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:
“... the Wall became a magnet for citizens of every generation, class, race, and relationship to the war perhaps because it is the only great public monument that allows the anesthetized holes in the heart to fill with a truly national grief.”
—Adrienne Rich (b. 1929)
“Only men of moral and mental force, of a patriotic regard for the relationship of the two races, can be of real service as ministers in the South. Less theology and more of human brotherhood, less declamation and more common sense and love for truth, must be the qualifications of the new ministry that shall yet save the race from the evils of false teaching.”
—Fannie Barrier Williams (1855–1944)
“Some people are under the impression that all that is required to make a good fisherman is the ability to tell lies easily and without blushing; but this is a mistake. Mere bald fabrication is useless; the veriest tyro can manage that. It is in the circumstantial detail, the embellishing touches of probability, the general air of scrupulous—almost of pedantic—veracity, that the experienced angler is seen.”
—Jerome K. Jerome (1859–1927)
“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)
“Most observers of the French Revolution, especially the clever and noble ones, have explained it as a life-threatening and contagious illness. They have remained standing with the symptoms and have interpreted these in manifold and contrary ways. Some have regarded it as a merely local ill. The most ingenious opponents have pressed for castration. They well noticed that this alleged illness is nothing other than the crisis of beginning puberty.”
—Novalis [Friedrich Von Hardenberg] (1772–1801)