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`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 52, NO. 12, DECEMBER 2004
`
`Concept and Application of LPM—A Novel
`3-D Local Position Measurement System
`
`Andreas Stelzer, Member, IEEE, Klaus Pourvoyeur, and Alexander Fischer
`
`Abstract—Precise measurement of the local position of moveable
`targets in three dimensions is still considered to be a challenge.
`With the presented local position measurement technology, a novel
`system, consisting of small and lightweight measurement transpon-
`ders and a number of fixed base stations, is introduced. The system
`is operating in the 5.8-GHz industrial–scientific–medical band and
`can handle up to 1000 measurements per second with accuracies
`down to a few centimeters. Mathematical evaluation is based on a
`mechanical equivalent circuit. Measurement results obtained with
`prototype boards demonstrate the feasibility of the proposed tech-
`nology in a practical application at a race track.
`
`Index Terms—Frequency-modulated continuous wave (FMCW),
`global positioning system (GPS),
`local position measurement
`(LPM), three-dimensional (3-D) position estimation.
`
`I. INTRODUCTION
`
`N UMEROUS applications require the knowledge of the
`
`exact position of moving targets. With the global posi-
`tioning system (GPS), there exists a widespread technology for
`global positioning with limited accuracy (without additional
`corrections) and measurement speed. For industrial tracking
`applications, it is often required to know the position of a
`target within a locally restricted area [1], [2]. The local position
`measurement (LPM) system fills this gap by providing the
`actual position of numerous targets in three dimensions with
`high accuracy and short measurement cycles [3], [4]. The LPM
`concept is, in some aspects, inverse to GPS as there are active
`transponders operating around 5.8 GHz, whose positions are
`measured, and as there are fixed passive base stations (BSs)
`around the covered field of view. The applications of LPM
`reach from the tracking of a single sportsman or a whole team
`in sports applications to the tracking of autonomous vehicles
`in industrial warehouses or the determination of the position of
`numerous vehicles and carts in operation on big airports.
`In Sections II and III, the LPM concept and measurement
`principle are presented, followed by a novel mechanical equiva-
`lency for the mathematical problem on hand in Section IV. Hard-
`ware details are given in Section V and measurement results are
`presented in Section VI.
`
`Manuscript received April 21, 2004; revised July 28, 2004. This work was
`supported in part by the Linz Center of Mechatronics (LCM) and by the Austrian
`Industrial Research Promotion Fund (FFF).
`A. Stelzer is with the Institute for Communications and Information
`Engineering, Johannes Kepler University Linz, A-4040 Linz, Austria (e-mail:
`a.stelzer@icie.jku.at).
`K. Pourvoyeur is with the Linz Center of Mechatronics GmbH, A-4040 Linz,
`Austria (e-mail: klaus.pourvoyeur@lcm.at).
`A. Fischer is with Abatec Electronic AG, A-4844 Regau, Austria (e-mail:
`fischer@abatec.at).
`Digital Object Identifier 10.1109/TMTT.2004.838281
`
`Fig. 1. Basic arrangement of transponders, BSs, and MPU, and the signal flow
`within the LPM system.
`
`II. OVERVIEW OF THE LPM CONCEPT
`
`The basic structure of the LPM system is sketched in Fig. 1.
`For simplicity, only one measurement transponder (MT) and
`four BSs are drawn. A master processing unit (MPU) is
`connected to the network and collects raw data for the final
`transponder position calculations.
`At least four BSs are arranged on exactly known positions
`around the field of interest. The unknown position of the MT
`is determined by means of time-of-flight (TOF) measurements
`of electromagnetic waves traveling from the transponder to the
`BSs.
`As the distances are short—the TOF is in the range of some
`hundreds of nanoseconds to microseconds—an evaluation in the
`frequency domain based on linear chirps is chosen. For TOF
`measurements, a common and highly accurate time base on the
`transponder and BSs would be necessary. To circumvent this,
`the time difference of arrival (TDOA) to different BSs is in-
`stead measured. Nevertheless, a synchronization of the BSs is
`required. As atomic clocks or high-speed optical fibers have to
`be ruled out due to cost reasons, the synchronization problem
`is solved by applying an additional low-cost transmitter, which
`serves as a reference transponder (RT) at a well-known and fixed
`position.
`From an operational point-of-view, the reference transmitter
`operates continuously to keep the BSs synchronized, whereas
`the individual MTs are activated by means of a trigger telegram.
