@InProceedings{8902938,
  author = {D. Reinhard and M. Fauß and A. M. Zoubir},
  booktitle = {2019 27th European Signal Processing Conference (EUSIPCO)},
  title = {Bayesian Sequential Joint Signal Detection and Signal-to-Noise Ratio Estimation},
  year = {2019},
  pages = {1-5},
  abstract = {Jointly detecting a signal in noise and, in case a signal is present, estimating the Signal-to-Noise Ratio (SNR) is investigated in a sequential setup. The sequential test is designed such that it achieves desired error probabilities and Mean-Squared Errors (MSEs), while the expected number of samples is minimized. This problem is first converted to an unconstrained problem, which is then reduced to an optimal stopping problem. The solution, which is obtained by means of dynamic programming, is characterized by a non-linear Bellman equation. A gradient ascent approach is then presented to select the cost coefficients of the Bellman equation such that the desired error probabilities and MSEs are achieved. A numerical example concludes the work.},
  keywords = {Bayes methods;dynamic programming;error statistics;estimation theory;gradient methods;mean square error methods;minimisation;nonlinear equations;probability;signal detection;MSEs;unconstrained problem;optimal stopping problem;nonlinear Bellman equation;error probabilities;signal-to-noise ratio estimation;sequential setup;sequential test;Mean-Squared Errors;Bayesian sequential joint signal detection;SNR;dynamic programming;gradient ascent approach;Bellman equation;cost coefficients;Estimation;Signal to noise ratio;Bayes methods;Error probability;Random variables;Cost function;sequential analysis;joint detection and estimation;signal-to-noise ratio estimation;Monte Carlo;optimal stopping},
  doi = {10.23919/EUSIPCO.2019.8902938},
  issn = {2076-1465},
  month = {Sep.},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570532715.pdf},
}

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The sequential test is designed such that it achieves desired error probabilities and Mean-Squared Errors (MSEs), while the expected number of samples is minimized. This problem is first converted to an unconstrained problem, which is then reduced to an optimal stopping problem. The solution, which is obtained by means of dynamic programming, is characterized by a non-linear Bellman equation. A gradient ascent approach is then presented to select the cost coefficients of the Bellman equation such that the desired error probabilities and MSEs are achieved. 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