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1 MASARYK UNIVERSITY FACULTY OF INFORMATICS }w!"#$%&'()+,-./012345<ya Positioning system for small devices using principles of inertial navigation system MASTER S THESIS Martin Veškrna Brno, 2013

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3 Declaration Hereby I declare, that this paper is my original authorial work, which I have worked out by my own. All sources, references and literature used or excerpted during elaboration of this work are properly cited and listed in complete reference to the due source. Advisor: RNDr. Zdeněk Matěj iii

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5 Abstract Inertial navigation is a technology which is able to track the position without the communication with any external systems. Its disadvantage is increasing inaccuracy with time of operation. This work integrates the inertial navigation and GPS to trace the device not only in an open space where the GPS signal is available. The GPS is used to track the device position in an open space and when the GPS signal is lost, the inertial navigation continues computing the position based on the force applied to the device. Keywords: INS, inertial navigation, GPS, MEMS, accelerometer, gyroscope, magnetometer v

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7 Contents 1 Introduction Navigation Principles GNSS (Global Navigation Satellite Systems) GPS (Global Positioning System) Inertial Navigation System Reference Frames Inertial System Configurations Stable Platform System Strapdown System Strapdown Attitude Representation Euler Angles Direction Cosine Matrixes Quaternions Gimbal Lock Attitude Computing Based on Gyroscope Output Tilt Computing Using Accelerometer Error Propagation Components for INS Construction Gyroscopes Conventional Sensors Other Types of Gyroscopes Accelerometers MEMS Technology MEMS Gyroscopes MEMS Accelerometers Calibration Compass Calibration Hard Iron Material Soft Iron Material Calibration Process Tilt Compensated Electronic Compass Align the Axis Accelerometer and Gyroscope Calibration Bias Scale Factor Axis Misalignment and Cross-Axis Sensitivity Accelerometer Calibration Gyroscope Calibration Requirements for equipment and Component Selection Requirements vii

8 5.1.1 Price Size Power Consumption Temperature Range Calibration INS Data Accurate Computing Position Obtained Using INS - Usable Time Component Selection Accelerometer Gyroscope Electronic Compass Voltage Regulator GPS Module UART/USB Transceiver Microcontroller Communication Interfaces Debugging Power Consumption Selected Microcontroller Summary Table Device for Data Acquiring Device Construction Firmware Detection of New Sample Data Acquiring from Sensors Using I 2 C GPS Serving Data Transferee to Computer Statistics Testing and Capturing Application Data Capturing and Internal Storing Data Visualization Gyroscope Data Visualization Accelerometer Data Visualization Magnetometer Data Visualization Statistics Calibration Assistance Data Saving Signal Processing Basic Schema of Data Processing File Loading Raw Data Calibration Tilt Computing (Roll and Pitch Angle) Fusion Algorithm Yaw Computing Position Computing Fusing GPS and Inertial Navigation System On-line Calibration viii

9 7.8.1 Gyroscope Calibration Accelerometer Calibration Testing and Results Results Gyroscope Calibration Accelerometer Calibration INS Error Comparing to Other Existing Devices Possible Future Improvement Sending Data via GSM Kalman Filtering INS/eCompass Fusing Algorithm Attitude Restriction and Representation Summary Bibliography A The Device B Testing and Capturing Application C Included Materials ix

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11 Chapter 1 Introduction Imagine the situation in which the small expensive device is situated at the place, where it is very complicated to protect it against the robbery. It is possible to track the device using the GPS, but when the robber walks into the building, the GPS signal will lose. The inertial navigation system (INS) is the technology which is able to track the device without communication with outer systems like GPS. It measures the force acting on the device and then computes the position. The position can be sent to the user via mobile phone (GSM). The first aim of this work is construct the prototype of device which includes GPS and inertial navigation system to track the position also in places where the GPS signal is not available. While the GPS signal is available, it will be used to position obtaining. At the moment when the GPS signal lost, the position will be computed using inertial navigation. The second aim is discussion about the way how to send the signal from sensors over the large distance and therefore make the device autonomous (chapter 9.1). The inertial navigation system consists of gyroscopes and accelerometers. Gyroscopes measure the attitude of the device (tilt and heading). The accelerometers measure the force acting on the device. Based on the attitude obtained using gyroscopes, this force is projected into the global coordinate system and then double integrated to compute the position of the device. Because of there are three consecutive integration (the first is when the attitude is computed from the gyroscope signal) the error in the result is propagated to the third power (chapter 2). The basic requirements for the device are low price, small size, low power consumption and wide temperature range. Therefore the INS sensors based on MEMS technology (Micro-Machined Electromechanical System) were selected. This technology satisfies all requirements, but the accuracy is the worst of all technologies. The calibration process used in this work do not use any external equipment. (chapter 3, 4 and 5.1). The signal from sensors is transmitted using the microcontroller into the computer where the off-line algorithm is implemented to compute the position. The communication protocol from the microcontroller to the computer is designated to easy change the communication through GSM to the computer (chapter 6). The off-line position algorithm consists of several steps. The first is attitude computing where the fusing of gyroscope, accelerometer and electronic compass signal is used to eliminate the gyroscope error propagation. Secondly, the initial position and velocity is determined using GPS. Then the acceleration applied to the device is double integrated to track the position (chapter 7). Two calibration procedures are used to eliminate the sensor errors. The first is provided during manufacturing the device and it does not need any tool or do any precious maneuvers. The second one is on-line calibration provided during the position computing. It is necessary because of the aging the sensors and temperature changing (chapter 7.8). 1

