IMU Filter. Michael Asher Emmanuel Malikides November 5, 2011
|
|
- Brittney Henderson
- 5 years ago
- Views:
Transcription
1 IMU Filter Michael Asher Emmanuel Malikides November 5, 2011 Abstract Despite the ubiquitousness of GPS devices, on board inertial navigation remains important. An IMU like the Sparkfun Ultimate IMU used, contains all the necessary sensors for inertial navigation. These sensors, particularly gyroscopes, are subject to error. An algorithm combining different modalities (acceleration, rotation, and the earth s magnetic field) to filter this error is developed. The possibility of parallelising the algorithm for implementation on a Field Programmable Gate Array is explored. Background Quaternions The issue of the updating and storing an attitude in 3 dimensional space was addressed through use of quaternions. Rotations can be stored as the a set of three rotations, each around a coordinate axis. However, when one of the angles approaches π 2, separate solutions for the other two angles for a given rotation cannot be found as their axes are parallel. To avoid this problem, known as gimbal lock, quaternions can be used to represent rotations. Quaternions are also more numerically stable than other possible representations. Quaternions can be described as extended complex numbers q = w + ix + jy + kz, with i 2 = j 2 = k 2 = ijk = 1 and w, x, y, z R. They can be computationally represented as quadruples of real numbers q = [x, y, z, w]. They have the following operations. Addition q + q = [v + v, w + w ]. Multiplication qq = [v v +wv +w v, ww v v ]. Norm N(q) = qq = w 2 +v v. Conjugate q = [v, w] = [ v, w]. Unit quaternions form a universal covering of the 3D rotations, capturing all their geometry, topology and group structure. This is represented through writing unit quaternions in the form q = [x, y, z, w] = [ v sin(θ), cos(θ)] for some vector v and angle θ. Now let p = [ v p, w p ] be some quaternion. Then conjugation of p by q represents a rotation by 2θ about v. These rotations can be composed through multiplication, as the rotation formed from first rotating with q 1 then q 2 is given by q 2 q 1 1
2 Equations of Motion for Inertial Navigation [TW04] An important aspect of navigation is the reference frame in which readings are taken. The two frames of reference we will refer to in this report are the navigation frame (denoted by subscript n), which has origin at the navigation system s location and axes along north, east and down, and the body frame (denoted by subscript b), which has origin at the location of the navigation system and axes aligned with roll, pitch and yaw of vehicle. Roll, pitch and yaw refer to counter clockwise angles of rotation about the x, z and y axes respectively. Navigation involves knowing the position p, represented as a vector from the original to the present origin in the navigation frame, and the posture q which is represented as a rotation which takes the axes in the body frame to those in the navigation frame. The available sensors give readings for the linear acceleration, f b, and angular velocity, ω b, of the system, and ultimately allow the estimation of position velocity and posture of the sensor. The angular velocity reading given by the gyroscopes is given by: ω b = d θ dt b Thus by integrating over one timestep we can find the change in angle about each θ, which defines a rotation r b that represents the change in attitude for that timestep in the body frame. Changing this rotation into the navigation frame, assuming the current attitude q is correct gives: r n = qrq 1 We can then update the attitude, q = r n q = qrq 1 q = qr. Now let g b denote the acceleration due to gravity, and a b the acceleration of the sensor without gravity. We have a b = g b + f b q a b = q g b + q f b a n = g n + q f b Now g n is a constant. So the above gives us a n. We also know that a n = d v n dt n = d2 p n dt 2 n so integrating twice gives the position p n. Hardware An inertial measurement unit (IMU) contains the sensors necessary for inertial navigation, at a minimum, 3 gyroscopes and 3 accelerometers with each set arranged orthogonally. The device used, Sparkfun s Ultimate IMU, also contains 3 magnetometers which can be used to filter the signal as detailed below. Sparkfun s Ultimate IMU, the IMU used, contains the following sensors. 2
3 Analog Devices 3-Axis ±2 to 16g Digital Accelerometer ADXL345 The sensor is a polysilicon surface-micromachined structure built on top of a silicon wafer. Polysilicon springs suspend the structure over the surface of the wafer and provide a resistance against acceleration forces. Deflection of the structure is measured using differential capacitors that consist of independent fixed plates and plates attached to the moving mass. Acceleration deflects the beam and unbalances the differential capacitor, resulting in a sensor output whose amplitude is proportional to acceleration. Phase-sensitive demodulation is used to determine the magnitude and polarity of the acceleration. Honeywell 3-Axis Digital Compass IC HMC5843 The HMC5843 utilizes Anisotropic Magnetoresistive (AMR) to measure magnetic fields from tens of micro-gauss to 6 gauss. The Honeywell HMC5843 magnetoresistive sensor circuit is a trio of sensors and application specific support circuits to measure magnetic fields. With power supply applied, the sensor converts any incident magnetic field in the sensitive axis directions to a differential voltage output. The magnetoresistive sensors are made of a nickel-iron (Permalloy) thin-film and patterned as a resistive strip element. In the presence of a magnetic field, a change in the bridge resistive elements causes a corresponding change in voltage across the bridge outputs. These resistive elements are aligned together to have a common sensitive axis that will provide positive voltage change with magnetic fields increasing in the sensitive direction. Because the output only is in proportion to the one-dimensional axis (the principle of anisotropy) and its magnitude, additional sensor bridges placed at orthogonal directions permit accurate measurement of arbitrary field direction. InvenSense ITG Axis gyro IC The sensor consists of three independent vibratory MEMS gyroscopes, which detect rational rate about the x (roll), y (pitch) and z (yaw) axes. When the gyros are rotated about any of the sense axes, the Coriolis Effect causes a deflection that is detected by a capacitive pickoff. The resulting signal is amplified, demodulated, and filtered to produce a voltage that is proportional to the angular rate. This voltage is digitized using the individual on-chip 16-bit ADCs to sample each axis. The basic principle of operation of such sensors is that the vibratory motion of part of the instrument creates an oscillatory linear velocity. If the sensor is rotated about an axis orthogonal to this velocity, a Coriolis acceleration is induced. This acceleration modifies the motion of the vibrating element and provided that this can be detected, it will indicate the magnitude of the applied rotation. [TW04] Magnetometer Calibration [RAL10] Antisotropic Magnetoresistive (AMR) sensors like the Honeywell model used have a number of sources of error. There is a offset error which is constant for the lifespan of the device. Four identical elements make up the sensor, and this error is due to difficulty in depositing the permalloy of which they are made evenly and of the same density. Sensitivity error refers to the nonlinear variation in the magnitude of the sensed magnetic field. A cross axis 3
