Method for determining route angles

Claim 1

A method for automatic calibration of the course accuracy of a three-axis magnetometer that is fixedly mounted in an aircraft and is subject to interference fields and instrumental errors comprising the steps of: (a) determining initial reference direction, at a preselected calibration location characterized by a homogeneous magnetic field of known intensity and inclination that is free from anomalies, by means of at least one gyroscope having short-term stability; then (b) determining the theoretical values of the mutually perpendicular reference components T x , T y and T z of the earth's magnetic field required for said calibration; then (c) sweeping over all route angles and course angle ranges, within established limiting roll and pitch angle values, required for said calibration during a flight maneuver; and (d) continuously observing during said flight maneuver the deviations ΔT x =T x '-T x , ΔT y =T y '-T y and ΔT z =T z '-T z of the instantaneous magnetic field components Tx', Ty', Tz' from the reference components T x , T y and T z ; and (e) reading said deviations into a computer; then (f) recurrently computing, after the occurrence of each observation triplet, ΔT x , ΔT y and ΔT z , in accordance with the calibration functions: ΔT.sub.x =T.sub.x '-T.sub.x =A.sub.x +B.sub.x.sin ψ+C.sub.x.cos ψ+D.sub.x.Φ+E.sub.x.Φ.sup.2 +F.sub.x.θ+G.sub.x.θ.sup.2 ( 1a) ΔT.sub.y =T.sub.y '-T.sub.y =A.sub.y +B.sub.y.sin ψ+C.sub.y.cos ψ+D.sub.y.Φ+E.sub.y.Φ.sup.2 +F.sub.y.θ+G.sub.y.θ.sup.2 ( 1b) ΔT.sub.z =T.sub.z '-T.sub.z =A.sub.z +B.sub.z.sin ψ+C.sub.z.cos ψ+D.sub.z.Φ+E.sub.z.Φ.sup.2 +F.sub.z.θ+G.sub.z.θ.sup.2 ( 1c) where ψ is the route angle, Φ is the roll angle and θ is the pitch angle, correction coefficients A x , B x , . . . G x A y , B y , . . . G y A z , B z , . . . G z having initial conditions: A x , B x , . . . G x =0 A y , B y , . . . G y =0 A z , B z , . . . G z =0 up to a predeterminable accuracy; then (g) transforming the instantaneous magnetic field components to corrected intensity components T x c , T y c , T z c in accordance with: T.sub.x.sup.c =T.sub.x '+V.sub.x ( 2a) T.sub.y.sup.c =T.sub.y '+V.sub.y ( 2b) T.sub.z.sup.c =T.sub.z '+V.sub.z ( 2c) with the correction values V.sub.x =-A.sub.x -B.sub.x.sin ψ-C.sub.x.cos ψ-D.sub.x.Φ-E.sub.x.Φ.sup.2 -F.sub.x.θ-G.sub.x.θ.sup.2 ( 3a) V.sub.y =-A.sub.y -B.sub.y.sin ψ-C.sub.y.cos ψ-D.sub.y.Φ-E.sub.y.Φ.sup.2 -F.sub.y.θ-G.sub.y.θ.sup.2 ( 3b) V.sub.z =-A.sub.z -B.sub.z.sin ψ-C.sub.z.cos ψ-D.sub.z.Φ-E.sub.z.Φ.sup.2 -F.sub.z.θ-G.sub.z.θ.sup.2 ( 3c); and then (h) determining a corrected route angle ψ c m from the equations of step (g).

