# A Self-Contained and Self-Checking LPS with High Accuracy

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. LOSNUS

#### 3.1. Design Rationale of LOSNUS

#### 3.2. Basic Principle of LOSNUS

#### 3.3. Signal Processing

**Figure 3.**(

**a**) 1-bit quantized linear frequency modulated chirp with Δ = 25 kHz, f

_{0}= 52.5 kHz and T = 256 μs; (

**b**) Binary autocorrelation function (Theoretical D = 6.4).

**Figure 4.**(

**a**) Directivity diagram without attached cone of Senscomp 600 electrostatic transducer; (

**b**) Directivity diagram after application of cone.

**Figure 5.**(

**a**) Received (analog) waveforms for burst with f

_{0}= 52.5 kHz and chirp with settings from Figure 3; (

**b**) Binary autocorrelation function showing pulse compression properties of the chirp compared to a burst.

#### 3.4. Transmitter Identification

**Figure 6.**(

**a**) Transmitter identification for n coding frequencies. Filter output values are only evaluated at discrete times as the starting time of the frame is known. (

**b**) Example transmitter decoding on binary input data using f

_{i}= 40 kHz + 4.5 kHz · i, 0 ≤ i ≤ 5. Identified transmitter is (40 kHz, 53.5 kHz). Red vertical lines mark sampling points.

#### 3.5. Localization

_{i}and T

_{j}, a receiver R and ToAs t

_{i}and t

_{j}the basic TDoA equation is given in Equation (3) where c is the speed of sound.

**Figure 7.**(

**a**) Calculation of the receiver positions by all fifteen combinations in case of no error. All positions are close and spread by the DOP. (

**b**) In case of a single outlier only five combinations are still valid and all others deliver different results. The assumed ToA error for this example was 1 cm.

## 4. Calibration

_{ij}be the ToF between transmitter i and receiver j. The defining equations are then given by

_{i}′, R

_{i}′ and a cone length l′. As the speed of sound was only relatively correct but not absolutely the output is a scaled version of the system. By calculation of the factor a according to Equation (7) the final calibrated transmitter and receiver positions as well as the cone length are given by

_{i}(k) are performed where the scaling factor c(k) is defined by the sum of the 24 ToFs where the first measurement is arbitrarily used as reference.

## 5. Uncertainty

#### 5.1. General Considerations

#### 5.2. Uncertainty in ToF and TDoA Measurements

_{0}described the unknown transmission time. In the case of ToF, the term t

_{0}contains any electrical and acoustic delays.

#### 5.3. Uncertainty in Calibration

_{i}is the coordinate of the transmitter, u

_{r}is the uncertainty of the reference path and r is the length of the reference path. The same applies for the receivers R

_{i}. All other systematic or random components are reduced either by the algorithms or averaging. A receiver-position used within the calibration is called reference position. Having two such positions available and a linear belt allows us to create arbitrary reference positions with a known uncertainty.

#### 5.4. Uncertainty in Localization

**Figure 8.**Graphical example for the calculation of uncertainty showing unknown value at the bottom, a systematic difference b(k) at each position, the uncertainty in determining b(k) as interval u

^{2}[b(k)] on the line tracking the value and the uncertainty of the individual measurements u

^{2}[P(k)].

_{c}is defined as the positive square root of Equation (15). This complicated expression is explained in Figure 8. The index k identifies the position on the belt (23 positions in our case) whereas P(k) defines a sufficient set of measurements at this position (20 in our case).

^{2}[P(k)] is simply the variance for the measurements mainly resulting from the uncertainty of the TDoA measurements and the DOP. At each position, a systematic correction factor b(k) can be determined being the mean distance of the measurements to the interpolated reference position. As the value is not known the uncertainty for determining this factor is expressed by u

^{2}[b(k)] resulting from the inaccurate reference positions and the variance of the mean value of the measurements. As only a single systematic value b is determined u

^{2}[b(k)] describes the variance of the factor itself. An important aspect of applying this formalism is that results can be transferred to different room positions as well. For example u

^{2}(P(k)) which is closely related to the DOP can be estimated by calculating the DOP and reevaluating Equation (15) again.

