2458-14
Workshop on GNSS Data Application to Low Latitude Ionospheric Research
6 - 17 May 2013
Inertial Navigation Systems
VAN GRAAS Frank
Ohio University
School of Electrical Engineering and Computer Science
345 Stocker Center
Athens OH 45701-2979
U.S.A.
Inertial Navigation Systems
Applications of GNSS
Workshop on GNSS Data Application to Low Latitude Ionospheric
Research
Trieste – Italy, 06-17 May 2013
Prof. Frank van Graas
Ohio University
Inertial Navigation Systems
p.1
Course Overview
•
•
•
•
•
•
•
•
•
•
•
Introduction to inertial navigation
Accelerometer operation and error sources
Gyroscope operation and error sources
Coordinate frames
Inertial navigation mechanization
Dynamics
Initialization
Strapdown terminology
Movement over ellipsoid
Attitude, velocity, and position updating
Future trends
Inertial Navigation Systems
p.2
Two Inertial Measurement Systems
Both systems use inertial sensors and know
about the orientation of the device, but only
the system on the left can be used to navigate
using inertial measurements only.
• Aviation Ring Laser Gyro Standalone Navigation Grade
Inertial Reference Unit
• 1 nautical mile per hour performance
• Outputs:
– 50Hz body rates and accelerations, pitch, roll
– 25Hz heading
– 20Hz velocities
An inertial navigation system has two
components:
1) Sensor package
2) Navigation computer
Autonomous navigation system
Inertial Navigation Systems
p.3
What Makes Inertial Navigation Work?
• In order to move, we first need to accelerate
• If we keep track of our acceleration over time,
then we can determine how much we move
» Use accelerometers to measure acceleration
• If we could also keep track of the direction in which
we accelerate, then we can determine how
much we move in a particular direction
» Use gyroscopes to measure changes in direction over time
• If we knew where we started and in which direction we were
pointing, then we can determine our position, velocity and
orientation as time goes on
» Use initial conditions
Inertial Navigation Systems
p.4
Inertial Application Areas
• Navigation Grade
» Spacecraft, sub-marine, military aircraft,
commercial aircraft, ship
• Tactical Grade
» Attitude and heading reference system
(artificial horizon), short-term tactical
guidance, land vehicles, aircraft autopilot,
guidance stabilization, GPS integration
• Short-term (Commercial Grade)
» Small unmanned aerial systems (UAS), camera stabilization,, airbag
g
sensors, car electronic
stability control, video games, smart phones,
athletic shoes, motion sensors (e.g. shipping
crates, electronics), medical
Inertial Navigation Systems
p.5
What About the Ionosphere?
• Primary application:
» Mitigate the effects of the ionosphere by aiding the
receiver tracking loop with inertial measurements
» First need to understand the ionosphere …
• Secondary applications:
» Earthquakes and nuclear detonations cause disturbances in
the ionosphere
• Earthquake detection networks are starting to use
inertial measurements to obtain the high-frequency
content of the quake along with GNSS measurements
for the lower frequencies
» Tsunami prediction networks are starting to use
accelerometers along with GNSS receivers
Inertial Navigation Systems
p.6
Short-Term, Tactical, Navigation Grade
Inertial Grade
Short-Term
Tactical
Navigation
Grade
Example
Applications
Flight Control
Consumer
Electronics
Missiles
AHRS
Aircraft
Navigation System
Gyroscopes
> 10 deg/hr
Silicon MEMS
> 1 mg
Accelerometers
Silicon MEMS
0.1 – 10 deg/hr
Fiber Optic,
Silicon MEMS
0.001 – 0.1 deg/hr
Fiber Optic,
Ring Laser
100 Pg – 1 mg
Quartz Resonant,
Silicon MEMS
10 – 100 Pg
Quartz Resonant,
Silicon MEMS
AHRS = Attitude and Heading Reference System (Artificial Horizon)
MEMS = Micro-Electro-Mechanical Systems
All numbers are root-mean-square (rms) values
Note: Navigation grade INS is integrated with airdata computer for vertical channel stabilization
