Abstract
A compound Poisson process is considered. We estimate the current position of the stochastic process based on past discrete-time observations (non-linear discrete filtering problem) in Bayesian setting. We obtain bounds for the asymptotic rate of the expected square error of the filter when observations become frequent. The bounds depend linearly on jump intensity. Also, estimation of process' parameters is addressed.
Highlights
Filtering of stochastic processes has attracted a lot of attention
One of the examples is target tracking, when a target is observed over a discrete time grid, corresponding to the successive passes of a radar
We deal with discrete observations
Summary
Filtering of stochastic processes has attracted a lot of attention. One of the examples is target tracking, when a target is observed over a discrete time grid, corresponding to the successive passes of a radar. B) A generalization to d-dimensional signal and observations is immediate when the density φ of the error distribution takes a special form: φ(x1, ..., xd) =. In this case, the optimal filter can be computed coordinate-wise. A special case of a piecewise-linear process with uniform observational errors was considered in [12], but their suggested asymptotics of O(n−2) appear to be incorrect. One of the questions is how much improvement does the (optimal) non-linear filter bring compared to (linear) Kalman filter Another is how does the error distribution affect this improvement. To clarify the role of the error distribution, consider a special case well-known in statistics: when the signal is constant over time.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
