Foot Mounted Pedestrian Navigation Systems

Foot Mounted Pedestrian Navigation
Systems
Final Report
April 30, 2015
Submitted by
Sailesh Kumar G, Shyam Sundar S
B.Tech Electronics and Communication Engineering
Department of Electrical Engineering
Project Mentor
Amit K Gupta
GT Silicon Pvt. Ltd-
Internal Supervisor
Prof. Vijay Kumar Chakka
Shiv Nadar University

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Table of contents:
1. Abstract
2. Introduction
3. Literature Survey
4. Inertial Navigation System (INS)
a) Coordinate systems and frames
b) Sensors
c) Accelerometer
d) Gyroscope
e) Block diagram of Inertial Navigation system
f) Dead Reckoning
g) Errors in INS
h) Errors in IMU
5. Mathematical model
a) Select sensors and mounting:
b) Choose a state space model
c) Define a Measurement model
d) Define a Process Model
e) Defining Pseudo measurements
f) Kalman Filter
6. Hardware
a) High level System Description
7. Software
a) Communication Protocol
i) Types of Commands
ii) Command Structure
iii) Command Reception/Transmission
b) IMU Interface
c) I2C protocol
d) Data storage mechanism
e) Calibration Compensation
i. Sensor Model
ii. Calibration matrix
iii. Fusion
iv. Bias compensation
8. Implementation:
a) Varying number of IMUs
9. Experimental Study
a) Design of the experiment
b) Results
c) Observations

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10. Conclusion
11. References

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1.Abstract:
Positioningis a fundamental component of human life to make meaningful interpretations of the
environment. Without knowledge of position, human beings are like machines and have very limited
capabilities to interact with the environment. Even machines in today’s world can be made smarter if
positioning information is made available to them.Indoor positioning of pedestrians is the broad area
considered in this thesis.A foot mounted pedestrian tracking device has been studied for this purpose. Systems
which utilize foot mounted inertial navigation system has been in the literature for more than two decades.
However very few real time implementations have been possible. The purpose of this thesis is to benchmark
and improve the performance of one such implementation.
The benchmarking of the device was carried out by incorporating varying number of sensors on board.For this
purpose the embedded software on the device was modified and the calibration compensation was carried
out correspondingly using a well-defined methodology. The height error is one of the most important metrics
in indoor navigation. The device currently suffers from a height error of roughly 2.5%. To minimise this error a
pressure sensor has been interfaced with the on-board microcontroller. Experimental study was then carried
out where the device was tested under different conditions by taking into account the parameters which affect
the tracking performance.
Prof. Vijay Kumar Chakka
2.Introduction:

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Human beings constantly need to acquire knowledge about their environment in order to interact with their
surroundings. In the absence of knowledge of location it would limit our interaction capabilities with the
physical world. Today machines face this problem and therefore require supervision of humans in order to
make meaningful inferences. By integrating machines with the knowledge of location they can be made to
autonomously interact with each other thus improving their efficiency. For human beings, Positioning
provides basic information that can be integrated into a diverse set of fields.
Global Positioning System (GPS) is the widely used technical standard for outdoor positioning. Any person with
an access to a system such as a mobile phone integrated with GPS receiver is provided positioning information
at free of cost with a horizontal accuracy of 3.5 metres. However atmospheric effects, sky blockage and
receiver quality affects the free LOS (Line Of Sight) communication between the transmitter and the receiver.
This situation degrades even more under circumstances such as moving underground, inside a tunnel or even
inside buildings. From this arises a need to deploy GPS integrated with other systems to improve the accuracy
for usage in indoor positioning. These systems can be categorised based on the nature of information sources.
The data from passive infrastructure based sources such as RFID (Radio Frequency Identification) tags, WLAN
are one of those. Also information from motion constraints such as building maps and pedestrian motion
models can be used. However the major problems with these systems are their cost in deployment and
maintenance. In case of emergency situations such as fire, the robustness of these systems fails destroying
their purpose. Designing a robust system which does not depend on infrastructure or prior knowledge about
the environment would satisfy a large scale of applications at a lower cost.
The advancements in MEMS Technology have paved the way for low cost sensors which can be integrated into
an Inertial Navigation System (INS). These sensors are also less power craving and occupy far lesser size. The
INSs apart from providing the possibility to integrate with GPS in fact provide a suitable alternative to the
same. Inertial Navigation Systems are self-contained systems that can operate in harsh radio environments
without pre-installed infrastructure and prior knowledge of the environment. Conventional Inertial Navigation
Systems calculate the change in position through Dead Reckoning. In Pedestrian Navigation this means
measuring the length of the steps and the direction of the pedestrian given the initial position and heading is
known. They calculate double integration of acceleration measurements and single integration of gyroscope
measurements which are noisy and therefore suffer from huge accumulation of position and heading errors
with time. This is because the new estimates of position and heading rely on previous estimates of the same.
The use of a complementary information source can mitigate this problem by providing absolute
measurements of position and orientation. However for emergency response situations the system has to be
completely self-sufficient at least for a short period of time.
Zero velocity detection (ZUPT) is one of the popular methods in literature to minimise the errors encountered
in position and heading estimates. By exploiting the standstill phase in the walking motion of the pedestrian
one can detect that the linear velocity of the foot at that instant is zero. This essentially means the sensor is
stationary at standstill position and therefore any estimated velocity or rotation is interpreted as error and is
used to recalibrate the estimated velocity to zero. ZUPT allows the device to estimate position only when the
device detects a step and thus the error encountered is directly proportional to the number of steps
measured. Without ZUPT the drift error would have grown cubic with time. It increases the accuracy of
conventional inertial navigation systems thus making it suitable for a large number of promising applications in
the area of indoor navigation in GPS denied environments.
The targeted applications include localisation in emergency response situations such as fire fighting missions
where prior knowledge of the environment or deploying costly infrastructure is not possible. This technology
can also be integrated into other research areas such as Biomechanics and Biomedicine where a person’s
walking patterns can be studied to connect it to various medical symptoms. Parkinson’s disease for example
studies the stability of the foot. Other fields include Sports medicine where gait analysis of the athlete is
performed and Behavioural Sciences where a person’s movement patterns are observed.