`For this reason, the BSs can also transmit control telegrams, but
`during the measurement cycle, they operate as receiver only.
`Furthermore, the transponder can send additional bytes of infor-
`mation to the BS, e.g., some measurement information captured
`by the mobile transponder.
`During each measurement slot, only one MT is active. This
`time sharing guarantees that several MTs do not interfere with
`
`0018-9480/04$20.00 © 2004 IEEE
`
`RFC - Exhibit 1020
`
`

`
`STELZER et al.: CONCEPT AND APPLICATION OF LPM
`
`Fig. 2. Sketch of ramp signals in the LPM system with frequencies plotted
`versus time.
`
`one another, moreover, the calculating time does not increase
`with the number of transponders.
`
`III. MEASUREMENT PRINCIPLE
`
`The basic concept of LPM relies on the well-known fre-
`quency-modulated continuous-wave (FMCW) radar [5] prin-
`ciple. In contrast to the FMCW principle, where the reflected
`and time shifted wave is mixed with a part of the transmitted
`signal, in LPM, the linear chirp received from the transponder
`is mixed in each BS with an independently generated chirp [6].
`Furthermore, the reference chirp is simultaneously sent with
`the measurement chirp and used for synchronization purposes.
`A detailed insight is given by the signal diagram depicted in
`Fig. 2.
`The RT continuously transmits reference chirps and each BS
`(
`) internally generates linear chirps with an unknown time
`shift
`. After having received an activation command, the
`selected measurement transponder (MT) responds with a linear
`chirp at time
`. The time of flight
`between RT and
`and MT and
`can be written in terms of distances
`
`as
`
`(1)
`
`(2)
`
`where
`is the velocity
`denotes the Euclidian distance, and
`of light. Mixing the received RT and MT signals with the inter-
`nally generated chirp leads to the following IFs:
`
`which leads, after a spectral evaluation, to a time difference
`of the corresponding signals in the time domain
`
`2665
`
`(6)
`
`Note that,
`are unknown, but identical for all BS
`and
`evaluations, resulting in a constant offset
`
`(7)
`
`IV. POSITION CALCULATION
`
`A. Geometrical Illustration
`Basically, LPM measures the time difference of electro-
`magnetic waves traveling from different transponders to the
`BSs, containing an unknown offset
`in the raw data.
`Because of a known and constant propagation velocity of the
`electromagnetic wave, these time differences can be viewed
`as distances.
`From a mathematical point-of-view, the position calculation
`in LPM is similar to the methods used in the GPS, as there are
`satellites with known positions and a receiver with an unknown
`position and a time offset due to a missing synchronization
`between the receiver and satellites. Therefore, the calculations
`for the dilution of precision (DOP) and all its derived quantities
`can be adapted from the mathematics used in the GPS [7].
`This can be used to optimize the arrangement of BSs for the
`problem on hand. For the GPS, it is possible to track this
`offset, whereas in LPM, the unknown offset is not determined
`by the past offsets.
`Due to the unknown offset, a measurement of a single BS
`contains no information about the position of the MT. Only a
`combined data set of several BSs allows us to compute the po-
`sition of the MT, e.g., for three-dimensional (3-D) applications,
`the result of two BSs restricts the solution of the MT position
`to a hyperboloid. Hence, for 3-D applications, the measurement
`results of at least four BS are necessary to calculate the three
`unknown coordinates of the MT and the offset. In case of only
`four BSs, no statement on the consistency of the measurement
`set is possible. Statements about the absolute accuracy are only
`possible by using calibrated reference points.
`Equation (6) describes the special case without measurement
`errors. This equation can be extended with an error-term
`representing the measurement error at
`by
`
`(3)
`
`(4)
`
`with
`
`defined by
`
`(8)
`
`(9)
`
`denotes the slope of the linear ramp—it is assumed that
`where
`all chirps have an identical slope. Now, each BS can calculate
`the frequency difference
`
`(5)
`
`.
`In Fig. 3, (8) is illustrated geometrically with
`From a mathematical point-of-view, it is irrelevant whether the
`offset is positive or negative— is assumed to be greater than
`zero.
