Indoor Positioning Using Frequency Translators Heinz Mathis, University of Applied Sciences Rapperswil, Switzerland Daniel Megnet, University of Applied Sciences Rapperswil, Switzerland Thomas Kneubühler, University of Applied Sciences Rapperswil, Switzerland Andreas Thiel, u-blox AG, Thalwil, Switzerland Etienne Favey, u-blox AG, Thalwil, Switzerland

BIOGRAPHIES

ABSTRACT

Heinz Mathis is a Professor of mobile communications at the University of Applied Sciences Rapperswil, Switzerland. He received the Diploma in electrical engineering from the Swiss Federal Institute of Technology (ETH), Zurich, in 1993, and the Ph.D. in EE at the same university in 2001, respectively. His research interests include signal processing for wireless communication systems and positioning systems.

Whereas most GPS repeater based indoor navigation systems apply time switching between the different repeaters, the proposed system uses different frequencies among the repeaters. Rather than cycling through the different repeaters, the repeaters all transmit simultaneously in time. However, prior to retransmission, each repeater translates the signal onto a different frequency location within the ISM band at 2.4 GHz. Such a system has a couple of significant advantages: First, precision accuracies reported in [ 2] and [5] are preserved since the fundamental arrangement (e.g., geometry, signal structure etc.) remains. Second, no time synchronization between the repeaters/translators is necessary. The receiver does not need to synchronize its time to the repeaters (apart from the usual GPS range/time reception and computation). Third, there is no danger of GPS interference. Other standard GPS equipment will either work undisturbed indoors if it has weak-signal capability or will not be interfered outdoors close to buildings containing the translator system. Fourth, the RF front-end of such a repeater/translator might potentially be combined with WLAN access points, since 802.11b/g use the same band. Coexistence of WLAN and GPS translator technology is provided through the spread-spectrum approach of either of the systems. Different navigation solutions are shortly discussed and convergence regions for a couple of setups of translator geometries are given based on Matlab simulations. Complying with FCC and other regulations as far as radiation in ISM bands are considered, the current approach is believed to gain more acceptance than other systems, where interference to the L1 band is a potential hazard.

Daniel Megnet received the Diploma in electrical engineering from the University of Applied Sciences Rapperswil, Switzerland, in 2002. He is working as a soft- and hardware research assistant at the University of Applied Sciences Rapperswil. Thomas Kneubühler received his Diploma in electrical engineering from the Swiss Federal Institute of Technology (ETH), Zurich, in 1992. He is working as a research assistant at the University of Applied Sciences Rapperswil. Andreas Thiel is head of hardware R&D at u-blox and co-founder of the company. He holds a Masters of Science in electrical engineering from Aachen Technical University. Until 1997, prior to founding u-blox, Mr. Thiel served as research assistant in the MCM research group at ETH Zurich. Mr. Thiel is member of IEEE and ION. Etienne Favey is a Research and Software Development Engineer at u-blox AG, Thalwil, Switzerland. He obtained his Ph.D-degree in Geodesy and Geomatics in 2001 from the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland. His research interests include innovative positioning techniques, and combination of GPS with other methods and sensors.

1 INTRODUCTION The current art of indoor positioning technology deploys one or several of the following principles: Weak-signal approach, repeater, WLAN access points navigation, mobile networks navigation, and pseudolites. Each of these approaches has its benefits but suffers from very distinct drawbacks: The weak-signal receiver uses long-time integration

∗ This project was supported by the Swiss research funding program CTI 6979.1.

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to overcome the low SNR associated with indoor signals. This comes at the cost of very slow acquisition times (due to the extensive search) or the need of aiding data such as rough position, ephemerides etc., which have to be provided by other networks. The pure GPS repeater impresses by its simple and robust appearing but delivers the position of the roof antenna, regardless of the actual position of the user within the building. Access points of WLAN networks might be used to do trilateration, but they are hardly ever time synchronized. Neither are GSM base stations, where the additional difficulty of non-line-of-sight and multipath propagation deteriorates the achievable position accuracy. Highest position accuracy can be achieved by so-called pseudolites. Pseudolites are like real GPS satellites using a distinct Gold code to make them appear unique within the environment used. However, the hardware associated with such a system is expensive. Also, exact time synchronization of the different pseudolites is paramount. Recently, another approach has appeared by two independent research groups [2], [5]. In their respective system both research groups apply a set of GPS repeaters that transmit their repeated GPS signal in their own disjoint timeslot. The GPS position obtained from each repeater is identical as long as they are attached to the same roof antenna. By measuring the clock bias values for each repeater and knowing the repeater location, a position relative to the roof antenna may be obtained. The arbitration of the time slots for the repeaters has to be administered centrally. Besides, the mobile unit needs a means to get to know about these cycling periods. Furthermore, the reradiation of signals at the GPS L1 frequency is a tricky business, a possible influence on the signals received outdoor close-by cannot be excluded.

