On the calibration problem
Bernard Friedland · IEEE Transactions on Automatic Control · 1977
First we consider estimating a constantn-dimensional parameter vectorxusing anm-dimensional observation vectory = Hxform < n. Unless H is time-varying,xcannot be estimated. This is the case addressed. It is shown that the Kalman filtering approach yields an estimation algorithm equivalent to a direct deterministic approach which may be more practical to implement. Using Friedland's "separate bias" algorithm [1], we extend the analysis to the problem of indirect observations, i.e., for\dot{z}= Az + Hxwithy = Cz + Dx+\upsilon(\upsilon=observation noise), and show that the results reduce to those for the first problem as observation noise\upsilontends to zero. As an illustration, the application to the calibration of four parameters in a two-axis gyro is presented.