A Kalman filter is an algorithm that we use to estimate the state of a system
By combining-
1) noisy measurement from sensor ( Gaussian distribution)
2) flawed prediction from process model ( linear + Gaussian error)
→ then linear Kalman filter = optimal state estimate
optimal state estimatino = product of 2 Gaussian distributions
linear Kalman filter = prediction step + Gaussian multiplication
First
1) we want accurate estimate of current state ( like to change temp, we need to know what the current temp is)
OBv- use sensor ot measure state
what not obv - can improve estimate by adding more info ( one of the methods for using some of the additional info is Kalman Filter)
Kalman filter - part of class of estimation filters
→ use 2 step process
1. prediction
2. correcion
→ to produce an optimal state estimate
the intuition you gain from understanding linear Kalman filters can help you to better understand their nonlinear counterparts like the extended Kalman filter, the sigma-point filter, and the particle filter.
They are separated into predict (using the model) and correct (using the measurements), hence the two-step process for estimating state
• A Kalman filter uses three different covariance matrices (measurement, model, final estimation) in order to maintain an estimate of the system state.
We can now frame all of these uncertainties (prediction error covariance, P, process noise covariance, Q, and measurement noise covariance, R) into a single coherent workflow.
So, now we can think of a Kalman filter as an algorithm that just runs a prediction model and then multiplies two Gaussian distributions: a prediction and its uncertainty distribution with a measurement and its uncertainty distribution.
Kalman gain
