Probabilistic models for IMU

Parent: IMU index Source: [MKok 2017 Using inertial sensors for position and orientation estimation](mkok 2017 using inertial sensors-for-position-and-orientation-estimation.md)

Three main components to the probabilistic models

1. IMU measurement model  (infer knowledge about pose from measurements) 
2. Prediction model  (how sensor pose changes over time)
3. Models of the initial pose (prior)

Knowledge we are interested in: pose of the sensor

• time-varying variables: states 
• constants: parameters 

Knowledge available to us: sensor dynamics, available sensor measurements 

Conditional probability distribution

• Smoothing problem (uses all measurements)

• Filtering problem (only up to t-th measurement) Parameters are treated as slowly time-varying —> incorporated into state vector x

• Variations: fixed-lag smoothing, MHE

Assumption: our models have the Markov property

The complexity of pose estimation can be mainly attributed to

• the nonlinear nature of orientation —> linearise the orientations
• the different available ways of parametrising orientation

Resulting probabilistic models Pose estimation

Initial conditions

Orientation at t=1 from QUEST algo

Orientation estimation