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This thesis is divided into the following sections. Chapter 3 provides a summary of the recent work in the area
of Pedestrian navigation few of which served as a reference in writing this thesis. Chapter 4 describes the
Inertial navigation system used in Osmium MIMU22BT with emphasis on the sensors and the equations used.
Chapter 5 derives the mathematical model using which the algorithm written in the Embedded software
operates. Chapter 6 outlines the hardware through a high level system description. Chapter 7 explains the
integral part of the Embedded software in the device which are the IMUs. Chapter 8 gives a detailed
description on the implementations carried out through writing Embedded Software code. Chapter 9 describes
the experimental study carried out to study and benchmark the performance of the device at different
conditions. Finally, Chapter 10 concludes this thesis with the evaluation of the objectives set.
3. Literature Survey:
Mathiassen et al. (2010) designed a low cost Inertial Navigation System in integration with GPS for
positioning. This system was able to track the position when GPS signals were lost. The IMU was supported by
external sensors such as Barometer and Magnetometer. The simulations showed good results when the

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gyroscope output was filtered. Position accuracy with a standard deviation of 8.5 m for 60s time was achieved.
But in the real world tests, the same system gave an error of 65 m for the same time. This is the reason
Magnetometers are not used in Osmium MIMU22BT. Even though position errors tend to grow out of bounds
and magnetometers can be used to bind the errors, they are not used so because during measurements they
suffer from errors which are difficult to model. One such example is the presence of any ferromagnetic
material near the pedestrian.
As Pedestrian dead reckoning requires estimation of Step length, studying and categorizing human
activity is essential before designing an algorithm for step detection. The variation in dynamics of movements
such as walking, running, loitering and the type of mounting affects the performance of the device. The drift
error measured as is less than 1% for many foot mounted systems in the literature compared to mounting on
other body parts which have more than 1% at least in all cases.
Nilsson et al. (2010) demonstrated that ZUPT aided foot mounted INS was able to achieve drift error
in the range of (0.1%-0.44%). The errors on the lesser side utilized information from external sources.
Problems are encountered in ZUPT algorithm when either the dynamics of the movement or speed or when
the pedestrian is walking on different surfaces. Skog et al. (2010) worked towards designing different Zero
velocity detectors and he achieved a position error of 0.14% in the acceleration magnitude detector and
angular rate energy detector. Both of these are used in the implementation of Open-shoe modules in 2012.
Wan and Foxlin (2010) used Intersense’s Navshoe
TM
to design a foot mounted system not dependent on
external sources giving a position error of 0.27% of the total distance.
In spite of the performance advantage in foot mounted systems these required specific arrangements
to integrate the IMUs into the sole of a shoe. Therefore Nilsson et al. (2012) presented the first open source
real time embedded implementation of a ZUPT aided foot mounted INS. By utilizing off-the-shelf components
and assembly methods the cost of a single unit was 800$ with a position accuracy of (0.2-1%). But it could only
be accessible using a USB interface. They also manufactured intelligent shoes to integrate the module close to
the heel. Nilsson et al. (2014) further improved the Open Shoe module by adding a Bluetooth interface and
flash memory to it and further reduced its cost to around 300$ while maintaining the Open source nature of
the module.
Skog et al. (2014) described a low cost calibration procedure by using a platonic solid icosahedron.
This novel method replaces the need for a high cost mechanical platform for calibrating the IMUs with a low
cost solution in which a trade-off for precision for reduction is cost is achieved. But the tradeoff in precision is
sufficient to compensate for all the observable errors in the device.
Angermann et al. (2010) presented a reference dataset for analysis and verification of different
algorithms on foot mounted inertial sensors. It also included data collection methodology which can be
applied to a large range of indoor applications. The reference data phase would help us understand the
performance of algorithms in Pedestrian dead reckoning specifically during the standstill phase of the motion
4. Inertial Navigation System:
The Inertial navigation system (INS) acts as the backbone of the device Osmium MIMU22BT. The ZUPT
algorithm aided kalman filter takes measurements from this system.This chapter explains the working of the
INS implemented inside the device. It describes the reference frames used for measurement, sensors used in
the system, block diagram of the complete system, errors inside the system and the errors in an IMU.

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Coordinate systems and frames:
The commonly used coordinate systems in inertial navigation are Cartesian, Curvilinear and spherical
coordinate systems. The commonly used frames include Sensor’s frame, Local tangent plane and Earth
centered Earth fixed frame.Local tangent plane refers to a frame fixed at a tangent point on the earth
reference to which Zero position and heading is defined. This necessarily means that with reference to latitude
and longitude values zero position and heading is defined.In addition to this, local gravity needs to be taken
into account during calibration. In Earth centered earth fixed frame, position is defined relative to the center
of the earth i.e a line passing from the Earth’s center through the equator. Sensor’s frame refers to the frame
which is moving with the sensor and hence relative to the sensitivity axes of the sensor.
In Osmium MIMU22BT the coordinate frame used is Local tangent plane. This essentially means that the
rotation of earth is neglected as the module is designed for pedestrian tracking for a short duration. The
coordinate system used is the Cartesian coordinate system.
Sensors:
The sensors in Osmium MIMU22BT are calledMEMS based Inertial Measurement Units (IMU). The
improvement in MEMS technology based sensors has revolutionized the field of pedestrian tracking due to less
cost, reduced power consumption andminiaturization. The IMU used here is Invensense’s MPU9150. Generally
an IMU contains Accelerometers and Gyroscopes in three orthogonal axes. But MPU 9150 has a
magnetometer in addition and therefore has nine degrees of freedom. However for the purpose of indoor
tracking magnetometer is not currently used as it is susceptible to disturbances from ferrous objects around
any building. The main utility of an IMU is to capture force and rotations in the three orthogonal sensitivity
axes. MIMU22BT is equipped with multiple IMUs which provide an opportunity to apply sensor fusion
techniques. Currently simple moving average is the fusion technique employed to fuse the data from IMUs.
The quality of tacking data indeed depends on number of IMUs on board. A detailed analysis on this has been
carried out in Section 7 & 8.
Accelerometer:

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An accelerometer is a sensor which provides specific force measurements when it is subjected to a force. It
contains a proof mass attached to a spring in each orthogonal axis. Therefore force measurements in three
orthogonal axes are observed (s
b
ε R
3
). The force each proof mass is subjected to is converted into an output
voltage depending on the force. But the force contains acceleration due to gravity in addition to the inertial
acceleration (actual acceleration of the body). Since the frame of the sensor changes continuously when the
body is moving, the orientation of the accelerometers with respect to the local tangent plane keeps on
changing. The inertial acceleration can be found only after knowing this orientation. s
t
ε R
3
provides
acceleration with respect to the local tangent plane. To get inertial acceleration, acceleration due to gravity
should be subtracted from this value.
Gyroscope:
The gyroscopes provide angular velocity measurements of a body whenit is moving with respect to a
coordinate frame. The MEMS gyroscopes used in the IMU are vibratory gyroscopes which operate on the basis
of Coriolis principle.According to Coriolis principle, an induced rotation in the velocity plane sets up a force
called coriolis acceleration. The angular velocity can then be calculated using the following formula.
Alternatively the circuits in MEMS sensors sense the coriolis acceleration and provide a value of capacitance
correspondingly. Like accelerometers three gyroscopes are present in three orthogonal axes in order to
measure angular velocity. The measured angular velocity is ω
b
ε R
3
.
Ω = acor/2v
where Ω refers to angular velocity
acor refers to coriolis acceleration
v refers to linear velocity

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Block diagram of an Inertial Navigation System:
The following block diagram of an inertial navigation system is widely used in the literature. The facts such as
neglecting the rotation of the earth simplify the inertial navigation system as follows.
Here S
n
represents transformed value of acceleration from sensor’s frame to the navigation frame.
S
b
represents acceleration measured in the sensor’s frame
is a rotation matrix for transforming the accelerations from sensor’s frame to the navigation frame
q defines quaternion which is taken as a function to the rotation matrix
g
n
denotes acceleration due to gravity
a
n
represents the true acceleration of the system
ω
b
represents angular velocity of the system
v
n
and q represent velocity and attitude of the system respectively
Dead reckoning:
Dead reckoning is an iterative process that has to be carried out with the values of position and heading
derived from the system. The drawbacks of this system are that it requires initial values of position and
heading and both these errors grow as a function of time. This can be attributed to the integrative nature of
the system. The total position error will depend on three error factors. These are initial position and heading
errors, translation errors when navigating from one frame to another and heading errors in the gyroscope. Out
of all these errors the attitude errors of a gyroscope is the most critical factor. Therefore choosing a gyroscope
with high accuracy will reduce the total position error.
Errors in INS:
The integrative nature of the inertial navigation system causes position error to grow as a cubic function of
time. This is because it involves integrating accelerometer measurements twice by also using gyroscope
measurements. This can be illustrated as follows.

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When the system moves from its initial position the frame of the sensor changes continuously and hence
therefore its axes loses its alignment with the local tangent plane frame. Due to this misalignment an error in
acceleration δωy t is observed. On double integration we get position error as a function of t
3
.
Errors in IMU:
The IMUs suffer from a certain set of errors after fabrication. The modeling of these errors and the calibration
compensation process are discussed in Section 6. In this section the focus is on providing a brief description of
the different types of errors.
Deterministic errors can be corrected using the calibration process while the non-deterministic errors are
taken care of during stochastic modeling and estimation (Kalman filter). Again determinsitic errors can be
classified as well as quantified. The following are the deterministic errors.
1. Bias
2. Gain
3. Non- orthogonality
4. Inter IMU Misalignment.
Note that Inter IMU misalignment occurs only when multiple IMUs are used on board.

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5.Mathematical Model:
A mathematical model was derived by Nilsson et al. (2013) to solve the problem of positioning. In spite of time
being a continuous quantity a mathematical model in continuous time is not suitable or it is laborious to
perform approximations. Positioning involves findingthe quantity position which varies with time. Therefore
time is required to be measured along with position. The information about the system is also required along
with the position which will be used in creating Process models involving system and Measurement models
which associate the system with the measurements. Thus the two fundamental quantities required to quantify
position are Measurements and Models.
The models create relations between measured quantities and the measurements measure those quantities.
For example position values are not directly available from the sensor measurements. Instead they need to be
derived from Acceleration and rotation measurements from accelerometer and gyroscope respectively. So
Measurements require measuring Accelerometer and Gyroscope values whereas Models process this
information and find out the position values.
1. Select sensors and mounting:
The measurements carried out, depending on the error sources in the measurements affect the statistical
models that are used to process this data. Therefore selecting the right kind of sensors and the mounting
scheme will generate confidence in the collected measurements and hence meaningful values of position can
be derived by the statistical models. IMUs when interfaced with a microcontroller to process the data and an
application platform to receive position values make a self-contained system which is not dependent on prior
knowledge of the environment or pre-installed infrastructure. Again mounting scheme cannot be overlooked.
2. Choose a state space model:
A State space model is required in order to make meaningful inferences out of the measurements. This is
because measurements cannot be infinite. Similarly the states are not absolute quantities and require a
reference coordinate system and frame. The coordinate frame used in Pedestrian navigation is Local Tangent
Plane. Here position and heading are initialized with reference to a tangent point on the earth. The coordinate
system used is Cartesian coordinate system.
3. Define a Measurement model:
The state space model can hold only static values of measurements. It cannot capture randomness in
measurements or how these measurements changes with time. Therefore a measurement model can be
defined to account for both these parameters.
The subscript k refers to the discrete time measurements.
Hk = (Xk,Uk,Nk)
Here Xk refers to the measurements, Uk refers to the change in measurements with time and Nk refers to the
randomness in the measurements.
4. Define a Process Model:
Even though the values of measurements change with time these measurements are temporal quantities and
hence the previous value of measurements heavily determines the current value of measurements. This
means that the current value of measurements can be estimated by its previous value, change in current
value with time and a random component.
Xk = Fk(Xk-1,Uk,Wk)

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Fk represents process model, Xk represents current value of measurement, Xk-1 represents previous value of
measurement, Uk refers to the change in measurements with time and Nk refers to the randomness in the
measurements.
5. Defining Pseudo measurements:
When the measurement values are complemented with the information about the environment and
the dynamics of the system, the resulting information cannot be covered within a process model. This
information is closely related to a measurement and hence the name Pseudo measurement. For
example when a zero velocity update is passed by comparing the acquired velocity with a threshold
value, the velocity value is not a measurement but a quantity derived from accelerometer and
gyroscope measurements and hence the update passed is a pseudo measurement.
6. Kalman Filter:
Utilizing the knowledge of process model, measurement model and pseudo measurement model
a statistical model can be used to derive the signals present in the state space model. These signals
represent the states of interest such as position that are to be estimated. One of the highly accurate
state estimation models is the Kalman filter which is applicable to linear stochastic systems. For non-
linear systems an extended kalman filter is used.
The state equations of the kalman filter consists of Time update and Measurement update equations.
The state prediction happens at time update .This value is fed into the measurement update where
the state correction takes place.