Figure 1: Indoor positioning using GPS repeaters.

the liberty, to adapt their multiplexing rate to their proper needs of fast acquisition, high precision, or any other navigation strategy. The intermediate baseband processing task remains unchanged. If only one repeater/translator station is received, the user can still fall back to the single repeater solution and obtain the position of the roof antenna at any time. • The FDMA approach within the 2.4 GHz ISM band is compatible to FCC and other regulations. The interference with the original GPS SPS signal is avoided, allowing the use of weak-signal receivers at the same location and having no negative influence to close-by outdoor locations. • An installed indoor navigation system using the proposed FDMA scheme can be extended with additional repeaters with no imperative need to change the configuration for any existing repeaters or indoor GPS receivers.

2 MOTIVATION Evaluating the time difference of arrival (TDOA) of repeated GPS signals coming from different indoor locations allows a GPS receiver to locate its position relative to these transmitters. The concept is illustrated in Figure 1. To prevent any contention between the signals of the different repeaters, a multiplexing scheme must be implemented in such an indoor navigation system. Using time division multiple access (TDMA) as proposed by [2] and [5] has the advantage that the GPS signal can be sent on the original L1 frequency without the need for modifying the GPS receiver’s RF frontend. In this paper, we propose a GPS-based indoor positioning system using frequency division multiple access (FDMA) in the 2.4 GHz ISM band. This approach needs a modification of the receiver’s RF frontend, as the GPS receiver must first mix the repeated signals down from the ISM band back to the original L 1 band before processing. However, this method has some important advantages from a system’s point of view:

• Extending the proposed system in a way that each repeater transmits the GPS signal on several assigned frequencies can improve the precision of the navigation solution, as this method has the potential to reduce multipath issues significantly.

3 SYSTEM SETUP Figure 2 shows a block diagram of the translator infrastructure installed within a building. The GPS signal is received by the roof antenna, amplified by a low noise amplifier and filtered by a bandpass filter centered at the L 1 frequency. From there, the signal is distributed to GPS repeaters having each preferably the same distance (i.e., the same signal propagation delay) from the roof antenna. Each GPS repeater translates the GPS signal into the 2.4 GHz ISM band using a mixer with a local oscillator. For FDMA, the frequencies f1 . . . fn can differ by some hundreds of kHz or several MHz. After filtering the mixed signal to the limits

• No frame synchronization is needed between the repeaters and the receiver, eliminating any additional synchronization concept and giving the GPS receiver ION GNSS 18th International Technical Meeting of the Satellite Division, 13-16 September 2005, Long Beach, CA

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4 FREQUENCY TRANSLATION GPS Satellite Signals

Roof-Top Antenna

GPS repeaters using frequency translation not only have the advantage to cause no interference with the original GPS SPS signal in the L1 band, but also allow a receiver to evaluate the signal of any repeater at any time, as the repeaters can transmit their signal simultaneously using an FDMA scheme. However, translating the GPS SPS signal to another frequency band introduces some additional effects that must be considered in the algorithms of the GPS receiver. Differences can be found in the Doppler measurement. Furthermore, the frequency offset between the mixers of the transmitting and receiving frontend must be taken into account when the navigation solution is evaluated.

Antenna

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4.1 Doppler Measurement

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A standard GPS receiver uses Doppler measurements to determine the velocity of the user [6]. Any difference of velocity ∆v between the transmitter and the receiver being projected to the direction of signal transmission e tr will generate a frequency shift due to the Doppler effect. For a carrier signal with the nominal frequency f c and a velocity of propagation c, the frequency shift ∆f results to: ∆f =

fn

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Figure 2: GPS repeaters using frequency translators.

