Joint state and measurement time-delay estimation of nonlinear state space systems

Sensor fusion algorithms often assume perfect time synchronization of the sensor clocks. In a practical sensor-actuator setup this is often difficult to achieve which in turn can give rise to systematic errors in the sensor fusion. In this article we suggest how the effect of the synchronization error from an unknown static or slowly varying measurement time-delays in a nonlinear state space system can be handled by linearizing the measurement equation in time. Based on the linearization an augmented system is constructed from which the system states and the delays can be jointly estimated. Expressions for the system, measurement, and covariance matrices of the augmented system are derived. Finally, the feasibility of the suggested approach is demonstrated by an example and a Monte-Carlo simulation.