4 sensitivity error occurs becaause over time, the sensor obtains uneven magnetization. While the errors above are deterministic, sensor measurement noise is a stochastic process. Lastly magnetic field specific errors result from magnetic perturbations in the vicinity of the sensor. These can be further classified into hard iron (permanent field independent of Earth s) and soft iron (induced field). These errors can be modelled mathematically as follows. The three instrumentation errors; offset, sensitivity and cross axis can be modelled by a bias b so, scale factor s and transformation M respectively. b = [ b sox b soy b soz ] T S = diag (s x s y s z ) M = [ɛ x ɛ y ɛ z ] 1 where ɛ x, ɛ y, ɛ z represent the sensors x, y, z axes in the body frame Magnetic deviation errors can be represented as a hard iron bias b hi = [ b hix b hiy b hiz ] T and a 3 3 matrix for soft iron errors which impact both the intensity and the direction of the sensed field. A complete error model for true heading h, magnetometer readings ĥ and error e is then, ĥ = SM(A si h + b hi ) + b so + e. For descriptive purposes we introduce, A = SMA si b = SMb hi + b so. So ĥ = Ah + b + e. (1) With only instrumental errors, the norm of the magnetometer reading should be equal to the magnitude of the Earth s magnetic field and so the locus described by its readings should be a sphere with centre equal to the bias in the body frame. When all errors are considered, Renaudin et. al [RAL10] show that the locus is an ellipsoid and that (1) can be solved using an adaptive least squares algorithm. Rotating the Ultimate IMU in place and plotting the magnetometer reading confirms this. See the below figure. Calibration as described by Renaudin was not implemented but a heuristic approach was attempted. 4
5 Kalman Filtering The standard approach to this problem involves the application of a Kalman filter. The Kalman filter functions, in essence, by keeping track of the state in question, predicting the state at a future timestep through some linear model, then combining the subsequent measurement of the state with the prediction via a weighted sum. More formally, the filter addresses the problem of tracking systems that can be represented by the following linear stochastic difference equation: x k = Ax k 1 + Bu k 1 + w k 1 Where x R n is the state vector at time k, u k 1 R l is an optional control input, A is a matrix representing the linear model that updates the state given the previous state, B is a matrix that relates the control input to the state and w k 1 is the process noise. This is accompanied by some measurement process: z k = Hx k + v k Where z k R m is the measurement vector, H is a m n matrix that predicts the next measurement given the current state vector, and v k is again some noise term, called the measurement noise. Crucially the noise terms are assumed to be gaussian, with distributions p(w) N(0, Q) and p(v) N(0, R). Here Q and R are called the process noise covariance, and measurement noise covariance,respectively. With the state defined as above, given some initial state vector x k, and measurement vector z k the Kalman filter combines the two through the update: 5
6 x + k = x k + K(z k Hx k ) where the superscript notation indicates x + k is the updated estimate of the state. Recall that the matrix H predicts the measurement given the previous state, thus the term (z k Hx k ) represents the difference between the prediction and the actual measurement. This is weighted with some matrix K. K, termed the kalman gain matrix, is determined to minimise the error covariance of x + k. This is roughly equivalent to minimising the expected magnitude of the error in the updated prediction. The result is given by: K = P k H T HP k H T + R The trouble with this technique is that one must find the covariance matrices. This is typically a difficult problem and the usually approached by guessing, or tuning until it works. Moving Average Filters Filters are processes that remove information from a signal. A moving average filter is a kind of low pass filter removes high frequency components from a signal. This is useful for removing random noise in measurements, which is often higher frequency than the underlying signal of interest. The moving average filter functions by performing a weighted sum over a fixed number of past samples. Let x(t) denote the input signal at timestep t, y(t) the output, and m the number of samples stored. Then the following is the result of the moving average at any time t: y(t) = 1 (x(t) + x(t 1) x(t m + 1)) m An important property of filters in the time domain is their step response. This is the output of the filter when the input is a step function. It is desirable to have a fast step response, an output that follows the input step function very closely. This is because it is desirable to have a filter that responds quickly to changes in the signal, while still filtering out the noise. The moving average filter is optimal in the sense that sense that it reduces random noise most efficiently while retaining a sharp step response. It is also simple, and can be implemented recursively, making it efficient compared to alternate filters. A variant of the moving average filter termed, for the purpose of this report, the weighted moving average filter gives preference to more recent data with the justification that it is more likely to represent the true state of the system, because it is strongly time-dependant. This can be simply implemented by changing the weights of each element of the sum. Let a (0, 1). The normalised weighted moving average filter output is given by: y(t) = 1 a 1 a m (x(t) + ax(t 1) + a2 x(t 2) a m 1 x(t m + 1)) a can now be tuned to by decreasing it to give faster response (higher weighting for more recent data), but less smoothing. 6
7 On an FPGA, however, the storage of previous inputs can be difficult. In this case the filter can be recursively implemented as: 1 y(t) = (x(t) + ay(t 1)) 1 + a Called an infinite impulse response filter, this results in similar behaviour to the weighted moving average with the exception that there is no bound on the number of previous data points incooperated into the sum. This means there is less flexibility when choosing a weight, because weights too close to 1 will result in a slow response, when compared with the moving average filter, where the number of past samples included is explicitly truncated. That is, the infinite impulse response filter sacrifices fast step response for fast computation time and less memory usage. Filtering Algorithm The algorithm developed aimed to overcome random error and long-term bias measurements in the accelerometer, gyroscope and compass measurements. The method by which each error was accounted for is detailed below. Random error in gyroscope, accelerometer and magnetometer This type of error was accounted for in all three cases with a recursive infinite impulse response filter. The weightings were determined by experiment, though bounds can be estimated as done for the acceleration, and subject to the assumptions of the application at hand. Gyro bias Tests demonstrated that the bias and random noise in the gyroscopes were the most significant, in the sense that they had the lowest signal to noise ratio. Thus the removal of this error was one of the prime goals of this design. The bias was accounted for by using the accelerometer and magnetometer readings to obtain an estimate of the orientation of the sensor. This estimate was then compared with that given by the integrated gyroscope signal, and updated according to a simple weighted sum: q = E M E g q Where q is the attitude, E g is a quaternion representing the error in the orientation as determined from the gravitational vector and E M is a quaternion rotation determined from the magnetometer reading. The quaternion E M was determined at each time-step by comparing the acceleration vector in the inertial frame as estimated by the updated attitude from the gyroscope reading with the initial stored acceleration reading. Assuming that the craft is not accelerating for long periods of time, the acceleration should, if the gyroscope reading were correct, point roughly in the same direction as this initial reading. Thus the rotation that takes the accelerometer reading to the initial value gives a measure of the error in the gyroscope reading. Let g n denote the normalised initial accelerometer reading, and a n denote the 7