∆v · etr · fc c

(1)

For our proposed indoor application, translating the carrier frequency f c from the L 1 band to the 2.4 GHz ISM band will also change the part of the measured Doppler frequency ∆f caused by the velocity of the user.

4.2 Mixer Frequency Offset For a cost-effective implementation of the frequency translation to the 2.4 GHz ISM band and back to the GPS L 1 band, the system should be insensitive to any low frequency offset generated by the mixers’ local oscillators being slightly out of tune. Every designer of a GPS receiver has to deal with frequency offsets of the GPS signals due to the Doppler effect caused by the motion of the satellites and possibly the user. The Doppler frequency from the satellites can reach up to 5 kHz with a maximum Doppler frequency change of about 1 Hz/s. For indoor applications, the maximum Doppler frequency caused by the user will be dominated by the rotation of the earth, which compensates the satellites’ Doppler shift for some part. However, the user can induce variations of the Doppler frequency that are distinctly higher than 1 Hz/s as an acceleration of 1 g can vary the Doppler frequency of a 2.4 GHz ISM signal by up to 78 Hz/s. These values provide a framework of requirements for a practical implementation of the mixers used for frequency translation. If an indoor positioning system using frequency translators shall be for the most part compatible with existing standard tracking-loop implementations, the mixer frequency offset should better not exceed about 1 kHz. This

of the 2.4 GHz ISM band, the signal is amplified and transmitted by the repeater antennas located at defined indoor positions.

Figure 3: GPS receiver using frequency translation.

Figure 3 shows a block diagram of the mobile indoor receiver. The signals within the 2.4 GHz ISM band are amplified and filtered before they are mixed down to the L 1 band and processed by a standard GPS receiver. The receiver can select the signals of any desired GPS repeater by choosing the appropriate mixer frequency f Rx .

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offset corresponds to a frequency accuracy of the mixer’s local oscillator of about 1 ppm. Furthermore, the frequency offset difference between any subsequent measurements should not exceed about 100 Hz/s. In the proposed indoor positioning system, the GPS repeaters are transmitting at different frequencies f Ij within the 2.4 GHz ISM band. The receiver is switching sequentially from one repeater frequency to the next. The faster switching occurs, the lower the frequency difference between the translated GPS signals need to be.

to fI of the ISM-Band and back to the L 1 frequency will not be completely synchronous. The offset between the transmitter’s and receiver’s mixer will be an additional portion of the measured Doppler frequency, the mixer frequency offset ∆f M . Taking these three effects into account and assuming a fixed roof antenna located at r r and a fixed repeater j located at rj , Equation (2) must be modified in the following way:

4.3 Navigation Solution

Di = −

Mixer frequency offset is a new element in the navigation solution, having no exact counterpart in the standard algorithms. To emphasize the differences to a classical navigation solution, the standard GPS application shall be considered first. The measured Doppler frequencies D i are used for calculating the user velocity v u , applying the following equations for each space vehicle i, according to [ 6]:
Di = −

v i − v u ri − ru · c |ri − ru |

with

ri − rr |ri − rr |

(4)

ep =

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Making a difference between the clock drift f u and the mixer frequency offset ∆f M is not only a question of systematic listing of different frequency offset sources but has a very practical impact for the design of the tracking loop and the Kalman filter of the navigation solution.

(2)

The satellite velocity vi can be calculated from ephemeris data. By subtracting the user velocity v u , dividing by the speed of light c, projecting this velocity vector to the line of sight r i − ru from the user to the satellite and multiplying it with the nominal L 1 -frequency, the effective Doppler frequency of the GPS signal seen by the user can be calculated. The measured Doppler frequencies D i will differ from this theoretical value due to the clock drift f i of the transmitting satellites and f u of the GPS receiver. The clock drift f i of the space vehicles is almost negligible and can even be corrected using ephemeris data. With the help of a known or estimated user position r u , the three coordinates of the user velocity v u and the user clock drift f u can be determined whenever the Doppler frequencies Di of a minimum of four different C/A coded signals are measured, normally implemented within the GPS receiver’s tracking loop. For the proposed GPS repeaters with frequency translation, three additional effects must be considered compared to the standard navigation solution:

