GPS/INS/Odometer Data Fusion for Land Vehicle Localization in GPS Denied Environment

The main purpose of this paper is to present a fusion approach to bridge the period of Global Positioning System (GPS) outages using two proprioceptive sensors that are the Inertial Navigation System (INS) and the odometer in order to assure a continuous localization for land vehicle in urban areas where GPS signal blockage is very often. Odometer and GPS measures are exploited to correct inertial sensor errors. In fact, during GPS availability, INS is integrated with GPS to provide accurate localization solution; whereas during GPS outages, the odometer measurements are used to correct the INS error thereby improving the positioning accuracy and assuring the continuity of navigation solution. The problem of estimation of vehicle localization is realized by Kalman Filter (KF) that merges sensor measurements. The paper thus introduces results from simulation and real data.


Introduction
Satellite navigation systems such as GPS or Galileo are increasingly popular and used in strategic as well as public applications.If the safety of persons or property is involved, like in civil aviation, the GPS accuracy is insufficient to be certified as primary means of navigation.One of the solutions is to integrate the GPS with other sensors that provide a good availability such as INS and odometry.Integrated navigation systems have been used intensively in many domains such as aeronautics.However, their application to the automotive industry shows a big increase due to the low cost inertial measurement units (IMU).INS is a system that delivers the position, velocity, and attitude of a vehicle by exploiting the output of inertial sensors.The measurements of the inertial sensors are affected by errors due to physical limitations.The accumulation of these errors leads to the decrease of the accuracy of navigation solution.Therefore, if the error is not compensated with additional sensors, the navigation solution of INS can only be trusted during a short period of time (Seo & Lee, 2005).Nowadays, GPS is very often used as an aiding source to the INS, and the GPS/INS integrated system with good GPS availability provides more precise dynamic positioning than a stand-alone GPS or INS.However, GPS has a low sampling rate thus the satellite signals are not always available due to high buildings, tunnels and mountains, multi-path reflections and bad weather conditions (Noureldin, El-Shafie & Taha, 2007) (Farrell, 1998).To achieve a high level of positioning estimation in an urban area, a new developed integration navigation system is detailed in this paper.Our proposed method is based on the use of an additional aiding source.This additional sensor is the odometer.All modern cars are equipped with the Antilock Braking Systems (ABS) that includes an odometer which measures wheel angular rates and estimate the traveled distance.It is an alternative to satellite-based navigation technology when the GPS measures are not available.The purpose of our work is to propose a global modeling of the GPS/INS/Odometer fusion problem with long GPS outages.The estimation of dynamic characteristics of the vehicle is solved by a KF that fuses the measurements of each sensor to estimate position, velocity and attitude of the vehicle.This paper traits the performance of the proposed method in terms of accuracy using both simulated and real data.For real tests we have used a Novatel GPS receiver and we estimated the INS and measurements from the real trajectory.In this work additional aiding source information is also considered as an aiding to the positions delivered by GPS receiver.This extra information is estimated by an odometer.There are four different categories of integration approaches: un-coupled (Titterton & Weston, 1996), loosely coupled (LC) (Wolf, Eissfeller & Hein, 1997) (Solimeno, 2007), tightly coupled (TC) (Li et al., 2006) (Petovello, 2003), and ultra-tightly coupled (UTC) techniques (Babu & Wang, 2007) (Pany, Kaniuth & Eissfeller, 2005) (Petovello & Lachapelle, 2006).The second approach uses GPS and odometer position measurements in addition to the heading angle estimated by the odometery in a Kalman filter that models INS error dynamics.In this paper we have implemented a Loosely Coupled algorithm that has the ability to exploit additional information when available.In such a case, a Kalman filter that uses the position and the heading angle, estimated by the odometer, as measurement has been designed in order to readjust the errors affecting the inertial sensors when GPS signals are absent.
The rest of this paper is organized as follows: Section 2 discusses the INS and the odometer sensor modeling.Section 3 describes the KF fusion algorithm and detailed the system model and the observation model.Section 4 offers simulation results.Finally, section 5 is dedicated to conclusions.

