Abstract
In various applications one faces the problem of estimating a signal from discontinuous observations. For example, in biomedical applications the signal may be the ‘state’ of a given organ and one observes through an external counter the amount of radioactivity sequestered by the organ after injection of a radioactive tracer. Here the problem is studied in the context of nonlinear filtering when the signal can be modelled as either a random variable or a diffusion process, and the observations have a continuous and a purely discontinuous component; both components may be affected by the signal. When the signal is a random variable an explicitly computable solution is obtained; for the diffusion case the solution is given as a sequence of approximating filters that can be computed recursively.
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Di Masi, G.B., Runggaldier, W.J. Non-linear filtering with discontinuous observations and applications to life sciences. Bltn Mathcal Biology 45, 571–577 (1983). https://doi.org/10.1007/BF02459588
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DOI: https://doi.org/10.1007/BF02459588