Random signals and systems
Elements of signal detection and estimation
Elements of signal detection and estimation
Detection in Sensor Networks: The Saddlepoint Approximation
IEEE Transactions on Signal Processing
| Hi-index | 35.68 |
Astronomical instruments able to detect the direct light of extra solar planets are currently under development. This paper focuses on instruments that will acquire a set of successive images where the planet (the source in more general purposes) moves in a known manner on a speckled background. Performant signal processing tools are required to account for the very low signal-to-noise ratio of the data. In the astrophysical context, the background arises mainly from the light scattered by the parent star. An accurate--but general--data model has been proposed in previous works to statistically describe optical images taking into account the spatial correlation of the wavefront complex amplitude. First, an estimator of the position and the intensity of the potential source is proposed. Because of several kinds of numerical constraints, it is derived from a simplified Gaussian data model. Under reasonable constraints on the motion of the source, the estimators are proved to be consistent, even under the accurate data model. For the detection test, we propose to threshold a linear statistics that arises from the intensity estimation. The threshold needs to be precisely related to the probability of false alarm (PFA) and the probability of detection (PD). Under the detailed model, the distribution of the data is only reachable through its moment generating function. We propose therefore to estimate analytically PFA and PD using the saddlepoint approximation. To evaluate the quality of these estimations, a Monte Carlo analysis is applied to monodimensional simulated data. The saddlepoint approximation proves to be very accurate, unlike the Gaussian approximation or even a low-order Gram-Charlier series approximation.