Inertial Navigation Systems
p.7
Accelerometer
• Consider a proof-mass glued to a scale that can measure both
positive (push) and negative (pull) weights
Proof mass
Scale
• Most accelerometers (like the one above) measure “specific
force,” or force per unit mass (in m/s2), which consists of:
» Acceleration specific force = acceleration = a (m/s2)
» Gravitation specific force ≈ 9.8 (m/s2)
• If the scale is at rest on the floor, then the
output of the accelerometer will be +g ≈ 9.8 (m/s2)
gravity
• If the accelerometer is in “free fall,” then there is no
force on the scale, such that the output = 0 (m/s2)
Inertial Navigation Systems
p.8
Accelerometer Technologies
• Several sensing technologies are in common use:
» Force-feedback pendulum
» Vibrating beam (or dual vibrating beam)
» Micro-machined with electrostatic control of proof mass
• In general, the force is measured indirectly by measuring how
much signal is required to keep the proof mass from moving
Pendulum pivot
Electromagnetic coil
Permanent magnet
Proof mass
Force
Feedback
Measured specific force
Capacitive displacement sensor
Sensitive axis
Differential
amplifier
Inertial Navigation Systems
p.9
Delta Velocity instead of Acceleration
• Most accelerometers output 'V instead of acceleration
'Vt2 ,t1
t2
³ a(t )dt
(m/s)
t1
• In words: 'V is the change in velocity over the time interval 't measured
from t1 to t2
» For most applications: 't = 0.01 (s) is sufficient
» High-dynamic applications use 't as small as 0.00025 (s)
• If an accelerometer measures gravity, then a ≈ 9.8 (m/s2), such that for 't
= 0.01 (s), 'V = 0.098 (m/s)
• Convenient format as it simplifies subsequent processing; some sensors
already directly measure change; reduces data rate and dynamic range
compared to implementation of the single integration outside the sensor
Inertial Navigation Systems
p.10
Example Inertial Measurement Unit
Miniature MEMS Quartz IMU
Systron Donner MMQTM 50
Accelerometers
Range
±10 g
Bias turn-on to turn-on stability
Bias in-run stability
≤ 3 mg, 1V
Velocity random walk
0.5 mg/√Hz
≤ 0.5%
Scale factor error
6.5 cm
≤ 2.5 mg, 1V
Alignment
≤ 5 mrad
Bandwidth
50 Hz
Gyroscopes
Range
200°/sec
Bias turn-on to turn-on stability
≤ 4-15°/hr
Bias instability
5 cm
From: www.systron.com
≤ 100°/hr, 1V
Angle random walk
0.3°/√hr
Scale factor error
≤ 0.5%
≤ 5 mrad
Alignment
Bandwidth (-90° phase shift)
50 Hz
Inertial Navigation Systems
p.11
Hardware Integration Research Platform
Inertial Navigation Systems
p.12
Inertial Navigation in the Vertical Direction
• Accelerometer sensitive axis in the Z direction
z
(perpendicular to local level defined by gravity)
• Scenario:
» t = 0: Start at height = 0 (h = 0)
» t = 1 s to 2 s: accelerate upwards, reach
highest point, stay for 2 seconds and return
to h = 0
h=0
Inertial Navigation Systems
p.13
MEMS Accelerometer: Vertical Acceleration
• Assume
» Accelerometer does not have any errors except for noise
» Gravity does not vary as a function of height
• Use first second of data to estimate gravity and subtract it
from the measured 'V ("zero-velocity update")
Inertial Navigation Systems
p.14
Vertical Velocity and Displacement
• To obtain velocity and displacement from 'V measurements:
vt2
rt2
'Vt2 ,t1 (t2 t1 )
vt1 'Vt2 ,t1
rt1 vt1 (t2 t1 ) 2
'Vt2 ,t1 (t 2 t1 )
2
v2
'v t 2 ,t1
v1
t1
t2
• Note that acceleration is time-varying, not constant
» In general, cannot directly use: r ( t ) r0 v0 t 1 at 2
2
(because it assumes constant acceleration)
» However, can use this by integrating in small steps and
assuming that acceleration is constant during each step
Inertial Navigation Systems
p.15
Measured Vertical Velocity and Displacement
z
Very good
short-term
performance
for
tracking
loop aiding
h=0
Drift = -0.6 m
Inertial Navigation Systems
p.16
What Happened in the X and Y Directions?
