Claim 1. A method for adjusting model and/or calibration parameters of a sensor system that is equipped with said model of external events that are taking place in the real world where:

• sensor output units of said system provide signals in response to said external events;
• N is greater than 50 where N is the total number of values from said sensor output units that are processed during any situation; and,
• said method makes use of adaptive Fast K- Filtering (FKF) that comprises steps a) to g):

a) provides a data base unit for storing information on:

- a plurality of test point sensor output signal values for some of said sensors and a plurality of values for external events that correspond to said test point sensor output signal values and/or simultaneous time series of sensor output signal values from adjacent sensors for comparison;

- values of said sensor output signals, values of said model and/or calibration parameters and values of said external events that correspond to a situation at time t; and,

- controls of said sensors and/or forcings of said external events that correspond to said situation at time t;

b) provides a logic unit for accessing both said sensor signal output values and said model and/or calibration parameter values, where said logic unit has both a two-way communications link to said data base unit and the capability of computing initial values for unknown model and/or calibration parameters, if required, by using Lange's High-pass Filter:

_i = (X_i'V_i^-1X_i)^-1X_i'V_i^-1(y_i - G_{i 0})

₀ = (G_i' R_i G_i)^-1G_i'R_i y_i

where
_i = computed initial values for unknown model and/or calibration parameters at an initial time i
₀ = computed initial values for those unknown model and/or calibration parameters that are common to all initial times i
y_i = vector of data obtained from said plurality of test point sensor output signal values for some of said sensors and/or said plurality of values for said external events corresponding to said test point sensor output signal values, and/or said simultaneous time series of said output signal values from adjacent sensors for comparison
X_i = Jacobian matrix for said state parameters s_i
G_i = Jacobian matrix for said state parameters c₀
R_i = V_i^-1-V_i^-1X_i(X_i'V_i^-1X_i)^-1X_i'V_i^-1
V_i = error covariance matrix of said vector of data y_i
= summation where the time index i runs over those time series of data that are used for initialising the FKF filter;

c) provides said sensor output signal values from said sensors, as available, to said logic unit;

d) provides information on said controls of said sensors and/or said forcings of said external events to said data base unit;

e) accesses current values of both model and/or calibration parameters and state transition matrices, and computes updated values of said model and/or calibration parameters by using FKF-formulas:

_{t - l} = (X_{t - l}'V_{t - l}^-1X_{t - l})^-1X_{t - l}'V_{t - l}^-1(Y_{t - l} - G_{t – l t})

_t = (G_{t - l}' R_{t - l} G_{t - l})^-1G_{t - l}'R_{t - l}Y_{t - l}

where
_{t - l} = filtered values of model and/or calibration parameters for time block t - l
_t = filtered values of those model and/or calibration parameters that are common for said situation at time t
Y_{t - l} = [y_{t - l}', (A _{t - l - 1} + B u_{t - l - 1})']' = vector of said sensor output signal values augmented with predicted model and/or calibration parameters
y_{t - l} = vector of said sensor output signal values for time block t - l
N_{t - l} = number of sensor output signal values in said vector y_{t - l}
A _{t - l - 1} + B u_{t - l - 1} = vector of said predicted model and/or calibration parameters for time block t – l
A = state transition matrix
_{t - l - 1} = filtered values of model and/or calibration parameters for previous time block t - l – 1
B = control gain matrix
u_{t - l - 1} = controls of said sensors or forcings of said external events for previous time block t - l - 1
X_{t - l} = [ H_{t - l}', I ]' = augmented Jacobian matrix for state parameters s_{t - l}
H_{t - l} = Jacobian matrix for said state parameters s_{t - l}
I = identity matrix
G_{t - l} = [ [F^y_{t - l}', F^s_{t - l}']', [   , M_{t - l - 1}']' ] = augmented Jacobian matrix for state parameters c_t
F_{t - l} = [F^y_{t - l}', F^s_{t - l}']' = matrix of common factors for error covariances between time block t - l and other blocks
M_{t - l - 1} = matrix of factors for correcting state transition error from time block t - l - 1 to time block t - l
R_{t - l} = V_{t - l}^-1-V_{t - l}^-1X_{t - l}(X_{t - l}'V_{t - l}^-1X_{t - l})^-1X_{t - l}'V_{t - l}^-1
V_{t - l} = error covariance matrix of said augmented vector of data in Y_{t - l}
= summation where the time block index t-l runs over those L time blocks of data that are used for said situation at time t;

wherein the improvement comprises the block-diagonalization of the error covariance matrix of Augmented Model (24):

of the description by exploiting any of said common factors F^y or F^s or said factors M by FKF-formulas, in said logic unit, for said situation at time t;

f) controls stability of said adaptive FKF-filtering by monitoring accuracy estimates of said updated values of model and/or calibration parameters, in said logic unit, and indicates needs for sensor output signal values, test point data, sensor comparisons or a system reconfiguration;

g) adjusts said model and/or calibration parameter values if stable updates are available.

Claim 2. A method for adjusting model and/or calibration parameters of a sensor system that is equipped with said model of external events that are taking place in the real world where:

• sensor output units of said system provide signals in response to said external events;
• N is greater than 50 where N is the total number of values from said sensor output units that are processed during any situation; and,
• said method makes use of adaptive Fast K- Filtering (FKF) that comprises steps a) to g):

a) provides a data base unit for storing information on:

- a plurality of test point sensor output signal values for some of said sensors and a plurality of values for external events that correspond to said test point sensor output signal values and/or simultaneous time series of sensor output signal values from adjacent sensors for comparison;

- values of said sensor output signals, values of said model and/or calibration parameters and values of said external events that correspond to a situation; and,

- controls of said sensors and/or forcings of said external events that correspond to said situation;

b) provides a logic unit for accessing both said sensor signal output values and said model and/or calibration parameter values, where said logic unit has both a two-way communications link to said data base unit and the capability of computing initial values for unknown model and/or calibration parameters, if required, by using Lange's High-pass Filter;

c) provides said sensor output signal values from said sensors, as available, to said logic unit;

d) provides information on said controls of said sensors and/or said forcings of said external events to said data base unit;

e) accesses current values of both model and/or calibration parameters and state transition matrices, and computes updated values of said model and/or calibration parameters by using FKF-formulas that are obtained by applying Frobenius Inversion Formula (26):

for solving the Normal Equation system, where the improvement comprises a partial diagonalization of the covariance matrix of the residual errors [e_t', (A (_{t - 1} - s_{t - 1}) - a_t)']' of Augmented Model (8):

by applying factors F^y, F^s or M to said Augmented Model, in said logic unit, for said situation;

f) controls stability of said adaptive FKF-filtering by monitoring accuracy estimates of said updated values of model and/or calibration parameters, in said logic unit, and indicates needs for sensor output signal values, test point data, sensor comparisons or a system reconfiguration;

g) adjusts said model and/or calibration parameter values if stable updates are available. 

* Last revised: May 23, 2004