12 1. INTRODUCTION The last chapter of this work describes the possible expansions. There are described sending signal from sensors through GSM, Kalman filtering, better attitude representation and better INS / ecompass fusing algorithm (chapter 9). 2

13 Chapter 2 Navigation Principles They [13] describe five types of navigations: 1. Pilotage. It is based on landmark recognizing to know where you are and how you are oriented. The animals use this type of navigation, it is older than humankind. 2. Dead reckoning. The starting point is known and the next position is estimated based on the heading information (azimuth) and estimate of speed. 3. Celestian navigation. It uses time and the angle between the local vertical and the known celestian objects (moon, sun, stars, etc.). Then the longitude and latitude are computed. 4. Radio navigation. It relies on some radiofrequency sources with known positions. Then the time to receive signal is measured and the position is computed. This type of navigation includes Global Navigation Satellite Systems (GNSS) too. 5. Inertial navigation. The initial position, speed and attitude (tilt and heading) are known. Then the attitude change and acceleration is measured. It is the only form of navigation that does not rely on external references. This work is based on the fourth and the fifth principles which will be described in the next chapters. 2.1 GNSS (Global Navigation Satellite Systems) It is based on radio navigation and uses satellites on orbit, control station and user receivers. Today (year 2013) there are four GNSS. The first Global Position System (GPS) was built by the U.S. Department of Defense. The second was Global Orbiting Navigation Satellite System (GLONASS), placed in orbit by the former Soviet Union. The Galileo (being built by European Union and European Space Agency) and Compass (Chinese satellite navigation system) are currently under construction. The principles of operation of all systems are similar, and then the most used GPS system will be described GPS (Global Positioning System) The space segment consists of 24 to 32 satellites which contains atomic clock to very accurate time measurement. The radio communication is realized on frequencies which are low influenced by meteorological phenomena. Satellites communicate between themselves, with users and the control segment. There are from 6 to 12 visible satellites above the Czech Republic. 3

14 2. NAVIGATION PRINCIPLES The control and monitoring system consist of stations whose positions are accurately known. It computes satellites position and synchronize atomic clock. In case the ground stations will be destroyed, the space segment could work up to 6 month independently. The user segment uses receivers that compute a position based on received values from the space segment. Users are divided into 2 basic groups. Authorized users (mainly from the army) have guaranteed higher accuracy to the unit centimeters. Unauthorized users (public) use a precision of unit meters. The user receives the information from each satellite that includes the sending time and the position of the satellite. Ideally values from three satellites is necessary, but the clock in the receiver is not as accuracy as in satellites. Then values from four satellites are used to compute the user position. R = (X r X s ) 2 + (Y r Y s ) 2 + (Z r Z s ) 2 + c δ r (2.1) R - the distance between receiver antena and satellite X s, Y s, Z s - satellite position X r, Y r, Z r - receiver antena position δ r - receiver clock skew c - velocity of light The accuracy of GPS is affected by atmosphere phenomena, clock accuracy in receiver, number of visible satellites and many others. To predict the atmosphere influence (specifically the ionosphere) to radio signal, the almanac is provided by satellites. To receive radio signal from satellites and compute the user position, the GPS modules are made. They communicate with user using NMEA protocol, see [21]. It defines a few sentences including actual position, speed, time, accuracy of position, number of visible satellites and information about them. 2.2 Inertial Navigation System There are a lot of situations where it is not possible to communicate with satellite navigation system or recognize landmarks to determine the position. The inertial navigation system (INS) is a self-contained navigation technique in which the measurement of force acting on the device is used to track its position. Let r(t) is the position vector of the tracked device. I except the three dimensional coordinate system which is fixed, non-rotating and non-accelerating. Then the device velocity v(t) and acceleration a(t) can be computed as: v(t) = d (r(t)) (2.2) dt a(t) = d2 (r(t)) (2.3) dt2 Acceleration can be measured by triad of orthogonally oriented accelerometers. The accelerometers output vector consists of force vector f acting to the device and gravity vector g. d 2 (r(t)) = f + g (2.4) dt2 4

