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Characterization of Accelerometers Using Nonlinear Kalman Filters and Position Feedback Morten Stakkeland, Gunnar Prytz, Member, IEEE, Wilfred E. Booij, and Steve Tveit Pedersen, Member, IEEE

Abstract—In this paper, we describe a method to test and characterize accelerometers using an accurate position sensor and nonlinear Kalman filters. The method is designed to estimate parameters in nonlinear accelerometers and could be a simpler alternative to methods using centrifuges or vibrational testing. The method makes it possible to do real-time parameter estimation. In addition, the method can be integrated into an inertial tracking or navigation system with sufficiently accurate position measurements. The estimation filters have been implemented and successfully tested using Monte Carlo simulations. An experimental setup has been built, and its functionality has been verified. Index Terms—Acceleration measurement, inertial navigation, Kalman filtering, nonlinear estimation, nonlinear filters, tracking.

I. I NTRODUCTION AND M OTIVATION

W

E DESCRIBE a new method of characterizing accelerometers using movements in one dimension in combination with accurate position feedback. The method makes use of extended Kalman filters (EKFs) of first and second order to obtain real-time estimates of the model parameters for the accelerometer under test. Three conventional methods of characterizing accelerometer are described by [1], [5], and [9]—multiposition tumble tests (MPTTs), vibrational testing, and experimental setups using centrifuges. The MPTT procedure uses the fact that the output
=p ¨ (t) − g, which means from the accelerometer is given by a that accelerometers using a proof mass cannot distinguish between accelerations relative to an inertial frame and specific acceleration due to gravity. Using the gravity vector as input, the accelerometer is rotated about an axis normal to the gravity vector. Experimental procedures applying vibrations as inputs generate zero-mean sinusoidal accelerations with the help of accurate mechanical equipment. The mean of the output from the accelerometer is then often calculated for a given orientation relative to the local gravity vector g [5]. The characterization of accelerometers with the help of centrifuges is probably the most versatile and accurate method; however, it requires a complex and expensive infrastructure [1], [5]. To obtain estimations of nonlinear parameters in an MPTT requires an extremely accurate experimental setup, whereas vibrational and centrifuge testing are more amenable for this

Manuscript received November 12, 2005; revised August 15, 2007. This work was supported by the Research Council of Norway. M. Stakkeland is with FMC Technologies, NO-1373 Asker, Norway. G. Prytz is with ABB Corporate Research, NO-1375 Billingstad, Norway. W. E. Booij is with Sonitor Technologies AS, NO-0314 Oslo, Norway. S. T. Pedersen is with Enfo Broadcast AS, NO-0213 Oslo, Norway. Digital Object Identifier 10.1109/TIM.2007.908145

purpose [5]. This paper demonstrates that it is possible to estimate nonlinear parameters using the methodology in this paper, potentially reducing the amount and complexity of necessary mechanical equipment. In addition, these methods make it possible to obtain real-time parameter estimates, which is of great importance in characterizing signal drift under dynamic conditions. In conventional methods, the bandwidth of detectable variations is limited upward by the duration of one experiment, which, in MPTTs, can be on the order of tens of minutes. Due to the proliferation of microelectromechanical systems (MEMS) based sensors in a wide variety of applications, the need for fast and accurate characterization and calibration of accelerometers is rapidly increasing. The authors propose that the methodology described in this paper presents a costeffective solution. An essential part of this novel method is the use of a 1-D inertial tracking system with an accurate position sensor in combination with advanced estimation routines. The experimental setup is described in Section II-A. In Section II-B1, the algorithms, system models, and state estimation filters are described. Some results are described in Section III; the discussion can be found in Section IV.

II. M ETHODS A. Experimental Setup The methods described in this paper were tested on two different accelerometers. The ADXL105 (Analog Devices, Norwood, MA) is a low-cost, one-axis capacitive MEMS accelerometer packed in a surface-mounted ceramic leaded capsule [13]. The ADXL105 has an input range of ±5 g, nominal cross-axis sensitivity of 5% of full scale, a bandwidth of √ 10 kHz, and a nominal noise density of 225–325 µg/ Hz. The Crossbow CXL02TG3 (Crossbow Technology Inc., San Jose, CA) is a low-noise MEMS three-axis accelerometer packed in an aluminum casing [12]. The CXL02TG3 has an input range of ±2 g, nominal cross-axis sensitivity of 3% of full scale, a√bandwidth of 200 Hz, and a nominal noise density of 20 µg/ Hz. A detail from the experimental setup is shown in Fig. 1. The accelerometers were mounted on a specially designed platform (see {3} in Fig. 1). This platform was moved along two parallel tracks (see {6} in Fig. 1) that are attached to a rigid metal profile. The motion of the platform was restricted to a motion parallel to the tracks through the use of ball bearings that are clamped around the tracks.

