Method and apparatus for finding aircraft position by integrating accelerations less time averages

Claim 1

A method for determining the position of an aircraft for radar mapping, comprising: providing a processor in the airplane; providing a master navigation system coupled to the processor and including an aircraft speedometer for measuring a forward x-speed v XUAX (t), a lateral horizontal position sensor for measuring a lateral y-position p YUAX (t), and an altimeter for measuring a vertical z-position p ZUAX (t); providing a slave system including an inertial measurement unit coupled to the processor and further including an x-accelerometer for generating a forward-direction horizontal acceleration signal a x (t), a y-accelerometer for generating a lateral horizontal acceleration signal a y (t), and a z-accelerometer for generating a vertical acceleration signal a x (t); (a) inputting the forward-direction acceleration signal a x (t) from the inertial system to the processor; time-averaging over a time interval T the acceleration signal a x (t) to obtain a first x-adjustment a x (t); subtracting the first x-adjustment a x (t) from the acceleration signal a x (t) to obtain an adjusted acceleration signal a' x (t); integrating the adjusted acceleration signal a' x (t) over the interval T to obtain a velocity v x "(t) according to ##EQU10## time-averaging the velocity v" x (t) over the interval T to obtain a v x -adjustment v x (t); subtracting the v x -adjustment v x (t) from the velocity v" x (t) to obtain a forward airplane speed v XIMU (t) in the desired flight direction according to ν.sub.XIMU (t)=ν.sub.X (t)-ν".sub.X (t) (5) estimating by method of least squares, from a difference between the speed v XIMU (t) and the speed measurement of the speedometer, an average acceleration a X0 and an average speed v X0 ; creating a correction term v XFIT (t) from a sum of the average speed v X0 and a time integration of a X0 according to ##EQU11## correcting the speed v XIMU (t) in the desired flight direction by adding the correction term v XFIT (t) thereto to obtain a corrected flight speed v XKORR (t) according to ν.sub.XKORR (t)=ν.sub.XIMU (t)+ν.sub.XFIT (t) (b) inputting the lateral-direction acceleration signal a y (t) from the inertial system to the processor; time-averaging over a time interval T the acceleration signal a y (t) to obtain a first y-adjustment a y (t); subtracting the first y-adjustment a y (t) from the acceleration signal a y (t) to obtain an adjusted acceleration signal a' y (t); integrating the adjusted acceleration signal a' y (t) over the interval T to obtain a velocity v y "(t) according to ##EQU12## time-averaging the velocity v" y (t) over the interval T to obtain a v y -adjustment v y (t); subtracting the first y-adjustment v y (t) from the velocity v" y (t) to obtain an adjusted velocity signal v' y (t); integrating the adjusted velocity signal v' y (t) over the interval T to obtain a position p y '(t) according to ##EQU13## time-averaging the position p' y (t) over the interval T to obtain a p y -adjustment p y (t); subtracting the p y -adjustment p y (t) from the velocity p' y (t) to obtain a forward airplane speed p YIMU (t) in the desired flight direction according to p.sub.YIMU (t)=p'.sub.Y (t)-p'.sub.Y (t) (9) estimating by method of least squares, from a difference between the speed p YIMU (t) and the speed measurement of the speedometer, an average acceleration a Y0 and an average speed v Y0 ; creating a correction term p YFIT (t) from a sum of the average speed v Y0 and a time integration of a Y0 according to ##EQU14## correcting the speed p YIMU (t) in the desired flight direction by adding the correction term p YFIT (t) thereto to obtain a corrected flight speed p YKORR (t) according to p.sub.YKORR (t)=p.sub.YIMU (t)+p.sub.YFIT (t) correcting the motion of the aircraft along the desired flight path according to the value of p YKORR (t); (c) inputting the lateral-direction acceleration signal a z (t) from the inertial system to the processor; time-averaging over a time interval T the acceleration signal a z (t) to obtain a first z-adjustment a z (t); subtracting the first z-adjustment a z (t) from the acceleration signal a z (t) to obtain an adjusted acceleration signal a' z (t); integrating the adjusted acceleration signal a' z (t) over the interval T to obtain a velocity v z "(t) according to ##EQU15## time-averaging the velocity v" z (t) over the interval T to obtain a v z -adjustment v z (t); subtracting the first z-adjustment v z (t) from the velocity v z (t) to obtain an adjusted velocity signal v' z (t); integrating the adjusted velocity signal v' z (t) over the interval T to obtain a position p z '(t) according to ##EQU16## time-averaging the position p' z (t) over the interval T to obtain a p z -adjustment p z (t); subtracting the p z -adjustment p z (t) from the velocity p" z (t) to obtain a forward airplane speed p ZIMU (t) in the desired flight direction according to p.sub.ZIMU (t)=p'.sub.z (t)-p'.sub.z (t) (15) estimating by method of least squares, from a difference between the speed p ZIMU (t) and the speed measurement of the speedometer, an average acceleration a Z0 and an average speed v Z0 ; creating a correction term p ZFIT (t) from a sum of the average speed v Z0 and a time integration of a Z0 according to ##EQU17## correcting the speed p ZIMU (t) in the desired flight direction by adding the correction term p ZFIT (t) thereto to obtain a corrected flight speed p ZKORR (t) according to p.sub.ZKORR (t)=p.sub.ZIMU (t)+p.sub.ZFIT (t) (29) and compensating the radar mapping according to the values of v XKORR (t), p YKORR (t), and p ZKORR (t).

