Abstract
We obtain a maximum likelihood algorithm for detecting a Gaussian stochastic signal with unknown appearance (disappearance) time and average power. Asymptotic expressions for the probabilities of the 1st- and 2nd-kind detection errors are found. Applicability limits for the derived expressions are found by statistical computer simulation.
Similar content being viewed by others
REFERENCES
van Trees, H.L., Detection, Estimation, and Modulation Theory, New York: Wiley, 1968, vol. 3. Translated under the title Teoriya obnaruzheniya, otsenok i modulyatsii, Moscow: Sov. Radio, 1977.
Sosulin, Yu.G., Teoriya obnaruzheniya i otsenivaniya stokhasticheskikh signalov (Theory of Detection and Estimation of Stochastic Signals), Moscow: Sov. Radio, 1978.
Voprosy statisticheskoi teorii radiolokatsii (Topics in Statistical Radar Theory), Tartakovskii, G.P., Ed., Moscow: Sov. Radio, 1963, vol. 1.
Repin, V.G. and Tartakovskii, G.P., Statisticheskii sintez pri apriornoi neopredelennosti i adaptatsiya informatsionnykh sistem (Statistical Synthesis under a priori Uncertainty and Adaptation of Information Systems), Moscow: Sov. Radio, 1977.
Tartakovskii, A.G., Posledovatel'nye metody v teorii informatsionnykh sistem (Sequential Methods in the Theory of Information Systems), Moscow: Radio i Svyaz', 1991.
Tartakovskii, A.G., Optimal Detection of Random-Length Signals, Probl. Peredachi Inf., 1987, vol. 23, no. 3, pp. 39–47 [Probl. Inf. Trans. (Engl. Transl.), 1987, vol. 23, no. 3, pp. 203-210].
Tartakovskii, A.G., Detection of Signals with Random Moments of Appearance and Disappearance, Probl. Peredachi Inf., 1988, vol. 24. no. 2, pp. 39–50 [Probl. Inf. Trans. (Engl. Transl.), 1988, vol. 24, no. 2, pp. 115-124].
Repin, V.G., Detection of a Signal with Unknown Moments of Appearance and Disappearance, Probl. Peredachi Inf., 1991, vol. 27, no. 1, pp. 61–72 [Probl. Inf. Trans. (Engl. Transl.), 1991, vol. 27, no. 1, pp. 49-58].
Teoriya obnaruzheniya signalov (Theory of Signal Detection), Bakut, P.A., Ed., Moscow: Radio i Svyaz', 1984.
Kulikov, E.I. and Trifonov, A.P., Otsenka parametrov signalov na fone pomekh (Estimation of Signal Parameters under Noise Background), Moscow: Sov. Radio, 1978.
Shiryaev, A.N., Minimax Optimality of the Cumulative Sum Method (CUSUM) in the Case of Continuous Time, Usp. Mat. Nauk, 1996, vol. 51, no. 4, pp. 173–174.
Trifonov, A.N. and Zakharov, A.V., Effciency of Detecting a Discontinuous Stochastic Radio Pulse with Unknown Arrival Time and Center Frequency, Radiotekhn. Elektron., 2000, vol. 45, no. 11, pp. 1329–1337.
Piterbarg, V.I., Asimptoticheskie metody v teorii gaussovskikh protsessov i polei (Asymptotic Methods in the Theory of Gaussian Processes and Fields), Moscow: Mosk. Gos. Univ., 1988.
Qualls, C. and Watanabe, H., Asymptotic Properties of Gaussian Random Fields, Trans. AMS, 1973, vol. 177, pp. 155–171.
Piterbarg, V.I. and Fatalov, V.R., Laplace Method for Probability Measures in Banach Spaces, Usp. Mat. Nauk, 1995, vol. 50, no. 6, pp. 57–156.
Pickands, J., Upcrossing Probabilities for Stationary Gaussian Processes, Trans. AMS, 1969, vol. 145, pp. 51–73.
Ibragimov, I.A. and Khas'minskii, R.Z., Asimptoticheskaya teoriya otsenivaniya (Asymptotic Estimation Theory), Moscow: Nauka, 1979. Translated under the title Statistical Estimation. Asymptotic Theory, New York: Springer, 1981.
Tikhonov, V.I. and Mironov, M.A., Markovskie protsessy (Markov Processes), Moscow: Sov. Radio, 1977.
Rights and permissions
About this article
Cite this article
Trifonov, A.P., Zakharov, A.V. & Pronyaev, E.V. Adaptive Detection of a Stochastic Signal under Parametric a priori Uncertainty. Problems of Information Transmission 38, 203–217 (2002). https://doi.org/10.1023/A:1020313202331
Issue Date:
DOI: https://doi.org/10.1023/A:1020313202331