Low-Complexity PDoA-based Localization

Transcription

1 1 Low-Comlexity PDoA-based Localization Benjamin Sackenreuter 1, Niels Hadaschik 1, Marc Faßbinder 1 and Christoher Mutschler 1, {firstname.lastname}@iis.fraunhofer.de 1 Fraunhofer Institute for Integrated Circuits IIS, Locating and Comm. Sys. Det., Nuremberg, Germany Friedrich-Alexander-University Erlangen-Nuremberg (FAU, Programming Systems Grou, Germany Abstract Localization of wireless nodes within the IoT received much attention lately. However, strong constraints on ower consumtion, scalability, and comlexity of the nodes ose a big challenge for localization techniques. This aer resents a concet for energy-efficient low-comlexity localization based on Phase Difference of Arrival (PDoA. Besides a novel method for reference transmitter selection we roose a waveform, wellsuited for PDoA measurements, and evaluate its ranging erformance. We comare multile signal classification (MUSIC, linear fitting, and mean hase difference and comare their estimation variance to the Cramer Rao Lower Bound (CRLB. Our system concet allows for the mitigation of near-far effects for reference and tag signals at the receiver nodes, and an efficient imlementation of a wideband frequency hoing scheme. I. INTRODUCTION Localization within the Internet of Things (IoT received much attention lately by standardization bodies and comanies involved in the field [1,. However, the tyically high bandwidth signals for accurate localization [3 contradict the objective of low-cost and low-ower devices for the IoT. Hence, WiFi-based localization, emloying its recently introduced ranging caabilities [4, or Ultra Wideband (UWB do not meet the requirements. Global Navigation Satellite Systems (GNSSs only rovide very limited indoor localization erformance. To mitigate some of these issues, there are localization systems that only rely on carrier hase measurements [5, 6. This aer resents a low-comlexity and energy efficient system concet for localization. It extends [7, consisting of a gateway, several beacon transmitters at known osition, and tags at unknown osition, see Fig. 1. In contrast, we use beacon transmitters that also act as reference transmitters for accurate localization, and anchor nodes to measure PDoA /16/$31.00 c 016 IEEE Beacon 1 Beacon 4 Tag M Tag 1 Beacon Beacon 5 Fig. 1: System Concet. Beacon 3 Beacon P Gateway PDoA Node 100m The rest of the aer is structured as follows. Sec. II reviews related work. Sec. III introduces the system comonents. Next, we resent our main contributions: We resent our localization rocedure and reference transmitter selection scheme to mitigate near-far effects (Sec. IV. We describe the hysical roerties of our roosed localization waveform (Sec. V. We outline a low-comlexity receiver architecture (Sec. VI, and analyze and simulate a set of ranging algorithms with resect to the CRLB (Sec. VII. Sec. VIII discusses the results and concludes. II. RELATED WORK GNSSs tag and reference station measure PDoA of at least two satellites [8, 9. By forming multile hase differences among the reference station and the tag, the clock biases cancel out and no dedicated synchronization among the receivers is needed. However, the obtained hase measurements are ambiguous within a very small range and if directly used, only allow for tracking relative movements of the tag. PDoA-based systems have also been used to estimate the range between reader and tag in assive backscattering RFID-systems [10, 11. However, for backscattering RFID-systems, transmitter, receiver, and PDoA anchors are integrated in one node. Other systems that use two

