Performance of a Precision Indoor Positioning System Using a Multi-Carrier Approach

Transcription

1 Performance of a Precision Indoor Positioning System Using a Multi-Carrier Approach David Cyganski, John Orr, William Michalson Worcester Polytechnic Institute Supported by National Institute of Justice, US Department of Justice ION-NTM 04

2 Presentation Outline Background/Motivation Overall System and Signal Architecture Performance Analysis Results, Further Work ION-NTM 04 2

3 Project Focus Precision, ad hoc, indoor/outdoor positioning and associated exchange of data for situational awareness and command/control for Firefighters Law enforcement officers Military First-responders Corrections officers ION-NTM 04 3

4 System Overview GPS Signal Personnel Unit Reference Unit, known location Phys Monitor Reference Unit, known location Reference Unit, known location Command and Control Unit GPS reference Positioning signal System control User-Commander link ION-NTM 04 4

5 Real-Time Deployable Personnel Geolocation Vehicles (red) drive up to a building and use reference units (blue) to locate and display tracks of fire fighters. Exits and other key building features may be marked on the fly. ION-NTM 04 5

6 with GIS (Geographic Info. Sys.) overlays. If GIS information such as complete floor plans are available, they can be integrated with the track display to assist route planning and other time-critical decisions. ION-NTM 04 6

7 System Requirements Number of dimensions: 3 Accuracy: +/- 1 ft Maximum range: 2000 ft Max number of simultaneous users: 100 Fundamental capabilities: 3-D location of each user relative to a chosen reference point Relative locations among users Graphical display at base station Graphical path information on all users Self rescue information to users (audio) Enhancements: Physiologic information telemetry Integration with stored databases: geographic and structural ION-NTM 04 7

8 Differences from GPS Small operational area (< ~1km 2 ) Major focus is indoors Absolute geo reference may not be needed User devices may be active Overall system cost must be kept low Entire system must be self-initializing, selfmonitoring ION-NTM 04 8

9 System Principles Positioning based on Time Difference of Arrival Roving Units are simple (transmitters of periodic signals) Signal processing is DFT-based as in OFDM (Orthogonal Frequency Division Multiplex) ION-NTM 04 9

10 Impulse-UWB vs. Multi-Carrier-UWB Wide (ultra-wide) bandwidth is needed for multipath rejection, but ultra-narrow time pulses are not needed. ION-NTM 04 10

11 The OFDM Concept ION-NTM 04 11

12 Lessons Learned from OFDM High data rate transmission via multicarrier modulation does not require a single wide band channel with: Low distortion (in amplitude and/or phase response) Narrow pulses Uniform noise Absence of interferers Precise synchronization ION-NTM 04 12

13 Proof of Concept Demonstration in Audio ION-NTM 04 13

14 Proof of Concept Demonstration Uses audio, not RF - greatly eased troubleshooting Top audio frequency has wavelength in air of 4.5 in. 1:1 scale behavior with an RF bandwidth of GHz Implements real-time location system using MATLAB Off the shelf microphone/speaker components can be used thanks to the OFDM like channelization Displays true location solution as well as multipath solutions ION-NTM 04 14

15 Transmitted Signal M # 1 s t = % Ae! " j f0 + m$ f t+ m ( ) m= 0 [2 ( ) ] M carriers Carrier spacing = Δf Each carrier has arbitrary phase Φ m ION-NTM 04 15

16 Signal Format Δf Carriers: M: # Carriers δf N: # DFT frequency samples Δf = Kδf δf = f s /N BW = B = M Δf ION-NTM 04 16

17 DFT Receiver Processing Architecture ION-NTM 04 17

18 Received Signal M $ 1 sk t = & Ak e! " # j f0 + m% f t+ t0 $ k 0 + m ( ) m= 0 t 0 : user clock offset; τ k0 : path delay [2 ( )( ) ] In the simple (no multipath) case, any 2 of the M carriers may be used to identify a phase difference and hence a time and distance difference between two receiver sites. There is phase and hence distance ambiguity, with ambiguity distance of c/δf where c is the velocity of the wave. For our situation, Δf may be chosen sufficiently small to eliminate the ambiguity. ION-NTM 04 18