Claim 2

A method for automatic calibration of the course accuracy of a three-axis magnetometer that is fixedly mounted in an aircraft and is subject to interference fields and instrumental errors comprising the steps of: (a) determining initial reference direction, at a preselected calibration location characterized by a homogeneous magnetic field of known intensity and inclination that is free from anomalies, by means of at least one gyroscope having short-term stability; then (b) determining the theoretical values of the mutually perpendicular reference components T x , T y and T z of the earth's magnetic field required for said calibration; then (c) sweeping over all route angles and course angle ranges, within established limiting roll and pitch angle values, required for said calibration during a flight maneuver; and (d) continuously observing during said flight maneuver the deviations ΔT x =T x '-T x , ΔT y =T y '-T y and ΔT z =T z '-T z of the instantaneous magnetic field components Tx', Ty', Tz' from the reference components T x , T y and T z ; and (e) reading said deviations into a computer; then (f) recurrently computing, after the occurrence of each observation triplet, ΔT x , ΔT y and ΔT z , in accordance with the calibration functions: ΔT.sub.x =T.sub.x '-T.sub.x =A.sub.x +B.sub.x.sin ψ+C.sub.x.cos ψ+D.sub.x.Φ+E.sub.x.Φ.sup.2 +F.sub.x.θ+G.sub.x.θ.sup.2 ( 1a) ΔT.sub.y =T.sub.y '-T.sub.y =A.sub.y +B.sub.y.sin ψ+C.sub.y.cos ψ+D.sub.y.Φ+E.sub.y.Φ.sup.2 +F.sub.y.θ+G.sub.y.θ.sup.2 ( 1b) ΔT.sub.z =T.sub.z '-T.sub.z =A.sub.z +B.sub.z.sin ψ+C.sub.z.cos ψ+D.sub.z.Φ+E.sub.z.Φ.sup.2 +F.sub.z.θ+G.sub.z.θ.sup.2 ( 1c) where ψ is the route angle, Φ is the roll angle and θ is the pitch angle, correction coefficients A x , B x , . . . G x A y , B y , . . . G y A z , B z , . . . G z having initial conditions: A x , B x , . . . G x =0 A y , B y , . . . G y =0 A z , B z , . . . G z =0 up to a predeterminable accuracy; then (g) transforming the instantaneous magnetic field components to corrected intensity components T x c , T y c , T z c in accordance with: T.sub.x.sup.c =T.sub.x '+V.sub.x ( 2a) T.sub.y.sup.c =T.sub.y '+V.sub.y ( 2b) T.sub.z.sup.c =T.sub.z '+V.sub.z ( 2c) with the correction values V.sub.x =-A.sub.x -B.sub.x.sin ψ-C.sub.x.cos ψ-D.sub.x.Φ-E.sub.x.Φ.sup.2 -F.sub.x.θ-G.sub.x.θ.sup.2 ( 3a) V.sub.y =-A.sub.y -B.sub.y.sin ψ-C.sub.y.cos ψ-D.sub.y.Φ-E.sub.y.Φ.sup.2 -F.sub.y.θ-G.sub.y.θ.sup.2 ( 3b) V.sub.z =-A.sub.z -B.sub.z.sin ψ-C.sub.z.cos ψ-D.sub.z.Φ-E.sub.z.Φ.sup.2 -F.sub.z.θ-G.sub.z.θ.sup.2 ( 3c); and then (h) determining a corrected route angle ψ c m from the equations of step (g).