8 normalised current reading, and w denote the weight. The corrective rotation is then given by: θ = Arccos(g n a n ) E g = [ g n a n sin( wθ ), cos(wθ 2 2 )] The error from the magnetometer reading was determined in an exactly analogous manner. This method was then further improved by storing the updates, and correcting the gyroscope reading in advance. Because the gyroscope data was determined to be roughly normally distributed, the mean of past values should serve as a reasonable estimate of future values. This learning of the gyro drift meant that the weights of the corrections due to the accelerometer and magnetometer readings can be reduced, allowing a relaxation of the assumption that the craft is only accelerating for short periods of time, and widening the applicability of the algorithm. The gyroscope bias was also learnt, along with the accelerometer bias, in an initial calibration stage, and taken as the mean of some number of initial samples. Bias in the accelerometer reading Initially the accelerometer reading was stored, and kept as a reference. As a reasonably accurate reading was needed this was taken over an average of some initial number of samples. This includes the initial bias value. However, as tests indicated this bias drifted over a period of 5 minutes or so, this initial value needed to be updated. This was done by performing a weighted update at each timestep of the initial accelerometer reading. The weighting was determined per dimension (individually for x, y and z) by the variance from the initial stored value over a long period of recorded data as below: w glearning = w gmax exp( V ariance(a t x a xi )) V ariance(a t, b) = mean((a t b) 2 ) Where w glearning is the final update weight w gmax is the maximum value this can take, a t x is a past list of stored data for the x values of accelerometer readings, and a xi is the accepted initial accelerometer reading; the accepted gravitational acceleration plus bias1. Bias in the Magnetometer reading This was determined in a calibration stage, run before the main loop began. It was determined based on the premise stated in the introduction that the bias vector can be determined as the centre of an ellipsoid comprised of the readings given by the magnetometer. This centre was simply computed by determining the maximum and minimum readings, and taking the middle of these two numbers along each axis. Thus during the initial calibration stage these maximum and minimum readings had to be detected, so the calibration 8
9 included revolving the sensor about each axis. Which should give a reasonable estimate of the bias, though it should be noted revolving about each axis does not guarantee the maximum and minimum values will be encountered. Parameter estimation For the purpose of this report some assumptions were made about the typical behaviour of the craft on which this filter was placed. This was necessary to justify otherwise arbitrary choices of constants. Firstly, for efficiency the infinite impulse response filter was used for filtering out random noise. The weight applied to each successive value reflects a compromise between effective noise filtration and step response of the filter. To quantify this it was assumed that the craft recieved position updates from an external source (for example a gps) every minute. Thus the acceptable amount of accumulated error in the position was assumed to be 1 metre per minute. This is equivalent to saying the maximum error in velocity is one metre per minute. Let dt be the update period of the sensor (assumed constant for the purpose of this estimate), a be the maximum error in the accelerometer reading. Then: S = 1 2 = 1 2 = /dt (a i + a)(dt) 2 i=1 60/dt i=1 60/dt i=1 a i (dt) /dt i=1 a i (dt) adt a(dt) 2 Thus 2ds 60dt = a This implies the error in each acceleration reading, for our timestep, which is at most s, can be at most 0.5 ms 2. With the goal of determining the weight of the infinite impulse response filter we now assume that the order of magnitude of the acceleration does not exceed 100ms 2, and further that the acceptable lag time in the response of our filter is 0.5 s. This means for our timestep, within roughly ten samples, the possibly erroneous past data samples must have negligible effect on the output of the filter, where negligible is quantified by the upper bound on the error in acceleration derived previously. Let w max be the weight of the infinite impulse response filter. Then 100wmax 10 i=0 wi max < 0.5 assuming all other terms of the infinite sum are negligible and we obtain w max < 0.5. The long term update of the bias in the accelerometer reading also hinged upon the assumption that the craft was not accelerating for long periods of time, as the update weight was made a function of the variance of past data, so if long term acceleration was sustained the bias might be updated to an incorrect value. It is assumed that the maximum time of continuous smooth acceleration for our craft is 10 seconds. Again, assuming that the maximum reading attained by the 9
10 accelerometers is 100ms 1, we require that the magnitude of the update of the bias vector 100w g exp( V ariance(a t d) << 0.5 where w gmax is the maximum gravitational learning weight and a ( t) is the past data over 10 seconds of the accelerometer values. If we assume the variance is zero over this time period, we reach the same conclusion as before, that w gmax < 0.5. Main loop The compilation of the above yields the main loop. while system is stationary and away from magnetic interference do read sensor data (gyroscope, accelerometer, magnetometer) accepted-gravity := sliding average of acceleration data accepted-heading := sliding average of magnetometer data gyro-drift := sliding average of raw (euler) gyroscope data end while while True do read sensor data (gyroscope, accelerometer, magnetometer) accelero-reading, magno-reading, gyro-reading := filtered data angle-change := (gyro-reading - gyro-drift) time-step (quaternion) attitude := attitude angle-change gravity-error := rotation from accelero-reading to accepted-gravity compass-error := rotation from magno-reading to accepted-heading gyro-drift := gyro-drift + ( weighted gravity-error and compass-error ) attitude := (c-1 compass-error) (c-2 gravity-error) attitude accepted-gravity := long term update of accelero-reading in inertial frame velocity + = (accelero-reading - accepted gravity) in inertial frame timestep position + = 1 2 velocity time-step end while 10
11 Experiments Analysis of Sensor Error If left stationary the sensor produces the following results. The approximate normal distributions produced by the gyroscopes indicate that learning the mean of past values will likely be an effective estimate of the future drift, at least over a short timescale. Demonstration of typical timescales involved in long term bias drift 11