INS Modeling
The equations modeling the INS sensors are used to obtain navigation solutions (position, velocity and orientation of the mobile) from the inertial sensors measurements, i.e. specific forces and angular rates.In this work these equations are expressed in the ENU frame (East, North and Up).In the following the ENU coordinate system will be considered as the navigation frame (n-frame).The body frame (b-frame) is defined at the INS centre.The dynamic equations in the n-frame are given by (Jekeli, 2001) (Abd Rabbou & El-Rabbany, 2015): Where en ω is the turn rate of the n-frame with the respect to the Earth, n g is the local gravity vector, D is the transformation matrix from the ENU frame to the LLa frame, it's given by (Titterton & Weston, 2004): (1 e sin ) m R and n R are the radii of curvature in the meridian and prime vertical, respectively (Tang et al., 2005).e is the eccentricity of the Earth, a and b are the semi-major axis and semi-minor axis of the Earth, respectively.
(1) Can be expressed in the ENU frame as: Where

[ ]
T n e n u P P P P = is the position vector in the navigation frame.

INS error equations
Eventually, the INS error equations are obtained by perturbing the kinematic equations, i.e. (1-3).These error equations are used in the construction of the GPS/INS/Odometer system model.The perturbation of the position in (1), velocity in (2) and attitude in (3) can be expressed as (5-7), (Angrisano, 2010): ) Where The INS mechanization in the navigation frame is summarized in figure 1 as follows:  (Schultz, 2006) (Quinchia et al., 2013)

Odometer Modeling
The kinematic equations of the char vehicle model figured in figure 2 are given by (Abuhadrous, 2005) Where R L and ω ω are the angular velocities of the right and left wheels, respectively.θ  is the heading angle rate Where k k x and y denote the position in the center of the axis, t Δ is the sampling time.

Kalman Filter Fusion Modeling
A KF is chosen to fuse the measurements of the INS and GPS when sufficient satellite signals are available and to integrate INS measures with odometer in the opposite case.The filter structure is shown in figure 3. The Kalman filter algorithm has two main steps: the first consists in predicting the state based on the system model and the second is dedicated to update the state based on the measurements (Grewal & Andrews, 1993).
 are the biases of accelerometers and gyroscopes, 3 0 and 3 I are zero and identity matrices of size 3, the drift of these biases can be modeled as a first-order Gauss-Markov process (Hou, 2004) represented as follow: Because the values of position error in ( 9) are very small, since they are expressed in radian, and can cause numerical instability inside the filter, to avoid this problem it is better to express the position error in the ENU frame (East, North and Up coordinates) (Shin, 2001), the new dynamic model is : Where The discrete form of the system model can be written as: Where t Δ is the sampling time.

GPS Measurements
When the GPS signals are available, position and velocity solution from GPS are integrated with INS at the rate of 1 Hz.The measurement model for GPS/INS loosely coupled scheme is: is a white Gaussian noise.
The observation matrix is: Where n is the size of the state vector, 3x 3 I is the identity matrix, 3x 3 0 is a zero matrix and the subscript (m n) × shows the number of matrix rows (m) and columns (n) .GPS measurements have as covariance matrix: Where 2 P GPS σ is the covariance of GPS P and P=x, y, z.

Odometer Measurements
In denied environments when GPS signals are not available, position solution from the odometer is integrated with the INS at the rate of 1 Hz.In this case, the measurement model is given by: is a white Gaussian noise.
The observation matrix has the following form: Where n is the size of the state vector.
The covariance matrix of odometer measurements is given by: Where 2 P Odo σ is the covariance of Odo P and P=x, y, z.

Simulation Results
The section below is dedicated to present some results from our fusion algorithm applied to simulation data in the purpose to quantify the contribution of the developed solution in terms of accuracy and availability of vehicle positioning in urban areas.