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Fig. 2. Overview of data acquisition setup.

the clock skew between the clock on the position sensor circuit card and the internal processor clock of the DS1102 board. Fig. 1.

Detail from experimental setup.

B. Accelerometer Models A custom accurate translational position sensor was mounted alongside the tracks, providing position feedback to the estimation filters. The position sensor had a resolution of 1 µm, an absolute accuracy of better than 10 µm, a bandwidth of 100 mm/s, and an output rate of 833 Hz. The rigid metal profile was aligned normal to the gravity vector using a Sola Lasertronic level instrument (Sola Messwerkzeuge GmbH, Goetzis, Austria). This level instrument had an accuracy of 0.05◦ . A Newport 481-A rotation stage (see {2} of Fig. 1; Newport Corporation, Irvine, CA) with 30-arcsec (approximately 0.008◦ ) sensitivity was used to adjust the yaw angle. The pitch angle was adjusted by means of a tilt platform (Fig. 1) {5} using a Starrett micrometer (see {4} of Fig. 1; L.S. Starrett Company, Athol, MA) with a resolution of 0.01 mm. As can be seen in Fig. 1, the tilt platform was mounted on top of the rotation stage to allow the input axis of the accelerometer to be aligned to the direction of the movement. The ADXL105 accelerometers were mounted inside an aluminum box (Fig. 1) {1} with outside measures of 24.9 × 56.8 × 36.5 mm. An MPT5000 temperature controller (Wavelength Electronics, Bozeman, MT) and a Melcor CP 1.0-31-08L 5.3-W Peltier element (Melcor Corporation, Trenton, NJ) were used to control the temperature of the accelerometer inside the aluminum box to within 0.1 ◦ C. An overview of the signal conditioning is shown in Fig. 2. The data from the position sensor and the accelerometer were logged using a DS1102 controller board, which is manufactured by dSPACE Inc. (Novi, MI). The data from the position sensor were processed by a circuit card, which communicated with the PC through the digital input of the DS1102. The position was sampled at a rate of 833 Hz. All analog signal conditioning was implemented on a separate circuit card. The output from the accelerometers was lowpass filtered by means of a passive RC filter with a cutoff frequency of 159 Hz. An Analog Devices AD620A (Analog Devices, Norwood, MA) instrumentation amplifier was used to amplify the signal. The output from the accelerometer temperature sensor was buffered to reduce noise pickup and drive the signal. All analog signals were sampled at a rate of 1667 Hz. The accelerometer output was oversampled to compensate for

The accelerometer models used in this paper were based on the IEEE standard 1293-1998 [5]. An extensive accelerometer model can be found in [5], with a selection of the parameters being estimated in this paper. As an example, a linear model of the accelerometer output in acceleration units
a is given by the following equation:
a = E/K = K0 + ai

(1)

where K is the scale factor, E is the accelerometer output in electrical units, K0 is the bias, and ai is the input acceleration. The applied nonlinear model is given by
a = E/K = K0 + ai + K2 a2i + K3 a3i

(2)

where K2 and K3 are the second- and third-order nonlinear coefficients, respectively. To estimate the scale factor, an initial guess of the scale factor K was used. A scale factor error k was then estimated, and the following two models were used:
a = E/K = K0 + (1 + k)a1

(3)


a = E/K = K0 + (1 + k)ai + K2 a2i + K3 a3i .

(4)

After an estimation of the scale factor error k has been obtained, the scale factor can be updated as K  = (1 + k)K. The estimated bias K0 is also a function of the initial scale factor, such that if the scale factor is updated, the estimated bias should be updated as K0 = K0 /(1 + k). To use the acceleration output as a deterministic control input to the system, as described in Section II-E1, the acceleration was modeled by the following linear and nonlinear equations: a −K0 ) ai =(1−k)(


(5)

ai =(1−k)(
a −K0 )+K2 (
a −K0 )2 +K3 (
a −K0 )3 .

