Distributed State Estimation for Dynamic Positioning Systems with Uncertain Disturbances and Transmission Time Delays

Algorithm 1

Distributed weighted fusion estimation using the ASS scheme.

	Input:
	The initial state , measurement , estimated state , and error covariance .
	Output:
	The local state estimation and the fused state estimation .
	(1) Perceive the measurements from sensor data packets with timestamp at the current time instant , which are transmitted over the networked systems.
	(2) Judge the received valid signals using the ASS scheme. The reorganized measurement is denoted as for the i-th subsystem.
	(3) Probe the filtering parameters , , , and according to Theorem 2.
	(4) Solve the filter and predictor in equations (8) and (9).
	(5) Obtain the weighted fusion estimation from equation (25).
	(6) Update at the next time instant. Return to Step 2.
	(7) return and in equations (8) and (9), respectively. , , and from equations (19)–(21).