#### 5.5. Computation of Uncertainty Parameters

_{1}and R

_{2}be two reference points. Then arbitrary reference points can be created in between if these two points are connected by a linear belt and the positions R

_{1}and R

_{2}have been part of the calibration (For accuracy reasons). An interpolated reference point at position k with a step size of Δ is given by

_{k}and the center of gravity of the measurement points.

_{1}and u

_{2}be the uncertainty of the reference points R

_{1}and R

_{2}. Assuming a simple linear interpolation the uncertainty for the point R

_{k}is given as

#### 5.6. Temperature Compensation during Operation

_{1}, T

_{2}, T

_{3}, T

_{4}, three time differences t

_{12}, t

_{13}, t

_{14}and the temperature T for calculating speed of sound.

#### 5.7. Impact of Motion and Doppler Effect

_{0}the Doppler shift can be approximated by [31] where is the direction and speed of motion of the receiver R. The direction of wave propagation between the transmitter and receiver is given by the unity vector .

_{0}. The error for a located position R can therefore be defined according to Equation (32).

**Figure 10.**Simulation Results: (

**a**) Effect of receiver motion with 0 ms interface spacing (only possible in CDMA system), (

**b**) Effect of receiver motion with 10 ms interframe spacing suitable for LPS LOSNUS with up to 3.4 m minimal spacing between consecutively firing transmitters.

## 6. Experimental Results

#### 6.1. System Configuration

**Figure 11.**(

**a**) Test system configuration consisting of six US transmitters. (

**b**) Ultrasonic transmitter adjustable in two direction including wiring.

#### 6.2. Calibration

**Figure 14.**(

**a**) Compensation factor c(k) calculated according to Equation (10); (

**b**) Example of two ToFs compensated with factor c(k). Data points marked with “x” are before compensation and data points marked with “o” are after compensation.

Tx1 | Tx2 | Tx3 | Tx4 | Tx5 | Tx6 | |
---|---|---|---|---|---|---|

x | 0 | 0 | 0.3221 | 0 | 0.1121 | 0.1762 |

y | 1.6126 | 0 | 0.0769 | 1.6271 | 2.903 | 3.8394 |

z | 0 | 0 | −0.9454 | −1.9408 | −1.9240 | −0.8845 |

#### 6.3. Localization

**Figure 16.**Correlation results of a complete LOSNUS sequence showing ToA for individual transmitters and an example for a Non Line of Sight (NLOS) signal for Tx1.

^{T}|| = 4.7 mm ± 1.3 mm. A graphical visualization of the uncertainty components is shown in Figure 19a. In this case b(k) calculated according to Equation (18) shows the systematic component of the uncertainty, i.e., the mean distance between the points and the reference position. The value of is the standard deviation of the measured points at position k. This value is closely related to the DOP by the standard deviation of the ToA measurements and the DOP for the transmitter/receiver combination used. Due to the large and accurate reference path used the component is rather small.

**Figure 18.**Measurement on linear belt at 23 positions with 20 measurements each. Temperature = 24.8 °C taken from Figure 17.

^{T}|| = 6 mm ± 2.2 mm. The deviations between the two results, although small, are due to the finite sample size. In addition modeling does not take into account all possible effects.

