Nonlinear Constrained Moving Horizon Estimation Applied to Vehicle Position Estimation

Abstract

The design of high–performance state estimators for future autonomous vehicles constitutes a challenging task, because of the rising complexity and demand for operational safety. In this application, a vehicle state observer with a focus on the estimation of the quantities position, yaw angle, velocity, and yaw rate, which are necessary for a path following control for an autonomous vehicle, is discussed. The synthesis of the vehicle’s observer model is a trade-off between modelling complexity and performance. To cope with the vehicle still stand situations, the framework provides an automatic event handling functionality. Moreover, by means of an efficient root search algorithm, map-based information on the current road boundaries can be determined. An extended moving horizon state estimation algorithm enables the incorporation of delayed low bandwidth Global Navigation Satellite System (GNSS) measurements—including out of sequence measurements—as well as the possibility to limit the vehicle position change through the knowledge of the road boundaries. Finally, different moving horizon observer configurations are assessed in a comprehensive case study, which are compared to a conventional extended Kalman filter. These rely on real-world experiment data from vehicle testdrive experiments, which show very promising results for the proposed approach.

Advanced Estimation Techniques for Vehicle System Dynamic State: A Survey

“…The performance of two estimators were compared according to the criterion of mean squared error and steady-state error. The work [79] proposed nonlinear constrained MHE to estimate mainly the vehicle position P p and vehicle sideslip angle for future autonomous vehicles; the delayed measurements from the global navigation satellite system (GNSS) and road boundary constraints can be directly incorporated into MHE, and real-world experiments show that the proposed MHE possesses improved estimation performance in comparison to the EKF.…”

A Physical Model-Based Observer Framework for Nonlinear Constrained State Estimation Applied to Battery State Estimation

“…The covariance matrices Qk and Rk are defined as normalE(wkwjT) = Qkδk−j and normalE(vkvjT) =Rkδk−j , where δk−j is the Kronecker delta function; that is, δk−j=1 if k=j , and δk−j=0 if k≠j . The operator normalE(·) calculates the expectation value of a random variable [8]. The notation wk~N(0,Q…”

“…The so-called sigma point transformation (SPT) is based on the idea that it is easier to approximate a Gaussian distribution than it is to approximate an arbitrary nonlinear function or transformation; see [8,29], and appendix Chapter A.4 in reference [2]. The parts of the unscented Kalman filter (UKF) algorithm, in which model evaluations are necessary, are given in Algorithm 3.…”

“…The textbooks [7,8,9] are excellent starting points for the theoretical background on Kalman filtering and optimal state estimation. For this reason, only the most important steps of discrete nonlinear estimation and their interface to the estimation framework are given in Chapter 2 to guarantee readability and comprehension.…”

“…In this work, a formulation and code generation framework is proposed that makes use of an estimation-problems-specific, extended FMU (Funtional Mockup Unit) 2.0 co-simulation interface [4], providing the possibility of formulating prediction model equations in continuous-time by means of the Modelica language. In addition to the implementation of the well-proven Kalman filter algorithms (e.g., in [8]), fast and reliable theory extensions for nonlinear constraint handling are given in Chapter 3.…”