Drift = 4.5 m
Drift = -5 m
Inertial Navigation Systems
p.17
Leveling Error
Z’: g cos(D) | g
Z’ Z
X’: g sin(D) | Dg
X’
D
g
X
If D = 2 degrees, then
X’ acceleration: 0.34 m/s2
After 5 s: 'X=4.28 m
Inertial Navigation Systems
p.18
Other Complications
• Accelerometers have many errors in addition to noise
• Gravity is not constant (anomalies), doesn't always point to the center of
the Earth (deflections), and varies as a function of height.
Gravity anomaly map
1 mGal = 10-5 m/s2
From:
http://mrdata.usgs.gov/
geophysics/gravity.html
For the WGS 84 Earth Gravitational Model: http://earth-info.nga.mil/GandG/wgs84/gravitymod/ and
http://www.ngs.noaa.gov/GEOID/GEOID96/ngdc-indx.html
Inertial Navigation Systems
p.19
Gyroscope
• Gyroscopes are used to measure orientation or
changes in orientation and are often based on the
principle of conservation of angular momentum.
Spinning wheel
Angle measurements (resolvers)
Gimbals
Note: Earth's rotation
rate ≈ 15° per hour
(7.292115×10-5 rad/sec)
Inertial Navigation Systems
p.20
Some Gyroscope Technologies
• Mechanical (see previous slide) – measures actual angles relative to some
orientation
• Micro Electro-Mechanical System (MEMS) Gyroscopes use the Coriolis
effect: F 2m(Z u v) on a vibrating proof mass
» Single beam oscillator, balanced or tuning fork oscillators, shell or
wine glass or cylindrical oscillators
F
Z
v
Oscillation axis
• Ring Laser Gyroscopes (RLG) and Fiber Optic Gyroscopes (FOG) use the
Sagnac effect to measure angular rate
» RLG: laser beam around a closed path with mirrors
» FOG: lasers through optical fiber
Inertial Navigation Systems
p.21
Fiber Optic Gyroscope
Fiber Optic Coil
CW Beam
Z
Laser
CCW Beam
• Path for the CW beam is
longer due to the rotation
• Path for the CCW beam is
shorter due to the rotation
Measure the interference
pattern between the CW
and CCW beam to
determine 'T
• Benefits include reliability and high bandwidth (small mass
enables strapdown without vibration isolation)
Inertial Navigation Systems
p.22
MEMS Gyroscope Example
• Stationary, followed by a clock-wise (CW) rotation of 90°
» t = 0: Start at angle = 0°
90°
» t = 1.5 s to 3.5 s: rotate CW up to 90°
• Use stationary portion to estimate the gyro bias
• Integrate (accumulate) 'T to determine the change in angle
Inertial Navigation Systems
p.23
Measured Angle (around Z Axis)
Inertial Navigation Systems
p.24
Gimballed and Strapdown
• Early days: gimballed
» Platform with accelerometers is held level and northpointing such that position is calculated "directly" by
integrating the 'V's
• Today: mostly strapdown
» Sensors are "rigidly" mounted to the vehicle/device and
leveling and north-pointing is implemented in software.
Inertial Navigation Systems
p.25
Strapdown INS Terminology
Ref: Proposed IEEE Inertial Systems Terminology Standard and Other Inertial Sensor Standards, Randall K. Curey, Michael E.
Ash, Leroy O. Thielman, and Cleon H. Barker, IEEE PLANS 2004 (IEEE Std 1559).
