Journal of Sensors

Volume 2018, Article ID 7368018, 7 pages

https://doi.org/10.1155/2018/7368018

## In-Motion Iterative Fine Alignment Algorithm for On-Board Vehicular Odometer-Aided SINS

^{1}Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China^{2}State Key Laboratory of Satellite Navigation System and Equipment Technology, Shijiazhuang 050081, China^{3}No. 454 Hospital of PLA, Nanjing 210002, China^{4}Institute of Air Combat, Naval Research Academy, Shanghai 200436, China

Correspondence should be addressed to Baichun Gong; nc.ude.aaun@gnog.nuhciab

Received 18 February 2018; Accepted 4 June 2018; Published 31 July 2018

Academic Editor: Giuseppe Maruccio

Copyright © 2018 Baichun Gong 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

This research proposes a novel in-motion fine alignment algorithm for vehicular dead reckoning (DR) with odometer-aided strapdown inertial navigation system (SINS) while the map matching result is used for a group of landmark points to estimate misalignment angles. The proposed algorithm is designed based on principle of similarity, that is, trajectory of DR is similar to the true trajectory that the main difference between these two trajectories is rotation and scale. Further, the results from map matching are introduced as a group of landmark points to estimate the residual of azimuth error angle after coarse alignment and the scale factor error of the odometer. It is theoretically proved that the alignment effectiveness based on the results from map matching is equivalent to that on single zero error landmark point. Finally, digital simulations are conducted to verify the presented algorithm and test the performance.

#### 1. Introduction

Strapdown inertial navigation system (SINS), considered as a dead reckoning system, utilizes the measurements from gyros and accelerometers to calculate the real-time attitude, position, and velocity of the vehicle. Initial alignment based on a preknown initial position directly determines the performance of SINS. Usually, methods for initial alignment are divided into two different types: self-alignment and transfer alignment. As to the autonomous vehicular application, self-alignment is required. Generally speaking, rapidity, accuracy, and autonomy are the basic requirements of the self-alignment methods. Especially rapid self-alignment is one of the key requirements for the circumstances such as military manoeuvers and rescue missions. However, rapidity and accuracy are contradiction to each other for the noise problem, that is, more time will be consumed to achieve an accurate self-alignment. Thus, in-motion alignment scheme is required for rapid response missions.

Many works have been done in field of in-motion alignment. Park et al. presented SINS/GPS alignment by using carrier phase rate information from on-boarded two-antenna GPS receiver [1]. Li et al. developed a DVL- (Doppler velocity log-) aided in-motion alignment algorithm [2]. Wan et al. presented an in-motion alignment method by using the position information from GPS [3]. Bimal and Ashok also studied DVL-aided in-motion alignment scheme [4]. Zhang et al. utilized the measurements from GPS and odometer (OD) to conduct fast alignment [5]. Cui et al. studied in-motion alignment for SINS/GPS under random misalignment [6]. Kaygısız and Şen presented in-motion alignment for a low-cost GPS/INS under large heading error [7]. Silson developed a rapid in-motion alignment method by using GPS position and velocity measurements [8]. Wang et al. proposed an odometer-aided in-motion alignment algorithm [9]. Yan presented an in-motion alignment algorithm for SINS/OD DR system utilizing a known landmark point based on principle of similarity [10].

It can be found that many of them require the information from GPS. However, GPS measurement information is not always available for signal blocking problem. Thus, more scholars put their attentions on the navigation without GPS that the self-alignment is independent to GPS. Inspired by the concept of principle of similarity using a known landmark point [10], a novel iterative in-motion fine alignment algorithm for vehicular DR based on SINS/OD is developed in this paper, where a group of virtual landmark points from the map matching result is used to estimate the azimuth error of SINS and the scale factor error of OD. Benefiting from the novel algorithm, the in-motion fine alignment can be achieved without GPS or even a zero velocity stop.

The formulation of the DR algorithm based on SINS/OD is reviewed firstly, and then positioning error analysis for DR is presented in Section 2. Novel iterative in-motion fine alignment algorithm utilizing a group of noised points from map matching result is presented in Section 3. Digital simulations are presented in Section 4. Conclusions are presented in Section 5.