15 2. NAVIGATION PRINCIPLES Reference Frames These equipments 2.2, 2.3 and 2.4 expect that the coordinate system of accelerometers (body frame or b-frame) is the same as the global frame (or n-frame, navigaional, reference frame) where axis are aligned with of directions of north, east and down. Due to the rotation of the device the alignment of accelerometer body frame is not same as the global frame. Then the attitude of the device is necessary to measure and then convert coordinate systems. It is possible to use a gyroscopes. The Earth rotates around its axis, then the global frame is rotated and then there is a Coriolis force. Sensors used in this work are not capable to measure this force. Therefore I expect non-rotating and fixed global frame Inertial System Configurations Nearly all the Inertial Measurement Units (IMU, consist of accelerometers and gyroscopes) can be divided into two basic categories. The difference is reference frame in which the gyroscopes and accelerometers work Stable Platform System The accelerometers are mounted on platform which is isolated from all external rotational motions. It means the platform is aligned witch global reference frame. It is achieved using gimbals which allow platform freedom in all three axes. The platform mounted gyroscopes detect rotation movement and the signal is propagated to the torque motors which rotate the platform to keep it aligned witch the global frame. Figure 2.1: Stable platform system, taken from [26] The device orientation can be read by the angle pich-off. To calculate the position of the device the signal from accelerometers are double integrated. Note the acceleration due 5

16 2. NAVIGATION PRINCIPLES to gravity is necessary subtract from the vertical channel before integrating. Figure 2.2: Schema of stable platform system, taken from [24] Strapdown System In strapdown systems the inertial sensors are rigidly mounted onto the device and therefore the accelerometer output is measured in the body reference frame. The gyroscopes provide the actual orientation of the platform and the accelerometer output is converted from body to global reference frame using microcontroller. Then the signal processing is same as in case of the stable platform. The advantage of strapdown system is reducting mechanical complexity and then tends to be physically smaller than the stable platform. Figure 2.3: Schema of strapdown platform system, taken from [24] 6

17 2. NAVIGATION PRINCIPLES Strapdown Attitude Representation The device is free to rotate about all directions. There are three basic types of rotation representations, the Euler angles, direction cosine matrixes and quaternions. It is possible to convert these representations from one to another, but there can be same numerical instability, see [24] Euler Angles The coordinate system is orthogonal and right-handled axis set. The positive rotation along each axes are taken to be in a clockwise direction looking along the axis from the origin as illustrate Figure 2.4. The change or attitude of the device body is not only the function of the angle through which it rotates about each axes, but the order in which the rotation occurs. See chapter 3.6 in [24]. Therefore the sequences of rotations are defined. To rotate the device from global reference frame to body reference frame is the sequence Oxyz (first roll angle, then pitch angle and last yaw angle). The reverse rotation from body reference frame to global frame is defined sequence Ozyx. Figure 2.4: Euler angles, taken from [24] Direction Cosine Matrixes A transformation from one reference frame to another can be carried out as three successive rotations about different axis. One Euler angle corresponds to each axis and the order of rotation is Oxyz or Ozyx. The first one is used to transferee coordinates from global to body frame and the second one to opposite direction. These three rotations can be expressed as matrixes cos ψ sin ψ 0 C 1 = sin ψ cos ψ 0 (2.5) cos θ 0 sin θ C 2 = (2.6) sin θ 0 cos θ 7

18 2. NAVIGATION PRINCIPLES C 1 - rotation ψ about z-axis C 2 - rotation θ about y-axis C 3 - rotation φ about x-axis C 3 = 0 cos φ sin φ (2.7) 0 sin φ cos φ And these separate transformations may be expressed together. The transformation from global to body frame is C b n = C 3 C 2 C 1 (2.8) And the transformation from body to global reference frame is Quaternions C n b = CT 3 C T 2 C T 1 (2.9) The quaternion representation is based on four parameters. The idea is that the transformation from one reference frame to another can be effected by one rotation about vector m. This vector m is defined with respect to the global reference frame. The quaternion is a four parameter vector µ x, µ y, µ z - the components of angle vector µ - the magnitude of m a cos(µ/2) q = b c = (µ x /2) sin(µ/2) (µ y /2) sin(µ/2) (2.10) d (µ z /2) sin(µ/2) The quaternion with components a, b, c, d can be expressed as a complex number with real part a and imaginary components b, c and d. Vector r b = (x, y, z) in body frame can be expressed as And then converted to global frame using q = a + ib + jc + kd (2.11) q = 0 + ix + jy + kz (2.12) Where q = (a ib jc kd) is the complex conjugate of q Gimbal Lock r n = qr b q (2.13) It is the lost of one degree of freedom in three-dimensional space. It occurs when two axes are driven into a parallel configuration. Then only a two-dimensional rotation is possible. If the rotation is expressed using Euler angles, gimbal lock occurs when the pitch angle is 90 or -90 degrees. If the quaternions are used, gimbal lock does not occur. 8

