performance evaluation of ins based memes inertial...

Abstract— Inertial navigation system (INS) is a self-contained

navigation system which provides position and velocity information

through direct measurements from an inertial measurement unit

(IMU). The advantage of INS is its independence from external

electromagnetic signals, and its ability to operate in all environments.

This allows an INS to provide a continuous navigation solution, with

excellent short term accuracy. However, the INS suffers from time-

dependent error growth which causes a drift in the solution, thus

compromising the long term accuracy of the system. The accuracy of

the INS is highly depends upon the grade of the IMU used, typical

IMU's are very expensive sensor, however, with a low cost version

comes low performance. In this paper, we will investigate the design

and implementation of 2-D INS navigation algorithm using MEMES

IMU. First, the inertial sensors and the errors subjected to their

measurement are discussed. Then importance of sensors calibration

as well as the alignment of the strapdown inertial navigation system

is illustrated. The mechanization equations in the navigation frame

are explained. simulation is carried out The limitations of the inertial

navigation systems are investigated in order to understand why INS

sometimes is integrated with other navigation aids and not just

operating in stand-alone mode. Finally, In order to perform numerical

simulations, A MATLAB® batch of M-file script and SIMULINK®

was used to model and simulate INS navigation algorithm. The paper

also provides experimental results. The relative effectiveness of the

INS navigation algorithm is highlighted. A field test on a four-wheel

drive car is carried out.

Keywords— Inertial Navigation; IMU; Strapdown INS

I. INTRODUCTION

HE basic principle of an INS is based on the integration of

accelerations observed by the accelerometers on board the

moving platform. The system accomplishes this task through

appropriate processing of the data obtained from the specific

force and angular velocity measurements. Thus, an

appropriately initialized inertial navigation system is capable

of continuous determination of vehicle position, velocity and

attitude without the use of the external information [1].

A major advantage of using inertial units is that given the

acceleration and angular rotation rate data in three dimensions,

Othman Maklouf is with the Aeronautical Engineering Department,

Faculty of Engineering. Tripoli University. LIBYA.

Salah Abdulhadi is with the Electronic Engineering Department,

Engineering Academy Tajoura. LIBYA.

Mahmoud Benhamid is with the Computer Engineering Department,

Engineering Academy Tajoura. LIBYA.

Hanin Shibl is with the Electronic Engineering Department, LIBYA.

the velocity and position of the vehicle can be evaluated in any

navigation frame. For land vehicles, a further advantage is that

unlike wheel encoders, an inertial unit is not affected by wheel

slip. However, the errors caused by bias, scale factors and non-

linearity in the sensor readings cause an accumulation in

navigation errors with time and furthermore inaccurate

readings are caused by the misalignment of the unit's axes with

respect to the local navigation frame. This misalignment blurs

the distinction between the acceleration measured by the

vehicles motion and that due to gravity, thus causing

inaccurate velocity and position evaluation. Since an inertial

unit is a dead reckoning sensor, any error in a previous

evaluation will be carried onto the next evaluation, thus as

time progresses the navigation solution drifts [2].

Rotational motion of the body with respect to the inertial

reference frame may be sensed using gyroscopic sensors and

used to determine the orientation of the accelerometers at all

times. Given this information, it is possible to transform the

accelerations into the computation frame before the integration

process takes place. At each time-step of the system's clock,

the navigation computer time integrates this quantity to get the

body's velocity vector. The velocity vector is then time

integrated, yielding the position vector. Hence, inertial

navigation is the process whereby the measurements provided

by gyroscopes and accelerometers are used to determine the

position of the vehicle in which they are installed. By

combining the two sets of measurements, it is possible to

define the translational motion of the vehicle within the inertial

reference frame and to calculate its position within that frame

[3].

II. COORDINATE FRAMES

Three coordinate frames are important for this work. These

include the ECEF (Earth-Centered Earth-Fixed) frame (e

frame), the body frame (b frame) and the local level frame

(LLF). The three frames are shown in Fig. 1. The origin of the

ECEF frame is the center of the Earth’s mass. The X-axis is

located in the equatorial plane and points towards the mean

Meridian of Greenwich. The Y–axis is also located in the

equatorial plane and is 90 degrees east of the mean Meridian

of Greenwich. The Z-axis parallels the Earth’s mean spin axis.