(6)

Instead of modeling the acceleration output as a function of input acceleration as
a = f (ai , α), where α is a vector consisting of the model parameters, as illustrated in Fig. 3, the acceleration is now fitted to the accelerometer output as a, β). It can be easily shown that the linear acai = f −1 (˜ celerometer model gives the same estimate of the bias and

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This shows that when the nonlinear coefficients are not included as part of the model, the estimated scale factor and bias will be corrupted by an error that is a function of the amplitude of the input acceleration. D. Parameter Models

Fig. 3. Acceleration output from the accelerometer as a function of the input acceleration and model parameters.

scale factor error. If the accelerometer model is a third-order polynomial√as given√by (4), f −1 would be a nonlinear func3 a, and
a. Equation (6) is then a Taylor series tion of
a,
expansion of third degree of f −1 about K0 . The acceleroma − K0 ) + etermodel given bythe equation ai = (1 + k)(
a − K0 ) + K3 3 (
a − K0 ) could have been also used as K2 (
an alternative. Polynomial and nonlinear fits using simulated data have been used to transfer the estimated parameter vectors between the two accelerometer models. 1) Correlated Scale Factor and Cross-Axis Sensitivity: The extended accelerometer model given in [5] includes sensitivity to accelerations that are normal to the input axis or the crossaxis sensitivity. In movements along one axis normal to the gravity vector, the cross-axis sensitivity for the axis along the gravity vector cannot be separated from the scale factor error. If cross-axis sensitivity along the axis normal to the input axis Kin [(m/s2 )−1 ] is added to the linear accelerometer model in (3), the output is given by the following equation, where g0 is the value of the local gravity vector:
a = E/K = K0 + (1 + k)ai + Kin ai g0 = K0 + (1 + k + g0 Kin )ai .

(7)

This means that the sum of the scale factor error and the cross-axis sensitivity is estimated. This can be solved by using movements along the gravity vector or a 180◦ rotation of the accelerometer about the input axis.

C. Fourier Coefficients To examine the dependence between the parameters with the nonlinear system given in (6), a Fourier expansion was done using a sinusoidal input acceleration: ai = A sin(ωt). This gave the following nonzero Fourier coefficients: a0 = 4K0 + 2K2 A2 b1 = A(k + 1 + 3/4K3 A2 ) a2 = − K2 A2 /2 b3 = K3 A3 /4.

(8)

The work described in this paper focused on characterizing the model parameters. The parameters were modeled as unknown constants, x˙ = 0. The methods could have been also used to examine long-time variations in accelerometer parameters, which means that the accelerometer parameters have to be modeled as time varying. A common way to model bias variations is to either add two distinct scalar Markov processes with different decorrelation time or simplify them as one Markov process [3]. E. System Models Two different system models were tried out during the estimation process. The first model used the accelerometer output as the deterministic control input to the system and did not include the acceleration as a state. Only the measured position was then fed as the measurement input to the Kalman filters. In this case, called the acceleration-as-control-input (ACI) model, the system equation becomes nonlinear, and the measurement update becomes linear. The second system model includes the acceleration in the state vector and models the acceleration as integrated white noise. Both the measured position and acceleration were used as measurement inputs, making the system linear with nonlinear measurement updates. This model is called the continuous Wiener-process acceleration (CWPA) model or the white noise jerk model [3]. 1) ACI System Model: The continuous system equation is a nonlinear function of the state vector and the acceleration input
where w ˜ is the input process noise u, i.e., x˙ = f (x, u) + w, ˜ 1 − t2 ). ˜ 2 )} = Qδ(t ˜ 1 )T w(t with covariance defined by E{w(t δ(τ ) is the Dirac delta function. For the linear accelerometer in (3) with all parameters modeled as unknown constants, the state vector is defined by the position p(t), the velocity v(t), the scale factor error k(t), and the bias K0 (t), i.e., x = [ p v k K0 ]T , where the time dependence of each parameter is left out for convenience. The system equation on state space form is then given by     v 0 (1 − k)(u − K )  1 0 
= x˙ = f (x, u) + w
(9)  +   w. 0 0 0 0 The measurement update to the Kalman filter is linear and is given by zk = [ 1 0 0 0 ]xk + vk , where vk is the measurement noise at time k with covariance defined by E{vkT vl } = Rk δkl (where δkl is the Kronecker delta). 2) CWPA System Model: Modeling the system acceleration as integrated white noise, the state vector is defined by x(t) = [ p v a k K0 ]T or x(t) = [ p v a k K0 K2 K3 ]T , depending on the chosen accelerometer model. The system equation on state space

