Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 515787, 14 pages

http://dx.doi.org/10.1155/2015/515787

## A Study on Maneuvering Obstacle Motion State Estimation for Intelligent Vehicle Using Adaptive Kalman Filter Based on Current Statistical Model

^{1}State Key Laboratory of Automobile Simulation and Control, Jilin University, Changchun 130022, China^{2}Ford Motor Research & Engineering (Nanjing) Co., Ltd., Nanjing 210000, China

Received 2 May 2015; Revised 7 August 2015; Accepted 9 August 2015

Academic Editor: Raffaele Solimene

Copyright © 2015 Bao Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The obstacle motion state estimation is an essential task in intelligent vehicle. The ASCL group has developed such a system that uses a radar and GPS/INS. When running on the road, the acceleration of the vehicle is always changing, so it is hard for constant velocity (CV) model and constant acceleration (CA) model to describe the motion state of the vehicle. This paper introduced Current Statistical (CS) model from military field, which uses the modified Rayleigh distribution to describe acceleration. The adaptive Kalman filter based on CS model was used to estimate the motion state of the target. We conducted simulation experiments and real vehicle tests, and the results showed that the estimation of position, velocity, and acceleration can be precise.

#### 1. Introduction

In recent years, the lane departure warning system, front collision warning system, adaptive cruise control system, and other automotive advanced driver assistance systems, which are based on the radar and computer vision, have become hot research topics in the international automotive safety technology [1–4].

In order to obtain the motion state information of the front vehicle comprehensively and achieve target identification effectively and accurately, the researchers of Bosch, Delphi, and other institutions proposed obstacle motion state estimation algorithm [5, 6]. And most of the studies use maneuvering target tracking methods from the military field, which are used to detect the aircraft, missile, and other flyers [7–11].

Friedland assumed that the target maintains a constant velocity relative to the radar, and the relative acceleration is considered to be the random interference in which the mean is zero. He established a two-order Kalman filter based on CV model [12]. The position and velocity estimation error are small when the velocity of the target is constant, but these estimation errors are larger when speed of the target changes.

Hampton assumed that the target maintains a constant acceleration relative to the radar, and the change of the relative acceleration is considered to be the random interference in which the mean is zero. He established a three-order Kalman filter based on CA model [13]. The position and velocity estimation error are small when the velocity or the acceleration of the target is constant, but these estimation errors are larger when the acceleration changes.

Singer proposed Singer model [14]. Singer model is a zero-mean model for motor acceleration, which is not reasonable to maneuvering target with mutative velocity and acceleration. It is generally agreed that the data range of next moment acceleration is limited.

Blom and Bar-Shalom proposed the Interactive Multiple Model (IMM) algorithm [15–18]. It allows for several parallel models which are combined to a weighted estimate. Choosing models for different driving modes, such as constant velocity, constant acceleration, and strong acceleration changes, the target state estimation can be optimized for highly dynamic maneuvers. But the amount of processing is large and if the weight set is not accurate enough, the estimation performance will decrease.

Hou of Tsinghua University assumed that the change rate of the acceleration is constant and he established a four-order Kalman filter [19]. When the acceleration of the target changes often, the position, velocity, and acceleration estimation is more accurate compared to the Kalman filter based on CV model or CA model. But it is a prior model and it is not an adaptive system according to the change of the acceleration. And if the change rate of the acceleration changes, the position, velocity, and acceleration estimation will be less precise.

In order to improve the accuracy of target state estimation, this paper introduces CS model [20, 21] from military and aerospace field, which is using the modified Rayleigh distribution to describe acceleration. Compared to the CA model, the CS model is more aligned with the actual acceleration change laws. The author established the adaptive Kalman filter based on the CS model. It uses the variance of the modified Rayleigh distribution to adjust the optimal Kalman gain at the next time, which improved the accuracy of the target motion state estimation. In addition, the motion modeling and filtering are based on absolute motion in absolute coordinate by using the GPS/INS, which can improve the accuracy.

The paper is organized as follows. In Section 1, a brief introduction on the target state estimation and modeling method is given. Section 2 presents the method for the target state estimation. In Sections 3 and 4 the simulation experiments and real vehicle test results are compared for CA model. Conclusions are presented in Section 5.

#### 2. Target Motion State Estimation Model

In this paper the object state estimation is to use the estimation algorithm based on the target motion model to identify the state (position, velocity, and acceleration) accurately and in real time. The key element is to find a suitable model for target and an appropriate estimation algorithm.

When driving on the road, the time that the vehicle maintains constant velocity and acceleration is always short and the acceleration changes a lot, such as overtaking. So when using the Kalman filtering algorithm based on the CV model or the CA model to estimate the state of real vehicle, the error is large. But that of the adaptive Kalman filtering algorithm based on the CS model is not.

##### 2.1. Target Motion Model

###### 2.1.1. The “Current” Probability Density Model of the Maneuvering Target

Probability density function of Rayleigh distribution is expressed as follows:

Figure 1 shows that if is determined, we can completely determine the statistical properties of Rayleigh distribution.