A State and Parameter Identification Scheme for Linearly Parameterized Systems

Abstract

This paper presents an adaptive algorithm to estimate states and unknown parameters simultaneously for nonlinear time invariant systems which depend affinely on the unknown parameters. The system output signals are filtered and re-parameterized into a regression form from which the least squares error scheme is applied to identify the unknown parameters. The states are then estimated by an observer based on the estimated parameters. The major difference between this algorithm and existing adaptive observer algorithms is that the proposed algorithm does not require any special canonical forms or rank conditions. However, an output measurement condition is imposed. The stability and performance limit of this scheme are analyzed. Two examples are then presented to show the effectiveness of the proposed schemes.

A study on lateral speed estimation methods

“…The equations are too numerous to recite completely in this paper. Interested readers are referred to the original paper by Liu and Peng for details [4]. This estimator, like most other adaptive algorithms, requires a persistent excitation condition to achieve small estimation errors.…”

“…However, this two-step approach relies heavily on the structure of the transfer function and might be very sensitive to uncertainties, such as variation in other vehicle parameters (m, I z , etc.) The adaptive algorithm developed by Liu and Peng [4] uses a one-step strategy. The algorithm was developed to estimate states and unknown parameters simultaneously for nonlinear time invariant systems which depend affinely on the unknown parameters.…”

“…Experimental results provided in their paper show that the side slip angle estimation error is roughly below 3 degrees. Liu and Peng [4] proposed a different identification scheme for simultaneous state and parameter estimation to overcome the unknown vehicle parameters. However, the observer stability is only proven for the case of time invariant cornering stiffness and/or road surfaces.…”

“…However, there have been few comparison studies between representative methods, and thus it will be the main focus of this paper. We will focus on the discussion and comparison of three representative methodologies: a transfer function approach, the state-space approach by Liu and Peng [4], and the kinematics approach by Farrelly and Wellstead [5]. First, simulations are performed under ideal conditions to see their best case performance by using clean data generated by the TruckSim 2 software (www.trucksim.com).…”

Kinematics-Based Analytical Solution for Wheel Slip Angle Estimation of a RWD Vehicle with Drift

“…However, the quality of estimation strongly depends on the accuracy of the vehicle and tire model parameters. Since most of the model-based estimation methods-i.e., linear state observer [26,28] and Kalman filter-relying on a linear vehicle model can work efficiently only under nominal vehicle operating conditions where tires operate within the linear slip-friction characteristic but no longer work reliably when the vehicle is skidding and the slip angle becomes large, other types of observer developed based on the extended nonlinear vehicle model such as nonlinear observer [29][30][31][32][33], extended Kalman filter [34], extended Luenberger observer and sliding-mode or adaptive observer have been proposed to overcome these constraints caused by the nonlinear tire characteristic. Nevertheless, these methods are too complicated and still have large error due to model parameters mismatching.…”