STAKKELAND et al.: CHARACTERIZATION OF ACCELEROMETERS USING FILTERS AND POSITION FEEDBACK

form with the scale factor error and bias modeled as unknown constants using the linear accelerometer model is now linear and stationary and is defined by ˙ x(t) = Ax(t) + D
q(t)  0 1 0 0 0 0 1 0  = 0 0 0 0  0 0 0 0 0 0 0 0

  0 0 0 0    0  x(t) +  1  q
(t).    0 0 0 0 

(10)

The process noise q
(t) is again defined by E{
q (t1 )T q
(t2 )} =
1 − t2 ), and the variance of the scalar white noise variable Qδ(t is chosen as σq2 T = ∆a, where ∆a is in the order of an acceleration increment over a sampling period [3]. The measurement input to the  is nonlinear and is defined

state observer
k . by zk = h(xk ) = (1+k)apkk +K0k + v The CWPA system model equation is linear and time invariant, which means that the system can be discretized with a constant transition matrix, and discrete estimation filters can be used. F. Vibrations and Nonlinear System Models The experiment showed that the accelerometer picked up the vibrations induced by the ball bearings, which connected the moving platform to the rig. The amplitude of these vibrations was a function of the velocity of the platform. Using the ACI system model, this makes the system a nonlinear function of the control input and the process noise, where the latter is correlated ˙
with the state vector x(t) = f (x(t), u(t), w(x(t), t)). Integrating a system on this form is very hard [6], and the chosen solution was to approximate the process noise as uncorrelated with the system state and increase the variance. Using the CWPA model, the measurement noise will be correlated with the state vector, i.e., zk = h(xk , vk (xk )). The chosen solution was, again, to approximate the measurement noise to be uncorrelated with the system state and increase the measurement noise variance. G. State Observers Different formulations and orders of the EKF were used as nonlinear observers throughout all the estimations done in this paper. A formulation of first- and second-order continuous–discrete EKF can be found in [3], whereas a discrete formulation is found in [4]. The CWPA system model, for instance, given in (10) is time invariant and linear. Thus, it was discretized, and the discrete EKFs of first and second order from [3] were used as nonlinear observers. The system equations in the ACI system model are neither linear nor time invariant, as shown in (9). The continuous–discrete Kalman filter was applied for these systems. If F is defined as the Jacobian of ˆ˙ = f (ˆ ˆ k , the time-update part x x, u) evaluated at x = x

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of a first-order EKF is defined by the following two equations [4]: ˆ˙ = f (ˆ x x, u)

(11)


P˙ = F P + P F T + DQD

(12)

˜ is defined by E{

1 − t2 ), where Q q (t1 )T q
(t2 )} = Qδ(t whereas D was defined in (10). The equations were numerically integrated using a second-order Runge–Kutta algorithm. The time update of the second-order EKF with linear measurement update is defined by the following two coupled equations [4]: 1 ˆ˙ (t) = f (ˆ x x(t), u(t)) + ∂ 2 (f (t), P (t)) 2 T ˙
P = F P + P F + DQD.

(13) (14)

The operator ∂ 2 is here defined by a vector where the ith component is given by ∂i2 (f , A) = trace([d2 fi /dxdxT ]A). These equations were integrated with a fourth-order Runge–Kutta algorithm. H. Filter Consistency Testing All estimation filters used in this paper underwent consistency evaluation to verify the filter design. As given by [3], the normalized state estimation error squared (NEES) can be used to verify that the estimation can be accepted as zero mean, and that the error is commensurate with the filter calculated vari˜k, ˜ Tk Pk−1 x ance. The NEES at time t = tk is defined by εk = x ˆ k is the estimation error [3]. As given by ˜ k = xk − x where x [3], the NEES can be used to verify that the estimation can be accepted as zero mean and that the error is commensurate with the filter calculated variance. The average NEES over N runs should be chi-square distributed with N nx degrees of freedom, where nx is the dimension of the state vector [3]. Using Monte Carlo analysis, the NEES was tested to be within the 95% probability concentration region. The rms error of an estimated parameter after N Monte Carlo runs at a specific time is defined by

