Incorporation of time delayed measurements in a discrete-time Kalman filter

TLDR

Sensor delays, such as those from vision systems, complicate Kalman filter fusion and require trade‑offs between optimality and computational load. The study compares existing delayed‑measurement Kalman filter techniques with a newly proposed method. The new approach extrapolates delayed measurements to the present using past and current filter estimates and computes an optimal gain for the extrapolated data.

Abstract

In many practical systems there is a delay in some of the sensor devices, for instance vision measurements that may have a long processing time. How to fuse these measurements in a Kalman filter is not a trivial problem if the computational delay is critical. Depending on how much time there is at hand, the designer has to make trade offs between optimality and computational burden of the filter. In this paper various methods in the literature along with a new method proposed by the authors will be presented and compared. The new method is based on "extrapolating" the measurement to present time using past and present estimates of the Kalman filter and calculating an optimal gain for this extrapolated measurement.