EXamples of Estimation Filters from Recent Aircraft Projects at MIT November 2004 Sanghyuk Park and Jonathan How
Examples of Estimation Filters from Recent Aircraft Projects at MIT November 2004 Sanghyuk Park and Jonathan How
Vehicles Navigation Sensors OHS(Outboard Horizontal stabilizer) Navigation Sensors(Piccolo from Cloudcap Tech) · GPS Motoro|aM12 Inertial 3 Tokin CG-16D rate gyros 3 ADXL202 accelerometers Navigation Sensors · Air data GPS Receiver(Marconi, Allstar) Dynamic& absolute pressure sensor ·| neria| Sensors Air temperature sensor Crossbow 3-axis Accelerometer MHX 910/2400 radio modem MPC555 CPU Tokin Ceramic Gyro MINior Crossbow IMU (OHS Pitot static Probe: measures Crista Inertial measurement Unit airspeed 3 Analog devices AdXL accelerometers Altitude Pressure sensor 3 ADXRS MEMS rate sensors
Vehicles & Navigation Sensors OHS (Outboard Horizontal Stabilizer) Navigation Sensors (Piccolo from Cloudcap Tech) • GPS Motorola M12 • Inertial • 3 Tokin CG-16D rate gyros • 3 ADXL202 accelerometers Navigation Sensors • Air Data • GPS Receiver (Marconi, Allstar) • Dynamic & absolute pressure sensor • Inertial Sensors • Air temperature sensor - Crossbow 3-axis Accelerometer, • MHX 910/2400 radio modem Tokin Ceramic Gyro (MINI) or • MPC555 CPU Crossbow IMU (OHS) • Pitot Static Probe: measures • Crista Inertial Measurement Unit airspeed • 3 Analog Devices ADXL accelerometers • Altitude Pressure Sensor • 3 ADXRS MEMs rate sensors
Complementary Filter(CF) Often, there are cases where you have two different measurement sources for estimating one variable and the noise properties of the two measurements are such that one source gives good information only in low frequency region while the other is good only in high frequency region You can use a complementary filter Example: Tilt angle estimation using accelerometer and rate gyro accelerometer rate gyro High Pass Filter for example 0≈| (angular rate) dt not good in long term due to integration 0≈sn- accel. output g only good in long term Low Pass Filter not proper during fast motion
Complementary Filter (CF) Often, there are cases where you have two different measurement sources for estimating one variable and the noise properties of the two measurements are such that one source gives good information only in low frequency region while the other is good only in high frequency region. Æ You can use a complementary filter ! Example : Tilt angle estimation using accelerometer and rate gyro ≈ ∫(angular rate) dt - not good in long term due to integration outputaccel. ⎞ ⎟ + ⎠ τ τ ⎛ ⎜ ⎝ s 1 examplefor, s = θ est accelerometer rate gyro High Pass Filter ⎛ ⎞ θ θ 1 g - not proper during fast motion ⎞ ⎟ τ ⎠ = ⎛ ⎜ ⎝ 1 s + − sin 1 - only good in long term Low Pass Filter ⎟ ⎟ ⎠ ⎜ ⎜ ⎝ θ ≈
Complementary Filter(cF)Examples CF1. Roll Angle Estimation CF2 Pitch Angle Estimation CF3. Altitude Estimation CF4. Altitude Rate Estimation
Complementary Filter(CF) Examples • CF1. Roll Angle Estimation • CF2. Pitch Angle Estimation • CF3. Altitude Estimation • CF4. Altitude Rate Estimation
CFI. Roll Angle estimation High freq. integrating roll rate(p) gyro output Low freq. using aircraft kinematics Assuming steady state turn dynamics roll angle is related with turning rate, which is close to yaw rate(r) Lsing=mvQ2 L≈mg g np≈p mg CF setup Roll Rate p HPF Gyro Roll angle Yaw r estimate Rate LPF yro
CF1. Roll Angle Estimation • High freq. : integrating roll rate (p) gyro output • Low freq. : using aircraft kinematics - Assuming steady state turn dynamics, roll angle is related with turning rate, which is close to yaw rate (r) L sin φ = mVΩ L ≈ mg V φ ≈ r g Ω ≈ r sin φ ≈ φ CF setup Roll Rate Gyro Yaw Rate Gyro 1 s HPF LPF V g + + Roll angle estimate p r φ
