Indoor Localization based on Multipath Fingerprinting. Presented by: Evgeny Kupershtein Instructed by: Assoc. Prof. Israel Cohen and Dr.
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1 Indoor Localization based on Multipath Fingerprinting Presented by: Evgeny Kupershtein Instructed by: Assoc. Prof. Israel Cohen and Dr. Mati Wax
2 Research Background This research is based on the work that was done in in the startup company: US Wireless Corp. by Wax et al. The work was driven by the FCC s 1996 mandate for localization of outdoor mobile users dialing 911. The work was documented in 10 US patents - it did not appear in a journal paper. Though more than 10 years have passed, the work is still relevant, especially for indoors localization. 2
3 Glossary Sound waves Microphone Speaker Antenna array Reverberation EM waves Rx antenna Tx antenna Microphone array Multipath 3
4 Multipath Fingerprinting A position location technique for rich multipath environments outdoors and indoors. The key idea: the characteristics of the multipath can serve as a unique identifier, i.e. as the location fingerprint. 4
5 What is it Good For? Excels where all other position location techniques suffer The classical techniques and technologies - GPS, TOA, DOA, DTOA are based on the assumption that the wireless signal travels from the source to the receiving antennas along the line-of-sight (LOS) path. In rich multipath propagation environment this basic assumption is void. Infrared Techniques Scales poorly due to limited range of IR. Installation and maintenance costs. Poor performance in direct sunlight. May be used as a single-site technology Other network-based techniques require multiple sites 5
6 Fingerprinting Positioning Algorithm Fingerprints Fingerprint 1 Fingerprint 2... Fingerprint N-1 Fingerprint N Locations Location 1 Location 2... Location N-1 Location N Fingerprints Database Positioning Signals Fingerprint Extraction Fingerprint Matching Picture source: IEEE SIGNAL PROCESSING MAGAZINE, JULY
7 The Proposed Fingerprints Spatial fingerprint The directions-of-arrival (DOAs) and powers of the multipath rays. Captured by the array covariance matrix. Time-delay fingerprint The time-delays and powers of the multipath rays Captured by the impulse response / power delay profile. 7
8 Signal Strength as Fingerprint Absolute signal strength has a poor fingerprint. Depends on many irrelevant parameters like Spatial orientation of the transmitter. Body shadowing. Varies significantly along a wavelength due to constructive and destructive multipath interference. 8
9 Fingerprints Extraction Approaches Explicit DOA, TOA estimation of multipath signals Computationally intensive. Highly sensitive to the correct detection of number of received multipath signals (signal subspace dimension). The solution: Use the signal subspace as the basis for the fingerprint. 9
10 Problem Formulation (I) Assuming that the medium is isotropic and homogeneous, the q multipath signals received at the i-th sensor, can be expressed as q x t t s t n t i im im i m1 s t q im im t n t i the transmitted signal. number of impinging multipath signals. the delay of the mth reflection with respect to the ith sensor. complex valued attenuation of the mth reflection with respect to the ith sensor. additive noise at the ith sensor independent of the source signal, (Complex Circular Gaussian Random Process). 10
11 Problem Formulation (II) Using narrowband assumption: j2 fc B 2 t s t 2 1 t s t 1 e We get q j2 fcim x t t s t e n t i m m i m1 m m im, where complex attenuation of the mth reflection at the reference sensor delay of the mth reflection at the reference sensor delay of the mth reflection between the ith and the reference sensor. 11
12 Problem Formulation (III) Finally the signal received by the r-antenna array is given by: q x t t a s t n t m1 2 Matrix form representation: x t A s t n t m m m j2 fc m j2 fc T rm 1,,, is a steering vector of the array a m e e, where, where toward direction. 1,..., q 1 1,..., q q A a a and s t t s t t s t m T 12
13 Maximum Likelihood DOA Estimation According to the Deterministic ML (DML) method [2]- [3]: N min x t A s t 2 ˆ DML H i1 1 H Rˆ, where P A A A A is the projection operator A arg max Tr P, s onto the space spanned by the columns of the matrix A. N ˆ 1 H R x ti x t N i i1 A i is the sample covariance matrix. i 13
14 Spatial Fingerprint Use the signal subspace A as the basis for the fingerprint - PA Example: assume a 3-antenna array and 2-ray multipath: xt ta st ta st nt
15 Fingerprinting Positioning Algorithm Data-base building: PA estimation. Localization: searching for the best matching projection matrix according to iˆ arg max Tr PR ˆˆ i location i 15
16 Projection Matrix Estimation (I) DOAs are captured by the array covariance matrix: x t A s t n t H H H 2 H H R E x t x t AE s t s t A E n t n t AA I R is a covariance matrix, hence it s Hermitian positivesemidefinite and its eigenvalue decomposition can be written as r H H R V V mvmv m m1 1, where diag,,..., eigenvalues ordered such that 1 1 r 1 2 and v,..., v corresponding eigenvectors. r r 16
17 Projection Matrix Estimation (II) Under appropriate assumptions [1]-[2], it can be shown that: 1 q 1 q Span a,..., a Span v,..., v, when r q Estimate the array covariance matrix: N ˆ 1 H R x t x t N i 1 Estimate the signal subspace dimension - Choose the first ˆq eigenvectors: Estimate the projection matrix by: i i V,..., L v1 v Pˆ A ˆq V V L H L qˆ 17
18 Estimating the Dimension of the Signal Subspace The dimension of the signal subspace is equal to the number of impinging multipath signals. The question is how to estimate it from the covariance matrix R. The problem is that typically there are many low energy multipath signals which are insignificant Solutions: Eigenvalues energy threshold. Eigenvalues ratio threshold. Information theoretic criteria. 18
