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A least-squares estimator of the intensity of a Poisson process is studied for a partially observed stochastic system, where the signal evolves as a jump-diffusion process and the observation is a diffusion process. Precisely, we establish the consistency and a central limit theorem of the least-squares estimator when a negative drift coefficient for the jump-diffusion process is considered. We also demonstrate that the variance and the fourth moment of the estimator is bounded but inconsistent when the drift coefficient of the jump diffusion is positive or data is collected within a fixed time horizon.

Network control systems are usually modeled as simple channels having limited transmission bandwidth, nonnegligible communication delays and random packet dropouts, when contaminated by disturbances with Gaussian distributions. However, wireless sensor networks undergo several abrupt jumps that appear as discontinuities that can be modeled as non-Gaussian processes, for which the estimation and identification problem is challenging. We consider a stochastic state space model in which the signal is disturbed with Lévy-type processes. An approximated ensemble Kalman filter is proposed and a method for the sequential importance sampling is given in the signal estimation stage. Comparison between two filtering methods is investigated, which then leads us to a study of particle MCMC method that is adjusted to achieve the model parameter identification.

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