Inertial Navigation Systems
p.26
IMU Accelerometer Parameters of Interest
•
•
•
•
•
•
•
•
•
•
•
Input dynamic range (g)
Bias stability during operation (mg)
Bias error at turn-on at room temperature (mg)
Bias error variation over temperature (mg)
Noise (mg, 1-V in a x-Hz bandwidth)
Velocity random walk (m/s/√hr)
Bias vibration sensitivity (mg/g2)
Scale factor error (% of full scale)
Scale factor linearity (%)
Frequency response (-3-dB bandwidth in Hz)
Cross-axis sensitivity (%)
Inertial Navigation Systems
p.27
IMU Gyroscope Parameters of Interest
•
•
•
•
•
•
•
•
•
•
•
•
Input dynamic range (deg/s)
Bias stability during operation (deg/s)
Bias error at turn-on at room temperature (deg/s)
Bias error variation over temperature (deg/s)
Noise (deg/s, 1-V in a x-Hz bandwidth)
Angular random walk (deg/s/√hr)
Bias vibration sensitivity (deg/s/g2)
g-sensitivity (deg/s/g)
Scale factor error (% of full scale)
Scale factor linearity (%)
Frequency response (-3-dB bandwidth in Hz)
Cross-axis sensitivity (%)
Inertial Navigation Systems
p.28
Gyroscope Drift & Angle Random Walk
• Gyroscope drift is expressed in terms of degrees per hour and
represents the long-term (average) angular drift of the gyro
• Gyroscope noise is the short-term variation in the output of the
gyro
»Can be measured in deg/sec
» Can be expressed as a Power Spectral Density (PSD) with
units of deg/sec/√Hz or (deg/sec)2/Hz to express the output
noise as a function of bandwidth
»To track angular changes, output is integrated over time to
find the angle as a function of time. Angular changes exhibit
Angle Random Walk (ARW) in units of deg/√hr
• If ARW = 1 deg/√s, then
»After 1 s, V of the angular change will be 1 deg
»After 100 s, V of the angular change will be 10 deg
»After 1000 s, V of the angular change will be 31.6 deg
Inertial Navigation Systems
p.29
Random Walk Process
• “Take successive steps in random directions”
• In continuous time, this process can be generated by feeding
an integrator with white noise.
t
³ w(u)du
w(t)
x(t)
o
t
³ w(u)du
x(t )
0
^
`0
E ^³ w(u )du ³ w(v)dv`
t
E^x(t )` E ³ w(u )du
E ^x (t )`
2
E ^x (t )`
2
0
t
t
0
0
t
t
t
0
0
0
t
t
0
0
³ ³ E^w(u )w(v)`dudv
³ ³ G (u v)dudv ³ dv
t
• Mean is zero, but variance increases linearly with time.
Inertial Navigation Systems
p.30
Gyro Random Walk
Angular noise in deg/s
Gaussian noise
5
0
-5
0
200
400
600
800
1000
Integrated Gaussian noise
Angle in degrees
50
0
-50
0
200
400
600
Time in seconds
800
1000
V of angular
change after
1000 s
Inertial Navigation Systems
p.31
Gyroscope and Accelerometer Time-Varying Biases
• Gyroscope and accelerometer biases are often modeled using
a first-order Gauss-Markov process: a stationary Gaussian
process with an exponential autocorrelation function.
t
w(t)
+
-
³ w(u)du
x(t)
o
E
• Continuous time: x Ex w
• Discrete time: xk 1 e E't xk wk
time constant = 1/E
Var(x) = V2/(2E)
where: wk is an uncorrelated zero-mean Gaussian sequence
Inertial Navigation Systems
p.32
1st Order Gauss-Markov Example
N = 7200*10; % 20 hours
beta = 1/7200; % time constant is 2 hours
dt = 1;
% time interval is 1 second
w = randn(N,1); % generate unity Gaussian
t= zeros(N,1);
% pre-allocate memory for speed
x = zeros(N,1); % pre-allocate memory for speed
x(1,1) = 0;
% initial condition
t(1,1) = 0;
% initial condition
for i = 2 : 1 : N
t(i,1) = i;
x(i,1) = exp(-beta*dt) * x(i-1,1) + w(i,1);
end
Var(x) = V2/(2E)=3600
Std(x) = 60
1st Order Gauss-Markov processes are often used in engineering problems
Mean and variance statistics are “stable”, but as can be seen from
the above example, the process is not always “well-behaved.”
Inertial Navigation Systems
p.33
INS Functional Components
Calibration of
inertial sensors;
realized postprocessing or
through bench test
Generic INS
computational process
Generic IMU
hardware
'V~A (t )
Conversion
IMU
~
'TA (t )
Pre-processing
(pre-integration
and instrument
compensation)
Coordinate
transformation
'TˆA (t)
Attitude
computation
(DCM)
TˆP/A (t )
'VˆN (t )
Compensation of
gravity and noninertial components
RˆN (t)
Integration
VˆN (t)
Inertial Navigation Systems
p.34
Conversion of Measured Data to State Estimates
• Gyro increments are converted into angular orientation
changes.
• Accelerometer outputs are combined with gravity effect and
transformed into velocity changes in navigation axes.
• Result is combined with known kinematical adjustments and
propagated into position increments.
• Current position estimate at each measurement time is used to
predict observations.
• Residuals (innovations) are formed by comparing predictions
versus measurements.
• Residuals (innovations) are weighted to produce updated
states.
• Position, velocity, and misorientation state updates are
assimilated into current estimates, resetting their a posteriori
estimates to zero.
Inertial Navigation Systems
p.35
Aircraft Euler Angles
>I@x
>\ @z
TA/P
0
0 º
ª1
«0 cos I sin I » >T@
y
«
»
«¬0 sin I cos I»¼
ª cos \ sin \ 0º
« sin \ cos \ 0»
«
»
«¬ 0
0
1»¼
Cnb
>I@x >T@y >\@z
ªcos T 0 sin Tº
« 0
»
1
0
»
«
«¬ sin T 0 cos T »¼
Roll
­I
°
Pitch
®T
°\
Heading
¯
Transformation from Platform to Aircraft
(Platform = Navigation Frame)
I
Roll
T
Pitch
\
Heading
TA / P
Cnb
Inertial Navigation Systems
p.36
Small Angles
TP / A
ªcos \ cos T sin \ cos I cos \ sin T sin I sin \ sin I cos \ sin T cos I º
« sin \ cos T cos \ cos I sin \ sin T sin I cos \ sin I sin \ sin T cos I»
«
»
«¬ sin T
»¼
cos T sin I
cos T cos I
• For small angles:
sin \ | \, sinT | T, sinI | I, cos\ | 1, cosT | 1, cosI | 1
TP / A
TA / P
ª 1 \
«\
1
«
«¬ T I
ª 1
TP' / A «« \
«¬ T
Tº
I»»
1 »¼
ª 0 \
0
I «« \
«¬ T I
\ Tº
ª 0
1
I »» I «« \
«¬ T
I 1 »¼
Tº
I»»
0 »¼
\
0
Tº
I »»
I 0 »¼
Inertial Navigation Systems
p.37
Gimbal Lock
TP / A
ªcos \ cos T sin \ cos I cos \ sin T sin I sin \ sin I cos \ sin T cos I º
« sin \ cos T cos \ cos I sin \ sin T sin I cos \ sin I sin \ sin T cos I»
«
»
«¬ sin T
»¼
cos T sin I
cos T cos I
When T
S
, then
2
TP / A
ª 0 sin(I \) cos(I \) º
« 0 cos(I \) sin(I \)»
«
»
«¬ 1
»¼
0
0
• Now only the difference between the roll and heading angle determines
the transformation from Aircraft to Platform.
• The roll and heading angles are not unique.
• Same occurs when the pitch angle = -90°, then the sum of the roll and
heading angles determines the transformation.
• For aircraft, both roll and heading undergo a discontinuity when the pitch
angle passes through ±90° Æ gimbal lock.
Inertial Navigation Systems
p.38
Four-Parameter Set (Quaternions)
• A quaternion is described by (nonsingular, unambiguous):
q
ª
§ T ·º
E
sin
« 1 ¨ 2 ¸»
© ¹»
«
«E sin §¨ T ·¸»
« 2 © 2 ¹»
«
T ·»
§
« E 3 sin ¨ ¸ »
«
© 2 ¹»
«
§T· »
cos
¨ ¸ »
«
©2¹ ¼
¬
ª q1 º
«q »
« 2»
« q3 »
« »
¬ q4 ¼
• Example:
TA / P
E1 1, E2
2q1q4
q42 q12
E3
q
1
TA / P E E
E12 E22 E32 1
§ T11 T22 T33 1 ·
T arccos ¨
¸
2
©
¹
ªq42 q12 q22 q32
«
« 2q1q2 q4 q3 « 2q1q3 q4 q2 ¬
0, then q1
sin(T / 2), q2
2 sin(T / 2) cos(T / 2) sin(T)
cos 2 (T / 2) sin 2 (T / 2) cos(T)
2q1q2 q4 q3 q42 q12 q22 q32
2q2 q3 q4 q1 q3
0
TA / P
2q1q3 q4 q2 º
»
2q2 q3 q4 q1 »
q42 q12 q22 q32 »¼
0
0 º
ª1
«0 cos(T) sin(T) »
«
»
«¬0 sin(T) cos(T)»¼
Inertial Navigation Systems
p.39
Inertial Navigation on a Flat Non-Rotating Earth
Zz
y
x
\
ZZ
FX , I
FX , A cos(\) FY , A sin(\ )
FY , I
FX , A sin(\) FY , A cos(\)
v X , I
FX , I
x X , I
vY , I
FY , I
xY , I
vX ,I
vY , I
YI
YA
XI
\
XA
Inertial Navigation Systems
p.40
Rotation around an Axis in Inertial Space
ω
ω angular velocity in rad/s
Zu Zu R
R
v
ωu R
a
ωu v
a
ω u ω u R Inertial Navigation Systems
p.41
Inertial Space & Earth-Centered-Earth-Fixed
As derived in: Goldstein, H., Classical Mechanics, 2nd Ed., 1980, pp. 174-176.
