On the Calibration Problem

Bernard Friedland

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


First we consider estimating a constant n-dimensional parameter vector x using an m-dimensional observation vector y = Hx for m<n. Unless H is time-varying, x cannot 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 ż = Az + Hx with y = Cz + Dx + ν (ν = observation noise), and show that the results reduce to those for the first problem as observation noise ν tends to zero. As an illustration, the application to the calibration of four parameters in a two-axis gyro is presented.

Original languageEnglish (US)
Pages (from-to)899-905
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Dec 1977
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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