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6. Hardware:
MIMU22BT is an embedded foot mounted navigation system having a combination of hardware and software
components which work together to give a superior tracking performance. In the hardware section only the
high level system design is the focus area in this thesis.
High level System Design:
The hardware in the module consists of 32-bit floating point capable AT32UC3C2512 Atmel
microcontroller which processes all the raw inertial data from the IMUs with the help of a navigation algorithm
written in Embedded software. There are four Invensense MPU9150 IMUs on board with a compass inside the
package which is connected to the microcontroller through the I2C buses initialised in the software. The
Bluetooth used is Bluetooth v3.0 and the module used is SPBT2632C2A from ST Microelectronics. An External
crystal oscillator provides a clock frequency of 16 MHZ to the microcontroller. It also contains a pressure
sensor LPS331AP from ST Microelectronics which is connected through TWI (Two Wire Interface) in the
microcontroller. The flash memory AT45DB081D is connected through the SPI interface in microcontroller.
Besides Bluetooth communication is also possible through USB interface.
Calculating position and performing dead reckoning is the sole purpose of the system. The computed
position values in microcontroller are captured by an external application platform which is an Android
powered device. This application sends commands to the module, which is provided with Bluetooth
connectivity, and is received by making use of the USART communication interface. The communication in this
interface between the two devices are performed by the TXD and RXD, transmitter and receiver pins
depending on the conditions of the CTS and RTS, Clear to Send and Ready to Send in both the devices.The
USART interface in the microcontroller is made up of Data Register, Control and Status Registers and Baud
Rate Registers. It used Serial communication at a baud rate of 9600 bps. USART usually inputs byte by byte and
reads the data from registers before further processing by the microcontroller. The Peripheral DMA controller
(PDCA) acts as an interface between USART module and memory. Handshake interface is used to connect
USART to Peripheral DMA. This essentially means that communication can only occur if valid data is present at
the transmitter and receiver is ready to receive the data. High Speed Bus Matrix is used to connect the PDCA
with on-board memory.

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7. Software:
In the software section, the communication protocol devised by the openshoe team serves as the backbone
for sending commands and receiving data at the application platform. IN communication protocol, the types of
commands, command structure and the transmission and reception logic of commands will be discussed. One
of the major interfaces in the device is the interface between the microcontroller and the IMUs. Though there
are no dedicated I2C pins used in this interface, the protocol is implemented in the software. A brief note on
the interface and the protocol is outlined. This is followed by the description on storing the data from the
IMUs in a suitable format which helps the user to send the data in a well-defined format to the application
platform. Next, calibration compensation discusses the methodology to remove the errors from the sensor’s
output data following which the process of fusion and bias compensation is explained.
Communication Protocol:
The communication between the INS and the Android device is defined in a protocol provided by the open
source embedded foot mounted INS system, Openshoe. This communication protocol provides a uniform
structure for receiving a command from the user and transmits the appropriate response to the command
received. The states where the raw and the computed results from the microprocessor is stored, the total lists
of various commands that the user can transmit and the different processing functions that influence in
tracking the pedestrians location are well defined in a framework of this protocol.
The user can have access to all the data which are received from the IMUs by the microcontroller which are
stored as variables in the system. Other computed data such as the fusion data and navigational states after
the error model data are also stored in the variables of its own which are also accessible. These states are
accessed by the user by transmitting the specific Command to the INS module. The user can request any
output of the state at a specified rate that can be transmitted, can change the value stored in a variable state
and even modify the processing sequence. A set of these commands together can be processed to perform a
certain function which in turn called the processing function and is specified for task to either perform for
computing the raw inertial values or even outputting the computed values. The states, commands and the
processing functions are identified as separate entity by the microprocessor with the help of a single byte
unique header assigned to each state, command and processing function respectively.
Types of Commands:
For the user’s convenience of handling the data there are five types of commands that can be used. For
example, the requirement of the Module Id and for pinging the device small commands are used which are
classified as Auxiliary commands. Since the users can modify the states stored in a variable and then check the
output of the processing function, a set of commands which serve the purpose of testing and debugging are
used. This is primarily used as to input a user defined inertial states of the IMUs and then compute the
required navigational equations for testing. The user can request a specific or a combination of states stored in
the microcontroller making use of Request data commands. Similarly a process function can be initiated by the
user which itself can output certain states is made possible by the Request Processing functions command. For
example Stepwise Dead Reckoning function can be initiated by the user which outputs the position of the
pedestrian at every step. Certain commands can perform both initiations of the processing function as well as
outputting the data for the user
Command Structure:
The command transmitted by the user is acknowledged by the module and then it retransmits the
appropriate response to the user. The command, Acknowledgement and the Response have a specific

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structure defined by the protocol. The command comprises of single byte header for identification followed by
payload which is of variable size depending on the command but specific for a particular command and then
the two byte checksum which is the sum of all byte received prior to it for error detection.
• Command Structure
CH PL CS
– CH – Command Header
– PL – Varying Payload
– CS - Checksum
• Acknowledgement Structure
A0 CH CS
• Response Function Structure
AA PN PS PL CS
– PN- Package Number
– Package Size
Command Reception/Transmission:
When receiving a command the module checks if the header corresponds to a valid command, if so it reads
the bytes within a time limit and then checks the checksum. If the checksum is valid it then continues to parse
the payload else it simply discards the bytes and waits for another header. If the command received is an
acknowledgement it doesn’t send a reply ACK else it does. While transmitting the states the module assembles
the data package in a buffer, allots a package number and adds the total bytes in the payload that is being
transmitted. Then the package number is incremented and the data package is pushed to an output buffer
which drops the packages once the buffer gets filled. Similarly if an ACK is needed to be transmitted it is
prepared by command reception logic and added to the buffer. If the packages are transmitted wirelessly i.e.
Bluetooth there are two modes of transmission. Lossy mode is where the packages are dropped and forgotten
which is followed when transmitting through USB. In Lossless mode the packages are added to a package
queue and then send the oldest package first. Once a command is reception is successful it then stores the
arguments of the command in a buffer of size 512 bytes. This buffer is then passed to the appropriate
response function that needed to be generated which executes the command sent by the user.
IMU Interface:
Following the command from application platform, the microcontroller reads raw data from the Inertial
Measurement Units (IMUs). Raw data refers to accelerations and rotations measured in x, y and z axes by

