Unconventional Positioning Technology

Transcription

1 Unconventional Positioning Technology Andrew Markham Department of Computer Science, University of Oxford Unconventional Positioning Technology (University of Oxford) 1 / 56

2 Overview Unconventional Positioning Technologies Magnetic Fields Geomagnetic Generated Applications Unconventional Positioning Technology (University of Oxford) 2 / 56

3 Section 1 Unconventional Positioning Technologies Unconventional Positioning Technology (University of Oxford) 3 / 56

4 Traditional positioning techniques Radio based position is the de facto solution for the majority of positioning applications GPS: Revolutionized the world Cell Tower/GSM: High density WiFi/BLE: Indoor positioning However, there are some applications where the dominant solutions perform poorly or simply fail: Underground Underwater Indoors Unconventional Positioning Technology (University of Oxford) 4 / 56

5 Alternative Techniques: Visible Light LEDs can be modulated to uniquely act as landmarks Unconventional Positioning Technology (University of Oxford) 5 / 56

6 Alternative Techniques: Passive Acoustic Fingerprinting A room has a unique acoustic transfer function. This can be used like a fingerprint. 2 2 Indoor localization without infrastructure using the acoustic background spectrum, Mobisys 11 Unconventional Positioning Technology (University of Oxford) 6 / 56

7 Alternative Techniques: Daylight length Geolocators are tiny (0.5g) devices that position migrating animals twice a day. 3 3 Bchler E, Hahn S, Schaub M, Arlettaz R, Jenni L, Fox JW, Afanasyev V, Liechti F Year-Round Tracking of Small Trans-Saharan Migrants Using Light-Level Geolocators. PLoS One 5 Unconventional Positioning Technology (University of Oxford) 7 / 56

8 Section 2 Positioning using the Geomagnetic field Unconventional Positioning Technology (University of Oxford) 8 / 56

9 Positioning using the Geomagnetic field The natural geo-magnetic field People have been using the Earth s magnetic field for navigation Animals too! They can sense the geomagnetic field (magnetoception) Photos: Wikipedia Unconventional Positioning Technology (University of Oxford) 9 / 56

10 Positioning using the Geomagnetic field Natural Magnetic Fields Earth s magnetic field can be well approximated by a magnetic dipole Earth's magnetic eld A coil's magnetic eld Photos: Wikipedia The intensity of the magnetic field varies from 0.25 (equator) to 0.65 (poles) Gauss Unconventional Positioning Technology (University of Oxford) 10 / 56

11 Positioning using the Geomagnetic field Natural Magnetic Fields Intensity of Earth s Magnetic Field Unconventional Positioning Technology (University of Oxford) 11 / 56

12 Positioning using the Geomagnetic field Natural Magnetic Fields The angle of the field also alters over the surface of the Earth Submarines in particular have exploited these microvariations to position themselves without suffering from Gyro drift Accuracy is relatively coarse (kilometres) Unconventional Positioning Technology (University of Oxford) 12 / 56

13 Positioning using the Geomagnetic field Distortions of the Earth s Magnetic Field Indoors, ferromagnetic material, especially in reinforced concrete, distorts the Earth s magnetic field Unconventional Positioning Technology (University of Oxford) 13 / 56

14 Positioning using the Geomagnetic field Distortions of the Earth s Magnetic Field A spatial map of these distortions can be built, using techniques very similar to HORUS The distortions themselves are not spatially unique However, for someone moving through the area, the sequence of distortions can be exploited to provide positioning Typical accuracy is around 2-3 m and various startups (IndoorAtlas) are exploiting this technique Unconventional Positioning Technology (University of Oxford) 14 / 56

15 Positioning using the Geomagnetic field Distortions of the Earth s Magnetic Field Advantages: No infrastructure needs to be deployed Virtually all smart-phones have a magnetometer for controlling screen rotation Adds absolute location to traditional IMU Unconventional Positioning Technology (University of Oxford) 15 / 56

16 Positioning using the Geomagnetic field Distortions of the Earth s Magnetic Field Disadvantages: Map has to be built and maintained Users can only be tracked when they move Accuracy is not good enough for many applications Unconventional Positioning Technology (University of Oxford) 16 / 56

17 Section 3 Generating our own magnetic fields Unconventional Positioning Technology (University of Oxford) 17 / 56

18 Generating Artificial Magnetic Fields We can produce magnetic fields using coils of wire B INA I = current, N = number of turns, A = cross-sectional area We can also sense a time-varying field using a coil of wire V B cos(θ) Unconventional Positioning Technology (University of Oxford) 18 / 56

19 Modulation Modulate the signal to make it easier to detect, especially compared with the strong Earth s magnetic field Unconventional Positioning Technology (University of Oxford) 19 / 56