**Figure 20.**(

**a**) Repeated measurement at different date and temperature; (

**b**) Temperature obtained by using reference position was 29.1 °C.

#### 6.4. Practical Realization Considerations

**Figure 21.**(

**a**) Picture showing a test realization of a sensor node with a ZigBee communication interface. (

**b**) Suggested software architecture for implementation.

## 7. Conclusion

## Conflicts of Interest

## References

- Mitilineos, S.; Kyriazanos, D.; Segou, E. Indoor localisation with wireless sensor networks. Prog. Electromagn. Res.
**2010**, 109, 441–474. [Google Scholar] [CrossRef] - Schweinzer, H.; Kastner, W. Systems with Numerous Low-Cost Sensors—New Tasks and Demands for Fieldbusses. In Proceedings of the 5th International Conference on Fieldbus Systems and Their Applications (IFAC), Aveiro, Portugal, 7–8 July 2003.
- Schweinzer, H.; Syafrudin, M. LOSNUS: An Ultrasonic System Enabling High Accuracy and Secure TDoA Locating of Numerous Devices. In Proceedings of the International Conference on Indoor Positioning and Indoor Navigation (IPIN), Zürich, Switzerland, 15–17 September 2010.
- Harter, A.; Hopper, A.; Steggles, P.; Ward, A.; Webster, P. The Anatomy of a Context-Aware Application. In Proceedings of the 5th ACM/IEEE International Conference on Mobile Computing and Networking (MobiCom), Seattle, WA, USA, 15–19 August 1999.
- Baunach, M.; Kolla, R.; Mühlberger, C. SNoW Bat: A High Precise WSN Based Location System; Technical Report; University of Würzburg: Würzburg, Germany, 2007. [Google Scholar]
- Lazik, P.; Rowe, A. Indoor Pseudo-Ranging of Mobile Devices Using Ultrasonic Chirps. In Proceedings of the 10th ACM Conference on Embedded Network Sensor Systems (SenSys), Toronto, ON, Canada, 6–9 November 2012.
- Woodman, O.; Harle, R.K. Concurrent Scheduling in the Active Bat Locating System. In Proceedings of the IEEE International Conference on Pervasive Computing and Communications Workshops (PERCOM), Mannheim, Germany, 29 March–2 April 2010.
- Priyantha, N.B.; Chakraborty, A.; Balakrishnan, H. The Cricket Location-Support System. In Proceedings of the 6th International Conference on Mobile Computing and Networking (MobiCom), Boston, MA, USA, 6–11 August 2000.
- Balakrishnan, H.; Baliga, R.; Curtis, D.; Goraczko, M.; Miu, A.; Priyantha, N.; Smith, A.; Steele, K.; Teller, S.; Wang, K. Lessons from Developing and Deploying the Cricket Indoor Location System. Available online: http://cricket.csail.mit.edu/ (accessed on 8 August 2003).
- Casas, R.; Marco, A.; Guerrero, J.; Falco, J. Robust estimator for non-line-of-sight error mitigation in indoor localization. EURASIP J. Adv. Signal Process.
**2006**. [Google Scholar] [CrossRef] - Ruiz, F.D.; Urena, J.; Jimenez, J.A.; Villadangos, J.M.; Garcia, J.J.; Hernandez, A.; Jimenez, A. Data Processing for the Calibration of an Acoustic Local Positioning System. In Proceedings of IEEE Instrumentation and Measurement Technology Conference Proceedings (IMTC), Victoria, BC, Canada, 12–15 May 2008.
- Casas, R.; Cuartielles, D.; Marco, A.; Gracia, H.J.; Falco, J. Hidden issues in deploying an indoor location system. IEEE Pervasive Comput.
**2007**, 6, 62–69. [Google Scholar] [CrossRef] - Nawaz, S.; Trigoni, N. In Robust Localization in Cluttered Environments with NLOS Propagation. In Proceedings of IEEE 7th International Conference on Mobile Adhoc and Sensor Systems (MASS), San Francisco, CA, USA, 8–12 November 2010.
- Mahajan, A.; Figueroa, F. An automatic self-installation and calibration method for a 3D position sensing system using ultrasonics. Robot. Auton. Syst.
**1999**, 28, 281–294. [Google Scholar] [CrossRef] - Fukuju, Y.; Minami, M.; Morikawa, H.; Aoyama, T. In DOLPHIN: An Autonomous Indoor Positioning System in Ubiquitous Computing Environment. In Proceedings of IEEE Workshop on Software Technologies for Future Embedded Systems (WSTFES), Hakodate, Hokkaido, Japan, 15–16 May 2003.
- Nishitani, A.; Nishida, Y.; Hori, T.; Mizoguchi, H. Portable Ultrasonic 3D Tag System Based on a Quick Calibration Method, Systems. In Proceedings of IEEE International Conference on Man and Cybernetics, The Hague, The Netherlands, 10–13 October 2004.
