Improvement of accuracy in aircraft navigation by data fusion technique

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 8, August (2014), pp. 35-46 © IAEME
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH
IN ENGINEERING AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 5, Issue 8, August (2014), pp. 35-46
© IAEME: http://www.iaeme.com/IJARET.asp
Journal Impact Factor (2014): 7.8273 (Calculated by GISI)
www.jifactor.com
35

IMPROVEMENT OF ACCURACY IN AIRCRAFT NAVIGATION BY DATA
FUSION TECHNIQUE
Mahasweta Bhattacharya1
1(Electronics and Communication Engineering, West Bengal University of Technology,
West Bengal, India)
ABSTRACT
Navigation of a aircraft is to reach a destination accurately and with minimum diversions.
This needs to guide the aircraft on the desired track. For a fighter aircraft which needs fast
manoeuvring to achieve the mission objectives need continuous and accurate position, attitude and
velocity updates.
The sensors used in an aircraft are GPS and Inertial Navigation System. The Inertial
Navigation System used in aircraft navigation provides parametric information in terms of
position(latitude, longitude and altitude), velocity(Velocity along north, east and vertical direction)
and attitudes(Pitch, roll, yaw). INS is working based on three gyroscopes and three accelerometers.
GPS works based on the satellite information of the aircraft position.
The update rate of INS solutions is high but in course of time, the accuracy of the
navigational solution degrades. GPS provides highly accurate position and velocity solutions but at a
slow update rate. Hence standalone use of either one for obtaining navigational solution is not
employed. This is a major problem in military navigation where highly accurate data with fast update
rate is necessary.
The solution to this problem can be obtained by designing a navigational algorithm which
performs sensor data fusion using the data from INS and GPS of an aircraft by means of a Kalman
Filter. In this project, a sensor data fusion algorithm for performing sensor fusion of INS and GPS
using 9th order Kalman filter has been developed. An initial estimation of the navigational
parameters that were needed to be corrected was taken. A process model using INS data and
measurement model using GPS data is formed. Using the process model, measurement model and
the Kalman filter, the errors in the INS data were corrected. The corrected navigational data thus
obtained is then compared with a standard system hybrid navigational data.
Keywords: INS, GPS, Kalman Filter, Estimation, Accuracy.
IJARET
© I A E M E

36
I. INTRODUCTION

Integration of INS and GPS has been indispensable because of the inherent drawbacks of the
individual system. INS has its inherent errors that gradually accumulate to finally give highly
erroneous data. GPS updates at a very slower rate of about 1sec. Both the drawbacks are
disadvantageous for successful military navigation. In general, an INS has a high update rate of
about 20ms and GPS has high accuracy in measurement. Thus using any one of them as a standalone
system hinders accurate and faster computation. Thus integration is needed.
If the errors in INS are not corrected then the error will go on accumulating thereby giving a
final data which will be highly erroneous and faulty. Thus the INS position and velocity data must be
corrected.
The main objective of the project was to improve the accuracy in measurement of a
navigational system by fusing the data coming from both INS and GPS so that an integrated system
through the fused data can be used in aircrafts where precise and fast computations are needed. To
accomplish this objective the following steps are involved:
• Design and develop the process model based on INS data
• Designing the measurement model based on GPS data
• Making an initial estimation based on the process model
• Feeding the estimation and measured data to Kalman Filter which minimizes the error between
the corrected and the actual data and provides a corrected estimate for the next state.
• The processes are continued in recursion for the whole set of data to arrive at a final corrected
set of data.
For testing the developed sensor data fusion algorithm, it has been coded in MATLAB. A set
of data relating to INS and GPS of a particular flight sortie of aircraft has been taken. The INS data
and the GPS data has been fused using the algorithm to give a corrected hybrid output. The algorithm
has been tested by comparing the computed hybrid data with the system hybrid data obtained from
INGPS system installed on the aircraft. It has been found that the error between computed hybrid
data and system hybrid data was very minimal and thereby establishing the success of the algorithm.
II. ERRORS OBSERVED IN SAMPLE INS DATA
As mentioned earlier, navigational data of a specific aircraft system has been taken as sample
in our project. The errors in the acceleration of the INS data were observed as such. The three plots
in the figure below show the INS acceleration measured by accelerometers. The plots show how
much the reading of the INS is full of errors. The above plots also are erroneous.
Errors in the accelerations and angular rates occur due to manufacturing error, biases etc
which lead to steadily growing errors in position and velocity components of the aircraft, due to
integration. These are called navigation errors and there are nine of them - three position errors, three
velocity errors, two attitude errors and one heading error. If an unaided INS is used, these errors
grow with time. It is for this reason that the INS is usually aided with GPS for accurate navigation
solutions.

