Method for calibrating a measuring apparatus

1 . A computer-implemented method for calibrating a microwave measuring apparatus for a plurality of products, the method being executed by a processor operatively connected to the microwave measuring apparatus, comprising:

measuring, using one or more sensors of the microwave measuring apparatus, a set of measured values (X P ={x P i,j }) for the plurality of products, wherein the set of measured values comprises one or more measured variables (j) corresponding to physical properties of the products;

providing a corresponding set of reference variables (Y P ={y P i i-th reference variable}) representing known reference parameters of the products;

determining, by the processor, at least one of the set of reference variables (Y) based on the one or more measured variables (x P i,j );

generating an expanded matrix of the set of measured values for the plurality of products;

determining a first set of calibration parameters (C′) comprising one or more weights

(

c

j

p

)

for one or more of the plurality of products (p), wherein the one or more of the plurality of products (p) is grouped within a first product family, wherein the one or more of the plurality of products in the first product family comprise an equal weight (c j ) that is independent of a product;

determining at least a second set of calibration parameters (C″) for a submatrix of the expanded matrix (X′) of the measured values to calibrate the microwave measuring apparatus with respect to a subset of the products;

determining one or more sets of additional weights within the first product family, wherein products (p) having equal weights

(

c

j

p

)

are grouped into a sub product family within the first product family;

determining weights for the plurality of products outside of the first product family, wherein products (p′) having equal weights

(

c

j

p

⁢

′

)

are grouped into another product family, until all weights are determined for the calibration of the microwave measuring apparatus;

identifying relationships between the measured values across product families using the expanded matrix; and

automatically adjusting one or more of first and second calibration coefficients of the microwave measuring apparatus based on the determined first and second sets of calibration parameters (C′, C″) and the identified relationships.

2 . The method according to claim 1 , further comprising determining the weights of the first set of calibration parameters and the additional weights inside and outside the first product family, wherein weights on which the set of reference variables least depend are determined first.

3 . The method according to claim 1 , further comprising:

determining one or more offset values (Δc); and

combining the one or more offset values to the measured values multiplied by the weights.

4 . The method according to claim 3 , further comprising grouping different products in a same product family when any weight difference or offset difference between them is determined to be statistically insignificant.

5 . The method according to claim 3 , further comprising testing a significance of the one or more offset values by formulating a null hypothesis such that a difference between the offset values (Δc) of two products is equal to zero.

6 . The method according to claim 1 , further comprising linking the weights to polynomials of the measured values, and wherein weights are provided for at least one of (i) products and (ii) quotients of measured values.

7 . The method according to claim 1 , further comprising determining the calibration parameters by multilinear regression.

8 . The method according to claim 1 , further comprising determining the submatrix of the measured values for determining the calibration parameters corresponding to the first product family or additional product families for a subset of the measured values (X p ).

9 . The method according to claim 1 , further comprising inserting the measured values and the products of the product family by non-numerical, categorical variables.

10 . The method according to claim 9 , further comprising inserting dummy variables to differentiate the products when grouping the expanded matrix.

11 . The method according to claim 1 , wherein the microwave measuring apparatus is configured as a microwave resonator that determines a shift in one of: (i) a resonance frequency; and (ii) a widening of a resonance curve.

12 . The method according to claim 1 , wherein the one or more measured variables of the microwave measuring apparatus are at least one of (i) temperature (T); and (ii) moisture angle (φ).