`
`

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`2666
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`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 52, NO. 12, DECEMBER 2004
`
`The rest position of the mechanical system is given by a min-
`imum of the total potential energy
`depending on the object
`position MT and the unknown offset
`
`Amazingly, for
`
`(12)
`
`(13)
`
`the two optimization problems (10) and (12) are identical. Based
`on the minimum of the total potential energy, it is possible to
`evaluate a mean error
`
`Fig. 3. Geometrical illustration of the LPM measurement principle in the 2-D
`case.
`
`of the measurement set with
`
`(14)
`
`(15)
`
`describes the consistency of the measure-
`This mean error
`ment set, it does not state anything about the absolute accuracy
`of the determined position.
`As a first approximation, the estimated object position can be
`distinguished as Gauss distributed. In this case, the variance
`of the estimated object position can directly be estimated by the
`mean error
`as follows:
`
`Fig. 4. Mechanical interpretation of the LPM measurement principle.
`
`(16)
`
`can
`The position of the MT, and the measurement offset
`by calculated, for example, by minimizing the weighted sum of
`the squared errors
`
`Additional information about the accuracy of the estimated
`position is of enormous importance to improve the performance
`of tracking filters.
`
`(10)
`
`represents
`of the quality function
`The weighting factor
`the measurement accuracy of
`, and
`is the number of
`BSs available.
`
`B. Mechanical Interpretation
`It is possible to interpret the measurement principle of LPM
`in a mechanical sense. The variable
`corresponds to the
`length of the spring . The weight representing the measurement
`accuracy corresponds to the spring stiffness
`. The error
`of
`corresponds to the expansion of the spring . Fig. 4
`sketches the mechanical interpretation of the measurement prin-
`ciple for LPM.
`The potential energy
`of all springs, representing the total
`energy of the mechanical system, is calculated as a sum of the
`potential energy
`of each individual spring as follows:
`
`(11)
`
`C. Solver
`During the last three centuries, mechanical engineers such
`as Euler, Lagrange, and others developed powerful methods to
`derive differential equations for mechanical systems and espe-
`cially to determine the rest position of these systems. The me-
`chanical interpretation of the LPM measurement principle gives
`us the ability to use these highly advanced methods directly [8].
`Hence, to solve the minimization problem of (12), we used
`a multidimensional damped Newton iteration for nonlinear re-
`gression [9], which was specially adapted to fit the demands of
`mechanical problems.
`The nonlinear and, in the general case, redundant opti-
`mization problem could also be solved, for example, by using
`advanced filter concepts [10]. The potential of the applied
`specially adapted multidimensional damped Newton iteration
`method for different starting points is shown in Fig. 5 based on
`a real BS arrangement and synthetic measurement data without
`measurement errors. Plotted are the target position (marked
`with a filled square), the position of a BS used for position
`detection (marked with a filled circle), and the position of a
`BS for which no measurement data is available (marked with
`unfilled circles).
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`

`
`STELZER et al.: CONCEPT AND APPLICATION OF LPM
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`
`Fig. 6. Block diagram of a transponder in the LPM system.
`
`Fig. 5. Ways of iteration for a damped Newton iteration method for different
`starting points.
`
`The quality function defined by the weighted sum of the
`squared errors can be interpreted as a potential field, its contour
`lines are visualized by solid lines. The gradient of the quality
`function is a vector valued function. For each point in the
`two-dimensional (2-D) plane, the direction of the arrows shows
`the direction of the gradient for this possible position of the MT,
`the lengths of these arrows correspond to the absolute value
`of the gradient. The measurement offset
`was calculated
`iteratively for each point in the plot. The rough positions of
`the available BS are chosen as starting points of the iteration.
`The ways of iteration are displayed by solid lines. As can be
`seen, the signals of four uneven distributed BSs were used to
`determine the position of the MT. This uneven distribution of
`the position of the BS around the target leads to a breaking up
`of the quality function on the opposite side of the BS. Such
`a BS distribution shows a worst case scenario; the breaking
`up effect can be suppressed by choosing the BS more uni-
`formly distributed around the MT. In the breaking-up area, the
`gradient becomes very small. As can be seen, our specially
`adapted multidimensional damped Newton iteration method
`can handle these small gradients almost perfectly. Within a very
`few number of iteration steps, the solution of the optimization
`problem has been found. Even the choice of the starting point
`of the iteration is uncritical.