37

Fig.1: The Accelerometer Reading along x, y and z axis respectively with respect to time
Fig. 2: The three plots above shows the turn angle rates about the three axes
III. ERRORS OBSERVED IN GPS DATA
Although GPS provides accurate navigational data free of errors but the GPS faces several
drawbacks. Firstly, the system consists of a constellation of fixed satellites which sends signals to
determine position. This takes higher computation time and thus the system has higher update rate.
The data rate is about 1sec. But even faster computation is necessary for military navigation. Thus
standalone GPS is not advantageous. In the system the GPS readings have been taken at t=20ms
which is the sample time for the INS system. We observe staircase type graph for the parameters.
This is because the update rate of GPS is much lower compared to the INS. While INS is updating at
20ms GPS is updating at 1s. Therefore, for 1s GPS keeps at data constant and data is updated after
that. This is the cause of the stairs. The values are updated after 50 such samples. So for 50 updated
values of INS, GPS data remains constant. At such a lower update rate we cannot get the proper
navigational details. Thus GPS also cannot be efficiently used as a standalone navigation system.
The figure below shows the nature of the data obtained from GPS.

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 8, August
Fig.3
3: Altitude obtained from GPS
IV. WORKING PRINCIPLE OF KALMAN FILTER
(2014), pp. 35-46 © IAEME
–

Kalman filter [3],[4],[6] estimates the state vector based on the knowledge of the
measurement model as well as on the knowledge of the process model. The process noise and
measurement noise are assumed to be independent of each other. The Kalman filter is a recursive
algorithm which makes predictions from previous state and then updates the prediction using
measurement to obtain an optimal state vector. The main objective of the Kalman Filter is
to find an
estimate of the n-state vector xk denoted by
which is a function of all the previous states and
minimizing the mean squared error between the estimated and the real value. in any system, the next
state is based on the previous state and is related to it through the state transition matrix. Presence
any input noise will affect the output state as well. Thus the process of the system can be modelled
as:
The noise is uncorrelated with respect to time and thus the covariance matr
Therefore,
of
ix is
Again, through the measurement model we can estimate a particular state at that very instant.
Noise in the model will affect the measurement and thus is
model thus can be formulated as:
Similarly, the covariance matrix associated with
objective is to make estimation such that the estimated value should be as close as possible to the
actual value of the erroneous data. Practically, it is difficult to make such close estimation and thus
there may be present some errors in our estimated value and th
so as to bring down that error to a minimum. We denote the error covariance matrix as
. The target is to minimize this error covariance matrix so that our estimation tallies
with the actual data.
Now, the function of a Kalman Filter is divided in two stages. The stages are: a). Updating
and b). Predicting. This stages occur in recursion and in every stage the Kalman Gain
38
(equation 1)
matrix associated with
(equation 2)
taken into account. The measurement
(equation 3)
is . Now the main
the e actual value. So we use a technique
is

computed and the state of the system as well as the associated Error C
for every state in the recursive loop. The equations associating with this updating stage are as
follows. (The superscript“-”denotes predicted state (priori state).
The equations that govern the stage of predicting are:
Equation shows that if is large, K
be less weighted. The estimated state will be nearer to predicted state. When K
term will have more weightage so the estimated state will be predicted state + weighted residual.
When Rk approaches zero then measurement more trus
zero then prediction is trusted more.
So in every stage the Kalman Filter narrows down the error between estimated and actual
data, updates the state and then predicts for the next state. This occurs in a
stages available finally giving a data which will match the actual data thereby filtering out the actual
data from the erroneous one.
In a system, an estimate about the next state can be determined using the process model. But
due to inherent error in the process model the estimated value at a particular instant will not be close
to the true value at that instant.
So we take another model known as the measurement model which gives measurement of
some of the parameters at that particu
models and corrects the estimated data.
In our project, the INS serves as the process model and the GPS serves as the measurement model.
V. PROCESS MODEL OBTAINED FROM INS SYSTEM
• Reference Ellipsoidal Model
Fig 3
(2014), pp. 35-46 © IAEME
39
Covariance Matrix is updated
”(equation 4)
(equation 5)
(equation 6)
(equation 7)
(equation 8)
Kk will be small. Therefore, the term
Kk is large then second
trusted than prediction. When
loop for the number of
particular instant. The Kalman Filter optimally combines these two
3: Reference earth model
–

