# OBU for Accurate Navigation through Sensor Fusion in the Framework of the EMERGE Project
## 3 Sensor Fusion: Loosely Coupled Algorithm Implementation
### The Initialisation Loop
; writing--review and editing, A.L.Z.S., V.I., M.P., M.B., F.V. and E.C. ; visualisation, all authors; supervision, M.P., R.A., F.V., E.C., C.A. and A.M.; project administration, F.V. and M.P. ; funding acquisition, all authors. All authors have read and agreed to the published version of the manuscript. This research was partly funded by the project \"Centre of Excellence on Connected, Geo-Localized and Cyber-secure Vehicles\"-Italian Government (Grant Number: CIPE Resolution 70/2017) and the project EMERGE-Navigation (Ministry of Innovation and Made in Italy and Regione Abruzzo). Not applicable. The data that support the findings of this study are available from the corresponding authors, A.Z. and V.I., upon reasonable request. The authors acknowledge the Ex-EMERGE centre, Radiolabs and Telespazio Spa for the support, resources and facilities provided. Special thanks to [PERSON]/DISIM-UNIVAQ for his invaluable technical assistance during this research. Their expertise and support have played a crucial role in successfully executing this work. The authors declare no conflict of interest. ## Abbreviations

The following abbreviations are used in this manuscript:

ADAS Advanced Driver Assistance System

AGNSS Augmented GNSS

AHRS Attitude and Heading Reference Systems

API Application programming interface

AV Autonomous Vehicle

C/N0 Carrier-to-Noise Density Ratio

CAD Connected and Automated Driving

COTS Commercial Off-The-Shelf

DOP Dilution Of Precision

ECEF Earth-centred, Earth-fixed Coordinate System

EKF Extended Kalman Filter

GNSS Global Navigation Satellite System

GPIO General Purpose Input/Output

GT Ground Truth

HW Hardware

IMU Inertial Measurement Unit

INS Inertial Navigation System

IoT Internet of Things

IP Internet Protocol

JSON JavaScript Object Notation

KPI Key Performance Indicators

MCU Microcontroller Unit

MQTT Message Queuing Telemetry Transport

MT Motion Trackers

NED North-East-Down

OBC On Board Computer

OBU On Board Unit

PNT Positioning, Navigation and Timing

PP PointPerfect

PPP Precise Point Positioning

PPP-RTK Precise Point Positioning - Real Time Kinematic

PVT Position, Velocity and Time

RMSE Root Mean Square Error

RTK Real Time Kinematic

SBC Single Board Computer

SDRAM Synchronous Dynamic Random Access Memory

SF Sensor Fusion

SMA SubMiniature version A - coaxial RF connector

SoC System-on-a-Chip

SVs Space Vehicles

SW Software

TTFF Time To First Fix

UAV Unmanned Aerial Vehicle

UBX u-blox proprietary binary protocol

UPS Uninterruptible Power Supply

V2V Vehicle to Vehicle communications

V2X Vehicle to Everything communications

XDA Xsens Device API

## Appendix A Extended Kalman Filter (NED Implementation)

In this appendix, the expressions for the matrices used in the Kalman filter prediction and correction steps when attitude and velocity are Earth-referenced and resolved in the local (NED) navigation frame, and the position is expressed using geodetic coordinates, are reported. The index denoting the epoch is omitted in the equations for readability. Prediction error covariance matrix:

\[\mathbf{Q}\approx \begin{bmatrix}S_{rg}\mathbf{I}&0&0&0&0\\ 0&S_{ra}\mathbf{I}&0&0&0\\ 0&0&0&0&0\\ 0&0&0&S_{bad}\mathbf{I}&0\\ 0&0&0&0&S_{bgd}\mathbf{I}\end{bmatrix} \tau, \tag{10}\]

where \(S_{rg}\), \(S_{ra}\), \(S_{bad}\), and \(S_{bgd}\) denote, respectively, the power spectral densities of the noise of the gyroscope and accelerometer, and the power spectral densities of the bias variations of the gyroscope and accelerometer. Vector of observations:

\[\delta\mathbf{z}_{k}= \begin{pmatrix}\hat{\mathbf{r}}_{GNSS}^{n}-\hat{\mathbf{r}}_{ eb}^{n}-\hat{\mathbf{C}}_{b}^{n}\hat{\mathbf{b}}_{ba}^{b}\\ \hat{\mathbf{v}}_{GNSS}^{n}-\hat{\mathbf{v}}_{eb}^{n}-\hat{\mathbf{C}}_{b}^{ n}(\hat{\mathbf{\omega}}_{ib}^{b}\times\mathbf{l}_{ba}^{b})+[\mathbf{\omega}_{ ie}^{n}]_{x}\hat{\mathbf{C}}_{b}^{n}\hat{\mathbf{l}}_{ba}^{b}\end{pmatrix}