Poisson source localization on the plane: the smooth case
Copyright policy )Poisson source localization on the plane: the smooth case
Consider the estimation of the unknown position \(\vartheta_0=(x_0,y_0)\) of a source emitting a Poisson signal. The emitter lies in a set \(\Theta\) of a plane. For the estimation of the unknown position \(\vartheta_0=(x_0,y_0)\), located at points \((x_j,y_j)\), \(j=1,\dots, k\), there are \(k\) sensors receiving data from the source which are modeled by independent, inhomogeneous Poisson processes \(X_j=X_j(t)\), having a certain intensity function \(\lambda_j=\lambda_j(\vartheta_0,t)\), \(j=1, \dots k, 0 \leq t \leq T\). After a detailed description of the statistical observation model, maximum likelihood and Bayesian estimators for the unknown source location \(\vartheta_0=(x_0,y_0)\) are presented. Moreover, several asymptotic properties of the estimators are shown.
- National Research University of Electronic Technology Russian Federation
- University of Maine France
- UNIVERSITE LE MANS France
source location, inhomogeneous Poisson process, Estimation in multivariate analysis, signals, maximum likelihood estimator, sensors, локализация источников, оценка максимального правдоподобия, неоднородный пуассоновский процесс, Bayes estimator, байесовские оценки, Point processes (e.g., Poisson, Cox, Hawkes processes)
source location, inhomogeneous Poisson process, Estimation in multivariate analysis, signals, maximum likelihood estimator, sensors, локализация источников, оценка максимального правдоподобия, неоднородный пуассоновский процесс, Bayes estimator, байесовские оценки, Point processes (e.g., Poisson, Cox, Hawkes processes)
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