Claim 3

A method for automatic calibration of the course accuracy of a three-axis magnetometer that is fixedly mounted in an aircraft and is subject to interference fields and instrumental errors comprising the steps of: (a) establishing an estimated initial reference direction at a preselected calibration location that is characterized by a homogeneous magnetic field of known intensity and inclination and free from anomalies; then (b) determining the theoretical values of the mutually perpendicular reference components T x , T y and T z of the earth's magnetic field required for calibration from said estimated initial reference direction by means of a gyroscope having short-term stability; then (c) sweeping all route angles and course angle ranges, within established limiting roll and pitch angle values, required for calibration during a flight maneuver; and (d) continuously observing during said flight maneuver the deviations ΔT x =T x '-T x , ΔT y =T y '-T y and ΔT z =T z '-T z of the instantaneous magnetic field components T x ', T y ', T z ' from the reference components T x , T y , T z ; and (e) reading said deviations into a computer; then (f) recurrently computing, after the occurrence of each observation triplet, ΔT x , ΔT y and ΔT z , in accordance with the calibration functions: ΔT.sub.x =T.sub.x '-T.sub.x =A.sub.x +B.sub.x.sin ψ+C.sub.x.cos ψ+D.sub.x.Φ+E.sub.x.Φ.sup.2 +F.sub.x.θ+G.sub.x.θ.sup.2 ( 1a) ΔT.sub.y =T.sub.y '-T.sub.y =A.sub.y +B.sub.y.sin ψ+C.sub.y.cos ψ+D.sub.y.Φ+E.sub.y.Φ.sup.2 +F.sub.y.θ+G.sub.y.θ.sup.2 ( 1b) T.sub.z =T.sub.z '-T.sub.z =A.sub.z +B.sub.z.sin ψ+C.sub.z.cos ψ+D.sub.z.Φ+E.sub.z.Φ.sup.2 +F.sub.z.θ+G.sub.z.θ.sup.2 ( 1c) where ψ designates the route angle, Φ designates the roll angle and θ designates the pitch angle, correction coefficients A x , B x , . . . G x A y , B y , . . . G y A z , B z , . . . G z having initial conditions A x , B x , . . . G x =0 A y , B y , . . . G y =0 A z , B z , . . . G z =0 up to a predeterminable accuracy; then (g) transforming the instantaneous magnetic field components to corrected intensity components in accordance with: T.sub.x.sup.c =T.sub.x '+V.sub.x ( 2a) T.sub.y.sup.c =T.sub.y '+V.sub.y ( 2b) T.sub.z.sup.c =T.sub.z '+V.sub.z ( 2c) with the correction values V.sub.x =-A.sub.x -B.sub.x.sin ψ-C.sub.x.cos --D.sub.x.Φ-E.sub.x.Φ.sup.2 -F.sub.x.θ-G.sub.x.θ.sup.2 ( 3a) V.sub.y =-A.sub.y -B.sub.y.sin ψ-C.sub.y.cos ψ-D.sub.y.Φ-E.sub.y.Φ.sup.2 -F.sub.y.θ-G.sub.y.θ.sup.2 ( 3b) V.sub.z =-A.sub.z -B.sub.z.sin ψ-C.sub.z.cos ψ-D.sub.z.Φ-E.sub.z.Φ.sup.2 -F.sub.z.θ-G.sub.z.θ.sup.2 ( 3c); then (h) determining a corrected route angle ψ c m from the equations of step (g) by inserting the uncorrected value of route angle ψ into equations 3(a), 3(b) and 3(c); then (i) performing a further calibration flight between at least two reference points (P 1 , P 2 ) of known coordinates (ρ 1 , ρ 2 ; λ 1 , λ 2 ); then (j) determining a course correction defined as ##EQU21## and where (ΔX-ΔX')=path difference in the latitudinal direction in flight between the reference points (P 1 , P 2 ); (ΔY-ΔY')=path difference in the longitudinal direction in flight between the reference points (P 1 , P 2 ); arc tan ΔY/ΔX=route angle; and S=path traversed between the reference points (P 1 , P 2 ); and then (k) determining said corrected route angle as ψ.sub.m.sup.c =f(T.sub.x.sup.c, T.sub.y.sup.c, T.sub.z.sup.c)+V.sub.A ( 5b).