4.4 Estimation of the Mixer Frequency Offset While the clock drift of the GPS receiver will continuously vary its time base compared to the absolute GPS time, the mixer frequency offset will not contribute to this change of clock bias. For indoor positioning systems using frequency translators, the total frequency offset can still be determined from Doppler measurements of the GPS SPS signal, but has no fixed relationship with the variations of the clock bias any more. The measured frequency offset as well as the carrier phase should not directly be used for augmenting the tracking loop control or for filtering the navigation solution with the Kalman filter, as this value must first be corrected by the part of deviation induced by the mixer frequency offset. With both, the frequency offset and the clock bias determined by the navigation solution, the mixer frequency offset ∆fM can be calculated by subtracting the change of user’s clock bias b˙ u (corresponding to the user’s clock drift fu ) from the total frequency offset f tot , which results as the least-squares adjustment solution of the velocity equations of the navigation solution:

• For any indoor application using GPS repeaters, the navigation solution will be accomplished for the roof antenna, which is typically a fixed position within the ECEF coordinate system. Therefore, the Doppler frequency consists of two parts, the velocity of the space vehicle projected to the line of sight from the roof antenna to the satellite and the velocity of the user’s motion toward the repeater.

Di = −

• Mixing up the GPS signal to the frequency f I within the 2.4 GHz ISM-Band will linearly increase the Doppler frequency caused by the user velocity.

v · e  v · e  i i u p · L1 + · fI + ftot − fi (6) c c ∆fM = ftot − b˙ u

(7)

An alternative way to determine the mixer drift is to compare the L1 carrier phase to the symbol phase of the C/A code, an approach which we have not further pursued.

• Assuming a practical implementation, the mixer frequencies fM used for the translation of the GPS signal

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 · L 1 + fu − fi

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fast as possible to maximally prevent disturbances in pseudorange measurement. Remaining transients within the pseudorange tracking must be settled first before evaluating a reliable distance from a newly selected repeater. Long settling times will not only lower the rate of locating the user’s indoor position, but will also decline the accuracy of the calculation, as small differences between the effective user clock drift f u and its estimation fˆu will not remain negligible anymore. Carrier aided pseudorange tracking will also lead to deviations in the pseudorange tracking, whenever a steady mixer frequency offset is present. Decoupling the measured carrier frequency from the pseudorange tracking is a key feature for frequency translation of GPS signals, therefore. Finally, the parameters of the Kalman filter must also be selected in a manner that this appearing discrepancy between the behaviour of the carrier frequencies and the pseudoranges will not lead to a degraded accuracy of pseudorange measurement.

5 TDOA DETERMINATION For indoor positioning systems using GPS repeaters, the pseudoranges are measured separately for each GPS repeater. The navigation solution results in the coordinates of the roof antenna and a total clock bias b tot that consists of the clock bias bu of the user’s time base compared to GPS time and the propagation delay d j from the roof antenna over the repeater j to the GPS receiver. When the system is implemented in a way that the delay from the roof antenna to each GPS repeater is identical, the time differences of arrival (TDOA) derived form the delays d j allow to determine the user’s position relative to these repeaters. For a two-dimensional solution, at least three GPS repeaters are needed, for three-dimensional calculations at least four of them. Details can be found in [2] and [5]. For an indoor navigation solution using GPS repeaters, the exact position of these transmitters must be communicated to the user, e.g., over a Wireless LAN. As the roof antenna is for most applications at a fixed position expressed in ECEF coordinates, too, the coordinates of the roof antenna can also be transmitted to the user at the same time. With the knowledge of these coordinates, a pseudo-range measurement from a single space vehicle would be enough to calculate the distance d j from the repeater j to the user. Using the signals from several satellites and taking an average of these measured pseudoranges results in a higher accuracy for this distance d j , however. As a cost-effective GPS receiver will measure only one frequency-translated group of GPS signals at once, the GPS receiver must switch sequentially from one repeater to the next and is not capable of evaluating the repeater-depending different time of arrival exactly at the same time. The variance of clock bias of a subsequent measurement will not only depend on the distance to the newly selected repeater but is also caused by the user clock drift compared to the absolute GPS time. As the mentioned mixer frequency offset prevents a direct determination of the user clock drift by means of the Doppler measurement, the user clock drift must be estimated first before switching to the next repeater. It can be expected that the effective clock drift fu will not significantly differ from the estimated clock drift fˆu during the short time ∆t of tuning from one repeater frequency to the other. The time difference of arrival (TDOA) d jk between the GPS repeaters j and k can then be calculated as: djk = dj − dk = btotj − btotk − fˆu · ∆t

