# Measurement Compression

One of the most costly opeerations in the EKF update is the matrix multiplication. To mitigate this issue, we perform the thin QR decomposition of the measurement Jacobian after nullspace projection:

This QR decomposition can be performed again using Givens rotations (note that this operation in general is not cheap though). We apply this QR to the linearized measurement residuals to compress measurements:

As a result, the compressed measurement Jacobian will be of the size of the state, which will signficantly reduce the EKF update cost: