# EKF SLAM Prediction Step

My question relates to the prediction step in EKF SLAM when we get measurements. This is a question I've encountered while implementing EKF SLAM in ROS.

At the beginning of the SLAM loop, we predict where we think the robot is by taking its expected location given the previous location and the previous controls. If we have valid measurements we then use those to compute the Kalman gain and update the robot position given these measurements.

These measurements, from a LIDAR scan, for example, will probably be captured in between SLAM loops, meaning that at time $$t$$ the measurements will be with respect to some time between $$t-1$$ and $$t$$.

Consider, for example, that the measurements come in at time $$t-0.1$$. In order to make the update step more accurate, shouldn't we predict up to time $$t-0.1$$, update, and then predict up to time $$t$$?

• No. If you are modeling a time dependent system then $t$ should creep into your propagation equations. Ultimately then the covariance should scale to be bigger or smaller depending on how big $t$ is. – edwinem Dec 19 '20 at 15:44