Definition of observability indices?

In summary, the Observability index (v) is the smallest natural number for which the rank of the matrix Ov is equal to the rank of the matrix Ov + 1. This index is closely related to the Kalman observability matrix and represents the maximum rank for a specific output vector (C).
  • #1
james1234
19
0
If someone could please provide me with a simple explanation for observability indices I would be most grateful!

According to wikipedia;

"The Observability index (v) of a linear time-invariant discrete system is the smallest natural number for which is satisfied that rank(Ov) = rank(Ov + 1)"

Can anyone tell me what is meant by the "smallest natural number"? according to slide 8/11 of this link - http://support.dce.felk.cvut.cz/pub/roubalj/teaching/SpaceMaster/lectures/SSMI_Observability.pdf

the observability index would appear to be the maximum rank for a specific output vector (C)? yes?

many thanks!

Jamie
 
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  • #2
james1234 said:
"The Observability index (v) of a linear time-invariant discrete system is the smallest natural number for which is satisfied that rank(Ov) = rank(Ov + 1)"

Hi,
Sorry for my Englsih.
Did you hear about Kalman observability matrix? Ov - like Kalman observability matrix, but the highest power of the matrix Ov is v.
 

1. What is the definition of observability indices?

The observability indices refer to a set of measures used to determine the extent to which a system's internal states can be determined from its outputs. In simpler terms, it is a way to assess how well we can observe or understand the behavior of a system.

2. Why do we need observability indices?

Observability indices are important because they allow us to evaluate the effectiveness and efficiency of a system's design. They help us identify potential issues or limitations in a system's observability, which can then be addressed to improve its overall performance.

3. What are the main types of observability indices?

The main types of observability indices are structural, modal, and Markovian. Structural observability indices are based on the system's structure, modal observability indices use the system's eigenvalues, and Markovian observability indices use the system's state transition matrix.

4. How are observability indices calculated?

The calculation of observability indices depends on the type of index being used. Structural observability indices can be calculated using graph theory algorithms, modal observability indices involve eigenvalue analysis, and Markovian observability indices use matrix operations.

5. What factors affect the observability indices of a system?

The observability indices of a system can be affected by various factors such as the number and location of sensors, the system's structural complexity, and the type of noise present in the system. These factors can impact the accuracy and reliability of the observability indices, and thus, the overall observability of the system.

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