12 Gyroscope Drift Learning To determine the effectiveness of learning the gyroscope drift, data from the stationary IMU was recorded and filtered with and without learning the gyroscope drift. The corrections obtained from the gravity and magnetometer reading were used as a measure of the effectiveness of the gyroscope drift update and plotted over time. If learning gyroscope drift is effective then the correction made according to gravity and magnetometer readings should grow smaller. The below graphics show the angles of rotations from the present heading and acceleration vectors to their long term averages. In order they are with no gyroscope drift learning and then with gyroscope drift learning and weights of 0.2, 0.5 and 0.7 on the acceleration vector correction. It is apparent that learning gyroscope drift is effective at reducing the need to correct attitude readings using gravity. This broadens the applicability of the algorithm since it is not necessary to weight the gravity correction as heavily. It also allows for the possibility of updating attitude from gyroscope readings at a higher frequency than quality acceleration data can be obtained. 12
13 13
14 14
15 Effectiveness of Learning Magnetometer Bias Bias was learnt by moving the device around and finding the center of the resulting locus of readings in the body frame. Once this calibration had been performed, the device was rotated once in the horizontal plane and the angle from its original position recorded. The below graphs plot this angle over time for correction weights of 0, 0.2 and 0.5 respectively. It can be seen that the magnetic correction results in less drift in the plane orthogonal to gravity. 15
16 16
17 Gravity Learning The next two graphs show the measured displacement values of a still device without changing the value for gravity and then with adjusting it using a long term average with weighting 0.3. Note the different vertical scales. It is clear that adjusting for varying accelerometer bias improves position estimates. An algebraic model like that suggested by Titteron [TW04] is inadequate in that it does not account for time dependent device bias. 17
18 18
19 Parallelising The end goal of the project was to parallelise the above algorithm in order to make its implementation on a Field Programmable Gate Array possible. Some considerations for programming in this environment and their respective implications are listed below. Memory is limited. Several kb total on chip. This constraint would limit such constructs as long term sliding averages. Data paths should be pipelined, there is no access to shared memory. Arithmetic operations on pipelines take up space. Space for operators is more important that time. Operator complexity should be minimised by using approximations, bit shifts and look up tables where possible. No floating point arithmetic. In order to parallelise the algorithm, the below data flow chart was developed. 19
20 Gyro Smoothing Gyro Reading Gryo Drift Drift Correct Time Stamp Accelerometer Attitude Integrate Magnetometer Smoothing Combine Smoothing Accelero Reading Attitude Magno Reading Rotate Rotate Gravity Accelero Reading (inerital) Heading Magno Reading (iinertial) Compare Compare Weighted Sum Rotate Weighted Sum Attitude Gryo Drift Transform Acceleration Subtract Weighted Sum Acceleration Gravity Integrate Velocity Add Velocity Integrate Position Add Position 20
21 Conclusion A simple and more parallelisable approach to the problem of inertial navigation has been developed. In contrast to the general approach in literature, the algorithm does not employ the kalman filter, resulting in more intuitive tuning, and less computation. The algorithm aims to compensate for random noise by employing simple smoothing filters. It accounts for time dependant drift in accelerometer reading and gyroscope readings. These aspects of the filter were tested yeilding positive results. It was shown that the method for accounting for time dependant bias in the gyroscope was effective at reducing the needed attitude adjustment. It was also shown by the implemented method for adjusting for compass bias that a relatively simple method for calibration can still be effective. References [RAL10] V. Renaudin, M.H. Afzal, and G. Lachapelle. Complete triaxis magnetometer calibration in the magnetic domain. Journal of Sensors, [TW04] D.H. Titterton and J.L. Weston. Strapdown inertial navigation technology, volume 17. Peter Peregrinus Ltd,
EE565:Mobile Robotics Lecture 6
EE565:Mobile Robotics Lecture 6 Welcome Dr. Ahmad Kamal Nasir Announcement Mid-Term Examination # 1 (25%) Understand basic wheel robot kinematics, common mobile robot sensors and actuators knowledge. Understand
More informationAttitude Estimation Version 1.0
Attitude Estimation Version 1. Francesco Farina May 23, 216 Contents 1 Introduction 2 2 Mathematical background 2 2.1 Reference frames and coordinate systems............. 2 2.2 Euler angles..............................
More informationEE C245 / ME C218 INTRODUCTION TO MEMS DESIGN FALL 2009 PROBLEM SET #7. Due (at 7 p.m.): Thursday, Dec. 10, 2009, in the EE C245 HW box in 240 Cory.
Issued: Thursday, Nov. 24, 2009 PROBLEM SET #7 Due (at 7 p.m.): Thursday, Dec. 10, 2009, in the EE C245 HW box in 240 Cory. 1. Gyroscopes are inertial sensors that measure rotation rate, which is an extremely
More informationQuaternion based Extended Kalman Filter
Quaternion based Extended Kalman Filter, Sergio Montenegro About this lecture General introduction to rotations and quaternions. Introduction to Kalman Filter for Attitude Estimation How to implement and
More informationApplication of state observers in attitude estimation using low-cost sensors
Application of state observers in attitude estimation using low-cost sensors Martin Řezáč Czech Technical University in Prague, Czech Republic March 26, 212 Introduction motivation for inertial estimation
More information1 Kalman Filter Introduction
1 Kalman Filter Introduction You should first read Chapter 1 of Stochastic models, estimation, and control: Volume 1 by Peter S. Maybec (available here). 1.1 Explanation of Equations (1-3) and (1-4) Equation
More informationAutonomous Mobile Robot Design
Autonomous Mobile Robot Design Topic: Inertial Measurement Unit Dr. Kostas Alexis (CSE) Where am I? What is my environment? Robots use multiple sensors to understand where they are and how their environment
More informationFundamentals of attitude Estimation
Fundamentals of attitude Estimation Prepared by A.Kaviyarasu Assistant Professor Department of Aerospace Engineering Madras Institute Of Technology Chromepet, Chennai Basically an IMU can used for two
More informationEE C245 / ME C218 INTRODUCTION TO MEMS DESIGN FALL 2011 C. Nguyen PROBLEM SET #7. Table 1: Gyroscope Modeling Parameters
Issued: Wednesday, Nov. 23, 2011. PROBLEM SET #7 Due (at 7 p.m.): Thursday, Dec. 8, 2011, in the EE C245 HW box in 240 Cory. 1. Gyroscopes are inertial sensors that measure rotation rate, which is an extremely
More informationAngle estimation using gyros and accelerometers
Lab in Dynamical systems and control TSRT21 Angle estimation using gyros and accelerometers This version: January 25, 2017 Name: LERTEKNIK REG P-number: Date: AU T O MA R TI C C O N T OL Passed: LINKÖPING
More informationAngle estimation using gyros and accelerometers
Angle estimation using gyros and accelerometers This version: January 23, 2018 Name: LERTEKNIK REG P-number: Date: AU T O MA RO TI C C O N T L Passed: LINKÖPING Chapter 1 Introduction The purpose of this
More informationPresenter: Siu Ho (4 th year, Doctor of Engineering) Other authors: Dr Andy Kerr, Dr Avril Thomson
The development and evaluation of a sensor-fusion and adaptive algorithm for detecting real-time upper-trunk kinematics, phases and timing of the sit-to-stand movements in stroke survivors Presenter: Siu
More informationFundamentals of High Accuracy Inertial Navigation Averil B. Chatfield Table of Contents
Navtech Part #2440 Preface Fundamentals of High Accuracy Inertial Navigation Averil B. Chatfield Table of Contents Chapter 1. Introduction...... 1 I. Forces Producing Motion.... 1 A. Gravitation......
