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
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