Method for thermal modeling and updating of bias errors in inertial navigation instrument outputs

Claim 1

A method for correcting the output of an inertial navigation instrument for temperature dependent bias comprising the steps of: a) making a plurality of measurements of instrument bias; and b) making a corresponding plurality of measurements of instrument temperature; then c) associating corresponding bias and temperature measurements to form a bias-temperature model; then d) encoding said model into spline parameters by (i) subdividing said temperature range into a plurality of equal temperature intervals, each of said intervals being defined by opposed interval boundaries, then (ii) determining a series of cubic polynomial functions over said intervals representing a fit to said measured values of bias versus temperature such that said functions and slopes of said functions versus temperature are continuous over said range, and then (iii) calculating the value and slope of each of said functions at each interval boundary; then e) storing said spline parameters; then f) making an estimate of instrument bias error while in use; and g) making a measurement of instrument temperature at a corresponding time; then h) coordinating said estimate of bias error with said temperature to form an update point; then i) revising said spline parameters in accordance with said update point; then j) reading the output of said instrument; and k) measuring the temperature of said instrument; then l) calculating an instrument bias value from said stored spline parameters in accordance with said measured temperature; and then m) adjusting said output in accordance with said calculated instrument bias value.

Claim 2

A method for correcting the output of an inertial navigation instrument for temperature dependent bias comprising the steps of: a) making a plurality of measurements of instrument bias; and b) making a corresponding plurality of measurements of instrument temperature; then c) associating corresponding bias and temperature measurements to form a bias-temperature model; then d) encoding said model into spline parameters by (i) subdividing said temperature range into a plurality of equal temperature intervals, each of said intervals being defined by opposed interval boundaries, then (ii) determining a series of cubic polynomial functions over said intervals representing a fit to said measured values of bias versus temperature such that said functions and slopes of said functions versus temperature are continuous over said range, and then (iii) calculating the value and slope of each of said functions at each interval boundary; then e) storing said spline parameters; then f) making an estimate of instrument bias error while in use; and g) making a measurement of instrument temperature at a corresponding time; then h) coordinating said estimate of bias error with said temperature to form an update point; then i) revising said spline parameters in accordance with said update point; then j) reading the output of said instrument; and k) measuring the temperature of said instrument; then l) calculating an instrument bias value from said stored spline parameters in accordance with said measured temperature; and then m) adjusting said output in accordance with said calculated instrument bias value.

Claim 12

A method for correcting the thermal model of bias of an inertial measurement device comprising a plurality of corresponding values of instrument bias and temperature, said method comprising the steps of: a) encoding said model as a spline by (i) subdividing said temperature range into a plurality of equal temperature intervals, then (ii) determining a series of cubic polynomial functions over said intervals representing a fit to said measured values of bias versus temperature such that said functions and slopes of said functions versus temperature are continuous over said range, and then (iii) calculating the value and slope of each of said functions at each interval boundary; then b) storing said parameters that define said spline; then c) estimating instrument bias at an observed instrument temperature; and d) associating said estimate with said observed temperature to form an update point; then e) revising said parameters in accordance with said update point; and then f) computing instrument bias as a function of temperature using said spline.

Claim 13

A method for correcting the thermal model of bias of an inertial measurement device comprising a plurality of corresponding values of instrument bias and temperature, said method comprising the steps of: a) encoding said model as a spline by (i) subdividing said temperature range into a plurality of equal temperature intervals, then (ii) determining a series of cubic polynomial functions over said intervals representing a fit to said measured values of bias versus temperature such that said functions and slopes of said functions versus temperature are continuous over said range, and then (iii) calculating the value and slope of each of said functions at each interval boundary; then b) storing said parameters that define said spline; then c) estimating instrument bias at an observed instrument temperature; and d) associating said estimate with said observed temperature to form an update point; then e) revising said parameters in accordance with said update point; and then f) computing instrument bias as a function of temperature using said spline.

Claim 23

A method for in-field updating of the thermal model of bias of an inertial measurement device comprising a series of parameters characterizing instrument bias over a predetermined temperature range, said method comprising the steps of: a) measuring the value of bias at a plurality of temperatures throughout said range; then b) subdividing said temperature range into a plurality of equal temperature intervals, each of said intervals being defined by opposed interval boundaries; then c) determining a series of cubic polynomial functions over said intervals representing a fit to said measured values of bias versus temperature such that said functions and slopes of said functions versus temperature are continuous over said range; then d) calculating the value and slope of each of said functions at each interval boundary; and e) storing said values and slopes; then f) estimating instrument bias error at an observed instrument temperature; then g) associating said estimate with said observed temperature to form an update point; and then h) revising at least one of said values and slopes in accordance with said update point.

Claim 24

A method for in-field updating of the thermal model of bias of an inertial measurement device comprising a series of parameters characterizing instrument bias over a predetermined temperature range, said method comprising the steps of: a) measuring the value of bias at a plurality of temperatures throughout said range; then b) subdividing said temperature range into a plurality of equal temperature intervals, each of said intervals being defined by opposed interval boundaries; then c) determining a series of cubic polynomial functions over said intervals representing a fit to said measured values of bias versus temperature such that said functions and slopes of said functions versus temperature are continuous over said range; then d) calculating the value and slope of each of said functions at each interval boundary; and e) storing said values and slopes; then f) estimating instrument bias error at an observed instrument temperature; then g) associating said estimate with said observed temperature to form an update point; and then h) revising at least one of said values and slopes in accordance with said update point.