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accelerometer and gyroscope respectively. The number of raw datasets read by the microcontroller in parallel
is equal to the number of IMUs on board. Before further processing occurs the raw data is fused and averaged
so that the navigation equations process a single datasetof accelerations and rotations in x, y and z axes (Ax , Ay
, Az , Gx , Gy , Gz).
In the following sections the process by which data is read from the IMU in parallel and stored in the
microcontroller will be described. Also the calibration procedure and data fusion methods followed in Osmium
boards in achieving a single raw dataset will be explained in detail.
I2C protocol:
The data is read from the IMU with the help of I2C buses initialized in the software. It makes use of a two wire
interface in which the serial pins SDA ( Serial data) and SCL ( Serial Clock) are interconnected between master
and slave devices. The microcontroller acts as the master device and the IMUs connected to the
microcontroller act as slave devices.
Data read from
IMU
Calibration
Compensation
Calibration
Matrix
Data fusion

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The command sequence used to transmit/receive data is as follows:
1. Send Start bit:
The microcontroller alone can initiate data transfer only when both the SDA and SCL pins are high. The Start
condition is generated when SDA is pulled to low by the microcontroller while the SCL pin is high. It is also a
signal to the IMUs (Slave devices) that a new communication session is about to begin.
2.Data Transfer:
• Data transfer begins when the microcontroller sends a byte . The most significant seven bits
corresponds to the Slave device address and the LSB corresponds to whether Read / Write operation
is taking place, 1 for Read, 0 for write.
• After this byte is sent, the microcontroller waits for an acknowledgement from the IMU .
• Once acknowledgement is received, the microcontroller waits for data serial data from the IMU.
• The Serial clock is always under the control of the microcontroller periodically changing from low to
high or from high to low and the data on SDA line can be changed only when SCL is low.
• This means the IMU can send data to the microcontroller only when SCL pin is low.
• For each byte of data received, the microcontroller has to send an acknowledgement.
3.Send Stop bit:
Once data transfer is complete, the Stop condition is generated by the microcontroller where the SDA pin is
set to high while the SCL pin is high. This is a signal that the bus is free once again and communication can be
started by initiating Start condition.

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Data Storage mechanism:
The data received from the IMUs in parallel through the SDA pins in the microcontroller are stored in a bit--
wise fashion in a data matrix.
1B1 1B2 1B3 …. …. 1B32
2B1 2B2 2B3 …. …. 2B32

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The 1
st
and 2
nd
elements of the data matrix will be in the above format each of size 32 bits where 1B1
represents 1st Bit sent from IMU 1, 1B2 represents 1st Bit sent from IMU 2. 2B1 represents 2nd Bit sent from
IMU 1, 2B2 represents 2nd Bit sent from IMU 2. In General,
nBm represents nth Bit sent from mth IMU.
The data matrix is a column matrix which means that each row in the matrix is taken as a single element of the
matrix. The number of bits in each row depends on the number of IMUs connected to the microcontroller.
Data is sent from the IMU registers in the following order to the microcontroller: Accelerometer values Ax, Ay,
Az followed by Temperature values and then the Gyroscope values Gx, Gy and Gz. Each measurement has a
size of 2 bytes. Therefore each IMU sends 14 bytes of data to the microcontroller.
The software now takes the first 32 elements in the column matrix and calculates the bitwise transpose of all
the elements in this matrix. The resultant matrix is again a column matrix in which each row corresponds to Ax,
Ay values from a particular IMU.
The same process is repeated till the remaining values Az, Temperature, Gx, Gy, Gz are isolated.
nBm nBm nBm …. …. nBm

22
The Ax, Ay, Az, Gx, Gy, Gz and Temperature values of IMU 1 which are 2 bytes each will be stored in the format
shown above where bytes from 1B1 to 16B1 represents Ax, 17B1 to 32B1 represents Ay, 33B1 to 48B1
represents Az, 65B1 to 80B1 represents Gx, 81B1 to 96B1 represents Gy, 97B1 to 112B1 represents Gz and
49B1 to 64B1 represents Temperature.
These values are sorted and stored in a 2-D mimu_data array of size 32x7 where each element is of size 16-bit
(2 byte) representing Ax,Ay,Az,Gx,Gy,Gz and Temperature.Here each element in the mimu_data matrix is of
size 16-bit i.e. 2 byte.
Axn Ayn Azn Gxn Gyn Gzn Tn
The first row corresponds to Ax1, Ay1, Az1, Gx1, Gy1, Gz1 and T1 values of IMU 1. In General, nth row
corresponds to the nth IMU.

23
Calibration Compensation:
The MEMS based IMUs used in the Pedestrian Navigation System (Osmium MIMU22BT) are generally not
calibrated before the fabrication process. Also imperfections in fabrication process and packaging results in
errorsin the sensitivity axes of the sensors present in the IMU.Calibration is required to be performed in order
to compensate for these errors.
The most popular method in literature for calibration is the usage of mechanical platforms to place the sensor
at accurate orientations and at known angular velocity values. The output of the sensors is compared with a
known force value which is applied as input. For a perfect sensor both the input force given and the output
measured should be the same. But due to observable and unobservable errors there is deviation in the
measured value. The accuracy of this platform is high but its cost exceeds the cost of an IMU.
A novel low cost calibration algorithm was then proposed by et al. (Skog 2009) by using a platonic solid
Icosahedron. The observable error parameters that can be estimated by this procedure are sensor gain, sensor
bias, non-orthgonality of sensitivity axis and Inter IMU misalignment. Since twelve parameters are required to
be estimated the IMU needs to be placed in atleast twelve different orientations. Using an icosahedron has
two advantages. One is it provides the maximum number of sides in a polyhedron. The other advantage is it
provides evenly distributed orientations.
The error in the sensitivity axis and the inter IMU misalignment is due to mounting of the device in random
orientations which also depends on the surface it is mounted. Since it is unlikely to calibrate the device in all
possible random orientations, a maximum likelihood based system is proposed to solve this issue by using an
icosahedron which consists of a number of evenly distributed yet unknown orientations.
Due to this, the raw data from sensors has many errors because of factors such as sensor gain, inter IMU
misalignment, sensitivity axis non-orthogonality and bias and hence the device requires calibration to
compensate for these errors in order to obtain accurate data from the sensors.
Sensor Model:
The IMU used in the device MIMU22BT is Invensense’s MPU9150. The IMU has nine degrees of freedom which
are accelerations from accelerometer, rotations from gyroscope and magnetic field from magnetometer. The
accelerometer measures acceleration in three dimensions as Ax, Ay, Az and similarly the gyroscope measures
rotations in three dimensions as Wx Wy Wz in the three sensitivity axes. The accelerometer can be digitally
programmed to measure ±2g, ±4g, ±8g, or ±16g m/s
2
and the gyroscope can be digitally programmed to ±250,
±500, ±1000, or ±2000 degrees per second. The sensor axes should be orthogonal to each other ideally. But
due to the reasons mentioned above there is a slight misalignment as represented below.