Inertial Navigation Systems
p.42
Apply to radius and inertial space velocity vectors
Inertial Navigation Systems
p.43
Force in Inertial Space (measured by accelerometer)
FI
ma I
with : a I a E 2(Ze u v E ) Ze u (Ze u r )
or : FI ma I ma E 2m(Ze u v E ) mZe u (Ze u r )
Fspecific ma E 2m(Ze u v E ) mZe u (Ze u r )
2
Note : 1 cm/s
after 5 min
displacement :
Coriolis force
2Ze v 1.5 u10 4 v
if v 300 m/s
Centrifugal force
(points outwards)
Ze2 r | 3.4 cm/s 2
Sum of earth’s gravitational
1
field and centrifugal force =
(0.01)(300) 2 450 m
2
gravity field
Based on: Goldstein, H., Classical Mechanics, 2nd Ed., 1980, pp. 177-179.
2Ze v 4.5 cm/s 2
Inertial Navigation Systems
p.44
Movement over Ellipsoid
Radius of curvature in a meridian
RM
>
a E (1 eE2 )
@
3/ 2
2
2
1 eE sin (Lat)
Radius of curvature in planes parallel to the equator
RP
aE
aE
1 eE2 sin 2 (Lat)
6378137 m; eE2
(2 f) f; f
1
298.257223563
Inertial Navigation Systems
p.45
Basis of Schuler Effect
Estimated
Position
True
Position
u uR̂
R
g
ĝ
horizontal position error :
g
r
r
R
frequency
Computed
gravity vector ĝ
has a backward
directional component
Position error
g
R
period | 84 minutes
Acceleration error
Inertial Navigation Systems
p.46
INS Functional Components
Calibration of
inertial sensors;
realized postprocessing or
through bench test
Generic INS
computational process
Generic IMU
hardware
'V~A (t )
Conversion
IMU
~
'TA (t )
Pre-processing
(pre-integration
and instrument
compensation)
Coordinate
transformation
'TˆA (t)
Attitude
computation
(DCM)
TˆP/A (t )
'VˆN (t )
Compensation of
gravity and noninertial components
RˆN (t)
Integration
VˆN (t)
Inertial Navigation Systems
p.47
Initialization
• Position is initialized with
» Estimated longitude
» Estimated geodetic latitude
» Estimated altitude above ellipsoid (baro-altimeter)
» Zero wander angle
• Pitch and roll angles are calculated from the accelerometers
(gravity defines the apparent vertical)
• Heading is obtained from gyrocompassing
» Need high-quality gyroscopes
» If not available Æ integration with other sensors
• Form corresponding matrix TP/E from Earth to nav-reference
(local level, wander-azimuth) coordinates
Inertial Navigation Systems
p.48
Short Term INS Position Error
Position Error in Cruise – Short Term (<< 84 min)
Position Error at time t =
Initial Position Error +
Velocity Error u t +
Leveling Error u g u ½ t2 +
Accelerometer Bias u ½ t2 +
Drift Rate u g u 1/6 t3
Inertial Navigation Systems
p.49
Future Trends
• Cost of inertial sensors continues to drop, while performance
continues to increase
» Non-tactical grade
» Automotive, consumer applications
• Low-cost navigation grade IMUs are not on the horizon
• Performance improvements feasible through advanced
calibration techniques
• Continued developments in the area of integration with GNSS
and other navigation sensors
» Ultra-tight integration with carrier phase
• Long signal integration and tracking loop design
» Integration with software-defined radios and batch
processing (open-loop tracking)
Inertial Navigation Systems
p.50