19 2. NAVIGATION PRINCIPLES Attitude Computing Based on Gyroscope Output Strapdown gyroscope output signal is angular speed, not the attitude of the device. Therefore it is necessary to compute attitude using integration of angular speed with knowing the initial attitude. Note the gyroscope output is measured in body reference frame, but the attitude of the device is in global frame. The second-order numerical integration algorithm uses a quaternion to attitude representation and the next state is related to the previous state. 0 σ x σ y σ z Σ = σ x 0 σ z σ y σ y σ z 0 σ x (2.14) σ z σ y σ x 0 q k+1 = e (Σ/2) q k (2.15) σ x, σ y, σ z - angular velocity in body reference frame (output signal from strapdown mounted gyroscopes) Tilt Computing Using Accelerometer When the device do not move, only the gravity is measured by the accelerometer. Then the angle roll and pitch can be computed using [20] tan φ = G y G z (2.16) tan θ = G x G 2 y + G 2 z (2.17) G x, G y, G z - accelerometer output φ - roll angle θ - pitch angle These equations are based on direction cosine matrixes and the numerical instability occurs if the G z is near zero Error Propagation The angular speed obtained from the gyroscope is integrated to get the attitude of the device. Then it is used to project the acceleration to the global reference frame, and then double integrated to compute the position. Errors in angular velocity cause a drift in attitude computing. An error in orientation causes an incorrect projection of the acceleration into the global reference frame. It causes two problems. Firstly, the acceleration is integrated in wrong direction and secondly, the gravity is not correctly removed from the vertical component of acceleration. Assume the ideal alignment of accelerometer body frame to global reference frame. Let the accelerometer measurement is a + ε, where the a is acceleration and ε is the error. When the device initially do not move, the position s in time t is s = (a + ε)t 2. (2.18) 9

20 2. NAVIGATION PRINCIPLES Assume the accelerometer which measurement range is ± 2 g and and the calibration is done with error 0.1%. It means the measurement is provided with error ε = ±( )m s 2 = ± m s 2 where g = 9.81m s 2 is gravity constant. Figure 2.5: Accelerometer error propagation, ε = m s 2 (author) 10

21 Chapter 3 Components for INS Construction The INS needs two types of sensors. The first are gyroscopes which measure the angular velocity and then the attitude of device can be computed. The second sensors are accelerometers which measure the linear acceleration acting on the device. 3.1 Gyroscopes Gyroscopes are used to sense angular turn or angular rate about some axis. There will be described some principles used to gyroscope construct Conventional Sensors These types of gyroscopes make use of the inertial properties of a wheel spinning at high speed. The spinning wheel tends to maintain the direction of its spin axis in space and defines the referent direction. Gyroscopic inertia is fundamental to the operation of all springing mass gyroscopes. It defines the fixed direction in space that remains fixed in the inertial reference frame. The practical construction may be designated by having the rotor supported in a set of frames or gimbals which are free to rotate. The orientation of the case with respect to the direction of spin axis may be measured with angle pick-off devices mounted on gimbals. One of the possible construction of convenctional gyroscope is illustrated in figure Other Types of Gyroscopes Vibratory gyroscopes use a vibration motion of the part of the instrument. It creates an oscillatory linear velocity. If the sensor is rotated about an axis orthogonal to this velocity, Coriolis acceleration is included. This acceleration changes the motion of the vibration element. Optical gyroscopes use an interferometer to sense angular motion. Optical gyroscopes rely upon the detection of difference between two counter-propagations beams of light in a closed path. 3.2 Accelerometers The basic principle of construction of accelerometer uses a proof mass and spring. The proof mass is situated in the case and confined only by the spring. The spring maintains the proof mass in a zero position. Then the acceleration is applied to the case, the proof mass is deflected from the zero position and the resultant spring force provides the necessary acceleration to move the proof mass in the case. For single axis accelerometer the displacement of the proof mass is proportional to force applied along the sensitive axis. 11

22 3. COMPONENTS FOR INS CONSTRUCTION Figure 3.1: Schematic diagram of 2-axis conventional gyroscope using spining wheel, taken from [24] This principle of accelerometer construction using a spring is named open-loop (figure 3.2). With a close-loop accelerometers, the spring is replaced by an electromagnetic device that produce a force on the proof mass to maintain it in its zero position. These types of accelerometers are more accurate than open-loop types. Vibratory accelerometers use a quartz technology. There are two crystals vibrating on the same frequency. When the acceleration is applied along the sensitive axis, the vibratory frequency changes and the different is measured. Other types of accelerometers technology are base on surface acoustic wave, silicon, fiber optics. 3.3 MEMS Technology Conventional inertial sensors focus on high precision, accurate, stable outputs and grate possibility of calibration. Then the price increase. MEMS (Micro-Machined Electromechanical System) uses a silicon as a base material and the manufacturing technology is the same as in the case of manufacturing of electronic integrated circuit. The most advantageous are low price, small size, rugged construction, short start-up time, low power consumption and low weight. 12

