Derivation of an optimal boundary layer width for the smooth variable structure filter - Gadsden SA; Sayed ME; Habibi SR (Institute of Electrical and Electronics Engineers (IEEE), 2011)
In this paper, an augmented form of the smooth variable structure filter (SVSF) is proposed. The SVSF is a state estimation strategy based on variable structure and sliding mode concepts. It uses a smoothing boundary to remove chattering (excessive switching along an estimated state trajectory). In its current form, the SVSF defines the boundary layer by an upper-bound on the uncertainties present in the estimation process (i.e., modeling errors, magnitude of noise, etc.). This is a conservative approach as one would be limiting the gain by assuming a larger smoothing boundary subspace than what is necessary. A more well-defined boundary layer will yield more accurate estimates. This paper derives a solution for an optimal boundary layer width by minimizing the trace of the a posteriori covariance matrix. The results of the derivation are simulated on a linear mechanical system for the purposes of control, and compared with the Kalman filter. © 2011 AACC American Automatic Control Council.
Keywords: 4901 Applied Mathematics; 40 Engineering; 49 Mathematical Sciences; 4001 Aerospace Engineering