More informationArrow Brasil. Rodrigo Rodrigues Field Application Engineer F: Date: 30/01/2014 TM 2
TM Arrow Brasil Rodrigo Rodrigues Field Application Engineer Rodrigo.rodrigues@arrowbrasil.com.br F:+55 11 3613-9331 Date: 30/01/2014 TM 2 State-of-the-art review Introduction How a Gyro Works Performance
More informationwith Application to Autonomous Vehicles
Nonlinear with Application to Autonomous Vehicles (Ph.D. Candidate) C. Silvestre (Supervisor) P. Oliveira (Co-supervisor) Institute for s and Robotics Instituto Superior Técnico Portugal January 2010 Presentation
More informationSilicon Capacitive Accelerometers. Ulf Meriheinä M.Sc. (Eng.) Business Development Manager VTI TECHNOLOGIES
Silicon Capacitive Accelerometers Ulf Meriheinä M.Sc. (Eng.) Business Development Manager VTI TECHNOLOGIES 1 Measuring Acceleration The acceleration measurement is based on Newton s 2nd law: Let the acceleration
More informationMEMS Tuning-Fork Gyroscope Mid-Term Report Amanda Bristow Travis Barton Stephen Nary
MEMS Tuning-Fork Gyroscope Mid-Term Report Amanda Bristow Travis Barton Stephen Nary Abstract MEMS based gyroscopes have gained in popularity for use as rotation rate sensors in commercial products like
More informationCalibration of a magnetometer in combination with inertial sensors
Calibration of a magnetometer in combination with inertial sensors Manon Kok, Jeroen D. Hol, Thomas B. Schön, Fredrik Gustafsson and Henk Luinge Division of Automatic Control Linköping University, Sweden
More informationSlide 1. Temperatures Light (Optoelectronics) Magnetic Fields Strain Pressure Displacement and Rotation Acceleration Electronic Sensors
Slide 1 Electronic Sensors Electronic sensors can be designed to detect a variety of quantitative aspects of a given physical system. Such quantities include: Temperatures Light (Optoelectronics) Magnetic
More informationVN-100 Velocity Compensation
VN-100 Velocity Compensation Velocity / Airspeed Aiding for AHRS Applications Application Note Abstract This application note describes how the VN-100 can be used in non-stationary applications which require
More informationTTK4190 Guidance and Control Exam Suggested Solution Spring 2011
TTK4190 Guidance and Control Exam Suggested Solution Spring 011 Problem 1 A) The weight and buoyancy of the vehicle can be found as follows: W = mg = 15 9.81 = 16.3 N (1) B = 106 4 ( ) 0.6 3 3 π 9.81 =
More informationCS491/691: Introduction to Aerial Robotics
CS491/691: Introduction to Aerial Robotics Topic: Midterm Preparation Dr. Kostas Alexis (CSE) Areas of Focus Coordinate system transformations (CST) MAV Dynamics (MAVD) Navigation Sensors (NS) State Estimation
More informationAutomated Tuning of the Nonlinear Complementary Filter for an Attitude Heading Reference Observer
Automated Tuning of the Nonlinear Complementary Filter for an Attitude Heading Reference Observer Oscar De Silva, George K.I. Mann and Raymond G. Gosine Faculty of Engineering and Applied Sciences, Memorial
More informationEE 570: Location and Navigation
EE 570: Location and Navigation Sensor Technology Stephen Bruder 1 Aly El-Osery 2 1 Electrical and Computer Engineering Department, Embry-Riddle Aeronautical Univesity Prescott, Arizona, USA 2 Electrical
More informationMAE 142 Homework #5 Due Friday, March 13, 2009
MAE 142 Homework #5 Due Friday, March 13, 2009 Please read through the entire homework set before beginning. Also, please label clearly your answers and summarize your findings as concisely as possible.
More informationChapter 4 State Estimation
Chapter 4 State Estimation Navigation of an unmanned vehicle, always depends on a good estimation of the vehicle states. Especially if no external sensors or marers are available, more or less complex
More informationDead Reckoning navigation (DR navigation)
Dead Reckoning navigation (DR navigation) Prepared by A.Kaviyarasu Assistant Professor Department of Aerospace Engineering Madras Institute Of Technology Chromepet, Chennai A Navigation which uses a Inertial
More informationAttitude Determination System of Small Satellite
Attitude Determination System of Small Satellite Satellite Research Centre Jiun Wei Chia, M. Sheral Crescent Tissera and Kay-Soon Low School of EEE, Nanyang Technological University, Singapore 24 th October
More informationEstimation and Control of a Quadrotor Attitude
Estimation and Control of a Quadrotor Attitude Bernardo Sousa Machado Henriques Mechanical Engineering Department, Instituto Superior Técnico, Lisboa, Portugal E-mail: henriquesbernardo@gmail.com Abstract
More informationOn the Observability and Self-Calibration of Visual-Inertial Navigation Systems
Center for Robotics and Embedded Systems University of Southern California Technical Report CRES-08-005 R B TIC EMBEDDED SYSTEMS LABORATORY On the Observability and Self-Calibration of Visual-Inertial
More informationA Study of Covariances within Basic and Extended Kalman Filters
A Study of Covariances within Basic and Extended Kalman Filters David Wheeler Kyle Ingersoll December 2, 2013 Abstract This paper explores the role of covariance in the context of Kalman filters. The underlying
More informationCharacterization of low-cost Accelerometers for Use in a Local Positioning System
Characterization of low-cost Accelerometers for Use in a Local Positioning System Morten Stakkeland Master Thesis Department of Physics University of Oslo 31. July 2003 Acknowledgements... i Mathematical
More informationNational Exams May 2016
National Exams May 2016 04-Agric-A5, Principles of Instrumentation 3 hours duration NOTES: 1. If doubt exists as to the interpretation of any question, the candidate is urged to submit with the answer
More informationTHE USE OF KALMAN FILTRATION TO ESTIMATE CHANGES OF TRUNK INCLINATION ANGLE DURING WEIGHTLIFTING 1. INTRODUCTION
JOURNAL OF MEDICAL INFORMATICS & TECHNOLOGIES Vol. 15/2010, ISSN 1642-6037 Kalman filtration, filter algorithm, accelerometric sensor Grzegorz SAPOTA 1, Anna SAPOTA 1, Zygmunt WRÓBEL 1 THE USE OF KALMAN
More informationDetermining absolute orientation of a phone by imaging celestial bodies
Technical Disclosure Commons Defensive Publications Series October 06, 2017 Determining absolute orientation of a phone by imaging celestial bodies Chia-Kai Liang Yibo Chen Follow this and additional works