rm

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TABLE I AVERAGE RMS ERROR OF ESTIMATED PARAMETERS RELATIVE TO THE P ARAMETER V ALUE , W ITH 200-Hz V IBRATIONS A DDED TO THE SYSTEM. A IS THE MAXIMUM AMPLITUDE OF THE VIBRATIONS

for the estimated nonlinear coefficients, the control input was calculated as (6), where
a = E/K was the accelerometer output. III. R ESULTS A. Simulations 1) Filter Consistency Testing: It was found that all the tested filters could be made consistent when the system model exactly matched the filter model using linear and nonlinear accelerometer models. From Monte Carlo analysis on systems with an exact system model, it was shown that filters using the CWPA system model, in general, converged faster than those using the ACI system model toward a stable error value when errors were added to the initial state x0 . 2) Mismatched Filters: As described in Section II-F, the tested accelerometers picked up vibrations from the ball bearings and other sources. The frequency of the vibrations was in the area 200–300 Hz and with amplitudes up to 2 m/s2 . To understand the effect of this unmodeled noise source on the parameter estimation methods, the effect of adding sinusoidal vibrations with frequency of 200 Hz and amplitude proportional to the square of the system velocity to the measured acceleration was simulated. The resulting rms error for the nonlinear parameter estimates was then calculated over five runs using (15), and the mean rms error over 120 s was estimated (Table I). The values of the nonlinear coefficients were chosen to be K2 = −1e − 4 (m/s2 )−1 and K3 = 1e − 5 (m/s2 )−2 . Adding other error components to the system showed that the ACI system model was more robust, with filters based on the CWPA model relatively often becoming unstable, given significant errors in the initial state or model mismatches.

Fig. 4. Estimated scale factor k, bias K0 of an Analog Devices ADXL105 accelerometer, and the normalized squared acceleration plotted as a function of time. Results were obtained from 130 s of real data.

B. Experimental Results 1) Linear Accelerometer Models: The accelerometer models from (3) and system models from Section II-E2 were used to estimate the parameters in a linear accelerometer model with the CWPA system model. The accelerometer model from (5) and the system model from Section II-E1 were applied when using the ACI system model. All parameters were modeled as unknown constants, as described in Section II-D. When estimating a linear accelerometer model, the secondand first-order EKFs gave the same results; however, the second-order filters were shown to converge more rapidly in the presence of significant errors in the initial guess of the system state.

Fig. 5. Estimation of nonlinear parameters, scale factor, and bias of an Analog Devices ADXL105 accelerometer plotted as function of time. Results were obtained from 250 s of real data.