19 The Research Objectives Extend the work of Wax et al. to wideband signals and exploit also the time-delay information for the fingerprint creation in addition to the DOA information. The work of Wax et al. concentrates on an urban environment, while we are going to apply this technique to an indoor environment, which differs in multipath characteristics as a number of paths and their delay spread. More specifically, the objectives of the proposed research are: Development of a new indoor localization technique based on a fingerprint, which exploits all information contained in the received signal: powers, angular distribution and delays of multipath rays. Development of time and frequency domain approaches to the fingerprint formation. Theoretical investigation and performance comparison of different pattern matching techniques. Investigation and performance assessment of the developed localization techniques with respect to the wireless system parameters such as SNR, bandwidth, array characteristics, etc. Conducting experiments with a base-station equipped with an antenna array. 19
20 Ray Tracing Radiowave Propagation Simulator 80x80x5[m] 20
21 Correlation: Trace(P i *R 555 ) Introducing the Similarity Vector The similarity vector is defined as T Sˆ Sˆ 1,..., Sˆ N Where Sˆ i Tr[ Pi Rˆ] is the similarity between the received data R and the i-th location subspace P i Reference similarity Profile of the location with index Location index (i) 21
22 Correlation: Trace(P i *R) Fingerprints Matching MLSE or maximum of the similarity vector iˆ arg max Tr PR ˆˆ i location i Often the similarity vector has ambiguous peaks: 1 Similarity Profile Ambiguities Location index (i) 22
23 How to Cope with the Ambiguities? Selecting the highest peak (MLSE) may result in high level of ambiguity There may be several peaks with slightly different heights The whole similarity vector provides useful identification information not only the peaks! Both similar and dissimilar fingerprints provide useful identification information The solution: use the similarity vector as fingerprint 23
24 The Similarity-Profile Matching Algorithm Select from the set of similarity-profiles S i the one which best matches the similarity vector S obtained from the received data: min i Sˆ Consider different norms: L, L 1, L 2 In a simple case of symmetric grid of Tx locations, L 2 norm and Gaussian i.i.d. noise it can be shown that S i p p Perror MLS Perror similarity profile 24
25 Signal subspace formation approaches Spatial correlation matrix: Time domain analysis. Signal subspace based on DOA information only. Spatio-Spectral correlation matrix: Frequency domain analysis. Signal subspace based on DOA and TOA information. Spatio-Temporal correlation matrix. Time domain analysis. Signal subspace based on DOA and TOA information. 25
26 Percent of locations [%] Percent of locations [%] Spatial correlation matrix approach intermediate results Percent of locations [%] Percent of locations [%] Cumulative distribution of position location error (Max of similarity profile (minimum of LS)) Cumulative distribution of position location error (L - infinity norm) Error [m] Cumulative distribution of position location error (L1 norm) Error [m] Cumulative distribution of position location error (L2 norm) Error [m] Error [m] 26
27 Spatio-Spectral approach Joint estimation of DOA and TOA. Frequency domain analysis. Per subcarrier signal subspace formation. M k 1 i 2 H 1 H D arg max Pˆ x, where P D D D D location i k D j k 1,..., Correlation matrix averaging. k D k a 1 e a q e j k q T 27
28 Percent of locations [%] Percent of locations [%] Spatio-Spectral approach intermediate results Percent of locations [%] Percent of locations [%] Cumulative distribution of position location error (Max of similarity profile (minimum of LS)) Cumulative distribution of position location error (L - infinity norm) Error [m] Cumulative distribution of position location error (L1 norm) Error [m] Cumulative distribution of position location error (L2 norm) Error [m] Error [m] 28
29 References (I) 1. H. Krim and M. Viberg, Two decades of array signal processing research: the parametric approach, IEEE Signal Processing Magazine, pp , July P. Tsakalides, Array signal processing with alpha stable distributions, Ph.D. thesis, Southern California Univ., M. Wax and I. Ziskind, Maximal likelihood Localization of multiple sources by alternating projection, IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp , Oct M. Wax and A. Leshem, Joint Estimation of Time Delays and Directions of Arrival of Multiple Reflections of a Known Signal, IEEE Trans. Signal Processing, vol. 45, pp , Oct M. Wax, T. J. Shan and T. Kailath, Spatio-Temporal Spectral Analysis By Eigenstructure Methods, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP 32, pp , Aug T. Oktem and D. Slock, Power delay doppler profile fingerprinting for mobile localization in NLOS, IEEE 21st International Symposium on Personal Indoor and Mobile Radio Communications, A. Hatami, Application of channel modeling for Indoor Localization Using TOA and RSS, Ph.D. thesis, Worcester Polytechnic Institute,
30 References (II) 8. P. Bahl and V. N. Padmanabhan, "RADAR: an in-building RF-based user location and tracking system," INFOCOM Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings. IEEE, 2000, pp vol O. Hilsenrath and M. Wax: Radio Transmitter Location Finding for Wireless Communication Network Service and Management, US Patent 6,026,304, Feb M. Wax, Y. Meng and O. Hilsenrath: Subspace signature matching for location ambiguity resolution in wireless communication systems US Patent 6,064,339, May M. Wax and O. Hilsenrath: Signature matching for location determination in wireless communication systems, US Patent 6,112,095, Aug M. Wax, O. Hilsenrath and A. Bar: Radio transmitter location finding in CDMA wireless communication systems, US Patent 6,249,680, June
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