Temperature correction of vertical speed of aircraft
The present disclosure provides methods and systems for correcting a vertical speed of an aircraft. An instantaneous vertical speed of the aircraft is obtained, based on inertial data from an inertial reference unit on the aircraft. A first correction is applied to the instantaneous vertical speed to generate a baro-inertial vertical speed, and a second correction is applied to the baro-inertial vertical speed based on an error between a geometric vertical speed and the baro-inertial vertical speed to obtain a temperature-corrected baro-inertial vertical speed.
1. A method for correcting a vertical speed of an aircraft, the method comprising:
obtaining an instantaneous vertical speed of the aircraft based on inertial data from an inertial reference unit on the aircraft;
applying a first correction to the instantaneous vertical speed to generate a baro-inertial vertical speed; and
applying a second correction to the baro-inertial vertical speed based on an error between a geometric vertical speed and the baro-inertial vertical speed to obtain a temperature-corrected baro-inertial vertical speed,
wherein:
applying the second correction to the baro-inertial vertical speed comprises applying a time-based function of the error between the geometric vertical speed and a pressure altitude vertical speed;
the time-based function of the error is estimated as a moving-average of an instantaneous error between the geometric vertical speed and the baro-inertial vertical speed, over a given portion of time prior to a current time; and
the instantaneous error corresponds to:
Err
inst
=
(
V
z
,
Geom
V
z
,
Press
·
V
z
,
BI
-
V
z
,
BI
)
where V z,Geom is the geometric vertical speed, V z,Press is the pressure altitude vertical speed, and V z,BI is the baro-inertial vertical speed.
2. The method of claim 1 , wherein the given portion of time is about 20 seconds.
3. The method of claim 1 , wherein the time-based function of the error is estimated as an output of a first order filter applied on the instantaneous error between the geometric vertical speed and the baro-inertial vertical speed, the first order filter having a time-constant that matches a time constant used to apply the first correction.
4. The method of claim 1 , wherein
V
z
,
Geom
V
z
,
Press
is computed as:
T
s
T
i
+
T
′
·
H
where T s is static temperature at a given altitude, T i is temperature at sea-level altitude, T′ is temperature lapse-rate, and H is altitude.
5. The method of claim 4 , wherein T s and H are measured from air data sensors on the aircraft, and H is approximated as pressure altitude.
6. The method of claim 1 , wherein applying the first correction to the instantaneous vertical speed comprises applying the first correction using pressure altitude data for the aircraft.
7. A system for correcting a vertical speed of an aircraft, the system comprising:
a processing unit; and
a non-transitory memory communicatively coupled to the processing unit and comprising computer-readable program instructions executable by the processing unit for:
obtaining an instantaneous vertical speed of the aircraft based on inertial data from an inertial reference unit on the aircraft;
applying a first correction to the instantaneous vertical speed to generate a baro-inertial vertical speed; and
applying a second correction to the baro-inertial vertical speed based on an error between a geometric vertical speed and the baro-inertial vertical speed to obtain a temperature-corrected baro-inertial vertical speed,
wherein:
applying the second correction to the baro-inertial vertical speed comprises applying a time-based function of the error between the geometric vertical speed and a pressure altitude vertical speed;
the time-based function of the error is estimated as a moving-average of an instantaneous error between the geometric vertical speed and the baro-inertial vertical speed, over a given portion of time prior to a current time; and
the instantaneous error corresponds to:
Err
inst
=
(
V
z
,
Geom
V
z
,
Press
·
V
z
,
BI
-
V
z
,
BI
)
where V z,Geom is the geometric vertical speed, V z,Press is the pressure altitude vertical speed, and V z,BI is the baro-inertial vertical speed.
8. The system of claim 7 , wherein the given portion of time is about 20 seconds.
9. The system of claim 7 , wherein the time-based function of the error is estimated as an output of a first order filter applied on the instantaneous error between the geometric vertical speed and the baro-inertial vertical speed, the first order filter having a time-constant that matches a time constant used to apply the first correction.
10. The system of claim 7 , wherein
V
z
,
Geom
V
z
,
Press
is computed as:
T
s
T
i
+
T
′
·
H
where T s is static temperature at a given altitude, T i is temperature at sea-level altitude, T′ is temperature lapse-rate, and H is altitude.
11. The system of claim 10 , wherein T s and H are measured from air data sensors on the aircraft, and H is approximated as pressure altitude.
12. The system of claim 7 , wherein applying the first correction to the instantaneous vertical speed comprises applying the first correction using pressure altitude data for the aircraft.