2 Ref Tag Fig. : Sequence diagramm for localization. active nodes for PDoA-based ranging imlicitely achieve synchronization by round-tri like measurements [5, 6. However, that not only causes that the first osition fix is obtained only after a long time. It also highly utilizes radio resources as each tag is required to communicate bidirectionally with sufficiently many anchor nodes (at least three in the case of D ositioning. Another method for PDoA-based ositioning is radiointerferometric distance estimation. [1 analyzes the signal atterns of the beat frequency of two suerimosed modulated signals, transmitted by a tag and a reference transmitter. PDoA measurement of suerimosed sinusoids is studied in [13, 14. [13 rooses a localization system based on PDoA measurements. However, they only consider a single, eriodically transmitting reference transmitter. This may cause near-far effects at the receiver nodes. The reference transmitter also occuies radio resources, even though no localization is requested. III. SYSTEM Fig. 1 deicts the roosed system, with the aforementioned extensions, i.e. the PDoA measurement nodes (the anchor nodes and enhanced beacon nodes. Here, beacon nodes not only allow for the Received Signal Strength (RSS-based localization of the tags but also act as reference transmitters that are used for the accurate localization of tags. We describe the basic elements of the system in the following. Tags are the devices that are to be located. They communicate with the gateway and can transmit secially designed localization signals. Beacons eriodically transmit low ower signals. They are equied with a wake-u receiver to trigger the transmission of a redefined reference signal. PDoA nodes are deloyed at known osition as anchor nodes. They erform PDoA measurements on the received signals and reort the results to a location server. IV. LOCALIZATION PROCEDURE The basis of our localization rocedure is an association of tags to reference beacons. The tags eriodically erform the association by measuring the RSS of all available beacons within their range. Based on these Frequency (f f c /f ste Time k Fig. 3: Transmit signals of beacon and tag. measurements the tag selects the closest beacon and stores its ID. From now this beacon serves as the reference transmitter for this tag. Assume that we want to locate Tag 1 in Fig. 1. Fig. shows our localization rocedure that works as follows. 1 The gateway activates the tag by transmitting the PositioningRequest message. Based on the reviously obtained ID, the tag derives the wake-u sequence of its associated reference transmitter. After the tag has transmitted the wake-u sequence of its reference transmitter in PreambleTx both the tag and the reference transmit the same localization signal concurrently with little temoral misalignment, thus occuying non-orthogonal ressources in frequency and time. 3 The PDoA node receives the suerimosed LocalizationSigTx and extracts hase differences from this signal. Finally, the obtained measurements are forwarded in the EstimationResult message to a common location server, which collects the results from several PDoA nodes. V. SIGNAL STRUCTURE For the remainder of this aer we use the signal shown in Fig. 3 and transmitted at center frequency f c. It can be defined by s[k = = [ k (n + 0.5L ex (+jω n k rect L n=1 [ k (n + 0.5L s n [k rect, L n=1 where k is the time index, L is the number of samles er subcarrier, ω n is the angular frequency of the n-th subcarrier and N is the number of subcarriers. The rect[

3 3 function ensures that only one subcarrier is active at a time and is defined as { [ k 1 if rect = L L < k L 0 else and ω n, with f ste being the subcarrier sacing, is given by ( N ω n = π (f c + f ste n. The samled receive signal at the -th PDoA node on the n-th subcarrier is collected in a vector x n = d n (r R, ϕ nr s n + d n (r T, ϕ nt s n + w n, where r R and r T denote the distance from the considered tag and the associated reference transmitter to the PDoA node, resectively. The influence of the channel and the transmitter oscillator on the signal hase can be modelled as ( ( d n (r, β = ex j π r + β + β n = e jθn λ n for the n-th subcarrier, where λ n denotes the wavelength of the signal, r is the Euclidian distance between transmitter and PDoA node, and β, β n denote the initial local oscillator hase of transmitter and PDoA nodes resectively. For the sake of simlicity, multiath roagation effects and noise are not considered here. VI. RECEIVER ARCHITECTURE Both tag and reference transmitter signals are received at the aroximate same signal strength as they are close to each other. We aly the signals to a mixing diode, see Fig. 4, and extract the intermodulation signal. For the next sections we