A Modified Unscented Kalman Filter Combined with Ant Lion Optimization for Vehicle State Estimation

Algorithm 1

The state estimation procedure based on the UKF algorithm.

	Step 1: initialization (k = 0)
	Step 2: time update (k = 0,1,2, ⋯)
	Generate sigma points:
	Calculate sigma points’ weight:
	The step prediction of sigma points:
	The state mean and error covariance matrix of step prediction: ,
	According to the step prediction, generate new sigma points:
	Step 3: measurement update (k = 0,1,2, ⋯)
	Propagate the new sigma points by h (∙), and the predicted observation is given by
	The mean of system observation:
	The error covariance matrix of system observation:
	Calculate the cross-correlation covariance matrix:
	Calculate the Kalman filter feedback gain matrix:
	The update of state estimation:
	The update of the error covariance matrix: