Why does sequential update of Kalman Filter work when you have multiple sensors?

1. Why covariance matrix is used in Kalman filter?
2. How does Kalman filter predict?
3. Why Kalman filter is optimal?
4. What are the different stages in Kalman filter?

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 does Kalman filter predict?

The filter estimates the current measurement by multiplying the predicted state by the measurement matrix. The residual, ∼yk , is later then multiplied by the Kalman gain, Kk , to provide the correction, Kk∼yk , to the predicted estimate ˆx−k .

Why Kalman filter is optimal?

Kalman filter is statistically optimal in a sense that it gives the minimum error covariance estimate, based on all available observation data at the present time step under the linear system.

What are the different stages in Kalman filter?

The Kalman filter can be written as a single equation; however, it is most often conceptualized as two distinct phases: "Predict" and "Update".