877 
CALIBRATION OF A LOW COST MEMS INS SENSOR FOR AN INTEGRATED 
NAVIGATION SYSTEM 
G. Artese a , A. Trecroci a 
a Land Planning Dept. - University of Calabria - Ponte Bucci cubo 46 B - 87036 Rende, Italy - (g.artese, 
aldo.trecroci)@unical.it 
Technical Session WgS-PS: ICWG V/I 
KEY WORDS: Calibration, Navigation, IMU, Integration, Multisensor, GPS/INS 
ABSTRACT: 
The method, the procedure and the results of the calibration of a low cost MEMS INS sensor are described and discussed. The 
reduced cost of the MEMSs sensors is very advantageous, but these sensors are characterized by much large errors. The accurate 
calibration of the sensors is very important for the determination of the systematic errors, like bias, scale factor and misalignment of 
the axes. For this aim, it has been used the multi-position calibration method, which doesn’t require the precise aligned mounting of 
the sensors with either local level frame or to the vertical direction. The equations in the static case, for the accelerometers sensors 
are shortly described; the results obtained with the Kalman filter in the experimentation of the tri-axial sensor ADIS 16350 are then 
illustrated. 
1. INTRODUCTION 
The integration of GPS and inertial systems is very interesting 
for several technological applications (Mohinder et al. 2001), 
(Mohinder et al. 2007), (Sanso, 2006) . The MEMS technology 
allows the realization of new miniaturized low cost sensors. 
Over the last few years many MEMSs systems have been 
developed with growing performances, very small size and light 
weight. These sensors, matched with miniaturized GPS 
receivers, are the basis of complete low cost and low weight 
navigation systems (Godha, 2006), (Niu and El-Sheimy, 2005), 
(Shin, 2001). 
The results obtained by such sensors are generally less accurate 
than the ones typically associated with tactical-grade inertial 
sensors. However, by means of high quality integration 
algorithms, it is possible to obtain significant positioning 
accuracy improvements with respect to GPS systems, when 
there is limited satellite availability. 
The IMU measurements are independent of the GPS signal 
outages and the frequencies of acquisition are very high. The 
IMU measures the angular velocities and linear accelerations. 
The matrix rotation is obtained using the angular rates by 
gyroscopes and the measured forces are rotated in the required 
frame using the rotation matrix. The velocities and positions of 
the body are obtained by integration of the accelerations and 
angular rates. 
Unfortunately the integration process is very sensible to the 
systematic errors of the IMU. The acceleration bias introduces 
an error in the velocity proportional to the time t, and an error 
in the position proportional to t 2 . Still worse the gyro bias 
introduces a quadratic error in the velocity and a cubic error in 
the position (El Sheimy, 2006). 
The position and velocity drift depends of bias, scale factor, 
misalignment and sensor noise. Then it is very important an 
accurate procedure of calibration for the initialization of the 
IMU. 
In the case of the gyroscopes generally the following equation 
is used: 
l m — (0+ b a + So) + No) + £ (co) (1) 
where /*,is the measured angular rate, co is the true angular rate, 
b M is the gyroscope instrument bias, S is the linear scale factor 
matrix, N is the non-orthogonality matrix and s(co) is the sensor 
noise. 
In the case of the accelerometers generally the following 
equation is used: 
//=/+ bf+ SJ-+ Sj + Nf+Sg + e(f) (2) 
where If is the measured acceleration,/is the true specific force, 
¿y is the accelerometer instrument bias, S/ and S 2 are the linear 
and non linear scale factor matrices, N is the non-orthogonality 
matrix, Sg is the deviation from theoretical gravity and e (j) is 
the accelerometer noise. 
Generally the position drift is estimated dependent of gyro and 
accelerometer bias instability, using the following approximate 
equation: 
Sp(t) * Sp 0 +Sv 0 At + Sb 0a ^-+Sb 0 g^- + 
l 6 
+ Sa,g^- + SH 0! (VM) + SF 0i ,^y+ < 3 > 
+ SF',(AH,Wto) 
The performance of integrated GPS/INS system depends of the 
signal quality of GPS and the correct prediction measurements 
of the INS, when the GPS signals are blocked.