consider the inverse Hilbert transform x (r n (t = H 1 {x n (t} of the signals, as we rocess real valued assband signals. The receive signal at one PDoA node on the n-th frequency ste is given by x (r (t = cos((ω + ω T t + Θ (R + cos((ω + ω R t + Θ (T = 1 ((ω+ ω [e j T t+θ (R ( + e j (ω+ ω R t+θ (T + e j ( (ω+ ω T t+θ (R + e j ( (ω+ ω R t+θ (T, (1 where ω T and ω R are the frequency offsets of tag and reference transmitter. The hase shift introduced by Fig. 4: Architecture of the PDoA measurement node. the channel and the local oscillators is denoted Θ (R and Θ (T for the reference transmitter and the tag to the PDoA node. For simlification, we omit n, i.e. x (r = x (r n, as we consider only one subcarrier. The mixing diode shows a nonlinear transfer function and is aroximated by taylor series exansion [15 i(t = u= u=1 a u (x (r (t u. ( Inserting (1 into (, limiting the number of terms to two and extracting the lowass comonents of interest, results in x (r n (t := 1 (ej((ω+ ω T t+θ n(ϕ R (ω+ ω R t Θ n(ϕ T + e j((ω+ ω Rt+Θ n(ϕ T (ω+ ω T t Θ n(ϕ R = cos(( ω T ω R t + (Θ (R Θ (T ( ( ωn = cos ( ω T ω R t + r RT + β R β T c 0. (3 As can be seen from (3, the unknown initial hase of the -th receiver cancels out. To also remove the initial hase β R and β T introduced by the transmitters, the differential hase estimate of multile PDoA nodes is calculated [9. The evaluation of the hase-term in (3 without any frequency offset, i.e. ω T = ω R = 0, and after removal of the clock biases translates to a magnitude roortional to the baseline distance r RT. This is true for tag, reference transmitter and PDoA nodes being located on a straight line. However, in ractical imlementations, the rocessing of DC signals oses a number of challenges. First, DC signals are more sensitive to noise comared to hase modulated signals, also a DC bias in the receiver circuit may cause roblems. Moreover, arccos( evaluation requires a roer scaling. Due to the difficulties involved in dealing with DC signals it is advantageous to select different frequencies for the reference transmitter and the tag. For a ractical imlementation it can be sufficient to rely on the different crystal oscillator frequencies due to manufacturing sread. This results in a lowass signal at the ADC with frequencies on the order of the carrier frequency offset between tag and reference transmitter. VII. SIMULATION In the following, we consider algorithms for 1Dositioning, see Fig. 5. We obtain the baseline distance between tag and reference transmitter by rocessing the measurements at two PDoA nodes (=1 and =. An estimation of a 3D osition can be obtained from baseline estimates among multile PDoA nodes and is

4 4 Fig. 5: Baseline r RT estimation with two PDoA nodes. beyond the scoe of this work but can be imlemented according to [16. The algorithms discussed in the following are different in comutational comlexity and traffic created in the backend between PDoA nodes and the location server. They range from low comlexity (Mean Difference to high comlexity (MUSIC [17. A. Mean Difference Mean difference relates the double difference carrier hase measurements erformed at two successive frequencies w n and w n+1. First, the baseband receive signal is segmented into single frequency stes, before the carrier hase is estimated for each signal segment individually by correlation r n [k = τ x n [k τs NF [k, where s NF [k is a comlex exonential for frequency ω NF = ω T ω R. The hase estimate for a single frequency ste is given by ϕ (n = arg(r n [argmax( r n and the combined measurements are given by r RT = λste 1 π N 1 ((ϕ 1 (n 1 ϕ (n 1 (ϕ 1 (n ϕ (n n= = λste π(n 1 ϕ(n, (4 n=1 where λ ste = c0 f ste. Rewriting (4 to ( λ ste r RT = (ϕ 1 (n 1 ϕ 1 (n π(n 1 n= ( λ ste (ϕ (n 1 ϕ (n, π(n 1 n= where only a single hase estimate er PDoA node must be transmitted to the location server. However, it is imortant to take care of a roer hase unwraing. PDoA nodes and collects the estimates in the unwraed hase vector (ϕ 1 (1 ϕ (1 (ϕ 1 ( ϕ ( b =.. (ϕ 1 (N 1 ϕ (N 1 (ϕ 1 (N ϕ (N A linear fit is erformed by min b ϕ RT f, ϕ RT where f = [1,,..., N contains the channel indices. The result is obtained from C. MUSIC r RT = ϕ RT c 0 