Error Simulation and Multi-Sensor Data Fusion AERO4701 Space Engineering 3 Week 6
Last Week Looked at the problem of attitude determination for satellites Examined several common methods such as inertial navigation, magnetometers, sun/star trackers, horizon scanners, attitude GPS etc.
Overview First Hour Look at modelling of sensor errors Multi-sensor data fusion, the alpha-beta filter and tuning Estimator performance evaluation
Modeling Sensor Errors Common sensor errors include: Noise: High frequency errors due to Biases: Constant offset error in sensor reading Scale factor errors: Error in conversion factors for sensor instrument reading into output quantity Sensor misalignments: Internal sensor axis misalignments for directional sensors
Data Fusion and Complimentary Filtering For attitude estimate we often require two different sensor readings for complete solution Often fuse sensor data from one sensor with high frequency errors and another sensor with low frequency errors Examples: INS-Star Tracker, INS-Sun Sensor- Magnetometers, INS-GPS
The Alpha-Beta Filter We have 2 observations of the state x: y and z Our estimate of x is simply a weighted sum of the two observations Our choice of the weight, α, depends on our confidence in each observation s accuracy All confidence in z when compared to y All confidence in y when compared to z Equal confidence in z and y
The Alpha-Beta Filter: Process and Observation Model Alpha-beta filter is often applied to estimating a state using a noisy process model with noisy observations Start off with Process Model: Initial condition errors and noise ω result in growth in estimate errors
The Alpha-Beta Filter: Process and Observation Model Predict forward state by integration: Periodically we get an observation: Observations has error ν. State estimate is updated: Predict forward until next observation:
The Alpha-Beta Filter: Choosing α Our choice of α depends on the relative errors in the observations of the state and the drift errors from the integration process As observations become more infrequent, α increases (weight more on observation) as estimate has drifted more in integration process In the scalar case, the optimal weighting is: assuming stochastic errors.
Case Study: Inertial-GPS Data Fusion System Common choice of sensor fusion for aircraft systems, provides complete position, velocity and attitude localisation data at high feedback rate Sensor errors for inertial and GPS can be simulated based on modeling from logged data Simple alpha-beta filter used for GPS update of inertial drift; choice of tuning depends on accuracies of each sensors and time between subsequent GPS measurements, thus drift
Sensor Error Modeling: INS Inertial sensor model includes noise, slowly drifting biases, scale factor errors and misalignments
Sensor Error Modeling: GPS GPS sensor model includes noise and a first order drift model
INS-GPS Data Fusion: Loosely Coupled GPS computed position regularly updates INS computed position for drift; update is a simple weighted combination of INS and GPS computed position IMU INS Accel. Co-ordinate Transform Velocity Rotation Rates Attitude Position GPS Position Solution Correction
INS-GPS Data Fusion: Tightly Coupled INS Accel. Co-ordinate Transform Velocity IMU Rotation Rates Attitude Position Filtering Predicted Pseudoranges GPS Pseudorange Measurement GPS Position Solution Correction
Monte Carlo Analysis From simulated vehicle trajectory, true accelerations, rotation rates and position, velocity and attitude are computed Errors added to these truth states to simulate sensor readings Sensor readings are then fed through data fusion and output statistics tested
Monte Carlo Analysis Mean Variance