24
In MPU9150, the Gyroscope is assumed to be free of all the errors except the Inter IMU misalignment which
occurs either during packaging of the sensor inside the IMU or when mounting the sensor on the MIMU
platform and bias. For accelerometers the calibration parameters are required to be estimated are sensor gain,
inter IMU misalignment, sensitivity axis non-orthogonality and bias.
The first step is to make sure that the three axes of a single IMU are orthogonal to each other before other
errors such as gain, bias or Inter IMU misalignment can be taken care of.
Because of this non-orthogonality, the accelerometer measurements in sensor’s frame are required
transformed to accelerometer measurements in navigation frame.
An = . Ai
An - Accelerometer measurements in navigation frame
Ai - Accelerometer measurements in sensor’s frame
=
1 −
1 −
− 1
Eliminating non-orthogonality requires the assumption that one of the axes of the sensor is aligned with the
same axis in the navigation frame.
Therefore the yn axis lying in the plane spanned by xi and yi and , , become zero. In the figure
described below x-axis is assumed to aligned between both the frames. Here xi, yi, zi, refer to the
accelerometers in X,Y and Z directions respectively in the frame of the sensor and xn, yn zn refer to the
acelerometers in X,Y and Z directions respectively in the navigation frame.

25
Following this, misalignment of Y-axis of the sensor can be calculated with respect to the X-Y plane of the
navigation frame. So, the Y-axis sensor will have components in both the X and Y axes of the navigation frame.
This X- axis component is added to the true force measurements in X-axis.
The misalignment in Z –axis is now calculated by projecting the value of Z-axis sensor in the X-Y plane and
measuring its components in both the X and Y axes. These two components now contribute to the true force
measurements in X and Y axes respectively.
In formulating the compensated acceleration equations, the misalignments in X, Y and Z axes between sensor’s
frame and navigation frame is assumed to be very small. Hence the compensated acceleration equations do
not have misalignment components about the same axis.
=
1 −
0 1 −
0 0 1
These equations clearly suggest that the X-axis acceleration depends on contributions from Y and Z axes true
force measurements which are evident from the methodology discussed above. Similarly the Y-axis
acceleration depends on contribution from Z axis true force measurements.

26
The calculation of Inter IMU misalignment axis requires choosing one of the IMU’s axes as the reference axis.
The remaining IMUs are calibrated based on this reference axis. Recalling the calibration methodology
followed, the only input to the accelerometer sensors is the gravity vector since the sensors are placed on a
table. The value of gravity vector in X,Y and Z directions in the reference IMU is measured and then the same
measurements are carried out in the remaining IMUs. By finding the deviation in X,Y and Z acceleration values
in comparison with the reference IMU, the Inter IMU misalignment is compensated.
=
1 −
− 1
− 1
, ` , refer to the misalignments in X, Y and Z directions of a jth IMU in comparison with the reference
IMU. Rij refers to the 3x3 rotation matrix representing the orientation between the ith and jth IMU chosen.
Following this, the individual gains in all the three axes are multiplied and then any calculated bias in the three
accelerometer axes are added or subtracted depending on its value.










±




















=










Bz
By
Bx
Az
Ay
Ax
Kz
Ky
Kx
Az
Ay
Ax
00
00
00
Here Kx, Ky and Kz refer to the gains of accelerometer in X,Y and Z axes respectively and Bx, By and Bz refer to
the bias of accelerometer in X, Y and Z axes respectively. Ax, Ay and Az on the left hand side refers to the final
compensated values of accelerations in X, Y and Z axes respectively.
The overall process can be summarised by the following equations.
Ai= K
i
(Li)
-1
An +b
i
where K
i
represents Gain, Li represents Non-orthogonality, represents Inter IMU misalignment, b
i
represents
bias , Ai and An represent Accelerometer measurements in sensor’s frame and navigation frame respectively.
(Note that An = . Ai and thus the inverse).
Here L
i
is dependent only on the mounting which is done physically whereas K
i
and b
i
are dependent on
variation in temperature in addition to the physical mounting.

27










−










=
Az
Ay
Ax
Yz
Yy
Yx
X
Here Yx,Yy and Yz are the known force measurements that are input to the IMU. The error value measures the
difference between the uncompensated and compensated acceleration output. This is calculated for all the
IMUs in 20 different orientations. The resultant matrix is of size No of IMUs * orientations *3 x 1. Then it is fed
into a non-linear equation solver with the initial guess value of unity gain and zero non-orthogonality, bias and
Inter IMU misalignment in the same order. The measured force from accelerometer should have been
independent of the orientation in which the IMUs are placed and should always be equal to the input force it is
subjected to. Hence the value of X serves as a cost function in calibrating the IMU.
The non-linear square equation solver takes the matrix of size No of IMUs * orientations *3 x 1 such that it is
of the form = 1 2 … " #
This cost function contains many local optima and if the summation has
to converge to the true parameters it must be initialised with the Initial Guess
Matrix.$ = 1 1 1 0 0 0 0 0 0 0 0 #
in which each parameter refers to
% & & & ' ' ' (
#
The initial guess matrix makes sure that the result
of non-linear equation solver converges to global minima. It contains unity gain and zero non-orthogonality,
bias and Inter IMU misalignment in X, Y and Z axes respectively when read from left to right. The value of initial
guess matrix is set from the datasheet of the IMU MPU-9150. The scaling factor is less than 3% (unit gain), The
bias is ±2 m/s
2
,non orthogonality is 0.5 % and Inter IMU misalignment is assumed to be close to zero as it is
dependent only on errors due to physical mounting.
)(
222
2
2
21minmin xnxxX K++=
θθ
∑∑= =
=
M
i
N
j
est X
1 1
2
2
minθ
θ
M represents total number of orientations, N- total number of IMUs , $ -Initial Guess Matrix $)*+ –Result of
Non- Linear Equation Solver which contains calibration parameters in the same order as Initial Guess Matrix.
The result of this non-linear equation solver is a matrix in the same form as initial guess matrix. Once these
parameters are estimated they can be put into the following matrices.
, =
& 0 0
0 & 0
0 0 &
=
1 −
0 1 −
0 0 1
=
1 −
− 1
− 1
' = ' ' ' #
Calibration Matrix:
The calibration matrix used for compensating the errors in gain, non orthogonality of sensitivity axis and inter
IMU misalignment is of size 32x18.

