A GMM-Based Secure State Estimation Approach against Dynamic Malicious Adversaries

Algorithm 1

The GMM-based state estimation against dynamic attacks.

1 // Run Kalman filter to steady state.

2: Initialize ;

3: fordo

4: // Local data reaches steady state.

5: Fordo

6:  

7:  

8: end for

9: // The remote estimator reaches steady state.

10: 

11: 

12: end for

13: // GMM clustering by the EM algorithm.

14: Set

15: fordo

16: fordo

17:  ;

18: end for

19: // the EM algorithm.

20: Initialize

21: while not achieve the maximum likelihood estimates do

22:  The expectation step: calculate and according to Equation (15)-(16).

23:  The maximization step: calculate by Equation (17)-(19).

24: end while

25: // the error compensator.

26: 

27: fordo

28:  ifthen

29:   ;

30:   ;

31:  else

32:   ;

33:   ;

34:  end if

35: end for

36: // Remote state estimation.

37: 

38: 

39: 

40: 

41: end for