23 3. COMPONENTS FOR INS CONSTRUCTION Figure 3.2: Schematic diagram of simple one axis open-loop accelerometer, taken from [24] The MEMS integrates the mechanical sensor and the control logic into one chip. This approach simplifies and makes cheaper the development of a target application. However the size reduction gives rise in decreases sensitivity / scale factor and increasing in noise MEMS Gyroscopes MEMS gyroscopes operate on a very similar principle as vibratory gyroscopes. It means there are no any rotating parts and the Coriolis acceleration is used to detect angular rate. There is a vibrating proof mass which is the subject of linear motion. In case of the rotating axis is perpendicular to the linear vibratory motion, the Coriolis force arises (figure 3.3). This is perpendicular to both the linear vibratory motion and rotation axis. Figure 3.3: The coriolis force, taken from [24] One of the types of MEMS gyroscopes are tuning fork MEMS gyroscopes. It consists of a silicone structure above the glass substrate. There are two vibrating proof masses made from silicon anchored to the substrate at specific points. These masses are made to oscillate by outer comb motor drivers and his phase is 180. When the angular rate is applied to the sensitive axis, which is perpendicular to the velocity of the vibrating proof mass, gives rise to Coriolis force. It acts on the mass and the resulting movement is measured by air capacitor (figure 3.4). The device is made from a single crystal of silicon. The size of vibrating proof mass is 13

24 3. COMPONENTS FOR INS CONSTRUCTION around 1000 µm x 1000 µm x 20 µm, the operating frequency is around 12 khz and the amplitude of the motion of the proof mass is around 10 µm. Figure 3.4: Schematic diagram of MEMS gyroscope, taken from [24] MEMS Accelerometers It can be divided into two main classes, reflecting the manner of acceleration application to the sensing element. Pendulous MEMS accelerometers use mechanical spring. When the acceleration is applied to the case, the displacement of the proof mass is supported by a flexure of the spring. Motion is detected by the change of the gap capacitance between the proof mass and the substrate using electrodes on a substrate. Resonant MEMS accelerometers using the change in the resonant frequency of beam oscillators under inertial loading of a proof mass, rather of the measurement of the displacement. Figure 3.5: Schematic diagram of MEMS accelerometer. Left part: gap capacitor, right part: proof mass. Picture is taken from [24]. 14

25 Chapter 4 Calibration There are various types of errors affecting on sensor output. Some of these are static and can be eliminated by calibration. These errors occur during manufacturing process or soldering. In case of magnetometer there are outer disturbing magnetic fields. 4.1 Compass Calibration There are two outside interference which change the magnetometer output; the first is named hard iron and is caused by permanently magnetized materials; and the second interference is caused by non-magnetized materials and is named soft iron. Only the output from magnetometer is not sufficient to compass making. There is necessary tilt compensation; it means use the accelerometer and the magnetometer output to implement the electronic compass. Magnetometer, accelerometer and gyroscope are independent components. It is very difficult during soldering it on PCB (printed circuit board) to align their axes. Therefore calibration process has to finds coefficients to align sensors axes Hard Iron Material Hard iron material makes a additional magnetic field. It can be permanent magnets, electromagnets etc. Figure 4.1: Material creating magnetic field. On the left side, it is not placed in outside magnetic field. On the right side, it is placed in homogenous magnetic field, taken from [15] Let B p is sensor output and V is interference caused by hard iron materials. Then it 15

26 4. CALIBRATION can be removed using B = B p V (4.1) B is calibrated output and it is a vector containing three components - value in axis x, y and z Soft Iron Material B x B = B y (4.2) B z This material does not create a magnetic field, but it changes the field which in are presented. This is normally unmagnetized ferromagnetic material and in presence of outside magnetic field, it is temporary magnetized and change the global magnetic field. Figure 4.2: Disturbance of a homogeneous magnetic field caused by soft iron material, taken from [15] Picture 4.2 illustrates distortion of a homogeneous magnetic field caused by soft iron material. On the left side, there are three bars made from ferromagnetic material. On the right side, there are the same three bars in the presence of a homogenous magnetic field. The bars become magnetized by external magnetic field and steer it along their axes. Soft iron disturbance can be modeled as a six-component symmetric matrix W 1. B = W 1 (B p V) (4.3) Calibration Process The algorithm which will be described, removes both hard and soft iron together. His output is W 1 matrix and V vector. The first step is data collection in many different orientation of the magnetometer. It is not important to measure data in precise rotations. In case of the magnetometer is not presented in any hard or soft iron disturbance, the measured data lies on a sphere and the radius is the size of the magnetic induction. Because there is hard and soft iron disturbance, the measured data lies on an ellipsoid. 16

27 4. CALIBRATION The ellipsoid is centered at the hard iron offset V. The shape of the ellipsoid is determined by the soft iron. Figure 4.3: Calibrated (blue) and raw data from sensor (red), taken from [15] If we modify the equation 4.3 into B 2 = (B p V) T (W 1 ) T W 1 (B p V) (4.4) And then the equation 4.5 is the standard ellipsoid equation. const = (R R 0 ) T A(R R 0 ) (4.5) R - measured data R 0 = V - hard iron disturbance A = (W 1 ) T W 1 - determine the shape of ellipsoid The calibration process is finding parameters V and A such that the equation 4.5 is constant for all measured data. Then the matrix W 1 is W 1 = A 1/2 (4.6) For more information about calibration process, see [15] and [17]. 17