28
















]17][31[]1][31[]0][31[
]17][1[]1][1[]0][1[
]17][0[]1][0[]0][0[
CCC
CCC
CCC
LL
MOMM
MOMM
LL
LL
All the values in the matrix help in compensating for the errors in accelerometer and gyroscope readings.
Each row in the matrix can only correct the value of a particular IMU. The first nine elements in all the rows
correct the accelerometer readings and remaining nine elements correct the gyroscope readings.
The first nine elements of an mth row where m is the IMU under consideration are generated using the
formula below
- 1: 9 = , 0 12
K
i
, L
i
, E
i
represents the gain, non-orthogonality and Inter-IMU misalignment repectively,where K
i
L
i
E
i
represents the matrix multiplication of the matrices K
i
, L
i
, E
i
in the same order and R is a 3x3 identity matrix if
the IMUs are placed on the top of the board and a 3x3 matrix of the form
0 −1 0
−1 0 0
0 0 −1
if the IMUs are
placed on the bottom.
The remaining nine elements of an mth row is generated by the formula below
- 10: 18 = 0 12
The resultant matrix is scaled by the value 32768 to convert it into a 16 bit number so that it can be multiplied
with the raw inertial readings. This is because each raw inertial reading has a size of 2 bytes.
The accelerometer readings are then corrected in the following manner.
[ ] [ ]










=
]8][[]7][[]6][[
]5][[]4][[]3][[
]2][[]1][[]0][[
nCnCnC
nCnCnC
nCnCnC
FzFyFxAzAyAx
Here Ax,Ay,Az refer to the corrected values of acceleration and Fx,Fy,Fz refer to the raw inertial readings of the
accelerometer. In the 3x3 matrix defined, each element is taken from the calibration matrix. The value of n
varies depending on the IMU chosen for calibration.
The following equation corrects the values of gyroscope readings.
[ ] [ ]










=
]17][[]16][[]15][[
]14][[]13][[]12][[
]11][[]10][[]9][[
nCnCnC
nCnCnC
nCnCnC
gzgygxGzGyGx

29
Here Gx,Gy,Gz refer to the corrected values of rotation and gx,gy,gz refer to the raw inertial readings of the
gyroscope. The defined 3x3 matrix again takes the remaining values from the calibration matrix.
Fusion:
The corrected values of accelerations and rotations from different IMUs are fused into a single entity by
calculating simple moving average of acceleration and rotation values in the three axes.
n
AnA2........A1
Aavg
+
=
n
GnG2........G1
Gavg
+
=
Aavg and Gavg refer to the fused value of acceleration and rotation in a particular axis respectively.
Bias Compensation:
Following fusion, bias compensation takes place where the mean values of accelerometer and gyroscope bias
is subtracted from the fused values of acceleration and rotation respectively.
Ax= Aavgx- Abx Gx= Gavgx-Gbx
Ay= Aavgy-Aby Gy= Gavgy-Gby
Az= Aavgz-Abz Gz= Gavgz-Gbz
Here Aavgx , Aavgy , Aavgz, Gavgx, Gavgy, Gavgz refer to the fused values of accelerations and rotations in x,y and z axes
respectively, Abx,Aby,Abz,Gbx,Gby,Gbz refers to the mean value of accelerometer and gyroscope biasin x,y
and z axes respectively. Ax,Ay,Az, Gx,Gy,Gz refer to the bias compensated values of acceleration and rotation
in x,y and z axes respectively.
These are the required values of acceleration and rotation on which processing happens through the use of
navigational algorithms to get the final values of displacement and heading change.

30
8. Implementation:
The previous sections on hardware and software provide sufficient background to complete the objectives set.
This chapter describes the evaluation of the objectives by summarizing the implementations carried out.
Varying number of IMUs:
Varying the amount of IMUs on board gives the user ability to check their performance individually or in
different combinations. The device currently performs bias compensation after fusion occurs. That is the bias is
compensated over averaged data. This would require the user to perform calibration every time if he/she
wishes to vary the amount of IMUs on board. To overcome this tedious process the Embedded software has to
perform calibration compensation individually for all IMUs before fusion. Also flexibility should be provided to
the users so that they will be able to choose any of the four IMUs in all different combinations. The command
supports a maximum of 32 IMUs which are the highest in the Osmium series.
Taking all these factors into account and the knowledge of the communication protocol, a command was
created to control the data read from the IMUs. Also a calibration script was created to generate a calibration
matrix suitable for compensating all the errors in the IMUs individually before fusion. Correspondingly the
application platform was enhanced to facilitate the user to choose the number of IMUs without which
implementation would just be a prototype. The application platform here refers to an Android powered device
with a minimum version of 1.1.

31
9. Experimental study:
Experiments were conducted on the foot mounted pedestrian navigation system Osmium MIMU22BT based
on the standard performance metrics used in the industry for analyzing the reliability of the device. For this
purpose the experiment was designed based on four main parameters which are the type of shoe that the
device is mounted on, type of surface the experiments were conducted, type of the path profiles used and
different speeds of motion during the experiment. The data from the device after processing is sent to the
Android application (DaRe) which then filters and displays the position values in terms of X, Y and Z co-
ordinates. Besides the application also captures the time taken, average speed and the distance covered by
the user and store it in a text format.
Design of the experiment: Path Profile:
Type of Shoes: Running and Formal Shoes
Type of Surface: Pavement and Grass
Type of motion: Fast (~5.8Kmph), Medium (~4.5Kmph) and
Slow (~3.5Kmph)
The chosen standard performance metrics are:
1. Distance between start point and end point per 100m meter distance covered
2. Distance measurement error (RMS) per 100m distance covered
3. Change in z axis value (RMS) per 100m distance covered
Images from left to right (Above): Formal Shoe, Running Shoe, DaRe Application. (Below) Real time tracking
using Rectangular and Straight Paths respectively, Test case as viewed from Google Maps
Rectangular Field Straight Path
Perimeter-129m Length-26m
Closed loop Path Sharp U turns
3 laps 2 laps
Total distance- 387m Total distance- 104m

