Relationship To General State Observers
More general state observers, such as the Luenberger observer for linear control systems, use a rigorous system model. Linear observers use a gain matrix to determine state estimate corrections from multiple deviations between measured variables and predicted outputs that are linear combinations of state variables. In the case of alpha beta filters, this gain matrix reduces to two terms. There is no general theory for determining the best observer gain terms, and typically gains are adjusted experimentally for both.
The linear Luenberger observer equations reduce to the alpha beta filter by applying the following specializations and simplifications.
- The discrete state transition matrix A is a square matrix of dimension 2, with all main diagonal terms equal to 1, and the first super-diagonal terms equal to ΔT.
- The observation equation matrix C has one row that selects the value of the first state variable for output.
- The filter correction gain matrix L has one column containing the alpha and beta gain values.
- Any known driving signal for the second state term is represented as part of the input signal vector u, otherwise the u vector is set to zero.
- Input coupling matrix B has a non-zero gain term as its last element if vector u is non-zero.
Read more about this topic: Alpha Beta Filter
Famous quotes containing the words relationship, general, state and/or observers:
“Some [adolescent] girls are depressed because they have lost their warm, open relationship with their parents. They have loved and been loved by people whom they now must betray to fit into peer culture. Furthermore, they are discouraged by peers from expressing sadness at the loss of family relationships—even to say they are sad is to admit weakness and dependency.”
—Mary Pipher (20th century)
“The tremendous outflow of intellectuals that formed such a prominent part of the general exodus from Soviet Russia in the first years of the Bolshevist Revolution seems today like the wanderings of some mythical tribe whose bird-signs and moon-signs I now retrieve from the desert dust.”
—Vladimir Nabokov (1899–1977)
“The judiciary has fallen to a very low state in this country. I think your part of the country has suffered especially. The federal judges of the South are a disgrace to any country, and I’ll be damned if I put any man on the bench of whose character and ability there is the least doubt.”
—William Howard Taft (1857–1930)
“An ... important antidote to American democracy is American gerontocracy. The positions of eminence and authority in Congress are allotted in accordance with length of service, regardless of quality. Superficial observers have long criticized the United States for making a fetish of youth. This is unfair. Uniquely among modern organs of public and private administration, its national legislature rewards senility.”
—John Kenneth Galbraith (b. 1908)