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Asynchronous Extended Kalman Filter

The Extended Kalman Filter (EKF) allow us to estimate the state of a system, known the inputs of the system and the measurements of the outputs of the system. A non-linear model can be used with EKFs. However, if the outputs of the system don't have the same rate, a non-linear model for each measurements state is needed.

This problem can be easily solved by modifying the equations of the Output Prediction, Output Matching and State Correction Steps, by introducing a binary vector of the enabled outputs measures.

Fig. 1: EKF loop

This Asynchronous EKF can be also used with continuous systems, discretizing the continuous model by the Euler method and calculating it with a fixed sample time having all the outputs unenabled between two measures.