developed essentially by Wald [1] in the late 1940s providing an alternative to the classical batch methods evolving from the basic Neyman–Pearson theory of the 1930s [2, 3]. From the detection theoretical viewpoint, the risk (or error) associated with a decision typically decreases as the number of measurements increases. Sequential detection enables a decision to be made more rapidly (in most cases) employing fewer measurements while maintaining the same level of risk. Thus, the aspiration is to reduce the decision time while maintaining the risk for a fixed sample size. Its significance was truly brought to the forefront with the evolution of the digital computer and the fundamental idea of acquiring and processing data in a sequential manner. The seminal work of Middleton [2, 4, 5, 6, 7] as well as the development of sequential processing techniques [8, 9, 10, 11, 12, 13] during the 1960s provided the necessary foundation for the sequential processor/detector that is applied in a routine manner today [7, 8, 9, 10, 11, 13].
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Notes
- 1.
This notation is defined in terms of predicted conditional means and covariances by: \(\hat{\mathbf{s}}({t}_{k}\vert {t}_{k-1})\) and \(\tilde{P}({t}_{k}\vert {t}_{k-1}) := \mbox{ cov}(\tilde{\mathbf{s}}({t}_{k}\vert {t}_{k-1}))\) for the predicted state estimation error, \(\tilde{\mathbf{s}}({t}_{k}\vert {t}_{k-1}) := \mathbf{s}({t}_{k}) -\hat{\mathbf{s}}({t}_{k}\vert {t}_{k-1})\).
- 2.
It is well known that some of the modern variants currently available offer alternatives such as the unscented Kalman filter or particle filter [14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26] that are better than the EKF but we choose this formulation since it easily tracks the linear case developed previously.
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Candy, J.V. (2012). Sequential Bayesian Detection: A Model-Based Approach. In: Cohen, L., Poor, H., Scully, M. (eds) Classical, Semi-classical and Quantum Noise. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6624-7_2
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