#### 2. Problem Statements

##### 2.1. Review of Dead Reckoning Algorithm Based on SINS/OD

First of all, the coordinate frames used in this paper are defined as follows [11]. The inertial frame is a stationary Earth-centered frame and shares its polar axis but not rotate with it. The Earth frame is an Earth-centered-Earth-fixed frame whose -axis points at the intersection of the Greenwich meridian and the equatorial plane -axis points to the North Pole. The navigation frame moves with the vehicle about the surface of the Earth. The axes of point to the direction of east, north, and geodetic latitude (radial). The vehicular body frame is a fixed frame to the vehicle body. The -axis is pointing forward along the symmetric axis of the vehicle while the -axis is orthogonal to the -axis and points to the right wing, and -axis completes the right-hand orthogonal set.

It is assumed that the wheels cling to the ground without any side skidding and jumping during moving, the frame of SINS is coincident with the body frame of the vehicle. Then, the vehicle’s velocity in the body frame can be governed by where is the speed of the vehicle measured by OD.

The velocity in navigation frame can be expressed by where , , and are the components along the three axes of navigation frame.

Thus, the position differential equations for DR are modeled as follows [10]: where , , and are the longitude, latitude, and height, respectively, and is the prime radius of curvature while is the meridian radius of curvature.

By assuming the updating period of OD is during which samples are available, the iterative updating algorithm can be governed by [10]

##### 2.2. Position Error Analysis for Dead Reckoning Algorithm Based on SINS/OD

###### 2.2.1. Sensor Error Models

Usually, initial attitude matrix for SINS from its body frame to the navigation frame can be obtained from coarse alignment by taking advantage of double-vector method, with the measurements of gyro and accelerometer [12]. Generally speaking, after a fast coarse alignment, horizontal attitude angle error would be small, but the azimuth angle error could not be well estimated. Thus, the main uncertainty for SINS after coarse alignment is the azimuth angle error. The residual of the azimuth angle error is modeled as a constant

Then, the attitude matrix approximates to the following expression where denotes the vector while stands for the cross-product operation.

Next, the accuracy of OD is another key parameter to the dead reckoning system. The speed accuracy of OD is mainly affected by the status of the road surface, tire inflation, and abrasion [13]. Because it is impossible to precisely model these factors, the scale factor error for OD is considered in this manuscript. The scale factor error is assumed to include two parts: random constant and noise which are modeled as a one-order Markov process where denotes the random constant, is the noise with a correlation time , and is a Gaussian noise.

###### 2.2.2. Error Model for Dead Reckoning

Defining the velocity measurement error of OD in the body frame is , and then the velocity in the navigation frame can modeled as

Substituting (6) into (8) yields and then the velocity error in navigation frame can be obtained

Substituting (1) into (10) produces

Next, by conducting partial differential operation to (3) with respect to the time variable, the position error equations for DR system based on SINS/OD can be achieved

Denoting , rephrasing (12) into matrix form, and substituting (11) into it yield where

#### 3. Iterative In-Motion Fine Alignment Algorithm for DR

As can be seen from (13), the position uncertainty of DR mainly depends on the azimuth error , the scale factor error , and the error of the preknown initial position, among which is usually unknown and can be considered to be pretty small. Thus, in order to achieve a good alignment performance, the azimuth error and scale factor error are required to be accurately estimated.

In [10], an in-motion alignment scheme is proposed where one accurate landmark point is required for the algorithm. However, accurate landmark point is usually unavailable if the vehicle does not pass by the required area. In [14], the experiments have shown that a couple of points can be obtained by map matching algorithm based on SINS/OD/Map database, where there is no requirement of appointed route for the vehicle. Thus, the map-matched points can be considered as a group of virtual landmark points to be used to estimate the misalignment error. In the following parts, the map-matched points are assumed to be available.

##### 3.1. Fine Alignment Method Based on Single Landmark Point

As depicted in Figure 1, the DR trajectory can be considered as the rotating and stretching trajectory of the true trajectory based on the principle of similarity [10], that is, where is the up-direction attitude error angle, and is the horizontal projection of the true trajectory, . It should be emphasized that this conclusion is under the assumptions: (a) azimuth angle error is a small constant; (b) horizontal attitude error can be ignored.