28 4. CALIBRATION Tilt Compensated Electronic Compass The accelerometer provides roll and pitch angle (tilt) which are used to correct the magnetometer output. It allows accurate computation of compass heading (yaw angle) when the magnetometer is not head flat [16]. This equation rotates the vector using direction cosine matrixes. B p = R x (φ)r y (θ)r z (ψ)b (4.7) B - the vector of magnetic field in the presence of magnetometer (global coordinate system) R x (φ), R y (θ) and R z (ψ) - direction cosine matrixes and φ, θ and ψ are Euler angles. B p - vector of magnetic field measured by magnetometer. We know that the roll and pitch angles are provided by the accelerometer. Then the B p vector can be de-rotated by φ and θ to compensate tilt. R z (ψ)b = R y ( θ)r x ( φ)b p (4.8) Equation 4.8 can be rewritten using Eqn. 2.6 and 2.7 to cos ψb cos δ cos θ 0 sin θ B px B fx sin ψb cos δ = cos φ sin φ B py = B fy (4.9) B sin δ sin θ 0 cos θ 0 sin φ cos φ B pz B fz B f - represents the magnetometer measurement after de-rotating to the flat plane where φ = θ = 0. cos δ - value of inclination of magnetic field. Then the compass heading can be computed as cos ψb cos δ = B fx (4.10) sin ψb cos δ = B fy (4.11) tan ψ = B fy B fx = B pz sin φ B py cosφ B px cos θ + B py sin θ sin φ + B pz sin θ cos φ (4.12) Align the Axis The hard and soft iron are eliminated and the compass is tilt-compensated. During the magnetometer and accelerometer soldering to PCB (printed circuit board), it is not guaranteed that their axes will be aligned. Then the tilt-compensation is not precise. If the compass heading is measured at the same place, the value of inclination will be still the same. If the accelerometer and magnetometer axes are misalignment, the inclination will be different in different rotation of compass. There is an algorithm which find direction cosine matrix to remove the axes misalignment. The first step is data acquisition. The compass lies on the flat plane and only the heading is changed by 10 degrees. The vector from magnetometer B i and accelerometer G i are acquired at each position. It means we have 36 twins of vectors. 18

29 4. CALIBRATION Then finding such matrix E where for all B i and G i the product EB i G i = cos α = const (4.13) is constant. Then the accelerometer and magnetometer axes are aligned. E - a symmetrical direction cosine matrix is a symbol for scalar product α - value of inclination 4.2 Accelerometer and Gyroscope Calibration For low-cost inertial sensors, it is not economical to build or buy expensive calibration equipment. These calibration equipments use precise movement or positioning to calibrate sensors. Because I do not have these expensive equipments, I need some calibration technique based on differential principles. I use a technique described in paper [25]. This paper presents method to compensate and calibrate bias, scale factor, axis misalignment and cross axis sensitivity of both tri-axis accelerometer and gyroscope. This method is based on Earth s gravity as a stable calibration method. The first step is accelerometer calibration using positioning into several prescribed positions. After the accelerometer is calibrated, it is used to gyroscope calibration. It is based on the comparison of the accelerometer measurement before and after the rotation based on the gyroscope data Bias Figure 4.4: Sensor error - bias, taken from [14] If there is no force acting on accelerometer or no rotation on gyroscope, the sensor output should be zero. The bias is the sensor output in this case. It can be split into static part called bias offset, a random part called bias drift and temperature varying part. [14] In case of the accelerometer, the effect of bias drift is very small but in case of the gyroscope the random part of bias is very significant. It is necessary to use special technique to eliminate the bias drift during the gyroscope operation. 19

30 4. CALIBRATION Scale Factor Figure 4.5: Sensor error - scale, taken from [14] Scale factor is a ratio of the change of the output o to the input i. As in the case of bias it can be split into three parts, static, random and temperature varying parts. Both in case of the accelerometer and the gyroscope, the effect of random scale is insignificant Axis Misalignment and Cross-Axis Sensitivity Misalignment is caused by imperfect sensor mounting on the printed circuit board. As a result, each axis is affected by measurements of other two axes in body frame. The influence of axis misalignment can be reduced using components including accelerometer and gyroscope into one component Accelerometer Calibration This technique is based on the property the magnitude of the static acceleration measured must be equal that of the gravity [25]. This is an orthogonal constraint where values measured by each axis are independent. There is a sensor error model used in this technique. a P,k = E(a S,k b a ) (4.14) e 00 e 01 e 02 E = e 10 e 11 e 12 (4.15) e 20 e 21 e 22 e 00, a 11 and e 22 - represents scale and other coefficients describe misalignment and cross-axis sensitivity b a - bias offset a S,k - noncalibrated accelerometer output a P,k - calibrated accelerometer output 20