19 Frequency Sampling of Received Signal The mth Fourier coefficient of the kth reference receiver: S km = A e k j[ % 2! ( f + m& f )" + # + $ ] 0 k 0 m m where the clock offset is! m = 2 " ( f0 + m# f ) t0 multiplied by results iṇ S = A e! m k j[ ] m ION-NTM 04 19

20 where Frequency Sampling of Received Signal (cont.) & S S = A A e & km m k = A A& e k = B e j' km, k # = 2! $ f ( t %" ) k jm( $ 2!% f" ) + # 0 k 0 Which represents samples of a sinusoid with sampling index m and frequency 2πΔf(t 0 -τ k0 ). Hence, given Δf, the time difference can be found. k 0 jm[2! (% ft $% f" )] + j2! f t 0 k Frequency m Delay ION-NTM 04 20

21 Sample Result for 1 Signal Freq Index corresponds to carrier frequencies in the transmitted signal comb. ION-NTM 04 21

22 Sinusoidal Frequency Estimation Estimation of the frequencies of sinusoids in noise (not necessarily harmonically related) is an old/fertile field We use the state space approach: Exact solution (without noise) for P frequencies given M > 2P Fourier samples (comb frequencies) Direct solution, good noise performance Model-based (P must be estimated a priori) ION-NTM 04 22

23 Positions from Frequencies Given the frequencies, TDOAs of all paths immediately follow Can reject multipath TDOAs based on inconsistency with a single source (computation-intensive) Given time synchronization with transmitter, TDOA becomes TOA and direct paths can be identified directly Or, make the system unambiguous range cell larger than the maximum physical operations area, and order solutions to identify shortest path ION-NTM 04 23

24 Steps in Determination of Position Errors Error in frequency estimation given signal structure, noise, signal strength Error in position estimate given frequency error, system geometry RF Channel performance: needed transmit power Engineering rules: position error vs. transmitted signal power given system structure Note: This initial analysis contains some simplying assumptions, including perfect synchronization among reference receivers ION-NTM 04 24

25 Bound on Frequency Estimate Cramer Rao Bound for a frequency estimate of one sinusoid: E { } n "# k = M 3! c 1 2 where σ n is the noise standard deviation c 1 is the amplitude of the sinusoid M is the number of carriers ION-NTM 04 25

26 Bound on Delay Estimate Put in terms of known or measurable parameters the bound on variance of the delay estimate is: 2 " # = 3 8! 2 N0 2 B TP s where N 0 is noise PSD B is signal bandwidth T is period of transmitted signal P s is received signal power ION-NTM 04 26

27 Position Estimate Error Standard deviation of the position estimate is approximately (asymptotically correct for large r 0 ): $ ˆ T = cr $ Tr[( A A) r 0 "#! 1 ] where c is the speed of light r 0 is the overall distance from target to references σ δτ is TDOA error standard deviation # "! $ 2#! A is the matrix of relative positions of reference stations ION-NTM 04 27

28 ION-NTM Example for a Particular Geometry h w 0 0 w 0 h 0 w 0 0 w h 0 0 A = PT Bh w h N c s r! " ˆ + = 6 reference stations: 1 at (0, 0, 0), 1 at (0, 0, h), etc.

29 RF Performance Effects Friis Transmission Formula for received power P s : P s = P trans G trans rec 2 2! 0 16 r G " 2 Noise power for given receiver noise figure (db) and antenna noise temperature (Kelvin): N 0 = 4!T a (10 NF /10 ) ION-NTM 04 29

30 Specific Example Same geometry, omnidirectional antennas Noise figure of 3 db, Antenna temperature of 290K Path attenuation of shortest wavelength (f max ) " ˆ r = 2.19X10! 2 8 5h + 2w Bh P 2 trans f T max w or " ˆ r = 2.19X10! 2 8 5h + 2w Fh E 2 w where F = (B/f max ) and E = P trans T ION-NTM 04 30

31 Performance Nomograph Nomograph for 6 sensor example geometry introduced earlier, h = 5 m, desired position std. dev. of 10 cm. Example: GHz BW, w = 21 m, energy needed is 2x10-12 W-sec or 2 µw for T=1 µsec ION-NTM 04 31

32 Conclusions This analysis provides encouraging results on system performance Analysis has been verified with simulation Continuing work will tighten the performance bounds and remove the simplifying assumptions Implementation of an RF proof-ofconcept system is underway ION-NTM 04 32