ovariance will
ted approaches
lar

(2014), pp. 35-46 © IAEME
Length of the semi-major axis, R=
Length of the semi-minor axis, r=6356752.3142 meters
Eccentricity of the Ellipsoidal Model, e=0.0818191908426
Meridian Radius of Curvature,
Transverse Radius of Curvature,
• Spherical Earth Model
6378137.0 meters
Where normal gravity at height h=0 i.e 9.81m/s
The design of the process model has been explained below.
INS Position error dynamics with respect to position, velocity and attitude are :
INS velocity error dynamics with respect to position, velocity and attitude are:
40
(equation 9)
2.
(equation 10)
(equation 11)
(equation 12)
(equation 13)
–

=
INS attitude error dynamics with respect
Thus, converting to skew symmetric form we get,
Therefore, the final process model,
Where state vector,
VI. MEASUREMENT MODEL
Measurement model is represented as
(2014), pp. 35-46 © IAEME
Where represent vector measurement of state xk at time tk. The measurement matrix is
represented as:
41
(equation 14)
to position, velocity and attitude are:
(equation 15)
(equation 16)
(equation 17)
(equation 18)
(equation 12)
(equation 13)
(equation 14)
- GPS ERROR MODELLING
(equation 15)
–

If INS and GPS are same with the difference in measurement leading to zero then that may
lead to instability of the system. To avoid the instability, first row of equation (6.15) and (6.16) is
multiplied with and second row with
And
VII. DESIGN OF THE KALMAN FILTER AND INS, GPS INTEGRATION
The F-matrix is in continuous time which is discretized as,
Kalman Filter estimates next state from previous state through the Kalman
equation (6.5),
The (k+1)th state can be estimated according to equation (6.7) as:
The corrected error covariance matrix is given as,
The Kalman Gain is calculated according to equation (6.4) as:
The updated error covariance matrix is given as:
(2014), pp. 35-46 © IAEME
42
(equation 16)
(equation 17)
. Therefore, the equation becomes
(equation 18)
(equation 19)
(equation 20)
Gain according to
(equation 21)
(equation 22)
(equation 23)
(equation 24)
–

(24)

VIII. BLOCK DIAGRAM
(2014), pp. 35-46 © IAEME
Fig. 4: Block Diagram of INGPS integrated circuit using Kalman Filter
–

The above figure shows the block diagram of the developed navigational algorithm for fusing
the INS and GPS data using Kalman Filter to obtain accurate navigational solution. The INS data in
terms of latitude, longitude, altitude, Vn, Ve and Vd. and the GPS data in terms of latitude, longitude,
altitude, Vn, Ve and Vd are used with 9
states i.e. .latitude, longitude, altitude, Vn, Ve, Vd, roll, pitch and yaw.
th order Kalman filter to compute the error rror in each of the
This is done by forming the process model using the INS data and the measurement model
using the GPS data. Further Kalman Filter is used for computing the erro
Kalman Gain. Using the process model, measurement model and the Kalman Gain the corrected
error is computed. This computed error is then added to the INS data to obtain the computed hybrid
data. To analyze the performance of the dev
is then compared with the system hybrid data.
IX. RECURSIVE FUNCTION OF THE KALMAN FILTER
r Fig. 5: Diagram of the Kalman Filter Recursive Cycle
43
error covariance matrix and
developed eloped navigational algorithm, the computed hybrid data

X. RESULT OBTAINED FROM SAMPLE
44

Fig. 6: Latitude and Longitude obtained from system and computation of algorithm
Fig. 7: Altitude and Velocity along north axis(Vn) obtained from system and computation of
algorithm
Fig. 7: Velocity along lateral and vertical axis(Ve and Vd) obtained from system and computation of
algorithm