LLF is a local geodetic frame serves as local reference

directions for representing vehicle attitude and velocity for

operation on or near the surface of the Earth; for this reason, it

is often referred to as navigation frame (n-frame). A common

Performance Evaluation of INS Based MEMES

Inertial Measurement Unit

Othman Maklouf1, Salah Abdulhadi

2 Mahmoud Benhamid

3 and Hanin Shibl

4

T

Int'l Journal of Computing, Communications & Instrumentation Engg. (IJCCIE) Vol. 2, Issue 1 (2015) ISSN 2349-1469 EISSN 2349-1477

http://dx.doi.org/10.15242/IJCCIE.E0915072 53

orientation for LLF coordinates is the North-East-Up (NEU)

system. The origin of the LLF frame is coincides with sensor

frame. The Z-axis is orthogonal to the reference ellipsoid

pointing up[2].

Fig.1 Coordinates frames [6]

III. TWO DIMENSIONAL REPRESENTATION OF INS

For a vehicle moving in 2D space, it is necessary to monitor

both the translational motion in two directions and the change

in the direction of vehicle (i.e. rotational motion). Two

accelerometers are required to detect the acceleration in two

directions. One gyroscope is required to detect the direction

of the vehicle (rotational motion) in a direction perpendicular

to the plane of motion[6]. Strap down systems mathematically

transform the output of the accelerometers attached to the body

into the navigation coordinate system before performing the

mathematical integration. These systems use the output of the

gyroscope attached to the body to continuously update the

transformation necessary to convert from body coordinate to

navigation. The derivation of the transformation matrix is

explained as follow.

Fig. 2 Two Dimensional vector representation of transformation

matrix. [5]

As seen from Fig. 2 the two accelerometers are fixed in X

and Y directions, these directions represent the body

coordinates. The measured acceleration will be transformed to

the navigation frame (ENU) using the following

transformation matrix[4].

y

x

N

E

a

a

a

a

cossin

sincos (1)

blb

n aRa (2)

Where

: are the accelerations in the (East and North

directions) navigation frame.

: is azimuth angle.

: is the acceleration in the body frame defined by the

accelerometers.

: is the rotation matrix which rotates to the navigation

frame.

IV. GENERAL CHARACTERISTICS OF INERTIAL SENSORS

An INS usually contains three accelerometers, placed

perpendicularly to one another, each of which is capable of

detecting acceleration in a single direction. The most

important characteristics describing the performance of each

inertial is given hereafter.

A. Bias

A sensor bias is always defined by two components: A

deterministic component called bias offset which refers to the

offset of the measurement provided by the sensor from the true

input; and a stochastic component called bias drift which refers

to the rate at which the error in an inertial sensor accumulates

with time. The bias offset is deterministic and can be

quantified by calibration while the bias drift is random in

nature and should be treated as a stochastic process [1].

B. Scale factor

The scale factor is the relationship between the output signal

and the true physical quantity being measured and it is usually

expressed in parts per million (ppm). The scale factor is

deterministic in nature and can be quantified or determined

through lab calibration. The variation of the scale factor with

the variation of the exerted acceleration/angular rate or

temperature represents the scale factor stability and is usually

called the non-linear part of the scale factor error [1].

C. Output stability

The output stability of a sensor defines the run-to-run or

switch-on-to-switch-on variation of the gyro-

drift/accelerometer-bias as well as in-run variation of gyro-

drift/accelerometer-bias. The run-to-run stability can be

evaluated from the scatter in the mean output for each run for a

number of runs given that the sensor is turned off then on

again between each two successive runs. The in-run stability of

a sensor is deduced from the average scatter of the measured

drift in the output about the mean value during a single run [1].



D. Thermal sensitivity

Thermal sensitivity refers to the range of variation of the

sensor performance characteristics, particularly bias and scale

factor errors, with a change in temperature. A bias or scale

factor correlation with temperature variation can be defined

graphically or numerically (using a mathematical expression)

through intensive lab thermal testing. Such correlations can be

stored on a computer for online use to provide compensation

for temperature variation, provided a thermal sensor is

supplied with the sensor [1].