Simulated Scenario
In the simulated trajectory of the vehicle, during 26 minutes and 37 seconds (figure 4), there are three zones where the GPS signals are not available mainly because of the masking of satellite signals or an insufficient number of visible satellites: the three zones have duration of 70 seconds each.During these periods, the estimator uses the odometer measures in order to correct inertial sensor errors. mas.ccsenet

Vehicle
Here we p filter uses reference t ectories meters/second in the presence of GPS signal blockages.The use of an additional aiding source, the odometer, leads to good results in terms of vehicle velocity estimation.In fact, the estimated error of the vehicle velocity is significantly reduced during GPS signal outages.As shown in figure 6, the proposed method improves significantly the vehicle positioning accuracy even during long GPS outages: the error does not exceed 0.3 meters for the horizontal component and the East and North components.A 2-D plot of the simulated trajectory and the estimated one are show below.It is clear by observing Fig. 7 and Fig. 8 that the position errors of the GPS/INS/Odometer integrated navigation system are smaller than those of GPS/INS integrated navigation system.Especially, where GPS signal is absent.From these results, it can be seen that the proposed algorithm fusion improves the accuracy of vehicle localization.In addition to this, the GPS/INS/Odometer integrated system realized by using the proposed data fusion methodology leads to good performance compared with the GPS/INS integrated system during GPS outages.

Real Data Test Results
This section is dedicated to the presentation of the results obtained by the application of the new method to a real trajectory.

Urban Transport Scenario
Tests were conducted along a track located within Calais city, France.Our test vehicle is equipped with a Novatel GPS receiver that calculates the position.The measurement campaign was conducted in an urban area during 5 minutes and 25 seconds.There are two areas where GPS positioning is absent due to an insufficient number of satellites: the first has duration of 40 seconds and the second 31 seconds.During these periods, the estimator uses odometer measurements which are delivered at a frequency of 1 Hz, as the GPS measurement when available.

Conclusion
In summary, this paper proposes a new technique for GPS/INS/Odometer integration based on Kalman filter that minimizes the INS error and provides continuous estimation of vehicle position, velocity and attitude.This combination permit to avoid disadvantages of a stand-alone sensor in order to establish long-term navigation in GPS denied environments.The proposed method is a loosely-coupled solution that fuses the available measures.As described earlier the system presented in our work consists of the GPS receiver, an INS, and a vehicle odometer.The new technique solution was tested with real and simulated trajectories.The results for both trajectories were presented.The first trajectory contains 3 simulated GPS outages of 40 seconds duration were introduced intentionally.This was repeated four different.The proposed solution based on KF achieves centimeter-level positioning accuracy.The second trajectory is an urban scenario with natural GPS absence because of satellites signal blockage, where the proposed system solution was tested to demonstrate its performance in such environments.
In this work we have examined the odometer bridging performance for the Inertial Navigation System during GPS outages, and the results obtained from simulation and real tests confirm that using an additional aiding source, the odometer, provides more accurate navigation estimation than GPS/INS integrated system can offer in urban areas.
The proposed GPS/INS/Odometer integrated navigation system overcomes the problems due to environment of GPS signals propagation and shows good performance for land vehicle navigation solution using inertial sensors and an odometer in urban environment where the blockage of GPS satellites signals is very often.
λ ϕ is the position in the navigation frame, expressed as latitude, longitude and altitude, function of the three orientation angles roll φ, pitch θ and yaw ψ and it's the transformation matrix from the b-frame to the n-frame and vice-versa for b n C .b nb ω is the vector of angular velocities about the axes of the INS provided directly by gyroscopes after removing b ie ω and b en ω , n ie ω is the Earth turn rate in the navigation frame, n

Figure 1 .
Figure1.INS mechanization in ENU frame, adopted from(Schultz, 2006) (Quinchia et al., 2013) Figu Figure 3.The filter structure Gauss-Markov process driving noises, Figu The test track is shown in figure9.It is clear from figure 10 that the performance of the proposed method (gray rectangles) improves significantly the performance of the GPS/INS/Odometer integrated system with GPS outages (the rest of figure10) in terms of velocity estimation.In fact, this method trusts the odometer measurements (East and North positions in addition to the heading angle) when GPS measures are not available and permits to readjust the INS navigation solution.