45

Fig. 8: Roll and Pitch obtained from system and computation of algorithm
Fig. 8: Yaw obtained from system and computation of algorithm
XI. ANALYSIS
Table 1: Tabular comparison of error deviation for the 3 samples of the computed data and the
hybrid data
PARAMETERS ERROR STANDARD DEVIATION IN
SAMPLE 1
Latitude, (degree) 6.287×10-5
Longitude, μ(degree) 4.378×10-5
Altitude, h(feet) 55.3443
Velocity towards north, Vn (m/s) 3.7069
Velocity towards east, Ve (m/s) 2.6915
Velocity towards the vertical, Vd (m/s) 1.9197
Roll, (degree) 0.2849
Pitch, (degree) 0.3369
Yaw, (degree) 0.1359
Standard deviation of errors for all these parameters were in acceptable range except the
altitude. The above table shows the mean error standard deviation computed using the three sample
data. In altitude a constant offset was observed in the standard error deviation because of the vertical
channel problem. The altitude result sows that the computed data deviates gradually from the system
hybrid data. This is because the system data is making its own correction based on the correction
algorithm installed where all the necessary factors have been considered, whereas, our algorithm has

considered only 9 parameters. Hence although in the beginning the two data are quite similar but
gradually deviation increases. Altitude errors can be corrected by introducing the vertical channel
modelling where the gravitational acceleration variation with respect to altitude is corrected by
introducing another observer. In some of the sample solutions noises were observed which led to the
high maximum value of error. This can be further removed by introducing digital smoothers as a next
module after the Kalman Filter module.
46
XII. CONCLUSION

The main aim of the project was to achieve successful data fusion for improvement of INS
and GPS systems. INS and GPS show their inherent disadvantages. While INS system leads to error
build up at the same time GPS despite its high accuracy, update rate is low. Precision and faster
computation are of utmost importance in military navigation which led to the need to fuse the INS
and the GPS for obtaining accurate navigational solution using INS and GPS. The fusion has been
achieved through Kalman Filter which works on the principle of estimation and update. The 9th order
Kalman Filter has been used to correct the 9 navigational parameters i.e. latitude, longitude, altitude,
velocities in three axes, roll, pitch and yaw subsequently by forming the process and the
measurement model. Observed algorithm was very good in latitude, longitude, altitude, vn, ve, vd,
roll, pitch and yaw. Further improvement can be made by introducing the accelerometer bias and
gyroscope sensitivity models. Observed errors in altitude and vd can be further minimized by
modelling the vertical channel. By fusion of INS and GPS thus we can aim to achieve accurate
navigation which can be employed in military. Data fusion can also be used in fields of medicine,
space research, economics etc where high precision data is important.
XIII. ACKNOWLEDGEMENT
I would like to offer my heartfelt gratitude to the Mission Combat and System Research and
Design Centre Department, Hindustan Aeronautics Limited, Bangalore for their guidance and
constant support for the execution of the project.
XIV. REFERENCES
1. David H. Titterton and John L. Weston, Strapdown Inertial Navigation Technology - 2nd
Edition(2004) The Institution of Electrical Engineers.
2. Elliott D. Kaplan and Christopher J. Hegarty, Understanding GPS Principles and
Applications- 2nd Edition(2006) Artech House.
3. Mohinder S. Grewal and Angus P. Andrews, Kalman Filter Theory and Practice using
MATLAB-3rd Edition(2008) John Wiley Sons, Inc.
4. Paul Zarchan Fundamentals of Kalman Filtering—A Practical Approach, 2nd Edition(2005)
American Institute of Aeronautics and Astronautics, Inc.
5. Robert M. Rogers, Applied Mathematics in Integration Navigation System- 2nd Edition(2003)
AIAA Education Series.
6. Eun-Hwan Shin, Accuracy Improvement of Low Cost INS/GPS for Land Applications(2001)
UCGE Reports.
7. Deepeshnamdev, Monika Mehra, Prerna Sahariya, Rajeshwaree Parashar and Shikha Singhal,
“Navigation System by using GIS and GPS”, International Journal of Electronics and
Communication Engineering Technology (IJECET), Volume 4, Issue 3, 2013,
pp. 232 - 243, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472.

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