Calibrating method and system, recording medium for this method

• US 8,577,635 B2
• Filed: 03/29/2011
• Issued: 11/05/2013
• Est. Priority Date: 03/29/2010
• Status: Active Grant

• Current Assignee: Commissariat a L'Energie Atomique (AES Corporation)
• Original Assignee: Commissariat a L'Energie Atomique (AES Corporation)
• Inventors: Lesecq, Suzanne
• Primary Examiner(s): Moffat, Jonathan C Teixeira
• Assistant Examiner(s): Zhang, Ruihua
• Application Number:
  US13/074,066
• Publication Number:
  US 20110238350A1
• Time in Patent Office: 952 Days
• Field of Search: 702/85
• US Class Current: 702/85
• CPC Class Codes: A61B 2560/0223 of calibration, e.g. protocols for calibrating sensors
• CPC Class Codes: A61B 5/062 using magnetic field
• CPC Class Codes: H03H 21/003 KALMAN filters

Abstract

A method for calibrating coefficients of an observer of a variable state of a physical system from measurements of physical quantities of the system, at different instants includes measuring a variable of the physical system at several instants, the variable being a function of a system state variable, and determining a vector of coefficients that minimizes a sum of the number of measurements of a square of a norm of a vector that is the difference between the measured variable and a function of the system state variable and the vector of coefficients. The minimization is subject to a constraint that the trajectory of the measured variable be within a corridor of uncertainty on either side of a trajectory of its estimate, at least for the measurement instants.

Claims

1. A method for calibrating coefficients of an observer of a variable state x_k of a physical system from measurements y_k of physical quantities of the system, wherein index k identifies an instant of measurement, the method comprising causing a sensor to measure a variable z_k of the physical system at N different instants, the variable z_k being a function of a state variable x_k, and causing a computer to determine a vector p of coefficients that minimizes the following criterion in complying with a predetermined set Δ

of one or more constraints;

2. The method of claim 1, wherein the predetermined set Δ

includes a constraint that dictates that the variable z_k be included between {circumflex over (z)}_k−

a and {circumflex over (z)}_k+b , wherein a and b are predetermined positive constants.

3. The method of claim 2, wherein the constants a and b are proportional to a mean square deviation σ

_{{circumflex over (z)}k} representing uncertainty in the estimation {circumflex over (z)}_k.

4. The method of claim 1, wherein the predetermined set Δ

of constraints includes a constraint that dictates that a mean of deviations between the variable z_k and its estimation {circumflex over (z)}_k be below a predetermined threshold S₁.

5. The method of claim 4, wherein the threshold S₁ is a function of the uncertainty in the estimation {circumflex over (z)}_k.

6. The method of claim 1, wherein the observer is a filter selected from a group consisting of a Kalman filter, an extended Kalman filter, and an unscented Kalman Filter, and wherein the coefficients to be calibrated are coefficients of the covariance matrices R and Q of the filter.

7. The method of claim 6, wherein the R and Q matrices are chosen to be diagonal matrices.

8. A manufacture comprising a non-transitory computer-readable medium having encoded thereon software for calibrating coefficients of an observer of a variable state x_k of a physical system from measurements y_k of physical quantities of the system, wherein index k identifies an instant of measurement, the software comprising instructions for causing a sensor to measure a variable z_k of the physical system at N different instants, the variable z_k being a function of a state variable x_k, and causing a computer to determine a vector p of coefficients that minimizes the following criterion in complying with a predetermined set Δ

of one or more constraints;

9. An apparatus for calibrating coefficients of an observer of a state variable x_k of a physical system from measurements y_k of physical quantities of the system, wherein index k identifies an instant of measurement, the apparatus comprising:

at least one sensor capable of measuring a variable z_k of the physical system at N different instants, the variable z_k being a function of a state variable x_k, and a computer capable of determining a vector p of coefficients that minimizes the following criterion in complying with a predetermined set Δ

of one or more constraints;