Hi Om Prakash
Upon reviewing the provided code, I see that there is an inconsistency in the number of states between the initial system dynamics and the state estimation process.
Initial System Dynamics:
State Transition Matrix – ‘A’ : 3 x 3
Control Input Matrix – ‘B’ : 3 x 1
Measurement Matrix – ‘C’ : 1 x 3
The dimensions of these matrices confirms that the original system is defined with three states.
Introduction of a Fourth State:
In the state estimation process, a fourth state is introduced. This is evident from the code segment where the state estimate ‘x_estimate’ is initialized and updated.
- The state vector ‘x_estimate’ is initialized with four elements, and the estimation process attempts to predict and update four states.
- The dynamics for the fourth state are defined as static (dx4 = 0;), indicating no actual dynamics are contributing to this state.
The estimation process might not accurately reflect the true system behaviour if it includes an unnecessary state.
Including a fourth state without proper integration into the system dynamics and measurement model can affect the system's observability, potentially making it impossible to accurately infer the system's complete state from the measurements.
Therefore, for any system, especially if additional states are introduced, the observability matrix should be calculated to ensure it has full rank, confirming that the system is fully observable.
It can be done as follows –
% Observability check
O = obsv(A, C);
rank_O = rank(O);
fprintf('Observability matrix rank: %d\n', rank_O);
if rank_O < size(A, 1)
warning('The system is not fully observable.');
end
For more information regarding observability, kindly refer the following documentation. https://www.mathworks.com/help/control/ref/statespacemodel.obsv.html
I hope this helps in resolving the issue.