Claim 2

A method for determining the position of an aircraft for radar mapping, comprising: providing a processor in the airplane; providing a master navigation system coupled to the processor and including an aircraft speedometer for measuring a forward x-speed v XUAX (t), a lateral horizontal position sensor for measuring a lateral y-position p YUAX (t), and an altimeter for measuring a vertical z-position p ZUAX (t); providing a slave system including an inertial measurement unit coupled to the processor and further including an x-accelerometer for generating a forward-direction horizontal acceleration signal a x (t), a y-accelerometer for generating a lateral horizontal acceleration signal a y (t), and a z-accelerometer for generating a vertical acceleration signal a x (t); (a) inputting the forward-direction acceleration signal a x (t) from the inertial system to the processor; time-averaging over a time interval T the acceleration signal a x (t) to obtain a first x-adjustment a x (t); subtracting the first x-adjustment a x (t) from the acceleration signal a x (t) to obtain an adjusted acceleration signal a' x (t); integrating the adjusted acceleration signal a' x (t) over the interval T to obtain a velocity v x "(t) according to ##EQU10## time-averaging the velocity v" x (t) over the interval T to obtain a v x -adjustment v x (t); subtracting the v x -adjustment v x (t) from the velocity v" x (t) to obtain a forward airplane speed v XIMU (t) in the desired flight direction according to ν.sub.XIMU (t)=ν.sub.X (t)-ν".sub.X (t) (5) estimating by method of least squares, from a difference between the speed v XIMU (t) and the speed measurement of the speedometer, an average acceleration a X0 and an average speed v X0 ; creating a correction term v XFIT (t) from a sum of the average speed v X0 and a time integration of a X0 according to ##EQU11## correcting the speed v XIMU (t) in the desired flight direction by adding the correction term v XFIT (t) thereto to obtain a corrected flight speed v XKORR (t) according to ν.sub.XKORR (t)=ν.sub.XIMU (t)+ν.sub.XFIT (t) (b) inputting the lateral-direction acceleration signal a y (t) from the inertial system to the processor; time-averaging over a time interval T the acceleration signal a y (t) to obtain a first y-adjustment a y (t); subtracting the first y-adjustment a y (t) from the acceleration signal a y (t) to obtain an adjusted acceleration signal a' y (t); integrating the adjusted acceleration signal a' y (t) over the interval T to obtain a velocity v y "(t) according to ##EQU12## time-averaging the velocity v" y (t) over the interval T to obtain a v y -adjustment v y (t); subtracting the first y-adjustment v y (t) from the velocity v" y (t) to obtain an adjusted velocity signal v' y (t); integrating the adjusted velocity signal v' y (t) over the interval T to obtain a position p y '(t) according to ##EQU13## time-averaging the position p' y (t) over the interval T to obtain a p y -adjustment p y (t); subtracting the p y -adjustment p y (t) from the velocity p' y (t) to obtain a forward airplane speed p YIMU (t) in the desired flight direction according to p.sub.YIMU (t)=p'.sub.Y (t)-p'.sub.Y (t) (9) estimating by method of least squares, from a difference between the speed p YIMU (t) and the speed measurement of the speedometer, an average acceleration a Y0 and an average speed v Y0 ; creating a correction term p YFIT (t) from a sum of the average speed v Y0 and a time integration of a Y0 according to ##EQU14## correcting the speed p YIMU (t) in the desired flight direction by adding the correction term p YFIT (t) thereto to obtain a corrected flight speed p YKORR (t) according to p.sub.YKORR (t)=p.sub.YIMU (t)+p.sub.YFIT (t) correcting the motion of the aircraft along the desired flight path according to the value of