31 4. CALIBRATION The model parameters in matrix E and vectorb a is collected in θ a to define the function h(a S,k, θ a ) = E(a S,k b a ) = a P,k (4.16) Assuming that the gravity force is the unity, the cost function for K sets of measurements is K 1 L(θ a ) = (1 h(as,k, θ a ) 2 ) 2 (4.17) k=0 Then several measurements are made in different position. There is important not to move during the measurement. Otherwise other force than gravity should acts on the accelerometer Gyroscope Calibration The most significant source of error for gyroscopic system is bias drift (random error). It can be easily measured by averaging static gyroscope signal; it means the gyroscope is not moved. However the bias drift is random over time; therefore it is not possible to predict it. There will be described the technique to calibrate the scale, misalignment and cross-axis sensitivity. The gyroscope error model is e 00 e 01 e 02 E = e 10 e 11 e 12 (4.18) e 20 e 21 e 22 The parameter s meaning is the same as the accelerometer. The calibration technique is based on property the gravity vector measured using a static tri-axial accelerometer must equal the gravity vector computed using the IMU orientation integration algorithm, which in turn uses the angular velocities measured using the gyroscopes. [25]. The first step is measuring the gravity vector u 0. Then the IMU (accelerometer and gyroscope) is rotated by prescribed angle. Finally the gravity vector u a is measured. Gyroscope output is angular velocity; then the second-order numerical integration algorithm (chapter ) is used to compute a quaternion representing the rotation. Then the quaternion is transformed to direction cosine matrix R. u a = Ru 0. (4.19) Then nine elements from matrix E is collected in form θ g. The cost function can be proposed as L(θ g ) = K 1 k=0 ua u g 2 (4.20) There is 18 prescribed movement of IMU. Then the minimum of this cost function is found. 21

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33 Chapter 5 Requirements for equipment and Component Selection 5.1 Requirements This work describes the prototype of equipment which could be constructible and salable. It is necessary to specify requirements based on real basis Price Assume that the smallest price of equipment which is profitable to observe is 500 EUR (approximately CZK). If we want to observe and find the device it is necessary to add some components. But the buyer is interested in the main equipment, not in added equipment. Then the price of added components enables observing and finding lost device should be in the order of magnitude smaller than the main device price. Then the price is approximately the same and equipment efficiency grows: it is approximately between 50 and 100 EUR (1000 and 2500 CZK) Size The device we want to observe can be smaller than a mobile phone. If the size of the additional system will be like the size of a credit card, it would be possible to observe and find devices like expensive camera, meteorological sensors, etc Power Consumption Assume the standalone meteorological sensor placed in a field. In the case of robbery, the time to the police start finding stolen device can be several days. The device has to send his position all the time Temperature Range In case of outdoor application, all the components have to be able to work at a low temperature (-40 C) and high temperature (80 C). It means all components have to operate in industrial temperature range, including batteries Calibration Due to temperature changes and aging, the calibration coefficients are changing. Because the device will work on standalone mode, the self-calibration method has to be implemented. In case of immobile application, there are limited possibilities to calibrate the device. 23

34 5. REQUIREMENTS FOR EQUIPMENT AND COMPONENT SELECTION INS Data Accurate Computing The position obtained from INS during the time lost accuracy. It is because of INS integrating the mechanical power acting on the device. The position is relevant information only if we know his accuracy. The system should compute the accuracy and display it to the user Position Obtained Using INS - Usable Time Position computing based on INS lost his accuracy in time. After some time an error is too big that the position information is not relevant. The device described in [26] has an error of 150 meters after 60 seconds sensing pedestrian movement. If the electronic compass is added and fusion algorithm used, the error decreases to 5 meters. 5.2 Component Selection The criteria listed in chapter 5.1 was used. Additional criterion is making the construction as easy as possible. It means use sensors with digital interface (accelerometer, gyroscope, compass) and difficult subsystems use as one module (GPS, GSM) Accelerometer The main criterion is price - then only accelerometers made by MEMS technology are acceptable. This type of accelerometer is used in mobile phone etc. The main parameters determining signal quality are measurement range and sensitivity. Measurement range is selected during manufacturing process by spring stiffens and mass weight. It is usual that accelerometers have more than one measurement range, typically three or four. Changing is provided by control registers. The typical sensed movement will be a walk. Signal on axis z (perpendicular to the ground) can look like on figure 5.1. The maximum signal is around 1.5 g. If the measurement range of accelerometer is from -2 g to 2 g, the sensitivity will be the highest possible. Wide measurement ranges are necessary too, for example for running sensing. In case of digital sensor, the sensitivity is determined by the number of bits of builtin analog-digital converter - existing accelerometers with 8, 10 and 12 bits AD converter. Another parameter influencing the sensitivity is noise. Other parameter determining signal quality is the zero-g level offset accuracy. It describes the deviation from ideal output signal if no acceleration is presented [22]. Consideration all parameters, chosen accelerometer is LIS331DLH made by ST Microelectronics. For more details see [22] Gyroscope The main selection criterion is price, as in the case of the accelerometer. MEMS technology is chosen. Figure 5.2 shows signal on gyroscope when pedestrian movement is captured. The range of this signal is approximately from -100 dps (degrees per second) to 100 dps. Therefore the minimal range should be ± 200 dps. It is typical that the gyroscope has more than one measurement range, like an accelerometer. 24