- Duff, P.; Muller, H. Autocalibration Algorithm for Ultrasonic Location Systems. In Proceedings of 7th IEEE International Symposium on Wearable Computers (ISWC), White Plains, NY, USA, 21–23 October 2003.
- Runge, A.; Baunach, M.; Kolla, R. Precise Self-Calibration of Ultrasound Based Indoor Localization Systems. In Proceedings of 2011 International Conference on Indoor Positioning and Indoor Navigation (IPIN), Guimarães, Portugal, 21–23 September 2011.
- Spitzer, G.; Schweinzer, H. LOSNUS: Ultrasonic Indoor Locating for Numerous Static and Mobile Devices. In Proceedings of 7th Workshop on Positioning Navigation and Communication (WPNC), Dresden, Germany, 11–12 March 2010.
- Hirata, S.; Kurosawa, M.K.; Katagiri, T. Accuracy and resolution of ultrasonic distance measurement with high-time-resolution cross-correlation function obtained by single-bit signal processing. Acoust. Sci. Technol.
**2009**, 30, 429–438. [Google Scholar] [CrossRef] - Elmer, H.; Schweinzer, H. Dependency of Correlative Ultrasonic Measurement Upon Transducer’s Orientation. In Proceedings of IEEE Sensors, Toronto, ON, Canada, 22–24 October 2003.
- Klauder, J.; Price, A.; Darlington, S.; Albersheim, W. The theory and design of chirp radars. Bell. Syst. Tech. J.
**1960**, 39, 745–808. [Google Scholar] [CrossRef] - Zhang, Y.; Abdulla, W. A Comparative Study of Time-Delay Estimation Techniques Using Microphone Arrays; The University of Auckland: Auckland, New Zealand, 2005. [Google Scholar]
- Tamim, N.; Ghani, F. Techniques for optimization in time delay estimation from cross correlation function. Int. J. Eng. Technol.
**2010**, 10, 49–54. [Google Scholar] - Walter, C.; Schweinzer, H. An Accurate Compact Ultrasonic 3D Sensor Using Broadband Impulses Requiring no Initial Calibration. In Proceedings of Instrumentation and Measurement Technology Conference (I2MTC), Graz, Austria, 13–15 May 2012.
- Kettlewell, J.; Seguin, H.J.J.; Schwidt-Weinmar, H.G. A device for point source simulation in a high frequency acoustical system. IEEE Trans. Sonics Ultrason.
**1972**, 19, 343–346. [Google Scholar] [CrossRef] - Bard, J.D.; Harn, F.M. Time difference of arrival dilution of precision and applications. IEEE Trans. Signal Process.
**1999**, 47, 521–523. [Google Scholar] [CrossRef] - Syafrudin, M.; Walter, C.; Schweinzer, H. Location Estimation Algorithms for the High Accuracy LPS LOSNUS. In Proceedings of International Conference on Indoor Positioning and Indoor Navigation (IPIN), Montbeliard, France, 28–31 October 2013. in press.
- Stephan, P.; Heck, I.; Kraus, P.; Frey, G. Evaluation of Indoor Positioning Technologies under Industrial Application Conditions in the SmartFactoryKL Based on EN ISO 9283. In Proceedings of 13th IFAC Symposium on Information Control Problems in Manufacturing, Moscow, Russia, 3–5 June 2009.
- Joint Committee for Guides in Metrology, Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measurement. 2008. Available online: http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf (accessed on 8 August 2013).
- Mahafza, B.; Elsherbeni, A.; Mahafza, C. MATLAB Simulations for Radar Systems Design; Chapman and Hall/CRC Press: Boca Raton, FL, USA, 2004. [Google Scholar]

© 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Walter, C.; Syafrudin, M.; Schweinzer, H. A Self-Contained and Self-Checking LPS with High Accuracy. *ISPRS Int. J. Geo-Inf.* **2013**, *2*, 908-934.
https://doi.org/10.3390/ijgi2040908

**AMA Style**

Walter C, Syafrudin M, Schweinzer H. A Self-Contained and Self-Checking LPS with High Accuracy. *ISPRS International Journal of Geo-Information*. 2013; 2(4):908-934.
https://doi.org/10.3390/ijgi2040908

**Chicago/Turabian Style**

Walter, Christian, Mohammad Syafrudin, and Herbert Schweinzer. 2013. "A Self-Contained and Self-Checking LPS with High Accuracy" *ISPRS International Journal of Geo-Information* 2, no. 4: 908-934.
https://doi.org/10.3390/ijgi2040908