ω ste. MUSIC has the highest comutational comlexity and introduces the most traffic as it requires the comlete receive signal x n (t of each PDoA node at the location server. In the location server, the combined signal of two PDoA nodes is given by x dd [k = x 1 [k x [k, (5 where x 1 and x are the analytic lowass comonents observed by two PDoA nodes. In MUSIC, the individual frequency comonents x [ dd are row-wise shifted into a matrix X dd = (x dd 1 T,..., (x dd N T T C N L. Next, MUSIC ossibly includes rerocessing stes of the covariance matrix, e.g. forward-backward averaging. The result is a trile-difference estimate for the hase shift between measurements on different frequencies in the staircaselike waveform. An estimate for the covariance matrix (assuming zero mean is given by ˆR = 1 L X ddx H dd. (6 The steering vector is given by a = [1, e jπ d jπn λ ste,..., e d T λ ste, and we maximize the MUSIC seudo-sectrum over the baseline length, here denoted by d. B. Linear regression Linear regression forwards (N 1 double differenced estimates er PDoA to the location server. The location server then comutes the trile difference among two D. Cramér-Rao Lower Bound In this section, we derive the CRLB to get a first imression of the estimator qualities. For the analysis, we assume erfect synchronization between the reference

5 Mean Difference Linear regression MUSIC CRLB Mean Difference Linear regression MUSIC CRLB m 10 0 m SNR SNR Fig. 6: Variance of the range estimate (5 subcarriers. transmitter and the tag. The discrete ADC signal after mixing and filtering is given by y[k = x (r [k + w[k = n x (r n [k + w[k = cos ( ω T ω R k + ωn r RT + β R β T c n 0 }{{} β [ k (n + 0.5L rect + w[k. L Note that at each oint in time, only one element of the sum is non-zero, due to the frequency hoing of the transmit signal. To obtain a lower bound for the range estimate, the likelihood function [18, 19 l(θ = ( 1 ex 1 (y[k x (r [k k πσ w σ w is derived wrt. the arameter of interest r RT. Taking the logarithm gives the log-likelihood function L(Θ = log l(θ = K log 1 πσ w k 1 (y[k x (r [k σ w. Deriving twice wrt. r RT and calculating the exectation yields { L(Θ } E L r RT σ w ( ω n c. (7 n 0 The CRLB for baseline estimation, based on hase measurements is then given by σ r 1 RT = { }, E L(Θ r RT where the factor of account for the two measurements obtained at different PDoA nodes. Fig. 7: Variance of the range estimate (101 subcarriers. The CRLB is evaluated for baseband signals for comarison of the three algorithms. Fig. 6 shows the erformance of the resented estimators for N = 5 subcarriers, f ste = 50kHz, the samling rate at the PDoA node is f s = 1000kHz and the signal duration is T = 15ms. From Fig. 7 it can be observed, that the range estimate imroves with a higher number of subcarriers and a higher bandwidth. For low SNR, MUSIC erforms better than Mean difference and Linear regression. For very low SNRs the variance of the estimate is uer bounded by the ambiguity free distance. E. Signal imairments Finally, we evaluate signal imairments that aear in a ractical system, and their imact on the ositioning erformance. A general frequency offset of one or both the tag and the reference transmitter does not deteriorate the erformance as differences between multile frequencies are formed. However, a mismatch of the channel sacing together with an unavoidable temoral synchronization mismatch between two PDoA nodes introduces a bias on the range estimate, that is calculated as t miss c 0 f miss f ste = d bias, where t miss is the synchronization missmatch between two PDoA nodes and f miss is the frequency difference of the channel sacing f ste between reference transmitter and tag. We only need to imose moderate accuracy on the PDoA node synchronization, i.e. that both nodes cut out the exact same window of the receive signal, see Fig. 8. VIII. CONCLUSION The main advantages of the outlined system are twofold: (1 the reference transmitter selection scheme