6 SOLUTIONS FOR THE NAVIGATION EQUATIONS Unlike the TOA measurements of a GPS receiver, TDOA measurements are used to calculate the navigation solution in a indoor situation. There are both iterative solutions and several closed-form solutions known. Reference [ 1] gives a summary. The properties of two of these algorithms are examined here in regard to indoor positioning. To simplify matters, only 2D solutions are calculated in this paper, thus all repeaters are located in a plane. A location (x, y) corresponds to a 3D position in this plane.

6.1 Taylor Approximation The iterative navigation equation solution is the well known Taylor approximation [4], [7], so the first step is to linearize the equations. The user location (x, y) is calculated by correcting an estimated location (x s , ys ) with a location error (ex , ey ), therefore x = xs + ex y = ys + ey .

The estimated range differences relative to repeater 1 are Rs21 and Rs31 , so the two navigation equations are  Rs21 = Rs2 − Rs1 = (X2 − xs )2 + (Y2 − ys )2 (10)  − (X1 − xs )2 + (Y1 − ys )2  Rs31 = Rs3 − Rs1 = (X3 − xs )2 + (Y3 − ys )2  − (X1 − xs )2 + (Y1 − ys )2 .

(8)

Tuning the mixer’s local oscillator of the receiving frontend from one repeater frequency to the next will also be detected by the tracking loop. As in standard GPS applications, transitions of the carrier frequency (and carrier phase) of the GPS signal are coupled in a rigid manner with changes of the pseudorange, most GPS receivers use carrier phase aiding or similar mechanisms for pseudorange tracking. As long as this coupled tracking of the carrier frequency and the pseudorange is not separated within the tracking loop, transitions of the mixer PLL should occur as ION GNSS 18th International Technical Meeting of the Satellite Division, 13-16 September 2005, Long Beach, CA

(9)

The applied first order Taylor polynomial for the true range difference is R i1 is Ri1 ≈ Rsi1 +

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dRsi1 dRsi1 ex + ey . dxs dys

(11)

Eq. (10) and Eq. (11) can be used to form a linear system of equations   R21 − Rs21 = (12) R31 − Rs31    ys −Y2 ys −Y1 xs −X2 xs −X1 ex Rs2 − Rs1 Rs2 − Rs1 · . ys −Y3 ys −Y1 xs −X3 xs −X1 ey Rs3 − Rs1 Rs3 − Rs1

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A reasonably small error value e can be reached after about 5 iterations, provided the initial estimation was chosen well. If the initial estimations are badly chosen, the solution will never converge. The next section gives some details on initial location estimation.

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Figure 4: Convergence performance of the Taylor approximation with an initial estimation in the balance point of the three repeaters. The repeaters are located at the corners of a right triangle. Convergence is reached for the blue user locations.

In the case of GPS, convergence performance is of no great concern. As long as the estimated position is somewhere near the earth, the geometrical constellation of the SVs and the estimated position does not change much. An indoor constellation with many repeaters can give a variety of different geometrical constellations. Two of them are shown in Figure 4 and Figure 5. These figures show the simulated convergence performance depending on the user location. The initial, estimated location is always in the balance point of the three repeaters. Dark blue regions show very fast convergence and light green regions never converge to the correct user location. Thus, an initial location in the balance point of three repeaters is a good estimation as long as the user is somewhere between these three repeaters. Figure 6 to Figure 9 show geometrical constellations with a fixed user location. The locations of the repeaters are on the corners of a right triangle and stay at the same location in each figure. The estimated location is variable and yields very fast convergence in the dark blue regions. The simulation results of the Taylor approximation show that both, initial estimation and actual user location should be within the area spanned by the three repeaters. Locations outside of the triangle are also acceptable, provided they are closest to the longest side of the triangle.