V. EFFECT OF INERTIAL SENSOR ERRORS ON NAVIGATION

PARAMETERS

An uncompensated accelerometer bias error (usually

expressed in terms of m/sec2) will introduces a linear error in

velocity and a quadratic error in the position. This is given in

fig. 3 [5].

Fig. 3 Effect Of un compensated accelerometer bias on position

determination [5]

In the other case an uncompensated gyro bias (usually

expressed in terms of deg/h or rad/sec) will introduces a

quadratic error in velocity and a cubic error in position [5].

The INS computation process is more complicated as it sounds

because any errors in the accelerometer or gyroscope

measurements will lead to errors in the determined position,

velocity and attitude. Gyroscope errors will result in errors in

the transformation matrix between body and navigation frame,

while accelerometer errors will result in errors in the integrated

velocity and position. The integration will result in errors

proportional to the integration time, t and its square, t² for

velocity and position respectively.

VI. HARDWARE

This section provides the necessary details on the hardware

and sensors implemented in this work. Fig. 4 shows

ADIS16334 Low Profile Six Degree of Freedom Inertial

Sensor from analog device. It is a low-profile, high-

performance IMU. This IMU uses a serial peripheral interface

for data communications. This interface enables direct

connection with a large variety of embedded processor

products.

Fig.4 ADIS16334 IMU

VII. 2-D SIMULATION OF INS

To understand the mechanization of the strap down INS in

(2-D model), an INS algorithm is carried out under

MATLAB/SIMULINK environment. The block diagram of

this algorithm is shown in fig. 5. In this computational

algorithm the raw measurement data from the IMU is

transformed from the body frame to the navigation frame using

the transformation matrix, this transformation matrix is simply

a direction cosine matrix given in (1), after this transformation

is done a double integration are performed to calculate the

position, velocity, and attitude in the navigation frame.

Fig. 5 Block diagram of INS algorithm using Simulink under

MATLAB

VIII. SIMULATION RESULTS

In order to validate the functionality of the proposal

navigation algorithm a car like robot model is used [7] , this

model is implemented using Simulink with MATLAB code see

fig. 6. For testing the INS algorithm the following steps are

carried out:

• Generation of the reference trajectory .

• Carry out the INS simulation in error free case (no sensor

error).

• Accelerometer bias, gyro bias, and initial tilt error were

taken as a case study and their effects on the derived INS

trajectory are illustrated.

A. Reference trajectory

In order to evaluate the INS algorithm, a reference

trajectory was generated. A Simulink code under MATLAB

environment is used to generate this reference trajectory. The

suggested reference trajectory has been adopted in all



simulation results for analysis and comparison studies. Fig. 7

shows the reference trajectory in the local level frame.

Fig. 6 Block diagram of INS algorithm validation using car like

robot model under Simulink with MATLAB

0 200 400 600 800 1000 1200 1400 1600 1800-600

-500

-400

-300

-200

-100

0

100

x(m)

y(m

)

Real

INS

INS compared with Real

Fig. 7 Reference and INS derived trajectories with .005μg

accelerometer bias

IX. ERROR ANALYSIS

The reference trajectory created earlier is applied as an

input for the proposed INS algorithm. Simulation runs have

been conducted to discuss the effect of various types of errors

that may degrade the performance of navigation system. First

an INS simulation is demonstrated without sensor errors. The

INS derived trajectory matches up quite closely with the

reference generated one as shown in Fig.7. Second, when

sensor’s errors are included, In this work the effects of the

various errors (accelerometer bias, , gyro bias, initial tilt) have

been studied. Table 3.1 gives the values of the mentioned

errors adopted in the simulation. The accelerometer bias, gyro

bias, initial tilt error have been chosen as case study for the

effect of the errors on the INS derived trajectory.

TABLE I

THE VALUES OF THE ERRORS

The Errors Minimum

The Values

Intermediate Maximum

Accelerometer

Bias(μg)

0.005 0.05 0.5

Gyro

Bias(Deg./hr)

0.0001 0.001 0.01

Initial Mis-

allignment(Dg)

30 45 60

A. Accelerometer's bias effect

In order to study the effect of the accelerometer bias on the

derived INS trajectory, three values have been adopted. The

adopted values are 0.005μg, 0.05μg and 0.5μg which

represented the low, medium and high error respectively. First,

0.005μg is set into the program. Figure 8 shows the reference

and the derived INS trajectories. Obviously there is a

difference between the two trajectories. Secondly 0.005μg and

0.5μg is set to the program respectively. It is clear that from

Figs. 9 and 10, the difference between the two trajectories is

increased as the accelerometer bias increased. This is due to

the improper measurement of the accelerometer which in turn,

results in improper computation in velocity and position.

