CALIBRATING METHOD AND SYSTEM, RECORDING MEDIUM FOR THIS METHOD

• US 20110238350A1
• Filed: 03/29/2011
• Published: 09/29/2011
• 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
• Granted Patent: US 8,577,635 B2
• Time in Patent Office: Days
• 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

This method for calibrating coefficients of an observer of a variable state comprises:

• the measurement (50) of a variable z_k of the physical system at N different instants, this variable z_k being a function of the state variable x_k,
• the determining (54) of a vector p of coefficients which minimizes the following criterion in complying with a predetermined set Δ of constraints:

$\left\{f\left(p\right)=\sum _{k=1}^N{z_k-\phi \left({\hat{x}}_k,p\right)}^2\right\}$

where:

• • {circumflex over (x)}_k is the estimation of the variable x_k built by the observer calibrated with the coefficients of the vector p at the instant k,
  • φ is a known function which links the estimation {circumflex over (x)}_k to an estimation {circumflex over (z)}_k of the variable z_k,
  • ∥ . . . ∥² is a norm, and
  • the constraint or the constraints of the set Δ dictate that the trajectory of the variable z_k should be included in a corridor of uncertainty situated on either side of the trajectory of the estimation {circumflex over (z)}_k at least for the majority of the instants k.

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, where the index k identifies the instant of measurement, the method comprising:

measuring a variable z_k of the physical system at N different instants, the variable z_k being a function of the state variable x_k, and

determining 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 set Δ

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

a and {circumflex over (z)}k+b, where 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 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 should 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 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, where the index k identifies the instant of measurement, the software comprising instructions for:

measuring a variable z_k the physical system at N different instants, the variable z_k being a function of the state variable x_k, and

determining 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, where the index k identifies the 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 the 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;