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Figure 5: Convergence performance of the Taylor approximation with an initial estimation in the balance point of the three repeaters. The repeaters are located at the corners of an obtuse triangle. Convergence is reached for the blue user locations.

6.3 Closed-Form Solution A closed-form solution for the navigation equation ( 10) has been proposed by [3]. The difference between an arbitrarily chosen repeater i and the user location (x, y) is  (14) Ri = (Xi − x)2 + (Yi − y)2 .

By squaring Eq. (15) and inserting Eq. (14) one gets 2 + 2Ri1 R1 + R12 = Ri1

Xi2

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6.2 Convergence Performance of the Taylor Approximation

Ri1 = Ri − R1 .

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− 2Xi x + x +

(16) Yi2

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− 2Yi y + y .

This equation can be simplified by subtracting R 12 in order to eliminate the quadratic term. We thus get a linear equa-

(15)

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Figure 6: Convergence performance depending on the chosen estimated location. Convergence is reached for the blue estimated locations. User location is (-8 / -8).

Figure 8: Convergence performance depending on the chosen estimated location. Convergence is reached for the blue estimated locations. User location is (5 / -15).

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Figure 7: Convergence performance depending on the chosen estimated location. Convergence is reached for the blue estimated locations. User location is (-0 / -0).

Figure 9: Convergence performance depending on the chosen estimated location. Convergence is reached for the blue estimated locations. User location is (-8 / 20).

tion in the unknown variables

In order to solve for the user location (x, y), matrix M must be inverted   X21 Y21
M= (19) X31 Y31   1
Y21 −Y31 L = − 1 · M −1 = . X31 −X21 det(M )

2 Ri1 + 2Ri1 R1 =

Xi2

+

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(17) −

Y12

− 2Xi1 x − 2Yi1 y.

By using two TDOA measurements, for example with repeater 2 and repeater 3, an equation system can be constructed with i = 2 or i = 3, respectively     2 1 X22 + Y22 − X12 − Y12 − R21 R21 − · R1 = 2 R31 2 X32 + Y32 − X12 − Y12 − R31     x X21 Y21 · . (18) X31 Y31 y ION GNSS 18th International Technical Meeting of the Satellite Division, 13-16 September 2005, Long Beach, CA

Thus, Eq. (18) is now    2    1 R21 + K1 − K2 x R21 R1 + =L· 2 R31 + K1 − K3 y 2 R31 Ki = Xi2 + Yi2 .

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(20)

Reordering Eq. (20) yields two linear equations x = aR1 + b

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y = cR1 + d 20

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Y21 R31 − Y31 R21 (22) det(M ) 2 2 − K2 + K1 ) + Y21 (R31 − K3 + K1 ) −Y31 (R21 2 det(M ) X31 R21 − X21 R31 det(M ) 2 2 − K2 + K1 ) − X21 (R31 − K3 + K1 ) X31 (R21 . 2 det(M )

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Figure 10: Situation with a valid closed-form solution at (4, 6) and a wrong solution at (-6.5010, -3.5736).

(23)

+ (aR1 + b)2 − 2Y1 (cR1 + d) + (cR1 + d)2 . So, Eq. (23) gives

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which can be inserted into Eq. (20) in order to solve for the user location (x, y).

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The closed-form solution produces two different solutions, but only one is valid. The distance R 1 obtained by Eq. (25) can be used to sort out the wrong solution, because R 1 can not be negative. However, there are special constellations that cause two positive solutions, which require special treatment. Figure 10 to Figure 13 show different user location and the corresponding plot of the equation system. The locations of the three repeaters are repeater 1: (-10, 10), repeater 2: (-10, -10), repeater 3: (10, 10). Valid solutions (R1 ≥ 0) are highlighted with a green  and wrong solutions (R1 < 0) are highlighted with a small red •. A small green • indicates a wrong solution with (R 1 ≥ 0). Both solutions are connected with a red line, in order to distinguish solutions obtained by the closed-form calculation from other intersections of the two hyperbolas. Figure 10 shows the normal situation with a valid and a wrong solution. They can be distinguished by the sign of R1 . Figure 11 shows a situation with the user location next to a repeater. Both solutions are on the same branch of the ION GNSS 18th International Technical Meeting of the Satellite Division, 13-16 September 2005, Long Beach, CA