p YKORR (t); (c) inputting the lateral-direction acceleration signal a z (t) from the inertial system to the processor; time-averaging over a time interval T the acceleration signal a z (t) to obtain a first z-adjustment a z (t); subtracting the first z-adjustment a z (t) from the acceleration signal a z (t) to obtain an adjusted acceleration signal a' z (t); integrating the adjusted acceleration signal a' z (t) over the interval T to obtain a velocity v z "(t) according to ##EQU15## time-averaging the velocity v" z (t) over the interval T to obtain a v z -adjustment v z (t); subtracting the first z-adjustment v z (t) from the velocity v z (t) to obtain an adjusted velocity signal v' z (t); integrating the adjusted velocity signal v' z (t) over the interval T to obtain a position p z '(t) according to ##EQU16## time-averaging the position p' z (t) over the interval T to obtain a p z -adjustment p z (t); subtracting the p z -adjustment p z (t) from the velocity p" z (t) to obtain a forward airplane speed p ZIMU (t) in the desired flight direction according to p.sub.ZIMU (t)=p'.sub.z (t)-p'.sub.z (t) (15) estimating by method of least squares, from a difference between the speed p ZIMU (t) and the speed measurement of the speedometer, an average acceleration a Z0 and an average speed v Z0 ; creating a correction term p ZFIT (t) from a sum of the average speed v Z0 and a time integration of a Z0 according to ##EQU17## correcting the speed p ZIMU (t) in the desired flight direction by adding the correction term p ZFIT (t) thereto to obtain a corrected flight speed p ZKORR (t) according to p.sub.ZKORR (t)=p.sub.ZIMU (t)+p.sub.ZFIT (t) (29) and compensating the radar mapping according to the values of v XKORR (t), p YKORR (t), and p ZKORR (t).

Claim 4

A device for determining the position of an aircraft for radar mapping, comprising: a processor in the airplane; a master navigation system coupled to the processor and including an aircraft speedometer for measuring a forward x-speed v XUAX (t), a lateral horizontal position sensor for measuring a lateral y-position p YUAX (t), and an altimeter for measuring a vertical z-position p ZUAX (t); a slave system including an inertial measurement unit coupled to the processor and further including an x-accelerometer for generating a forward-direction horizontal acceleration signal a x (t), a y-accelerometer for generating a lateral horizontal acceleration signal a y (t), and a z-accelerometer for generating a vertical acceleration signal a x (t); (a) means for inputting the forward-direction acceleration signal a x (t) from the inertial system to the processor; means for time-averaging over a time interval T the acceleration signal a x (t) to obtain a first x-adjustment a x (t); means for subtracting the first x-adjustment a x (t) from the acceleration signal a x (t) to obtain an adjusted acceleration signal a' x (t); means for integrating the adjusted acceleration signal a' x (t) over the interval T to obtain a velocity v x "(t) according to ##EQU19## means for time-averaging the velocity v" x (t) over the interval T to obtain a v x -adjustment v x (t); means for subtracting the v x -adjustment v x (t) from the velocity v" x (t) to obtain a forward airplane speed v XIMU (t) in the desired flight direction according to ν.sub.XIMU (t)=ν.sub.x (t)-ν".sub.X (t) (5) means for estimating by method of least squares, from a difference between the speed v XIMU (t) and the speed measurement of the speedometer, an average acceleration a X0 and an average speed v X0 ; means for creating a correction term v XFIT (t) from a sum of the average speed v X0 and a time integration of a X0 according to ##EQU20## means for correcting the speed v XIMU (t) in the desired flight direction by adding the correction term v XFIT (t) thereto to obtain a corrected