More informationChapter 7 Vibration Measurement and Applications
Chapter 7 Vibration Measurement and Applications Dr. Tan Wei Hong School of Mechatronic Engineering Universiti Malaysia Perlis (UniMAP) Pauh Putra Campus ENT 346 Vibration Mechanics Chapter Outline 7.1
More informationSensors: a) Gyroscope. Micro Electro-Mechanical (MEM) Gyroscopes: (MEM) Gyroscopes. Needs:
Sensors: Needs: Data redundancy Data for both situations: eclipse and sun Question of sampling frequency Location and size/weight Ability to resist to environment Low consumption Low price a) Gyroscope
More informationThe Fiber Optic Gyroscope a SAGNAC Interferometer for Inertial Sensor Applications
Contributing International Traveling Summer School 2007, Pforzheim: The Fiber Optic Gyroscope a SAGNAC Interferometer for Inertial Sensor Applications Thomas Erler 12th July 2007 1 0. Outline 1. Scope
More informationLocating and supervising relief forces in buildings without the use of infrastructure
Locating and supervising relief forces in buildings without the use of infrastructure Tracking of position with low-cost inertial sensors Martin Trächtler 17.10.2014 18th Leibniz Conference of advanced
More informationTwo dimensional rate gyro bias estimation for precise pitch and roll attitude determination utilizing a dual arc accelerometer array
Rochester Institute of Technology RIT Scholar Works Theses Thesis/Dissertation Collections -- Two dimensional rate gyro bias estimation for precise pitch and roll attitude determination utilizing a dual
More informationTracking for VR and AR
Tracking for VR and AR Hakan Bilen November 17, 2017 Computer Graphics University of Edinburgh Slide credits: Gordon Wetzstein and Steven M. La Valle 1 Overview VR and AR Inertial Sensors Gyroscopes Accelerometers
More informationTransduction Based on Changes in the Energy Stored in an Electrical Field
Lecture 6- Transduction Based on Changes in the Energy Stored in an Electrical Field Actuator Examples Microgrippers Normal force driving In-plane force driving» Comb-drive device F = εav d 1 ε oε F rwv
More informationEE C245 ME C218 Introduction to MEMS Design Fall 2007
EE C45 ME C8 Introduction to MEMS Design Fall 007 Prof. Clark T.C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 9470 Lecture 3: Input Modeling
More informationVisual Feedback Attitude Control of a Bias Momentum Micro Satellite using Two Wheels
Visual Feedback Attitude Control of a Bias Momentum Micro Satellite using Two Wheels Fuyuto Terui a, Nobutada Sako b, Keisuke Yoshihara c, Toru Yamamoto c, Shinichi Nakasuka b a National Aerospace Laboratory
More informationNAWCWPNS TM 8128 CONTENTS. Introduction Two-Dimensinal Motion Three-Dimensional Motion Nonrotating Spherical Earth...
CONTENTS Introduction... 3 Two-Dimensinal Motion... 3 Three-Dimensional Motion... 5 Nonrotating Spherical Earth...10 Rotating Spherical Earth...12 WGS84...14 Conclusion...14 Appendixes: A. Kalman Filter...15
More informationMeasurement Techniques for Engineers. Motion and Vibration Measurement
Measurement Techniques for Engineers Motion and Vibration Measurement Introduction Quantities that may need to be measured are velocity, acceleration and vibration amplitude Quantities useful in predicting
More informationMiscellaneous. Regarding reading materials. Again, ask questions (if you have) and ask them earlier
Miscellaneous Regarding reading materials Reading materials will be provided as needed If no assigned reading, it means I think the material from class is sufficient Should be enough for you to do your
More informationStochastic Models, Estimation and Control Peter S. Maybeck Volumes 1, 2 & 3 Tables of Contents
Navtech Part #s Volume 1 #1277 Volume 2 #1278 Volume 3 #1279 3 Volume Set #1280 Stochastic Models, Estimation and Control Peter S. Maybeck Volumes 1, 2 & 3 Tables of Contents Volume 1 Preface Contents
More informationSensors for mobile robots
ROBOTICS 01PEEQW Basilio Bona DAUIN Politecnico di Torino Mobile & Service Robotics Sensors for Robotics 2 Sensors for mobile robots Sensors are used to perceive, analyze and understand the environment
More informationMEMS Gyroscope Control Systems for Direct Angle Measurements
MEMS Gyroscope Control Systems for Direct Angle Measurements Chien-Yu Chi Mechanical Engineering National Chiao Tung University Hsin-Chu, Taiwan (R.O.C.) 3 Email: chienyu.me93g@nctu.edu.tw Tsung-Lin Chen
More information10 Measurement of Acceleration, Vibration and Shock Transducers
Chapter 10: Acceleration, Vibration and Shock Measurement Dr. Lufti Al-Sharif (Revision 1.0, 25/5/2008) 1. Introduction This chapter examines the measurement of acceleration, vibration and shock. It starts
More informationModule I Module I: traditional test instrumentation and acquisition systems. Prof. Ramat, Stefano
Preparatory Course (task NA 3.6) Basics of experimental testing and theoretical background Module I Module I: traditional test instrumentation and acquisition systems Prof. Ramat, Stefano Transducers A
More informationObjectives. Fundamentals of Dynamics: Module 9 : Robot Dynamics & controls. Lecture 31 : Robot dynamics equation (LE & NE methods) and examples
\ Module 9 : Robot Dynamics & controls Lecture 31 : Robot dynamics equation (LE & NE methods) and examples Objectives In this course you will learn the following Fundamentals of Dynamics Coriolis component
More informationAttitude Estimation for Augmented Reality with Smartphones
Attitude Estimation for Augmented Reality with Smartphones Thibaud Michel Pierre Genevès Hassen Fourati Nabil Layaïda Université Grenoble Alpes, INRIA LIG, GIPSA-Lab, CNRS June 13 th, 2017 http://tyrex.inria.fr/mobile/benchmarks-attitude
More informationAdaptive Unscented Kalman Filter with Multiple Fading Factors for Pico Satellite Attitude Estimation
Adaptive Unscented Kalman Filter with Multiple Fading Factors for Pico Satellite Attitude Estimation Halil Ersin Söken and Chingiz Hajiyev Aeronautics and Astronautics Faculty Istanbul Technical University
More informationVariable Capacitance Accelerometers: Design and Applications
Variable Capacitance Accelerometers: Design and Applications Micromachined silicon variable-capacitance accelerometers are designed for easy manufacture and demanding applications. Tom Connolly, Endevco
