EXAMPLE FROM GREWAL CH 9 GREWAL SEC 9
- Slides: 14
EXAMPLE FROM: GREWAL (CH. 9) GREWAL, SEC. 9. 5. 4. 1: VERTICAL CHANNEL DAMPING WITH BAROMETRIC ALTIMETER EXPO. CORR. PROCESS OF ALTIMETER (NO INS ACCELEROMETER) SEC. 9. 5. 4. 2 CAROUSELING FEBRUARY 6, 2012, IITB AE 457 M, AE 641: Navigation and Guidance March 11, 2011
Grewal, Sec. 9. 5. 4. 1: Vertical Channel Damping with Barometric Altimeter Measurement interval: Delta. T = 10 s; Altimeter process noise: modeled as an exponentially correlated error with parameters : variance: sigma altitude^2 = (100 m)^2 altimeter offset correlation time, Tau. Altimeter = 10*3600 s; % [10 hours] white noise sequence that generates exponentially correlated process : Qaltimeter m^2; = Sigma. Altitude^2 * (1 -exp(-2*Delta. T/Tau. Altimeter)) = 2. 36^2 Altimeter measurement white noise variance : Raltimeter = 10^2 meter^2; % Caution: There is an error in Grewal's formulation; Instead of 1/Tschuler, he should have 8^0. 5 * pi/TSchuler, and TSchuler = 5066 s Schuler period [sec] according to Grewal: TSchuler. M = 5066/(8^0. 5*pi) s; = 5046 s; % to correct for Grewal’s error
Expo. Corr. Process of Altimeter (No INS accelerometer): true, measurements, and estimate; altimeter Expo-Corr. Steady-state measurement error variance: Sigma. Altitude^2 = (100 m)^2; Tau Altimeter = 10 hrs; Input white sequence process noise variance: Qaltimeter = Sigma. Altitude^2 *(1 -exp( -2*Delta. T/Tau. Altimeter))= 2. 36^2 m^2; Altimeter measurement white noise sigma : 10 meter
Expo. Corr. Process of Altimeter (No INS accelerometer): Its estimation Kalman Gain
Expo. Corr. Process of Altimeter (No INS accelerometer): true, measurements, and estimate; altimeter error variance: Sigma. Altitude^2 = (100 m)^2; Tau Altimeter = 10 hrs; Input white sequence process noise variance: Qaltimeter = Sigma. Altitude^2 *(1 -exp(2*Delta. T/Tau. Altimeter))= 2. 36^2 m^2; Altimeter measurement white noise sigma : 10 meter
Grewal, Sec. 9. 5. 4. 1: Vertical Channel Damping with Barometric Altimeter: Original Incorrect Code [T_Schuler should be T_Schuler/(8^0. 5*pi)]
Grewal, Sec. 9. 5. 4. 1: Vertical Channel Damping with Barometric Altimeter: Corrected Code [T_Schuler is T_Schuler/(8^0. 5*pi)]: Altitude error
Grewal, Sec. 9. 5. 4. 1: Vertical Channel Damping with Barometric Altimeter: Corrected Code [T_Schuler is T_Schuler/(8^0. 5*pi)]: Velocity error
Grewal, Sec. 9. 5. 4. 1: Vertical Channel Damping with Barometric Altimeter: Corrected Code [T_Schuler is T_Schuler/(8^0. 5*pi)]: Kalman Gains
In steady-state, INS altitude error is the same as baro-altimeter error, as expected intuitively
Brown & Hwang, Prob. 10. 1: Baro-Inertial Vertical Channel Stabilization: delta. T = 1 s; accelerometer white noise PSD = 0. 13889 (m/s^2)/(rad/s); Baro errors: exp. corr. variance sig^2 = (100 m)^2; tau_altim = 300 s; q_baro=sig^2 * (2*beta*dt)=8. 16^2 m^2; meas. white noise variance = R = (10 m)^2
Nav errors caused by 10 μg north accelerometer bias: with and without platform carousel; carousel period 5 minutes (1/3)
Nav errors: north error vs. time; east error vs. time
Carousel rotation angle α
