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 to, relationship, general, state and/or observers:
“Sometimes in our relationship to another human being the proper balance of friendship is restored when we put a few grains of impropriety onto our own side of the scale.”
—Friedrich Nietzsche (1844–1900)
“Harvey: Oh, you kids these days, I’m telling you. You think the only relationship a man and a woman can have is a romantic one.
Gil: That sure is what we think. You got something better?
Harvey: Oh, romance is very nice. A good thing for youngsters like you, but Helene and I have found something we think is more appropriate to our stage of life—companionship.
Gil: Companionship? I’ve got a flea-bitten old hound at home who’ll give me that.”
—Tom Waldman (d. 1985)
“At that,
his small size,
keen eyes,
serviceable beak
and general truculence
assure his survival—”
—William Carlos Williams (1883–1963)
“It should be noted that when he seizes a state the new ruler ought to determine all the injuries that he will need to inflict. He should inflict them once and for all, and not have to renew them every day.”
—Niccolò Machiavelli (1469–1527)
“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)