Towards affordable on-track testing for autonomous vehicle — A Kriging-based statistical approach

Abstract

This paper discusses the use of Kriging model in Automated Vehicle evaluation. We explore how a Kriging model can help reduce the number of experiments or simulations in the Accelerated Evaluation procedure. We also propose an adaptive sampling scheme for selecting samples to construct the Kriging model. Application examples in the lane change scenario are presented to illustrate the proposed methods.

Synthesis of Different Autonomous Vehicles Test Approaches

“…6, where we use yellow asterisk to represent the experiments from h 1 . Compared to the response surface in Fig 5, this response surface has better prediction in the region [4,5], while it has a similar response in rest of the design space. The improvement of the tail region further decreased the MSE to 0.0087 (compare to 0.0093 in Fig 5).…”

“…We observe that the mean of the response surface (blue solid line) is not close to the real function (green dash line) in most part of the region (e.g. [−5, 1] and [4,5]) and the 95% confidence interval (red dot line) does not contain the real function in [−1, 3]. Note that the Kriging model is built with only 4 data points (the Fig.…”

“…We need to decide the fidelity levels t's and the value of x in X new , so that we can do experiments on those t's and x's to collect the response Y new . In [4], [18], an experiment design scheme for Kriging based on the information gain (IG) is discussed. Here, we define IG at point x for model with fidelity t as IG(x, t) = E y∼yt(x) (p n −p n+1 (x, y)) 2 |(X, Y ) , (14) wherep denotes the probability estimation with n samples in the samples set (X, Y ) andp n+1 (x, y) denotes the probability estimation with sample set (X, Y ) and an additional sample (x, y).…”

“…[4] discussed an approach that uses response surface model in the accelerated evaluation context, and used a single type test results. This paper extends the use of response surface model in [4]. Besides results of on-road tests, the proposed approach also obtains information from other test resources, which improves the accuracy of the response surface.…”

“…This model utilizes Kriging model or Gaussian process in constructing the response surface. We also discuss the extension of the design of experiments scheme in [4] to multi-source tests. The scheme can help us smartly select design points and therefore avoid unnecessary experiments in the model constructing procedure.…”