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GNC > State Estimation > Flashcards

State Estimation Flashcards

1
Q

Define:

State Estimation

A

Determining the spacecraft’s current position, velocity, and orientation.

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2
Q

What methods are used for state estimation?

A
  • Kalman Filters
  • Particle Filter
  • Bayesian Estimation
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3
Q

Define:

Kalman Filter

A

A recursive algorithm that uses a series of measurements over time, incorporating noise and other inaccuracies, to produce estimates of unknown variables.

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4
Q

What are the two steps of a kalman filter?

A
  1. Prediction or propagation - State and error
  2. Update - State update, gain calculation, error update
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5
Q

What sensors provide input to a kalman filter?

A
  • IMUs
  • GPS
  • Star Trackers
  • Sun Sensors
  • Magnetometers
  • Ground-Based Tracking
  • Control inputs
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6
Q

What is the GNC data flow?

A
  1. Sensor data collection
  2. Data pre-processing - filters to remove noise and baises
  3. Prediction - Prediction of the satellite’s next state
  4. Update - Updates state estimate using new measurements.
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7
Q

Define:

Extended kalman filter

A

A non-linear adaptation of a kalman filter.

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8
Q

How do you tune a kalman filter?

A

Sytematically optimize.
Use cross validation (train & test sets)

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9
Q

Define:

Process Noise Covariance

A

Matrix Q, represents uncertainty in the model in the state space

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9
Q

Define:

Measurement Noise Covariance

A

Matrix R, represent the uncertainty in measurements based on sensor specifications or empirical measurements.

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10
Q

What are three examples of optimization techniques?

A
  • Grid search
  • Genetric algorithms
  • Gradiant-based optimization
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11
Q

What are computational challenges of implementing kalman filters on satellites?

A
  • Limited processing power
  • Memory contrainsts
  • Power
  • Thermal
  • Radiation
  • Cost.
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12
Q

What can make a kalman filter fail to converge?

A
  • Poorly modeled systems dynamics
  • Incorrect initial error state
  • Improper noise covariance matrices.
  • measurement outliers
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13
Q

What’s the difference between a direct and indirect kalman filter?

A

A direct filter estimates the state, while and indirect measures the error.

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14
Q

What is another name for an indirect kalman filter?

A

Error-state kalman filter

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15
Q

Why is an indirect kalman filter helpful in collision avoidance?

A

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.

16
Q

What happens to gain when measurement error covariance goes to infinity?

A

The gain goes to 0.

16
Q

What is Kalman sensor gain?

A

Gain is the filter’s sensitivity to inputs. A high gain means that small sensor changes have a large effect on state.

17
Q

What is an intertial navigation system?

A

An inertial navigation system is the suite of sensors aiding in state determination, including:
* IMUs
* Star trackers
* GPS
* Range
* Altimeter
* Cameras

18
Q

What is an intertial measurement unit?

A

An IMU contains gyroscope and accelerometers to measure rotation and translational displacement.

19
Q

Define:

Invariant

A

A variable that remains the same after a specific transformation

20
Q

What are examples of invariance in GNC?

A
  • Angular momentum
  • Total Mechanical Energy
  • Keplereian element (except true anomaly)
  • Attitude (quaternion)
21
Q

What is an Invariant Kalman Filter?

A

A filter which preserves geometric properties and symmetries of the system during the estimation process.

22
Q

Why use an Invariant Kalman Filter?

A

It improves estimation accuracy and robustness for systems with inherent symmetries, such as those involving rotational dynamics.

23
Q

How does an Invariant Kalman Filter differ from a standard EKF?

A

An Invariant Kalman Filter preserves system invariances during linearization, while a standard EKF does not.

24
Q

How do Invariant Kalman Filters contribute to the robustness of state estimation?

A

By accounting for and preserving system symmetries, they reduce the impact of modeling errors and disturbances.

25
Q

What is the difference between velocity estimated by a KF and instantaneuous velocity?

A

KF velocity is smooth, and instant velocity is noisy. The KF accounts for error.

26
Q

How does a KF combine measurements?

A
  • Sequential Update - process each measurement 1 by 1.
  • Combined Update - combine all measurements in a larger measurement vector and process them in one update.
27
Q

What should you consider when picking sensors for a KF?

A
  • Accuracy and precision
  • Noise
  • Measurement frequency
  • Sensor range
  • Redundancies
  • Latency
  • Environmental durability
  • Cost and availibility
28
Q

List:

5 examples of process noise in a spacecraft

A
  • Thrust noise
  • Atmospheric drag
  • Solar radiation pressure
  • Gravitational pertubations
  • MMOD Impacts
29
Q

What is a covariance matrix?

A

A square matrix that represents the covariance between each pair of elements in a given multivariate random variable.

GNC (3 decks)

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