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system. The reason is probably that the Kalman filter of the CWPA system model has measurement updates during these periods, whereas the ACI system model uses the predicted state vector. Still, the ACI model may be more suited to estimating nonlinear and linear parameters, as it is less sensitive to system model mismatches. As seen in Table III, the linear accelerometer model seems to perform better than the nonlinear model, although estimations indicate that the very same accelerometer has significant nonlinear components, as shown in Fig. 5. This may be due to relatively high frequency variations in the parameters of the ADXL105 accelerometer, as the ADXL is a low-cost and, in an inertial tracking and navigation context, a low-performance component. Another explanation may be that a nonlinear model in an inertial tracking system is more sensitive to parameter errors. As given by [4], choosing a suboptimal system design may reduce the sensitivity to uncertain parameters. Thus, a linear model may be preferred in inertial navigation or tracking applications, unless the errors in the estimated nonlinear model parameters are sufficiently small. ACKNOWLEDGMENT The authors would like to thank Eng. F. Bakken and Eng. S. Gundersen for help and valuable craftsmanship during the construction of the experimental setup and for conducting most of the experiments, as well as Assoc. Prof. T. Lindem from the Physics Department, University of Oslo. R EFERENCES [1] D. H. Titterton and J. L. Weston, Strapdown Inertial Navigation Technology. London, U.K.: Peregrinus, 1997. [2] N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors J., vol. 1, no. 4, pp. 332–339, Dec. 2001. [3] Y. Bar-Shalom, X.-R. Li, and T. Kirubarajan, Estimation With Applications to Tracking and Navigation. New York: Wiley, 2001. [4] A. Gelb, Ed., Applied Optimal Estimation. Cambridge, MA: MIT Press, 1974. [5] IEEE Standard Specification Format Guide and Test Procedure for Linear, Single-Axis, Nongyroscopic Accelerometers, IEEE Std. 1293, 1999. [6] A. H. Jazwinski, Stochastic Processes and Filtering Theory. London, U.K.: Academic, 1970. [7] A. Savitzky and M. J. E. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem., vol. 36, no. 8, pp. 1627–1639, 1964. [8] B. P. Flannery, W. Press, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing. Cambridge, U.K.: Cambridge Univ. Press, 1992. [9] A. Lawrence, Modern Inertial Technology: Navigation, Guidance, and Control, 2nd ed. New York: Springer-Verlag, 1998. [10] M. Shuster, B. Briano, and C. Kitchin, Mounting considerations for ADXL series, accelerometers, Analog Devices. AN-379 Application note. [Online]. Available: http://www.analog.com [11] J. A. Farrell and M. Barth, The Global Positioning System & Inertial Navigation. New York: McGraw-Hill, 1998. [12] Crossbow Technology, Inc. (2003). Accelerometers. High Performance, Tactical Grade, TG Series. [Online]. Available: http:// www.xbow.com/products/product_pdf_files/accel_pdf/6020-0006-01_a_ tg%20series.pdf [13] Analog Devices, Inc. (1999). ADXL105 Datasheet. [Online]. Available: http://www.analog.com/UploadedFiles/Data_Sheets/ADXL105.pdf

Morten Stakkeland was born in Flekkefjord, Norway, in 1976. He received the Cand. Scient. (M.Sc.) degree in physics from the University of Oslo, Oslo, Norway, in September 2003. He is currently working toward the Ph.D. degree at the University Graduate Center (UniK), Kjeller, Norway, in cooperation with the Department of Engineering Cybernetics, Norwegian University of Science and Technology (NTNU), Trondheim, Norway. His Ph.D. research is focused on sensor modeling and target tracking using multiple radars and transponders in sea, air, and land surveillance systems. He is currently with FMC Technologies, Asker, Norway, where he is working on advanced subsea instrumentation and control systems. His research interests include sensor modeling, estimation, multisensor fusion, and instrumentation.

Gunnar Prytz (A’02–M’03) was born in Aalen, Norway, in 1972. He received the M.Sc. and Ph.D. degrees in experimental physics and biophysics from the Norwegian University of Science and Technology, Trondheim, Norway, in 1997 and 2001, respectively. Since 2001, he has been with the ABB Corporate Research, Billingstad, Norway, as a Scientist. His research interests include industrial communication, instrumentation, signal processing, and robotics. He is also actively involved in standardization within the International Electrotechnical Commission (IEC), where he is a Project Member of the IEC 62439: high availability automation networks standardization project.

Wilfred E. Booij received the M.Sc. degree in applied physics from the University of Twente, Enschede, The Netherlands, in 1994 and the Ph.D. degree in applied superconductivity from the University of Cambridge, Cambridge, U.K., in 1997. The work described in this article resulted from his engagement as a Senior Scientist with the Microsystems and Nanotechnology group of Stiftelsen for industriell og teknisk forskning ved Norges Tekniske Høgskole (SINTEF): a large contract research organization based in Oslo and Trondheim, Norway. The SINTEF group has a long history in the design and manufacture of microsystems solutions for industry going back to the late 1950s. He is currently the Chief Technology Officer with Sonitor Technologies AS, Oslo: a company that develops and markets indoor positioning systems based on ultrasound. He has published over 30 articles in refereed journals in the areas of applied superconductivity, nanometer-scale structuring, and instrumentation.

Steve Tveit Pedersen (M’99) was born in Stavanger, Norway, in 1969. He received the M.Sc. degree in electrical engineering from Delft University of Technology, Delft, The Netherlands, in 1997. From 1997 to 2006, he was with ABB Corporate Research, Billingstad, Norway, focusing on instrumentation for the control of industrial robots. Since 2006, he has been the Head of product development with Enfo Broadcast AS, Oslo, Norway: a company providing products and services for the energy market.