CF2. Pitch Angle estimation High freq. integrating pitch rate(q gyro output Low freq: using the sensitivity of accelerometers to gravity direction gravity aiding accelerometer In steady state gsin 6 0= tan A,=-g cos 8 A Ax, A,-accelerometer outputs Roll angle compensation is needed CF setup eas COS HPF A.口b,=tan cOS LPF
CF2. Pitch Angle Estimation • High freq. : integrating pitch rate (q) gyro output • Low freq. : using the sensitivity of accelerometers to gravity direction - “gravity aiding” In steady state AX = g sin θ − x θ = tan 1 ⎛ ⎜ ⎜− A ⎞ ⎟ AZ = −g cos θ ⎝ Az ⎠ ⎟ AX , AZ − accelerome outputs ter • Roll angle compensation is needed CF setup qmeas ≈ qmeas θ cos φest θ φest est + + s 1 HPF A A x ⎛ ⎞ − x θ = tan 1 ⎜ ⎜− A cos φest ⎟ ⎟ z ss φest ⎝ Az ⎠ LPF
CF3. Altitude estimation In order of overcome this, pressure sensor was added onds of delay Motivation: GPS receiver gives altitude output but it has0. 4 sec Low freq. from GPS receiver High freq: from pressure sensor CF setup flight data GPS+Pressure from Pressure Sensor HPF est from GPS KF LPF
CF3. Altitude Estimation • Motivation : GPS receiver gives altitude output, but it has ~0.4 seconds of delay. In order of overcome this, pressure sensor was added. • Low freq. : from GPS receiver • High freq. : from pressure sensor CF setup & flight data hfromPressure Sensor LPF HPF + + h h KF GPS from est
CF4. Altitude rate Estimation Motivation: GPS receiver gives altitude rate but it has -0. 4 seconds of delay In order of overcome this inertial sensor outputs were added Low freq. from GPS receiver High freq. integrating acceleration estimate in altitude direction from inertial sensors CF setup Angular Transform HPF est 2 est from GPs KF LPF note: a A, -LEs ees r o Ar, A- accelerometer outputs
CF4. Altitude Rate Estimation • Motivation : GPS receiver gives altitude rate, but it has ~0.4 seconds of delay. In order of overcome this, inertial sensor outputs were added. • Low freq. : from GPS receiver • High freq. : integrating acceleration estimate in altitude direction from inertial sensors CF setup az Angular Transform ah s 1 a HPF est , φ θ est + + hest y ax LPF h KF GPS from Ax ⎧a x ⎫ ⎧ ⎫ ⎧ 0 ⎫ ⎪ ⎨ ⎪ = ⎨ ⎪ ⎬ ⎪ ⎩ ⎪ ⎭ ⎪ ⎬ − [φest][θ est ⎪ ]⎨ ⎪ ⎬ A A x z , − accelerome outputs ter Ay A z : note a y 0 [φ ] est ,[θ est ⎪ ] angular : transforma tion matrices ⎩ ⎪ ⎩ ⎪ ⎭ ⎪ − ⎭ a g z
Kalman Filter(KF) EXamples KF1. Manipulation of GPS Outputs KF2 Removing Rate Gyro Bias Effect
Kalman Filter(KF) Examples • KF1. Manipulation of GPS Outputs • KF2. Removing Rate Gyro Bias Effect
KF 1. Manipulation of GPS Outputs Background motivation Stand-alone gps receiver gives position and velocity These are obtained by independent methods position t pseudo-ranges elocity doppler effe and are certainly related(=v) Kalman filter can be used to combine them! · Motivation Typical Accuracies Position 30 velocity 0.15m/s Many gps receivers provide high qual ity velocity information > Use high quality velocity measurement to improve position estimate
KF 1. Manipulation of GPS Outputs Background & Motivation • Stand-alone GPS receiver gives position and velocity • These are obtained by independent methods : • position Å pseudo-ranges • velocity Å Doppler effect and are certainly related ( x = v) Æ Kalman filter can be used to combine them ! • Motivation : Typical Accuracies Position ~ 30 m Velocity ~ 0.15 m/s Many GPS receivers provide high quality velocity information Æ Use high quality velocity measurement to improve position estimate