6 6 Fig. 8: Range estimation bias due to signal imairments. leads to a reduced utilization of radio resources, as a higher ower reference signal is only transmitted, if triggered by the tag beforehand. Otherwise, the reference transmits a very low ower beacon signal. The selection further maximizes the number of PDoA nodes which receive the tag signal and the reference signal. Besides the selection ste, the system allows for the imlementation of very low ower PDoA nodes as a result of the waveform design and the overla of tag signal and refernce signal. ( The roosed signal is simle and can be generated by an energy efficient device. We require no digital modulation. Instead a single hase locked loo with a channel sacing of f ste suffices. Hoing only to the adjacent channel also greatly reduces settling times of the transmitter loo. However, a downside of the roosed receiver lies in its sensitivity to two or more closely saced interferers within the band of interest. Devices suitable to act as tags and beacons are currently under develoment. Next stes involve a measurement camaign to thoroughly investigate the achievable erformance under real world conditions, esecially in harsh multiath environments. IX. ACKNOWLEDGEMENT This contribution is suorted by the Bavarian Ministry of Economic Affairs and Media, Energy and Technology as a art of the Bavarian roject Leistungszentrum Elektroniksysteme (LZE. [3 B. Sadler and R. Kozick, A survey of time delay estimation erformance bounds, in Proc. 4th Worksho Sensor Array and Multichannel Processing, (Waltham, MA,. 8 88, 006. [4 Wireless LAN Medium Access Control (MAC and Physical Layer (PHY Secifications, [5 M. Pelka, C. Bollmeyer, and H. Hellbruck, Accurate radio distance estimation by hase measurements with multile frequencies, in Proc. Intl. Conf. Indoor Positioning and Indoor Navigation (IPIN, (Busan, South Korea, , 014. [6 X. Li, Y. Zhang, and M. Amin, Multifrequency-based range estimation of RFID Tags, in Proc. Intl. Conf. RFID, (Orlando, FL, , 009. [7 J. Robert, T. Lindner, and H. Milosiu, Sub 10µw wakeu-receiver based indoor/outdoor asset tracking system, in Proc. 0th Conf. Emerging Technologies & Factory Automation, (Luxembourg,. 1 3, 015. [8 J. P. Collins, An overview of GPS inter-frequency carrier hase combinations, tech. re., University of New Brunswick, Canada, [9 G. Blewitt, Basics of the GPS technique: observation equations, tech. re., Deartment of Geomatics, University of Newcastle, UK, [10 A. Povalac and J. Sebesta, Phase difference of arrival distance estimation for RFID tags in frequency domain, in Proc. Intl. Conf. RFID-Technologies and Alications, (Sitges, Sain, , 011. [11 R. Miesen, F. Kirsch, P. Groeschel, and M. Vossiek, Phase based multi carrier ranging for UHF RFID, in Proc. Intl. Conf. Wireless Information Technology and Systems, (Maui, HW,. 1 4, 01. [1 M. Schneider and R. Salomon, Theoretical analysis and validated exeriments of the localization by suerosing beats, in Proc. 010 Intl. Conf. Indoor Positioning and Indoor Navigation, (Zurich, Swiss,. 1 7, 010. [13 B. Kusỳ, G. Balogh, J. Sallai, Á. Lédeczi, and M. Maróti, intrack: High recision tracking of mobile sensor nodes, in Proc. 4th Euroean Conf. Wireless Sensor Networks, (Delft, Netherlands, , Sringer, 007. [14 C. Wang, Q. Yin, and W. Wang, An efficient ranging method for wireless sensor networks, in Proc. Intl. Conf. Acoustics Seech and Signal Proc., (Dallas, TX, , 010. [15 S. Maas, Nonlinear Microwave and RF Circuits. Artech House, 685 Canton Street Norwood, MA, USA, 003. [16 Ming and Yang, Noniterative Method of Solving the GPS Double-Differenced Pseudorange Equations, Journal of surveying engineering, vol. 131, no. 4, , 005. [17 R. Schmidt, Multile emitter location and signal arameter estimation, IEEE Transactions on Antennas and Proagation, vol. 34, no. 3, , [18 D. Rife and R. Boorstyn, Single tone arameter estimation from discrete-time observations, IEEE Transactions on Information Theory, vol. 0, no. 5, , [19 S. Kay, Fundamentals of Statistical Signal Processing: Detection theory. Fundamentals of Statistical Signal Processing, Prentice-Hall, REFERENCES [1 3GPP, 3GPP TR.891: Feasibility Study on New Services and Markets Technology Enablers; Stage 1, tech. re., ETSI, 015. [ L. Sellier and C. Fourtet, Method for synchronizing time measurements carried out in a radio communication network for geolocation uroses, 014.