0 200 400 600 800 1000 1200 1400 1600 1800 2000-600

-500

-400

-300

-200

-100

0

100

200

east (m)

north

(m)

Reference

INS

Accelerometer Bias (x,y) = 0.005

Fig.8 Reference and INS derived trajectories with .005μg

accelerometer bias

0 500 1000 1500 2000 2500 3000 3500 4000 4500-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

east (m)

north

(m)

Reference

INS

Accelerometer Bias (x,y) =0.05

Fig.9 reference and INS derived trajectories with 0.05μg

accelerometer bias



As one would expect, the difference between the two

trajectories as well as the error in both horizontal and vertical

positions will increase. This is clear in Figs 11and 12 where

the values are list on these figures.

0 0.5 1 1.5 2 2.5 3

x 104

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4x 10

4

east (m)

north

(m)

Reference

INS

Accelerometer Bias (x,y) = 0.5

Fig.10 reference and INS derived trajectories with 0.5μg

accelerometer bias

Fig.11 Error in horizontal position due to accelerometer bias

Fig. 12 Error in vertical position due to accelerometer bias

B. Gyro's bias effect

The same scenario is adopted. Three values of gyro bias

have been selected. These values are 0.0001 rad/hr,

0.001rad/hrand 0.1 rad/hr which represented the low, medium

and high respectively. Fig. 13 shows the difference between

the reference and the derived INS trajectories when a 0.0001

rad/hr gyro drift is set. Due to this drift which in turn results in

improper projection of the accelerometer measurement into the

reference frame, a deviation between the two trajectories has

been occurred. This deviation is increased as the bias

increased. This is illustrated in Figs 14 and 15. Clearly when

the gyro bias is increased to 0.1 rad/hr the deviation between

the two trajectories as well as the error in the horizontal and

vertical position are increased. In this case the derived INS

trajectory couldn't match up the reference trajectory due to the

large drift of gyro bias. This is illustrated in Figs 16 and 17,

where the values are listed in these figures.

0 200 400 600 800 1000 1200 1400 1600 1800-600

-500

-400

-300

-200

-100

0

100

east (m)

north

((m

)

Reference

INS

Gyroscope Bias (x,y) = 0.0001

Fig.13 Reference and INS derived trajectories with .0001 rad/h gyro

bias

0 200 400 600 800 1000 1200 1400 1600 1800-600

-500

-400

-300

-200

-100

0

100

200

east (m)

nort

h (m

)

Reference

INS


Fig. 14 Reference and INS derived trajectories 0.001 rad/h gyro bias

-200 0 200 400 600 800 1000 1200 1400 1600 1800-600

-500

-400

-300

-200

-100

0

100

200

east (m)

nort

h (

m)

Reference

INS


Fig. 15 .Reference and INS derived trajectories with 0.1 rad/h gyro

bias



Fig.16 Error in horizontal position due to gyro bias

Fig.17 Error in vertical position due to gyro bias

C. Initial tilt error

Also three values 30 deg,45 deg and 60 deg as initial tilt

error are set to the program. Figs 18, 19 and 20 show the

difference between the two trajectories with tilt error equal to

30 deg, 45 deg, and 60 deg respectively. Obviously, the

derived INS trajectory is deviated too much from the reference

trajectory. This is also shown in Figs 21 and 22 as error in the

horizontal and vertical position. The reason is that, since the

horizontal plane is unleveled, the east and north accelerometer

will read a component of the gravity from the beginning

instead of reading zero component if the horizontal plane is

leveled. Then these components will results in error which

accumulated with time. Clearly, the computed horizontal and

vertical position will behave in similar manner. Increasing this

tilt error the results get worst.