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Figure 11: Situation with a valid closed-form solution at (-9, 8) and a wrong solution at ( -32.4697, 29.9710).

hyperbola and both solutions for R 1 are positive, so there are two possible solutions. This ambiguity can be solved by restricting the possible user locations to an area near the repeaters used. Figure 12 shows another situation with the user location next to a repeater but outside of the area defined by the three repeaters. Both solutions are again on the same branch of the hyperbola, therefore the sign of the solutions for R 1 is the same. Furthermore, the two possible user locations are close to each other. In such a case, the ambiguity can not be reliably resolved. Figure 13 shows again a situation with a valid and a wrong solution that are distinguishable. The valid solution is far away from the three repeaters. So restricting the

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7 MULTIPATH CONSIDERATIONS

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Multipath propagation of the GPS signals is a limiting factor for indoor positioning based on GPS repeaters. Even when a direct line of sight between the GPS repeater and the user’s position is present, the receiver will not unconditionally track on this direct signal as this signal path can be strongly faded due to standing waves. Frequency translators can potentially help to detect such faded signals by the following method: Each repeater j is sending simultaneously the same GPS signal mixed to different dedicated frequencies f Ijk assigned to repeater j. These transmitted signals within the 2.4 GHz ISM-Band will have different patterns of standing waves within an indoor location. From this generated variety of GPS signals with identical C/A code coming from the same repeater but on different ISM frequencies f Ijk the receiver selects for each C/A code those exponents with lowest propagation delay. Eliminating in this way additional multipath delays should statistically improve precise indoor positioning. This proceeding is for further study.

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Figure 12: Situation with a valid closed-form solution at (13, 9) and a wrong solution at (23.2033, 12.4994).

8 DEMONSTRATOR ARCHITECTURE

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As a standard GPS-receiver, we used the ANTARIS evaluation kit from u-blox containing a TIM-LP GPS module. The evaluation kit together with the PC-based software u-center allowed us to have access to raw data, i.e., unfiltered pseudo-range and Doppler data measured within the tracking loop. To prevent any undesired effects of the Kalman filter and to fix known parameters (e.g., the position of the roof antenna), the navigation solution was calculated with a MATLAB algorithm on a PC. We made no effort to improve the performance of the MATLAB algorithm, but stored the measured data first in a logfile and did the calculation off-line. The tracking loop of the TIM-LP GPS was unmodified, with the exception that settling time was accelerated at the cost of a slightly higher noise level. Note that the structure of the algorithm using carrier aiding remained unmodified, with the effect that a mixer frequency offset of a few hundred Hertz sufficed to bring the pseudorange tracking completely out of control. For this reason, we synchronized the mixers of the transmitting repeaters and the receiver by using the same reference frequency as a time base for the local oscillators.

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Figure 13: Situation with a valid closed-form solution at (15, -20) and a wrong solution at (-4.4983, 7.3721).

possible user locations and neglecting the sign of R 1 could wrongly eliminate this valid solution. Unfortunately, the closed form and the Taylor approximation solutions show difficulties in similar situations. Constellations with the user and the repeaters located nearly on a straight line result in poor performance. In these particular situations, another set of three repeaters should be chosen to make sure that the constellation is as good as possible for the calculation of the navigation solution.

9 MEASUREMENT RESULTS The first measurement result illustrated below was made with a setup of three repeaters located at an identical short distance to the receiver. The L 1 carrier of 1.57542 GHz has been mixed up with local oscillator frequencies of 840, 848, and 856 MHz giving transmitted frequencies of 2.41542, 2.42342, and 2.43142 GHz, respectively. Multipath effects have been eliminated by running the transmitters and the receiver in an anechoic environment. The GPS receiver was

For both methods, restricting the user to within the polygon area spanned by the repeaters likely yields correct results. ION GNSS 18th International Technical Meeting of the Satellite Division, 13-16 September 2005, Long Beach, CA