More informationUAV Navigation: Airborne Inertial SLAM
Introduction UAV Navigation: Airborne Inertial SLAM Jonghyuk Kim Faculty of Engineering and Information Technology Australian National University, Australia Salah Sukkarieh ARC Centre of Excellence in
More informationECEN 420 LINEAR CONTROL SYSTEMS. Lecture 6 Mathematical Representation of Physical Systems II 1/67
1/67 ECEN 420 LINEAR CONTROL SYSTEMS Lecture 6 Mathematical Representation of Physical Systems II State Variable Models for Dynamic Systems u 1 u 2 u ṙ. Internal Variables x 1, x 2 x n y 1 y 2. y m Figure
More informationFigure 1: Inverted Pendulum. Why not just make a 4-wheeled or 3-wheeled robot? The following aresome reasons:
AIM As the name suggests, the robot would be a bicycle balancing autonomously.the self stabilizing bicycle will employ a control system to keep itself from falling over while in motion. INTRODUCTION Bicycles
More informationQUESTION BANK DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING UNIT I - INTRODUCTION SYLLABUS
QUESTION BANK DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING YEAR/SEM NAME OF THE SUBJECT NAME OF THE FACULTY : II / IV : EE6404 MEASUREMENTS AND INSTRUMENTATION : K.M.S.MUTHUKUMARA RAJAGURU, AP/EEE
More informationPSE Game Physics. Session (3) Springs, Ropes, Linear Momentum and Rotations. Atanas Atanasov, Philipp Neumann, Martin Schreiber
PSE Game Physics Session (3) Springs, Ropes, Linear Momentum and Rotations Atanas Atanasov, Philipp Neumann, Martin Schreiber 20.05.2011 Session (3)Springs, Ropes, Linear Momentum and Rotations, 20.05.2011
More informationCalibration and data fusion solution for the miniature attitude and heading reference system
Sensors and Actuators A 138 (2007) 411 420 Calibration and data fusion solution for the miniature attitude and heading reference system David Jurman, Marko Jankovec, Roman Kamnik, Marko Topič Faculty of
More informationAnalog Signals and Systems and their properties
Analog Signals and Systems and their properties Main Course Objective: Recall course objectives Understand the fundamentals of systems/signals interaction (know how systems can transform or filter signals)
More informationState Estimation for Autopilot Control of Small Unmanned Aerial Vehicles in Windy Conditions
University of Colorado, Boulder CU Scholar Aerospace Engineering Sciences Graduate Theses & Dissertations Aerospace Engineering Sciences Summer 7-23-2014 State Estimation for Autopilot Control of Small
More informationAn Adaptive Filter for a Small Attitude and Heading Reference System Using Low Cost Sensors
An Adaptive Filter for a Small Attitude and eading Reference System Using Low Cost Sensors Tongyue Gao *, Chuntao Shen, Zhenbang Gong, Jinjun Rao, and Jun Luo Department of Precision Mechanical Engineering
More informationResearch Article Complete Triaxis Magnetometer Calibration in the Magnetic Domain
Journal of Sensors Volume 21, Article ID 967245, 1 pages doi:1.1155/21/967245 Research Article Complete Triaxis Magnetometer Calibration in the Magnetic Domain Valérie Renaudin, Muhammad Haris Afzal, and
More informationInertial Odometry using AR Drone s IMU and calculating measurement s covariance
Inertial Odometry using AR Drone s IMU and calculating measurement s covariance Welcome Lab 6 Dr. Ahmad Kamal Nasir 25.02.2015 Dr. Ahmad Kamal Nasir 1 Today s Objectives Introduction to AR-Drone On-board
More informationLecture 9: Modeling and motion models
Sensor Fusion, 2014 Lecture 9: 1 Lecture 9: Modeling and motion models Whiteboard: Principles and some examples. Slides: Sampling formulas. Noise models. Standard motion models. Position as integrated
More informationInertial Navigation and Various Applications of Inertial Data. Yongcai Wang. 9 November 2016
Inertial Navigation and Various Applications of Inertial Data Yongcai Wang 9 November 2016 Types of Gyroscope Mechanical Gyroscope Laser Gyroscope Sagnac Effect Stable Platform IMU and Strapdown IMU In
More informationStudy on Tire-attached Energy Harvester for Lowspeed Actual Vehicle Driving
Journal of Physics: Conference Series PAPER OPEN ACCESS Study on Tire-attached Energy Harvester for Lowspeed Actual Vehicle Driving To cite this article: Y Zhang et al 15 J. Phys.: Conf. Ser. 66 116 Recent
More informationPHYSICS ASSIGNMENT ES/CE/MAG. Class XII
PHYSICS ASSIGNMENT ES/CE/MAG Class XII MM : 70 1. What is dielectric strength of a medium? Give its value for vacuum. 1 2. What is the physical importance of the line integral of an electrostatic field?
More informationElectrostatic Microgenerators
Electrostatic Microgenerators P.D. Mitcheson, T. Sterken, C. He, M. Kiziroglou, E. M. Yeatman and R. Puers Executive Summary Just as the electromagnetic force can be used to generate electrical power,
More informationCalibration of a magnetometer in combination with inertial sensors
Calibration of a magnetometer in combination with inertial sensors Manon Kok, Linköping University, Sweden Joint work with: Thomas Schön, Uppsala University, Sweden Jeroen Hol, Xsens Technologies, the
More informationLecture 19. Measurement of Solid-Mechanical Quantities (Chapter 8) Measuring Strain Measuring Displacement Measuring Linear Velocity
MECH 373 Instrumentation and Measurements Lecture 19 Measurement of Solid-Mechanical Quantities (Chapter 8) Measuring Strain Measuring Displacement Measuring Linear Velocity Measuring Accepleration and
More information(Refer Slide Time: 00:01:30 min)
Control Engineering Prof. M. Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 3 Introduction to Control Problem (Contd.) Well friends, I have been giving you various
More informationLecture 20. Measuring Pressure and Temperature (Chapter 9) Measuring Pressure Measuring Temperature MECH 373. Instrumentation and Measurements
MECH 373 Instrumentation and Measurements Lecture 20 Measuring Pressure and Temperature (Chapter 9) Measuring Pressure Measuring Temperature 1 Measuring Acceleration and Vibration Accelerometers using
More informationLecture Module 5: Introduction to Attitude Stabilization and Control
1 Lecture Module 5: Introduction to Attitude Stabilization and Control Lectures 1-3 Stability is referred to as a system s behaviour to external/internal disturbances (small) in/from equilibrium states.