-500 0 500 1000 1500 2000-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

200

east (m)

north

(m)

INS

Reference

Initial Tilt Alignment = (30deg)

Fig.18 reference and INS derived trajectories with 30 deg tilt error

0 200 400 600 800 1000 1200 1400 1600 1800-600

-400

-200

0

200

400

600

800

1000

1200

1400

east (m)

north

(m)

INS

Reference

Initial Tilit Aligment = (45deg)

Fig. 19 reference and INS derived trajectories with 45 deg tilt error

-2000 -1500 -1000 -500 0 500 1000 1500 2000-600

-500

-400

-300

-200

-100

0

100

200

300

east (m)

north

(m)

INS

Reference

Initial Tilit Alignment = (60deg)

Fig. 20 reference and INS derived trajectories with 60 deg tilt error



Fig.21 error in horizontal position due to tilt error

Fig. 22 Error in vertical position due to tilt error

X. EXPERIMENTAL WORK

The experiments are conducted using a car with the IMU

mount on it fig.23. A laptop is the host computer is connected

to IMU and the data are recorded.

Fig. 23. experimental setup

The data was then taken and analyzed in MATLAB using

the developed model. The recorded data from the IMU is

consists of the two readings from the accelerometers and the

one rate gyro, these readings are shown in fig 24. Closly

looking in the IMU output data reveals that, these data are

highly corrupted with noise which is the main feathres of

MEMES IMU, this will result in a very high drift in stand

alone INS systems.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

-0.5

0

0.5

Time

m/s

ec2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

-0.5

0

0.5

m/s

ec2

Time

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

-100

0

100

rad/

sec

Time

Fig.24 The recorded data from ADIS16334 IMU

The recorded data from the IMU is set in to the SIMULINK

with MATLAB block diagram shown in fig. 25, this block

diagram contains the INS navigation algorithm discussed

previous section. The out put of this block diagram will

express the real trajectory of the moving land vehicle. Fig. 26

shows the car trajectory estimated by the INS algorithm.

Fig. 25 The SIMULINK block diagram used for analyzing the

recorded data.

-5000 0 5000 10000 15000 20000-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

4

Nort

h (

m)

East (m)

Estimated Land Vehicle

Trajectory using INS

Fig. 26 INS trajectory estimated of the of the moving land vehicle.



XI. CONCLUSION

In this work, the limitations of the inertial navigation

systems are investigated in order to understand why INS

sometimes is integrated with other navigation aids and not just

operating in stand-alone mode. Accelerometer bias, gyro bias

and initial tilt error are taken as a case study and their effects

on the derived INS trajectory are studied. The deviation of the

derived INS trajectory from the reference one is due to the

values of these errors. Errors analysis shows that the initial tilt

error has significant effect on the derived INS trajectory so the

accurate alignment is necessary to minimize this effect. The

low cost IMU used in this work is not capable of running by

itself and providing accurate positioning information. The

system therefore sees to drift with time. In order to minimize

these errors, external measurements at regular time intervals

must be utilized. Different types of update measurements can

be used in order to update the position, the velocity or the

attitude. GPS is one of the main position update methods.

Other methods could be velocity update from a wheel speed

sensor or attitude update from a compass.

REFERENCES

[1] Titterton D.H. and Weston, J.L. ―Strapdown inertial navigation

technology;‖ Peter Peregrinus Ltd., London, UK, 1997 .

[2] MohanderS.Grewal, Lawrance R. Weill, Angus P. Anderws ―Global

positioning system inertial navigation system and integration‖

Copyright © 2nd Edition 2007, A John Wiley &Sons, Inc

[3] A. D. King, B.Sc., F.R.I.N., ―Inertial Navigation – Forty Years of

Evolution” Marconi Electronic Systems Ltd. GEC REVIEW, VOL. 13,

NO. 3, 1998.

[4] El-Sheimy.‖ Inertial techniques and INS/DGPS Integration‖. ENGO

623- Lecture Notes, the University of Calgary, Department of

Geomatics Engineering, Calgary (2004)

[5] El-Sheimy, N., ―The Potential of Partial IMUs for Land Vehicle

Navigation.‖, Geomatics department, University of Calgary (2008)

[6] Eric N Moret., ―Dynamic Modeling and Control of a Car-Like Robot‖

M.Sc. Thesis, Virginia Polytechnic Institute and State University‖,

(2003).



performance evaluation of ins based memes inertial...

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