35 5. REQUIREMENTS FOR EQUIPMENT AND COMPONENT SELECTION Figure 5.1: Signal from accelerometer while pedestrian movement sensign on axix z which is perpendicular to the ground (author) Selected gyroscope is L3G4200D made by ST Microelectronics. For more details see [23] Electronic Compass Besides the price, the measurement range and sensitivity are the main selection criterion. They [7] show the total magnetic field intensity in the world. It is from 23µT (micro Tesla) to 66µT or from 0.23 Ga (Gauss) to 0.66 Ga. Magnetic sensor HMC5883L made by Honeywell has the lowest measurement range ± 0.88 Ga and therefore sensitivity is 1370 bits per Gauss. They [8] claims that it is possible to construct electronic compass with a 1 to 2 heading accuracy Voltage Regulator Accelerometer, compass and gyroscope are sensitive to the input voltage changing. Operational power supply is wide, for example from 2.16 V to 3.16 V in case of accelerometer [22]. But the output signal is changed with the change of power supply. Therefore accuracy of output voltage of the voltage regulator should be the highest. Accuracy of voltage regulator TLV700xx is ±2% in the whole operational temperature range (-40 to 125 C). For more information see datasheet [9] GPS Module Because the GPS is very complicated and a wide used system, there are modules processing GPS signal and providing GPS information like a position, speed, accuracy, etc. It is not necessary to compute this information from RAW GPS signal. It is expected that this constructed equipment will stay for a long time in the same place and GPS will be off. It is due to power saving. Typical cold start (the time from power on to 25

36 5. REQUIREMENTS FOR EQUIPMENT AND COMPONENT SELECTION Figure 5.2: Signal from gyroscope while pedestrian movement sensign (author) getting useable position information) of GPS module is 30 seconds. The method providing the decrease this time is named assisted GPS. Initial information about satellites (named almanac) are loaded from the internet into GPS module. For more information see [1]. GPS module L10 made by Quectel is used; it supports assisted GPS and active antenna [19] UART/USB Transceiver The easier way haw to communicate with PC is UART/USB transceiver. UART (Universal asynchronous receiver/transmitter) is usually the available microcontroller interface. The module PU232F made by Pandatron is used [18] Microcontroller Communication Interfaces The communication interface of compass is I 2 C. Accelerometer and gyroscope support both I 2 C and SPI. Baud rate of SPI is higher than I 2 C. SPI supports higher clock frequency. In case of accelerometer and gyroscope, it is 10 MHz [22], [23]. I 2 C clock frequency is supported at 100 khz (standard mode) and 400 khz (fast mode). The maximum sample rate of accelerometer is 1000 Hz, gyroscope is 800 Hz and compass is 80 Hz. In all cases, there are 3 axes. 16 bits is used per one axis. Then baud rate is ( ) 16 3 = bps. (5.1) It is the baud rate without addressing and other overhead. Assume using maximum sample rate of accelerometer, gyroscope and compass: then the microcontroller has to support I 2 C fast mode or both I 2 C and SPI interfaces. 26

37 5. REQUIREMENTS FOR EQUIPMENT AND COMPONENT SELECTION The GPS module supports only the UART interface. Because there is an USB/UART transceiver, two UART ports are necessary in microcontroller Debugging One of the techniques how to decrease development time of the device is in-circuit debugging. The microcontroller is placed in the final application and communication with the computer is provided using interface named debugger. MPLAB ICD 3 In-Circuit Debugger [12] made by Microchip is available to me; therefore the microcontroller made by Microchip will be used Power Consumption Most of the time the device will be run in sleep mode. It means that there is no data transmission, no computing, only waiting for device movement. Accelerometer supports generating interrupt signal when some movement is presented [22]. This interruption can be used for waking-up of the processor. To minimize the power consumption, it is important to microcontroller support any advanced power management mode. In case of Microchip, it is named nanowatt XLP [10] Selected Microcontroller Summarize all requirements, the PIC18F26J11 [11] was selected. It is a cheap 8bit microcontroller and it supports I 2 C, SPI, UART, nanowatt and has 28 pins Summary Table This table contains the most important components. The table does not contain GSM module (not implemented) CZK and other components like resistors, LEDs, printed circuit boards etc. Microcontroller PIC18F26J11 Accelerometer LIS331DLH Gyroscope L3G4200D Compass HMC5883L GPS module Quectel L10 Power consumption Standby mode Normal mode Price * Interfeace 100 na 23 ma 81 CZK UART, I 2 C, (deep sleep mode) (maximum SPI frequency) 1 µa 250 µa 152 CZK I 2 C, SPI 5 µa 6 ma 265 CZK I 2 C, SPI 2 µa 100 µa 152 CZK I 2 C 0 ma (not used in standby) 43 ma 520 CZK UART Total 8.1 µa 72 ma 1170 CZK * april 2013, cz.farnell.com, retail price 27