flight speed v XKORR (t) according to ν.sub.XKORR (t)=ν.sub.XIMU (t)+ν.sub.XFIT (t) (b) means for inputting the lateral-direction acceleration signal a y (t) from the inertial system to the processor; means for time-averaging over a time interval T the acceleration signal a y (t) to obtain a first y-adjustment a y (t); means for subtracting the first y-adjustment a y (t) from the acceleration signal a y (t) to obtain an adjusted acceleration signal a' y (t); means for integrating the adjusted acceleration signal a' y (t) over the interval T to obtain a velocity v y "(t) according to ##EQU21## means for time-averaging the velocity v" y (t) over the interval T to obtain a v y -adjustment v y (t); means for subtracting the first y-adjustment v y (t) from the velocity v y (t) to obtain an adjusted velocity signal v' y (t); means for integrating the adjusted velocity signal v' y (t) over the interval T to obtain a position p y '(t) according to ##EQU22## means for time-averaging the position p' y (t) over the interval T to obtain a p y -adjustment p y (t); means for subtracting the p y -adjustment p y (t) from the velocity p' y (t) to obtain a forward airplane speed p YIMU (t) in the desired flight direction according to p.sub.YIMU (t)=p'.sub.Y (t)-p'.sub.Y (t) means for estimating by method of least squares, from a difference between the speed p YIMU (t) and the speed measurement of the speedometer, an average acceleration a Y0 and an average speed v Y0 ; means for creating a correction term p YFIT (t) from a sum of the average speed v Y0 and a time integration of a Y0 according to ##EQU23## means for correcting the speed p YIMU (t) in the desired flight direction by adding the correction term p YFIT (t) thereto to obtain a corrected flight speed p YKORR (t) according to p.sub.YKORR (t)=p.sub.YIMU (t)+p.sub.YFIT (t) means for correcting the motion of the aircraft along the desired flight path according to the value of p YKORR (t); (c) means for inputting the lateral-direction acceleration signal a z (t) from the inertial system to the processor; means for time-averaging over a time interval T the acceleration signal a z (t) to obtain a first z-adjustment a z (t); means for subtracting the first z-adjustment a z (t) from the acceleration signal a z (t) to obtain an adjusted acceleration signal a' z (t); means for integrating the adjusted acceleration signal a' z (t) over the interval T to obtain a velocity v z "(t) according to ##EQU24## means for time-averaging the velocity v" z (t) over the interval T to obtain a v z -adjustment v z (t); means for subtracting the first z-adjustment v z (t) from the velocity v z (t) to obtain an adjusted velocity signal v' z (t); means for integrating the adjusted velocity signal v' z (t) over the interval T to obtain a position p z '(t) according to ##EQU25## means for time-averaging the position p' z (t) over the interval T to obtain a p z -adjustment p z (t); means for subtracting the p z -adjustment p z (t) from the velocity p' z (t) to obtain a forward airplane speed p ZIMU (t) in the desired flight direction according to p.sub.ZIMU (t)=p'.sub.Z (t)-p'.sub.Z (t) means for estimating by method of least squares, from a difference between the speed p ZIMU (t) and the speed measurement of the speedometer, an average acceleration a Z0 and an average speed v Z0 ; means for creating a correction term p ZFIT (t) from a sum of the average speed v Z0 and a time integration of a Z0 according to ##EQU26## means for correcting the speed p ZIMU (t) in the desired flight direction by adding the correction term p ZFIT (t) thereto to obtain a corrected flight speed p ZKORR (t) according to p.sub.ZKORR (t)=p.sub.ZIMU (t)+p.sub.ZFIT (t) and means for compensating the radar mapping according to the values of v XKORR (t), p YKORR (t), and p ZKORR (t).