`
`V. LPM HARDWARE
`
`In Fig. 6, the block diagram of the transponder is shown. The
`receive path with a low-noise amplifier (LNA) for the recep-
`tion of the activation command sent by the actual master BS is
`sketched in the upper half of the block diagram. The RF paths
`are separated by a switch. When activated, a measurement chirp
`is generated by the chirp generator, amplified by the power am-
`plifier (PA), and finally transmitted via the antenna.
`Fig. 7 shows the small and lightweight transponder printed
`circuit board (PCB).
`The elementary function blocks exist in both the device’s
`transponder and BS, mostly with an inverted signal flow path.
`
`Fig. 7. Transponder PCB.
`
`A power supply, programmable logic device (PLD), master con-
`trol unit (MCU), and clock and chirp generator are common to
`both devices.
`In the BS, which works as a receiver during the measurement
`cycle, the measurement chirp transmitted by the transponder is
`mixed with an internally generated chirp. Coherent mixing of
`these signals demands extremely high linearity of the generated
`chirps [6]. The digitized IF signal is pre-evaluated using a digital
`signal processor (DSP) and preprocessed data is transmitted to
`the MPU via the network.
`In the current development state, the transponder hardware is
`as small as a credit card and weighs approximately 75 g. The
`BSs are slightly larger, but fit into approximately 1 dm and are
`generally mounted on masts around the field of view.
`
`VI. MEASUREMENT RESULTS
`
`The motor sports center at the Wachau Race Track, Melk,
`Austria, has been equipped with a prototype LPM system. An
`aerial view is shown in Fig. 8. The LPM control unit was in-
`stalled at the paddock club above the pit lane.
`The measurement accuracy was tested with a transponder
`mounted on a precision rail. The results obtained show a posi-
`tion error in the range of few centimeters at measurement rates
`of up to 1000 per second. The coverage of a single measurement
`cell is up to 500 m 500 m. Larger areas can be monitored by
`combining basic measurement cells.
`A more illustrative example is tracking of a car on an infield
`lap on the race track, as shown in Fig. 9.
`The solid line visualizes the trajectory of the car in the 2-D
`plane, a filled circle marks the position of a BS. The start and
`finish points of the car on the home straight are nearly identical;
`the track was driven clockwise. The maximum velocity of the
`
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`IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 52, NO. 12, DECEMBER 2004
`
`Fig. 8. Aerial view of the Wachau Race Track (reprinted with permission of
`the Austrian automobile club ÖAMTC).
`
`Fig. 10. Detailed view of a section for the infield lap on the Wachau Race
`Track.
`
`Fig. 9. Measured position data of a car on an infield lap on the Wachau Race
`Track.
`
`car was approximately 80 km/h. The area surrounded by dashed
`lines is shown in detail in Fig. 10.
`As we can see, almost all estimated positions are in a tube
`of
`10 cm, visualized by dashed lines. These results where
`achieved without any tracking. Fig. 11 shows the corresponding
`total potential energy. To improve the comparableness to
`Fig. 10, the abscissa was scaled in -coordinates of the object
`and not in samples, as it would be the nature of this signal.
`As we can see, the total potential energy increases clearly
`around
`m and
`m. These increases are di-
`rectly related to prongs of the estimated -coordinate of the ob-
`ject position.
`By using
`, or Kalman filters for object tracking
`,
`[11], the precision of the position detection can be increased
`clearly. Another advantage of such filters would be an estima-
`tion of the velocity and the acceleration of the target. To achieve
`an adequate performance of such tracking filters, the approx-
`imate knowledge of the accuracy of the estimated position is
`needed. By using (14) and (16), the total potential energy can
`be directly converted into the variance
`of the object posi-
`tion.
`The LPM systems gives us the ability to determine the po-
`sition of several cars or other targets for each moment, for ex-
`
`Fig. 11. Total potential energy of the spring-based model for position
`evaluation with abscissa scaled in x-coordinates of the object.
`
`ample, time differences of two cars are now available for every
`point in time and are no longer restricted to the end of certain
`sectors.
`
`VII. CONCLUSION
`
`With local position measurements, a novel technology for
`fast and accurate LPMs is available. The LPM system operates
`within a license-free industrial–scientific–medical (ISM) band
`and the current design is compliant to European regulations.
`Within a covered range of 500 m in square, the accuracy is
`better than 10 cm, depending on multipath and line-of-sight
`connections. Applications spread from analyzing movements
`in sports over industrial positioning to autonomous vehicle and
`cart control.
