Qualitative State Estimation from corrupted Data with Uncertain Parameters

1. Kuwait University
Dec 19, 2011 ICGS Conference
Qualitative State Estimation from
corrupted Data with Uncertain Parameters
By
Mohamed F. Hassan Hala A. Mourad
Presented By
Prof. Mohamed F. Hassan
Faculty of Engineering and Petroleum
Electrical Engineering Department

2. Presentation Outline

3. Presentation Outline

4. Introduction
• Since most, if not all, real control systems are stochastic by
their nature, it has been essential not only to develop and
enhance stochastic control theory but also the estimation
theory in order to deal with this type of problems.
• For linear dynamical system with random disturbances,
where the stochastic phenomena appears, the state
estimation problem is solved using Kalman filter.
• In standard Kalman filter, all the system characteristics (i.e.
system model, initial conditions, and noise characteristics)
have to be specified a priori. However, if there is uncertainty
in any of these characteristics, the filter may not be robust
enough.

5. Introduction
• In this paper, a new approach is proposed to estimate the
states of linear stochastic discrete-time dynamical system
with uncertain parameters. The system model and the
measurements are assumed to be corrupted by uncorrelated
zero mean white Gaussian noise sequences. The parameters
of the system are assumed to be uncertain, which leads to a
nonlinear (bilinear) estimation problem. The new filter
handles this problem and its performance is compared with
that of the KF, when the parameters are assumed to be
certain, and with the EKF, when the parameters are decided
to be estimated.

6. Presentation Outline

7. Problem Formulation

8. Problem Formulation

9. Problem Formulation

10. Presentation Outline

11. The Developed Estimator

12. The Developed Estimator

13. The Developed Estimator

14. The Developed Estimator

15. Presentation Outline

16. The Developed Recursive Algorithm

17. Presentation Outline

18. Simulation Results

19. Simulation Results
Table 1: RMSE index (MI = 100)

20. Simulation Results

21. Simulation Results

22. Simulation Results

23. Simulation Results

24. Simulation Results

25. Simulation Results

26. Simulation Results

27. Simulation Results

28. Simulation Results

29. Simulation Results

30. Simulation Results
Table 2: RMSE index, Q=0.1, R=0.01 (MI = 100)
The average values of the RMSE indices of the states, calculated over 100
Monte Carlo iterations using the three filters, are shown in Table 2. RMSE
plots for Case-b are shown in Figures (7-9).

31. Simulation Results

32. Simulation Results

33. Simulation Results

34. Presentation Outline

35. Conclusion
In this paper, an approach is developed to estimate the states of
linear stochastic discrete-time dynamical systems with uncertain
parameters. The system model and the measurements are
assumed to be corrupted by uncorrelated zero mean white
Gaussian noise sequences with known statistical data. Although
this problem is treated in the literature as a nonlinear estimation
problem which intern increases the dimensionality of the
problem; with the developed approach the system is still treated
as linear and without any increase in the dimensionality of the

36. Conclusion
Therefore, it is expected that the developed algorithm leads to
less computational time and has better numerical properties
due to the resulting estimator dimensionality. Simulation results
showed that the state estimation using the developed filter is
better than that of KF, where the EKF diverged and failed to
estimate the system states.

37. Kuwait University
Dec 19, 2011 ICGS Conference