Claim 5

A device for determining the position of an aircraft for radar mapping, comprising: a processor in the airplane; a master navigation system coupled to the processor and including an aircraft speedometer for measuring a forward x-speed v XUAX (t), a lateral horizontal position sensor for measuring a lateral y-position p YUAX (t), and an altimeter for measuring a vertical z-position p ZUAX (t); a slave system including an inertial measurement unit coupled to the processor and further including an x-accelerometer for generating a forward-direction horizontal acceleration signal a x (t), a y-accelerometer for generating a lateral horizontal acceleration signal a y (t), and a z-accelerometer for generating a vertical acceleration signal a x (t); (a) means for inputting the forward-direction acceleration signal a x (t) from the inertial system to the processor; means for time-averaging over a time interval T the acceleration signal a x (t) to obtain a first x-adjustment a x (t); means for subtracting the first x-adjustment a x (t) from the acceleration signal a x (t) to obtain an adjusted acceleration signal a' x (t); means for integrating the adjusted acceleration signal a' x (t) over the interval T to obtain a velocity v x "(t) according to ##EQU19## means for time-averaging the velocity v" x (t) over the interval T to obtain a v x -adjustment v x (t); means for subtracting the v x -adjustment v x (t) from the velocity v" x (t) to obtain a forward airplane speed v XIMU (t) in the desired flight direction according to ν.sub.XIMU (t)=ν.sub.x (t)-ν".sub.X (t) (5) means for estimating by method of least squares, from a difference between the speed v XIMU (t) and the speed measurement of the speedometer, an average acceleration a X0 and an average speed v X0 ; means for creating a correction term v XFIT (t) from a sum of the average speed v X0 and a time integration of a X0 according to ##EQU20## means for correcting the speed v XIMU (t) in the desired flight direction by adding the correction term v XFIT (t) thereto to obtain a corrected flight speed v XKORR (t) according to ν.sub.XKORR (t)=ν.sub.XIMU (t)+ν.sub.XFIT (t) (b) means for inputting the lateral-direction acceleration signal a y (t) from the inertial system to the processor; means for time-averaging over a time interval T the acceleration signal a y (t) to obtain a first y-adjustment a y (t); means for subtracting the first y-adjustment a y (t) from the acceleration signal a y (t) to obtain an adjusted acceleration signal a' y (t); means for integrating the adjusted acceleration signal a' y (t) over the interval T to obtain a velocity v y "(t) according to ##EQU21## means for time-averaging the velocity v" y (t) over the interval T to obtain a v y -adjustment v y (t); means for subtracting the first y-adjustment v y (t) from the velocity v y (t) to obtain an adjusted velocity signal v' y (t); means for integrating the adjusted velocity signal v' y (t) over the interval T to obtain a position p y '(t) according to ##EQU22## means for time-averaging the position p' y (t) over the interval T to obtain a p y -adjustment p y (t); means for subtracting the p y -adjustment p y (t) from the velocity p' y (t) to obtain a forward airplane speed p YIMU (t) in the desired flight direction according to p.sub.YIMU (t)=p'.sub.Y (t)-p'.sub.Y (t) means for estimating by method of least squares, from a difference between the speed p YIMU (t) and the speed measurement of the speedometer, an average acceleration a Y0 and an average speed v Y0 ; means for creating a correction term p YFIT (t) from a sum of the average speed v Y0 and a time integration of a Y0 according to ##EQU23## means for correcting the speed p YIMU (t) in the desired flight direction by adding the correction term p YFIT (t) thereto to obtain a corrected flight speed p YKORR (t) according to p.sub.YKORR (t)=p.sub.YIMU (t)+p.sub.YFIT (t) means for correcting the motion of the aircraft along the desired flight path according to the value of p YKORR (t); (c) means for inputting the lateral-direction acceleration signal a z (t) from the inertial system to the processor; means for time-averaging over a time interval T the acceleration signal a z (t) to obtain a first z-adjustment a z (t); means for subtracting the first z-adjustment a z (t) from the acceleration signal a z (t) to obtain an adjusted acceleration signal a' z (t); means for integrating the adjusted acceleration signal a' z (t) over the interval T to obtain a velocity v z "(t) according to ##EQU24## means for time-averaging the velocity v" z (t) over the interval T to obtain a v z -adjustment v z (t); means for subtracting the first z-adjustment v z (t) from the velocity v z (t) to obtain an adjusted velocity signal v' z (t); means for integrating the adjusted velocity signal v' z (t) over the interval T to obtain a position p z '(t) according to ##EQU25## means for time-averaging the position p' z (t) over the interval T to obtain a p z -adjustment p z (t); means for subtracting the p z -adjustment p z (t) from the velocity p' z (t) to obtain a forward airplane speed p ZIMU (t) in the desired flight direction according to p.sub.ZIMU (t)=p'.sub.Z (t)-p'.sub.Z (t) means for estimating by method of least squares, from a difference between the speed p ZIMU (t) and the speed measurement of the speedometer, an average acceleration a Z0 and an average speed v Z0 ; means for creating a correction term p ZFIT (t) from a sum of the average speed v Z0 and a time integration of a Z0 according to ##EQU26## means for correcting the speed p ZIMU (t) in the desired flight direction by adding the correction term p ZFIT (t) thereto to obtain a corrected flight speed p ZKORR (t) according to p.sub.ZKORR (t)=p.sub.ZIMU (t)+p.sub.ZFIT (t) and means for compensating the radar mapping according to the values of v XKORR (t), p YKORR (t), and p ZKORR (t).