`
`REFERENCES
`[1] M. Vossiek, L. Wiebking, P. Gulden, J. Wieghardt, and C. Hoffmann,
`“Wireless local positioning—Concepts, solutions, applications,” in
`Proc. Radio Wireless Conf., Aug. 2003, pp. 219–224.
`
`

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`STELZER et al.: CONCEPT AND APPLICATION OF LPM
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`2669
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`Klaus Pourvoyeur was born in Ehenbichl, Austria,
`in 1977. He received the Dipl.-Ing. (M.Sc.) degree in
`mechatronics from Johannes Kepler University Linz,
`Austria, in 2004.
`He was with the Institute for Communications
`and Information Engineering, University of Linz.
`In 2004, he joined the Linz Center of Mechatronics
`GmbH, Linz, Austria. His research interests are
`position measurement for real-time applications and
`object tracking.
`
`Alexander Fischer was born in Grieskirchen, Aus-
`tria, in 1973. He received the Dipl.-Ing. degree in
`mechatronics from the Johannes Kepler University
`of Linz, Linz, Austria, in 1999.
`He is currently with Abatec Electronic AG, Regau,
`Austria, where he is responsible for the development
`of a LPM system. His primary scope of functions is
`the design of LPM technology and the coordination
`of development in the fields of radar sensors, data
`transfer, and position evaluation.
`
`[2] M. Vossiek, R. Roskosch, and P. Heide, “Precise 3-D object position
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`1999, pp. 234–237.
`[3] A. Stelzer, A. Fischer, M. Vossiek, and A. Söser, “A novel 3-D local
`position measurement (LPM) technology,” in Proc. Sensor Congr., vol.
`I, Nuremberg, Germany, May 2003, pp. 341–344.
`[4] A. Stelzer, A. Fischer, and M. Vossiek, “A new technology for precise
`local position measurement—LPM,” in IEEE MTT-S Int. Microwave
`Symp. Dig., vol. 2, June 2004, pp. 655–658.
`[5] M. I. Skolnik, Introduction to Radar Systems, 3rd ed. Boston, MA:
`McGraw-Hill, 2001.
`[6] A. Stelzer, K. Ettinger, J. Höftberger, J. Fenk, and R. Weigel, “Fast and
`accurate ramp generation with PLL-stabilized 24-GHz SiGe VCO for
`FMCW and FSCW applications,” in IEEE MTT-S Int. Microwave Symp.
`Dig., vol. 2, June 2003, pp. 893–896.
`[7] E. D. Kaplan, Understanding GPS: Principles and Applica-
`tions. Boston, MA: Artech House, 1996.
`[8] A. I. Lurie, Analytical Mechanics. Berlin, Germany: Springer-Verlag,
`2002.
`[9] G. A. Seber and C. J. Wild, Nonlinear Regression. Hoboken, NJ:
`Wiley, 2003.
`[10] L. Wiebking, M. Vossiek, L. Reindl, M. Christmann, and D. Mastela,
`“Precise local positioning radar with implemented extended Kalman
`filter,” in Proc. 33rd Eur. Microwave Conf., Oct. 2003, pp. 459–462.
`[11] E. Brookner, Tracking and Kalman Filtering Made Easy. Hoboken,
`NJ: Wiley, 1998.
`
`Andreas Stelzer (M’00) was born in Haslach an der
`Mühl, Austria, in 1968. He received the Diploma
`Engineer degree in electrical engineering from the
`Technical University of Vienna, Vienna, Austria, in
`1994, and the Dr.techn. degree (Ph.D.) in mecha-
`tronics (with honors sub auspiciis praesidentis rei
`publicae) from Johannes Kepler University Linz,
`Linz, Austria, in 2000.
`In 1994, he joined Johannes Kepler University, as
`an University Assistant. Since 2000 he has been with
`the Institute for Communications and Information
`Engineering, Johannes Kepler University. In 2003, he completed his habilitation
`thesis and became an Associate Professor with Johannes Kepler University.
`His research focuses on microwave sensors for industrial applications, RF and
`microwave subsystems, electromagnetic compatibility (EMC) modeling, digital
`signal processing (DSP), and microcontroller boards, as well as high-resolution
`evaluation algorithms for sensor signals.
`Dr. Stelzer is member of the Austrian Engineering Society (OVE). He is an as-
`sociate editor for the IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS.