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:
“Film music should have the same relationship to the film drama that somebody’s piano playing in my living room has to the book I am reading.”
—Igor Stravinsky (1882–1971)
“But the relationship of morality and power is a very subtle one. Because ultimately power without morality is no longer power.”
—James Baldwin (1924–1987)
“In the drawing room [of the Queen’s palace] hung a Venus and Cupid by Michaelangelo, in which, instead of a bit of drapery, the painter has placed Cupid’s foot between Venus’s thighs. Queen Caroline asked General Guise, an old connoisseur, if it was not a very fine piece? He replied “Madam, the painter was a fool, for he has placed the foot where the hand should be.””
—Horace Walpole (1717–1797)
“Such is the state of life, that none are happy but by the anticipation of change: the change itself is nothing; when we have made it, the next wish is to change again. The world is not yet exhausted; let me see something tomorrow which I never saw before.”
—Samuel Johnson (1709–1784)
“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)