More informationModeling and Experimentation: Mass-Spring-Damper System Dynamics
Modeling and Experimentation: Mass-Spring-Damper System Dynamics Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin July 20, 2014 Overview 1 This lab is meant to
More informationLecture D21 - Pendulums
J. Peraire 16.07 Dynamics Fall 2004 Version 1.1 ecture D21 - Pendulums A pendulum is a rigid body suspended from a fixed point (hinge) which is offset with respect to the body s center of mass. If all
More informationThe Basic Research for the New Compass System Using Latest MEMS
International Journal on Marine Navigation and Safety of Sea Transportation Volume 4 Number 3 September 21 The Basic Research for the New Compass System Using Latest MEMS G. Fukuda Graduate Student in
More informationAP Physics C Mechanics Objectives
AP Physics C Mechanics Objectives I. KINEMATICS A. Motion in One Dimension 1. The relationships among position, velocity and acceleration a. Given a graph of position vs. time, identify or sketch a graph
More informationRobotics Errors and compensation
Robotics Errors and compensation Tullio Facchinetti Friday 17 th January, 2014 13:17 http://robot.unipv.it/toolleeo Problems in sensors measurement the most prominent problems
More informationHS AP Physics 1 Science
Scope And Sequence Timeframe Unit Instructional Topics 5 Day(s) 20 Day(s) 5 Day(s) Kinematics Course AP Physics 1 is an introductory first-year, algebra-based, college level course for the student interested
More informationTheory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati
Theory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 2 Simpul Rotors Lecture - 2 Jeffcott Rotor Model In the
More informationCHAPTER 4 DESIGN AND ANALYSIS OF CANTILEVER BEAM ELECTROSTATIC ACTUATORS
61 CHAPTER 4 DESIGN AND ANALYSIS OF CANTILEVER BEAM ELECTROSTATIC ACTUATORS 4.1 INTRODUCTION The analysis of cantilever beams of small dimensions taking into the effect of fringing fields is studied and
More informationModel Reference Adaptive Control of Underwater Robotic Vehicle in Plane Motion
Proceedings of the 11th WSEAS International Conference on SSTEMS Agios ikolaos Crete Island Greece July 23-25 27 38 Model Reference Adaptive Control of Underwater Robotic Vehicle in Plane Motion j.garus@amw.gdynia.pl
More informationPRATHAM IIT BOMBAY STUDENT SATELLITE. Critical Design Report Attitude Determination and Control System (ADCS) for Pratham
PRATHAM IIT BOMBAY STUDENT SATELLITE Critical Design Report Attitude Determination and Control System (ADCS) for Pratham Indian Institute of Technology, Bombay 26 June, 2010 Chapter 1 Objectives of ADCS
More informationMARKING SCHEME SET 55/1/RU Q. No. Expected Answer / Value Points Marks Total Marks
MARKING SCHEME SET 55//RU Q. No. Expected Answer / Value Points Marks Total Marks Set, Q Set2,Q5 Set,Q4 Section A Self inductance of the coil is numerically equal to magnetic flux linked with it when unit
More informationCalibration and Uncertainty Analysis of a Spacecraft Attitude Determination Test Stand
Calibration and Uncertainty Analysis of a Spacecraft Attitude Determination Test Stand Charles T. Pope Space Engineering, masters level 2017 Luleå University of Technology Department of Computer Science,
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level *8055009334* PHYSICS 9702/43 Paper 4 A2 Structured Questions May/June 2012 2 hours Candidates answer on
More informationReview of modal testing
Review of modal testing A. Sestieri Dipartimento di Meccanica e Aeronautica University La Sapienza, Rome Presentation layout - Modelling vibration problems - Aim of modal testing - Types of modal testing:
More informationExtension of Farrenkopf Steady-State Solutions with Estimated Angular Rate
Extension of Farrenopf Steady-State Solutions with Estimated Angular Rate Andrew D. Dianetti and John L. Crassidis University at Buffalo, State University of New Yor, Amherst, NY 46-44 Steady-state solutions
More informationAdaptive Estimation of Measurement Bias in Six Degree of Freedom Inertial Measurement Units: Theory and Preliminary Simulation Evaluation
Adaptive Estimation of Measurement Bias in Six Degree of Freedom Inertial Measurement Units: Theory and Preliminary Simulation Evaluation Andrew R. Spielvogel and Louis L. Whitcomb Abstract Six-degree
More informationThe secondary winding have equal no. of turns. The secondary windings are placed identically on either side of the primary winding.
UNIT 4 DISPLACEMENT MEASURMENT Electrical comparator Working principle of Electrical comparators: These instruments are based on the theory of Wheatstone A.C. Bridge. When the bridge is electrically balanced,
More informationEE 570: Location and Navigation
EE 570: Location and Navigation Aided INS Aly El-Osery Kevin Wedeward Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA In Collaboration with Stephen Bruder Electrical and Computer
More informationLecture 13 Visual Inertial Fusion
Lecture 13 Visual Inertial Fusion Davide Scaramuzza Outline Introduction IMU model and Camera-IMU system Different paradigms Filtering Maximum a posteriori estimation Fix-lag smoothing 2 What is an IMU?
More informationChapter 2 Math Fundamentals
Chapter 2 Math Fundamentals Part 5 2.8 Quaternions 1 Outline 2.8.1 Representations and Notation 2.7.2 Quaternion Multiplication 2.7.3 Other Quaternion Operations 2.7.4 Representing 3D Rotations 2.7.5 Attitude
More informationLAWS OF GYROSCOPES / CARDANIC GYROSCOPE
LAWS OF GYROSCOPES / CARDANC GYROSCOPE PRNCPLE f the axis of rotation of the force-free gyroscope is displaced slightly, a nutation is produced. The relationship between precession frequency or nutation
More informationPLANAR KINETIC EQUATIONS OF MOTION (Section 17.2)
PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2) We will limit our study of planar kinetics to rigid bodies that are symmetric with respect to a fixed reference plane. As discussed in Chapter 16, when
More informationLecture Notes 4 Vector Detection and Estimation. Vector Detection Reconstruction Problem Detection for Vector AGN Channel
Lecture Notes 4 Vector Detection and Estimation Vector Detection Reconstruction Problem Detection for Vector AGN Channel Vector Linear Estimation Linear Innovation Sequence Kalman Filter EE 278B: Random
More information