Role of Riccati Equations in Kalman Filter Design

1. Why do we use Riccati equation?
2. What are Q and R matrices in Kalman filter?
3. Why covariance matrix is used in Kalman filter?
4. How do you find the Riccati equation?

Why do we use Riccati equation?

The algebraic Riccati equation determines the solution of the infinite-horizon time-invariant Linear-Quadratic Regulator problem (LQR) as well as that of the infinite horizon time-invariant Linear-Quadratic-Gaussian control problem (LQG). These are two of the most fundamental problems in control theory.

What are Q and R matrices in Kalman filter?

R expresses how accurate your sensors are. Q is a measure of how accurate your model is - some dynamics are too complicated to be modelled and are assumed as process noise. By comparing your model predictions with real measurements you could estimate Q.

Why covariance matrix is used in Kalman filter?

The Kalman Filter (KF) is a recursive scheme that propagates a current estimate of a state and the error covariance matrix of that state forward in time. The filter optimally blends the new information introduced by the measurements with old information embodied in the prior state with a Kalman gain matrix.

How do you find the Riccati equation?

The given Riccati equation can be solved by substitution y=x2+1/v(x), where y₁ = x² is a particular solution of the given Riccati equation.