Claim 4

A method for automatic calibration of the course accuracy of a three-axis magnetometer that is fixedly mounted in an aircraft and is subject to interference fields and instrumental errors comprising the steps of: (a) establishing an estimated initial reference direction at a preselected calibration location that is characterized by a homogeneous magnetic field of known intensity and inclination and free from anomalies; then (b) determining the theoretical values of the mutually perpendicular reference components T x , T y and T z of the earth's magnetic field required for calibration from said estimated initial reference direction by means of a gyroscope having short-term stability; then (c) sweeping all route angles and course angle ranges, within established limiting roll and pitch angle values, required for calibration during a flight maneuver; and (d) continuously observing during said flight maneuver the deviations ΔT x =T x '-T x , ΔT y =T y '-T y and ΔT z =T z '-T z of the instantaneous magnetic field components T x ', T y ', T z ' from the reference components T x , T y , T z ; and (e) reading said deviations into a computer; then (f) recurrently computing, after the occurrence of each observation triplet, ΔT x , ΔT y and ΔT z , in accordance with the calibration functions: ΔT.sub.x =T.sub.x '-T.sub.x =A.sub.x +B.sub.x.sin ψ+C.sub.x.cos ψ+D.sub.x.Φ+E.sub.x.Φ.sup.2 +F.sub.x.θ+G.sub.x.θ.sup.2 ( 1a) ΔT.sub.y =T.sub.y '-T.sub.y =A.sub.y +B.sub.y.sin ψ+C.sub.y.cos ψ+D.sub.y.Φ+E.sub.y.Φ.sup.2 +F.sub.y.θ+G.sub.y.θ.sup.2 ( 1b) T.sub.z =T.sub.z '-T.sub.z =A.sub.z +B.sub.z.sin ψ+C.sub.z.cos ψ+D.sub.z.Φ+E.sub.z.Φ.sup.2 +F.sub.z.θ+G.sub.z.θ.sup.2 ( 1c) where ψ designates the route angle, Φ designates the roll angle and θ designates the pitch angle, correction coefficients A x , B x , . . . G x A y , B y , . . . G y A z , B z , . . . G z having initial conditions A x , B x , . . . G x =0 A y , B y , . . . G y =0 A z , B z , . . . G z =0 up to a predeterminable accuracy; then (g) transforming the instantaneous magnetic field components to corrected intensity components in accordance with: T.sub.x.sup.c =T.sub.x '+V.sub.x ( 2a) T.sub.y.sup.c =T.sub.y '+V.sub.y ( 2b) T.sub.z.sup.c =T.sub.z '+V.sub.z ( 2c) with the correction values V.sub.x =-A.sub.x -B.sub.x.sin ψ-C.sub.x.cos --D.sub.x.Φ-E.sub.x.Φ.sup.2 -F.sub.x.θ-G.sub.x.θ.sup.2 ( 3a) V.sub.y =-A.sub.y -B.sub.y.sin ψ-C.sub.y.cos ψ-D.sub.y.Φ-E.sub.y.Φ.sup.2 -F.sub.y.θ-G.sub.y.θ.sup.2 ( 3b) V.sub.z =-A.sub.z -B.sub.z.sin ψ-C.sub.z.cos ψ-D.sub.z.Φ-E.sub.z.Φ.sup.2 -F.sub.z.θ-G.sub.z.θ.sup.2 ( 3c); then (h) determining a corrected route angle ψ c m from the equations of step (g) by inserting the uncorrected value of route angle ψ into equations 3(a), 3(b) and 3(c); then (i) performing a further calibration flight between at least two reference points (P 1 , P 2 ) of known coordinates (ρ 1 , ρ 2 ; λ 1 , λ 2 ); then (j) determining a course correction defined as ##EQU21## and where (ΔX-ΔX')=path difference in the latitudinal direction in flight between the reference points (P 1 , P 2 ); (ΔY-ΔY')=path difference in the longitudinal direction in flight between the reference points (P 1 , P 2 ); arc tan ΔY/ΔX=route angle; and S=path traversed between the reference points (P 1 , P 2 ); and then (k) determining said corrected route angle as ψ.sub.m.sup.c =f(T.sub.x.sup.c, T.sub.y.sup.c, T.sub.z.sup.c)+V.sub.A ( 5b).