Longitudinal-lateral-cooperative estimation algorithm for vehicle dynamics states based on adaptive-square-root-cubature-Kalman-filter and similarity-principle

•ASRCKF observation is proposed to estimate vehicle states.•The SP algorithm is put forward to calculate the μmax.•ASRCKF can improve the estimation accuracy, especially for vehicle sideslip angle.•Accurate μmax can always be obtained by the proposed algorithm.•Co-simulation and experiments are designed to verify the algorithm validation. It is infeasible to measure vehicle dynamics states (VDS) directly without expensive measurement instruments, especially for the tire-road peak adhesion coefficient (μmax). However, four-wheel-independent-drive-electric-vehicle (4WIDEV) provides convenience for the observation of these dynamic states, because the rotation rate and torque of the in-wheel motor can be acquired directly. Vehicle nonlinear longitudinal-lateral dynamics, the single estimation method for all VDS and the time-varying measurement noise of sensors cause difficulties for the observation. Common the extended-Kalman-filter (EKF) is unsuitable to estimate VDS in strong nonlinear region. This paper propose a longitudinal-lateral cooperative estimation algorithm based on adaptive-square-root-cubature-Kalman-filter (ASRCKF) and partitioned similarity-principle (SP) to estimate the vehicle states and the tire-road peak adhesion coefficient sequentially for 4WIDEV. Firstly, a nonlinear 7-degree-of-freedom (7DOF) vehicle model and magic-formula (MF) tire model are built as the base of the successive estimation scheme. Then, recursive-least-squares (RLS) is adopted to estimate the tire longitudinal force. With the estimated tire longitudinal force, an ASRCKF which can be adjusted adaptively by the feedback dynamics states, is designed for the estimation of vehicle states. Next, the SP algorithm combined with the characteristic of longitudinal-lateral dynamics, which is benefit for μmax estimation when tire dynamics enters the nonlinear region, is proposed. Finally, experiment and simulation results show that excellent performance can be achieved with the proposed estimation method in varying driving conditions.