State Estimation Flashcards
Define:
State Estimation
Determining the spacecraft’s current position, velocity, and orientation.
What methods are used for state estimation?
- Kalman Filters
- Particle Filter
- Bayesian Estimation
Define:
Kalman Filter
A recursive algorithm that uses a series of measurements over time, incorporating noise and other inaccuracies, to produce estimates of unknown variables.
What are the two steps of a kalman filter?
- Prediction or propagation - State and error
- Update - State update, gain calculation, error update
What sensors provide input to a kalman filter?
- IMUs
- GPS
- Star Trackers
- Sun Sensors
- Magnetometers
- Ground-Based Tracking
- Control inputs
What is the GNC data flow?
- Sensor data collection
- Data pre-processing - filters to remove noise and baises
- Prediction - Prediction of the satellite’s next state
- Update - Updates state estimate using new measurements.
Define:
Extended kalman filter
A non-linear adaptation of a kalman filter.
How do you tune a kalman filter?
Sytematically optimize.
Use cross validation (train & test sets)
Define:
Process Noise Covariance
Matrix Q, represents uncertainty in the model in the state space
Define:
Measurement Noise Covariance
Matrix R, represent the uncertainty in measurements based on sensor specifications or empirical measurements.
What are three examples of optimization techniques?
- Grid search
- Genetric algorithms
- Gradiant-based optimization
What are computational challenges of implementing kalman filters on satellites?
- Limited processing power
- Memory contrainsts
- Power
- Thermal
- Radiation
- Cost.
What can make a kalman filter fail to converge?
- Poorly modeled systems dynamics
- Incorrect initial error state
- Improper noise covariance matrices.
- measurement outliers
What’s the difference between a direct and indirect kalman filter?
A direct filter estimates the state, while and indirect measures the error.
What is another name for an indirect kalman filter?
Error-state kalman filter
Why is an indirect kalman filter helpful in collision avoidance?
An indirect kalman filter returns the errors in the states, rather than the states them selves. State error is the primary input into the alfano collision method.
What happens to gain when measurement error covariance goes to infinity?
The gain goes to 0.
What is Kalman sensor gain?
Gain is the filter’s sensitivity to inputs. A high gain means that small sensor changes have a large effect on state.
What is an intertial navigation system?
An inertial navigation system is the suite of sensors aiding in state determination, including:
* IMUs
* Star trackers
* GPS
* Range
* Altimeter
* Cameras
What is an intertial measurement unit?
An IMU contains gyroscope and accelerometers to measure rotation and translational displacement.
Define:
Invariant
A variable that remains the same after a specific transformation
What are examples of invariance in GNC?
- Angular momentum
- Total Mechanical Energy
- Keplereian element (except true anomaly)
- Attitude (quaternion)
What is an Invariant Kalman Filter?
A filter which preserves geometric properties and symmetries of the system during the estimation process.
Why use an Invariant Kalman Filter?
It improves estimation accuracy and robustness for systems with inherent symmetries, such as those involving rotational dynamics.
How does an Invariant Kalman Filter differ from a standard EKF?
An Invariant Kalman Filter preserves system invariances during linearization, while a standard EKF does not.
How do Invariant Kalman Filters contribute to the robustness of state estimation?
By accounting for and preserving system symmetries, they reduce the impact of modeling errors and disturbances.
What is the difference between velocity estimated by a KF and instantaneuous velocity?
KF velocity is smooth, and instant velocity is noisy. The KF accounts for error.
How does a KF combine measurements?
- Sequential Update - process each measurement 1 by 1.
- Combined Update - combine all measurements in a larger measurement vector and process them in one update.
What should you consider when picking sensors for a KF?
- Accuracy and precision
- Noise
- Measurement frequency
- Sensor range
- Redundancies
- Latency
- Environmental durability
- Cost and availibility
List:
5 examples of process noise in a spacecraft
- Thrust noise
- Atmospheric drag
- Solar radiation pressure
- Gravitational pertubations
- MMOD Impacts
What is a covariance matrix?
A square matrix that represents the covariance between each pair of elements in a given multivariate random variable.