32
Results:
Sample tracking data obtained from the device (above) and Graphs plotted based on the experimental
results (below)
Observations:
1. Errors in X-Y axes are independent of errors in Z-axis. The accumulation in Z-error is higher than the
distance and drift errors because the Z-axis accelerometer is not at par in performance when
compared to X-Y axes as fabrication of Z- axis accelerometer inside the MEMS IC is tedious [3].
2. Less Z-axis errors are observed while walking on pavement compared to on grass. The distance and
drift errors are comparable in both the cases.
3. A formal shoe performs better compared to a running shoe. As running shoes are designed for the
user to be in motion continuously at a higher speed, the heels are elastic in nature and do not provide
firm footing with the ground. Conversely a formal shoe provides the same at every step as it is meant
for walking.
-10
-5
0
5
10
15
20
25
30
35
40
45
-30-25-20-15-10 -5 0 5 10
Rectangle
-3
0
3
6
9
12
15
18
21
24
27
-5 0 5 10 15 20
Straight
0
1
2
3
4
Z-error Distance Drift
Shoe Running shoe
Formal shoe
0
1
2
3
4
Surface Pavement
Grass
0
1
2
3
4
Z- error Distance Drift
Path profile Rectangle
Straight
0
2
4
6
Speed Slow
Medium
Fast

33
4. The walking speeds indeed matter as at a higher walking speed the device does not have ample time
to sense Zero-Velocity. In ZUPT algorithm errors are corrected only when step is detected. In spite of
that, the drift error is almost the same for all walking speeds. This proves that even though error is
accumulated till the detection of next step, the presence of an on board floating point 32-bit
processor, Multiple IMUs and the static calibration performed helps in better dead reckoning.
5. The device performs best at a medium walking speed as the algorithm is tuned on the device for this
speed. Higher the mounting position, higher is the velocity detected as in the case of running shoes. If
the threshold velocity of step detection is increased better results will be observed for fast motion
whereas it degrades for slower motion.

34
10. Conclusion:
The knowledge of communication protocol was crucial in carrying out the implementations in Embedded
software. The integration with the application platform (Android) also provides the ease of use from the end
user’s perspective to incorporate varying amount of IMUs on board. Currently, data from the IMUS is fused by
means of a simple moving average and the averaging factor is dependent on the number of IMUs selected by
the user. Experimental study was indeed required to verify the implementation. It was also done to benchmark
the performance of the device under various conditions by taking into account the parameters that directly or
indirectly affect the tracking output data. The implications of these results discussed in Chapter 9 help us draw
valid conclusions from the derived data.
The device was programmed in Atmel Studio 6.2 using a custom made JTAG programmer at GT Silicon Pvt Ltd
and the application platform was designed using Eclipse IDE.

35
11. References:
1. Atmel,”32-bit AVR Microcontroller”,AT32UC3C datasheet, Oct. 2010 [Revised January.2012]
2. InvenSense, “MPU 9150 Product Specification”, PS-MPU-9150A-00 [Revised September. 2013]
3. InvenSense, “MPU 9150 Register Map and Descriptions”, RM-MPU-9150A-00[Revised September.
2013]
4. John-Olof Nilsson “ZUPT aided INS software components for an embedded platform”sourceforge.net,
Nov. 11, 2011. [Online]. Available: http://sourceforge.net/projects/openshoe/
5. I2C info – I2C Bus, Interface and Protocol [online], Available:http://i2c.info/
6. John-Olof Nilsson, “Communication Protocol for the open shoe modules”openshoe.org, Jan.30, 2015.
[Online]. Available: http://www.openshoe.org/wp-
content/uploads/2015/01/OpenShoe_communication_protocol.pdf
7. Oliver J. Woodman. An Introduction to inertial navigation. Technical Report. University of Cambridge,
UK, Computer Laboratory, August 2007.
8. Frequently Answered Questions, Inertial Elements, [online] 2012,Available:
http://www.inertialelements.com/faq.php
9. GPS Accuracy, GPS.GOV,[online] 2014, Available:
http://www.gps.gov/systems/gps/performance/accuracy
10. Foot Mounted INS for every foot, Open Shoe, [online] 2011,Available: http://www.openshoe.org/
11. John-Olof Nilsson, Amit K Gupta, Peter Handel, "Foot mounted inertial navigation made easy”. In Proc
Indoor Positioning & Indoor Navigation (IPIN), Busan, Korea, 2014.
12. Mathiassen, K., Hanssen, L. and Hallingstad, O. (2010): “A Low Cost Navigation Unit for Positioning of
Personnel After Loss of GPS Position”, Proceedings of the 2010 International Conference on Indoor
Positioning and Indoor Navigation (IPIN), September 15–17, 2010, Campus Science City, ETH Zurich,
Switzerland.
13. Nilsson, J.O., Skog, I. and Händel, P. (2010): “Performance Characterisation of Foot-Mounted
ZUPT-Aided INSs and Other Related Systems”, Proceedings of the 2010 International Conference on
Indoor Positioning and Indoor Navigation (IPIN), September 15–17, 2010Campus Science City, ETH
Zurich, Switzerland.
14. Skog, I., Nilsson, J. O. and Händel, P. (2010): “Evaluation of Zero-Velocity Detectors for Foot-Mounted
Inertial Navigation Systems”, Proceedings of the 2010 International Conference on Indoor Positioning
and Indoor Navigation (IPIN), September 15–17, 2010 Campus Science City, ETH Zurich, Switzerland.
15. Wan, S. and Foxlin, E. (2010): “Improved Pedestrian Navigation Based on Drift-Reduced MEMS IMU
Chip”, Proceedings of ION 2010 International Technical Meeting, January 25–27, 2010,San Diego,
California, USA, pp. 365–374.
16. J.-O. Nilsson, I. Skog, P. Handel, and K. Hari, “Foot-mounted INS for everybody – An open-source
embedded implementation,” in Position, Location and Navigation Symposium (PLANS), 2012
IEEE/ION, (MyrtleBeach, SC, USA), 23-26 Apr. 2012.
17. J.-O. Nilsson, I. Skog and P. Handel, “Aligning the forces – Eliminating the misalignments in IMU
Arrays” Instrumentation and Measurement, IEEE Transactions on , vol.63, no.10, pp.2498 —
2500, 2014

36
18. I. Skog and P. Handel, “Calibration of a MEMS Inertial Measurement Unit” XVII IMEKO World
Congress, pages 1-6, 2006.

Foot Mounted Pedestrian Navigation Systems

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