The answer is clarified in the attached image; but in any case the Probabilistic Density Function in the state space is supposed Gaussian.

Dear Abedallatif, Thank you for the illustration which is simply clarifying. But still the question remains for me unanswered. Do you mean assuming Gaussian probability density function is a deficiency of unscented Kalman filter (UKF) ?

I repeat again, is UKF the final alternative to Kalman filter or there are somethings negative about (UKF), needing another alternative? Simply I want to know whether UKF is the end point of Kalman filtering or there are some alternatives? If yes, then why we need an alternative for UKF?

In my opinion; no body can say UKF is the endpoint of Kalman filtering. Form time to time we read some new researches in this field. But we can simply distinguish between the "Kalman family" that suppose the Gaussian function as a probabilistic distribution in the state space and the other filters like particle filters who are applicable to any p.d.f. in the state space. In my opinion; the main draw back of the family of Kalman filters is the heavy computational burden because of the "big matrix" which have been initialized at the beginning of our model.

You can also read the first and second chapters of the following book:

Beyond the Kalman Filter: Particle Filters for Tracking Applications.

Thanks for your comprehensive insight on the subject. I am now in possession of the answer to my query. Also thanks for the reference.

In general, there are no generic or standard solutions for nonlinear problems, as every nonlinear system is unique. Neither Extended Kalman filters (including UKFs) nor particle filters give you any guarantees of convergence or performance beyond local stability/convergence in restricted conditions. However, small modifications to system design often permit building state estimators that converge predictably and globally. Look up Kreisselmeier K-filters and Marino-Tomei filters for nonlinear systems.

@Kartik B Ariyur,

as I see, these (Kreisselmeier, Marino-Tomei) are observers, not filters.

Dear Saeb AmirAhmadi Chomachar ,

For more information about your question i suggest you to see link and attached files in subject.

http://ieeexplore.ieee.org/abstract/document/1271397/?reload=true

good luck

One of the deficiency of UKF is that it cannot handle constraints. But there are research papers, which shows how UKF is modified to handle such situations.

in my experience and through reading in this field I suggest the drawbacks of UKF is to get a better accurate need propagate a large number of sigma point which is become the highly coast.