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Figure 14: TOA measurement for 3 equidistant repeaters Figure 15: Evaluated results (red) for a fixed indoor position (blue) used with its original firmware version, i.e., for this measurement, the settling time was not accelerated by higher gains in the pseudorange tracking loop. Every 300 ms, the clock bias was calculated. After 20 measurement points (i.e., 6 seconds), the receiver selected a new repeater. Figure 14 shows the transitions within the calculated time of arrival TOA (referenced to t = 0) caused by the finite settling time of the mixer frequency. Whenever the receiver changes from one repeater frequency to the next, the evaluated TOA can momentarily differ several meters from the effective distance between the GPS repeater and the receiver before converging back to a more precise value. The sketched trend line drawn in red corresponds to a small drift, caused by a tiny deviation of the estimated user clock drift. As the algorithms for the indoor navigation uses TDOA instead of TOA, this small error of the estimated drift will not significantly affect the accuracy of the final results. The second measurement result shows a real 2dimensional application of indoor positioning using frequency translators. The measurement has taken place in an office with the repeaters in a relatively short distance of each other compared to the accuracy reported for typical indoor applications. The mixer frequencies are the same as in the measurement before and the local oscillator of the receiver’s mixer was synchronized again to the same time base as the mixers of the GPS repeaters. Additionally, the firmware with the modified tracking-loop gain was used for the GPS receiver. In Figure 15, the real positions of the repeaters and the user position are drawn in blue, the calculated results in red, having an accuracy of a few meters. However, the indoor navigation solution did only converge after multipath effects were suppressed using absorbers and directive antennas. We assume that the distance of 1.35 m between the averaged results and the real user position is still caused by remaining multipaths. The measured standard deviation was 1.06 m. ION GNSS 18th International Technical Meeting of the Satellite Division, 13-16 September 2005, Long Beach, CA

The figure shows that indoor navigation using frequency translators is an alternative approach to other so far proposed solutions. Improvements by the help of using a decoupled tracking loop and by increasing the insensitivity to multipath effects are for further study.

10 CONCLUSIONS Indoor positioning using frequency translators has not only the advantage of being compliant with FCC and other regulations, as it can be operated without license in the 2.4 GHz ISM band, but permits the different GPS repeaters to transmit their signals simultaneously using an FDMA scheme. The FDMA approach allows the GPS receiver to switch independently from one GPS repeater to another, without the need of any additional synchronization and the possibility for each GPS receiver to track a repeater signal as long as necessary for the evaluation of the pseudo-range. This concept can be further expanded, when each repeater is transmitting the GPS signal on several carrier frequencies with the potential to minimize multipath effects. For 2-dimensional navigation, the Taylor approximation as well as the studied closed form solution yield correct results if the user location is within the area spanned by the three repeaters. Locations outside of the triangle are also acceptable, provided they are closest to the longest side of the triangle. With the demonstrator built, we have shown the principle performance of an indoor system using frequency translators and got an insight as to what implications are caused by this method, if a standard GPS receiver is used for signal tracking and evaluating the navigation solutions. Adapting a standard GPS receiver to avoid offsets and transients in pseudorange tracking caused by the mixer’s local oscillator as well as strategies for the elimination of multipath effects are for further study.

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References [1] M. Aatique, “Evaluation of TDOA techniques for position location in CDMA systems,” Master’s thesis, Virginia Polytechnic Institute and State University, September 1997. [2] J. Caratori, M. Francois, N. Samama, and A. VervischPicois, “UPGRADE RnS indoor positioning system in an office building,” in Proceedings of ION GNSS 2004, Long Beach, CA, September 2004, pp. 1959–1969. [3] Y. T. Chan and K. C. Ho, “A simple and efficient estimator for hyperbolic location,” IEEE Transactions on Signal Processing, vol. 42, no. 8, August 1994, pp. 1905–1915. [4] W. H. Foy, “Position-location solutions by Taylorseries estimation,” IEEE Transactions on Aerospace and Electronic Systems, March 1976, pp. 187–194. [5] G.-I. Jee, J.-H. Choi, and S.-C. Bu, “Indoor positioning using TDOA measurements from switching GPS repeater,” in Proceedings of ION GNSS 2004, Long Beach, CA, September 2004, pp. 1970–1976. [6] B. W. Parkinson and J. J. Spilker, Jr., eds., Global Positioning System: Theory and Applications, Vol. I. American Institute of Aeronautics and Astronautics, 1996. [7] D. J. Torrieri, “Statistical theory of passive location systems,” IEEE Transactions on Aerospace and Electronic Systems, March 1984, pp. 183–198.

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