20 RSSI vs MI: Decay Magnetic fields fall off more rapidly RSSI MI RSSI 1 r 2 40 db/decade B 1 r 3 60 db/decade Unconventional Positioning Technology (University of Oxford) 20 / 56

21 RSSI vs MI: Decay Magnetic fields fall off more rapidly Range less than traditional radio RSSI MI RSSI 1 r 2 40 db/decade B 1 r 3 60 db/decade Unconventional Positioning Technology (University of Oxford) 20 / 56

22 RSSI vs MI: Antennas Magnetic field controlled by size and shape of generating coil RSSI MI Unconventional Positioning Technology (University of Oxford) 21 / 56

23 RSSI vs MI: Antennas Magnetic field controlled by size and shape of generating coil RSSI MI Unconventional Positioning Technology (University of Oxford) 21 / 56

24 RSSI vs MI: Antennas Magnetic field controlled by size and shape of generating coil RSSI MI Unconventional Positioning Technology (University of Oxford) 21 / 56

25 RSSI vs MI: Antennas Magnetic field controlled by size and shape of generating coil RSSI MI Unconventional Positioning Technology (University of Oxford) 21 / 56

26 RSSI vs MI: Antennas Magnetic field controlled by size and shape of generating coil Simple to alter field patterns to optimize localization RSSI MI Unconventional Positioning Technology (University of Oxford) 21 / 56

27 RSSI vs MI: Multipath and Penetration MI penetrates any non-metallic objects and does not suffer from multipath RSSI MI RSSI Distance B-field Distance Unconventional Positioning Technology (University of Oxford) 22 / 56

28 RSSI vs MI: Multipath and Penetration MI penetrates any non-metallic objects and does not suffer from multipath Environmental obstacles do not affect MI localization accuracy RSSI MI RSSI Distance B-field Distance Unconventional Positioning Technology (University of Oxford) 22 / 56

29 RSSI vs MI: Properties MI is a vector field i.e. it has magnitude and direction Unconventional Positioning Technology (University of Oxford) 23 / 56

30 RSSI vs MI: Properties MI is a vector field i.e. it has magnitude and direction Using a triaxial sensor, we can make the device rotationally invariant Unconventional Positioning Technology (University of Oxford) 23 / 56

31 Magnetic Fields for Navigation Low-Frequency Magnetic Fields We can electronically control the orientation and the magnitude of the magnetic moment by using 3 mutually perpendicular coils Triaxial coils TX IMU RX Figure : Triaxial magnetic transmitter (TX) and receiver (RX) operating at 2.5 khz The sensor is also equipped with a triaxial coil The total received power is invariant to TX and RX orientation Unconventional Positioning Technology (University of Oxford) 24 / 56

32 Typical Measurements Overall RSSI The abrupt decay of the magnetic field db-magnitude corresponds to a path-loss exponent of 6 limits the transmission range enables easy detection of tiny changes in distance (few cm) Estimated channel model TX1 Estimated channel model TX estimated model measurements free space model estimated model measurements free space model 0 0 RSSI [db] RSSI [db] log distance [meters] log distance [meters] Figure : The overall magnetic RSSI measured outdoor decays at 60 db/decade. Unconventional Positioning Technology (University of Oxford) 25 / 56

33 Section 4 Applications of MI positioning Unconventional Positioning Technology (University of Oxford) 26 / 56

34 Above-ground tracking Tracking animals above ground is relatively well researched ZebraNet - GPS-WSN Virtual Fencing - GPS-WSN TurtleNet - GPS-WSN WildSensing - RFID-WSN... Unconventional Positioning Technology (University of Oxford) 27 / 56

35 What about burrowing animals? Example burrowing species: badgers Nocturnal medium sized carnivores (8 kg) Live in extensive (20 m x 10 m) setts Tunnels between 1 and 3 m deep typically 1 to 20 badgers in a sett Unconventional Positioning Technology (University of Oxford) 28 / 56

36 Animal Tag: MI Sensor MI sensor detects signals from three orthogonal transponders Simultaneously measures RSSI Vector magnitude taken to ensure rotational invariance B = B 2 x + B 2 2 y + B z Unconventional Positioning Technology (University of Oxford) 29 / 56

37 Antennas Unconventional Positioning Technology (University of Oxford) 30 / 56

38 Positioning Using signal strengths from 4 or more antennas, we can work out likely location of animal This is done using a simple particle filter approach Not limited to 2-D, but can also be used in 3-D Unconventional Positioning Technology (University of Oxford) 31 / 56

39 Results 20 badgers tagged, each generates about 1 million readings per day Typical 3-D positioning accuracy of 30 cm RMS Underground Localization in 3D using magneto-inductive tracking, IEEE Sensors Unconventional Positioning Technology (University of Oxford) 32 / 56

40 2-D Accuracy Actual Estimated 10 Y co-ord [m] X co-ord [m] Unconventional Positioning Technology (University of Oxford) 33 / 56

41 Behaviour Unconventional Positioning Technology (University of Oxford) 34 / 56

42 Summary Using MI tracking solved a previously impossible problem Leading to novel insights about animal behaviour Latest generation also have accelerometer, so we can also mine activity Unconventional Positioning Technology (University of Oxford) 35 / 56

43 Section 5 Precise 3-D localization in Challenging Environments Unconventional Positioning Technology (University of Oxford) 36 / 56

44 3-D Magnetic Vector Modulation As previously mentioned we can: Generate and steer a magnetic vector using 3 orthogonal transmitting coils Sense and recover the magnetic vector using 3 orthogonal receiving coils This provides the unique ability to localize a receiver using a single transmitter Unconventional Positioning Technology (University of Oxford) 37 / 56

45 Magnetic Positioning With 3 transmitting antennas and 3 receiving antennas, we have a total of 9 measurements, of which 6 are unique Using some physics 5 we can work out the 6 degrees of freedom in the receiver (position and orientation) Due to symmetry, we have a hemispherical ambiguity, which can be solved with some prior knowledge 5 in the appendix Unconventional Positioning Technology (University of Oxford) 38 / 56

46 Applications: Worker Safety Workers underground cannot currently be localized - major safety issue for railway and mining industries 6 6 TrackSafe Project Unconventional Positioning Technology (University of Oxford) 39 / 56

47 Applications: Structural Deformations Embed tiny triaxial magnetic sensors in concrete structures to measure deformation Unconventional Positioning Technology (University of Oxford) 40 / 56

48 Results: Outdoor tracking Walking in a circle around the transmitter Y (East) 3 X (North) 2 1 Z [m] 0 1 O TX x z y X [m] 2 Z (Down) Y [m] Unconventional Positioning Technology (University of Oxford) 41 / 56

49 Results: Indoor tracking Operating through solid concrete over two floors Unconventional Positioning Technology (University of Oxford) 42 / 56

50 Results: Precision tracking Precision (cm-level) ranging at a distance of 3 m. RSSI [db] RSSI sensitivity to tiny displacements estimated distance RSSI [db] true distance time [seconds] distance [meters] Unconventional Positioning Technology (University of Oxford) 43 / 56

51 Section 6 Conclusions Unconventional Positioning Technology (University of Oxford) 44 / 56

52 Summary If some property varies over space, then there is a strong chance that someone has or will use it for positioning! Magneto-Inductive positioning has some unique properties which make it an interesting alternative Positioning itself though is just another sensor - it is what we do with it that is important Unconventional Positioning Technology (University of Oxford) 45 / 56

53 Section 7 Appendix Unconventional Positioning Technology (University of Oxford) 46 / 56

54 Free-space Magnetic Channel Model Position Estimation Consider TX located at the origin (x, y, z) = (0, 0, 0) Let RX position in 3D be described by the position vector r = (x r, y r, z r ) The range is r = r 2 = x 2 r + y 2 r + z 2 r TX is energized in each axis, and the corresponding magnetic moments are: m i = N TX I TX A TX e i, (1) where N TX = number of turns of the TX coil I TX = the coil input TX coil current A TX = the area of the TX coil e i, i = 1, 2, 3 are the standard Euclidean basis vectors (excitations) Unconventional Positioning Technology (University of Oxford) 47 / 56

55 Free-space Magnetic Channel Model Position Estimation GOAL: estimate the 3D position of RX The B-field at an arbitrary position r, given an arbitrary magnetic moment m is: B(r, m) = µ [ TX 3r(m T r) 4π r 5 m ] r 3 = µ [ TX 3rr T ] 4πr 3 r 2 I 3 m, (2) where µ TX is the magnetic permeability of the TX coil core I 3 denotes the 3 3 identity matrix ( ) T denotes the matrix transpose For each TX magnetic moment m i, i = 1, 2, 3, we get a vector b i = B(r, m i ) Unconventional Positioning Technology (University of Oxford) 48 / 56

56 Free-space Magnetic Channel Model Position Estimation Define the matrix whose columns are b i, i = 1, 2, 3 B 1,2,3 [b 1, b 2, b 3 ] = µ TXN TX I TX A [ TX 3rr T ] 4πr 3 r 2 I 3 [e 1, e 2, e 3 ] }{{} I 3, (3) Let Ω SO(3) be an orthogonal matrix describing the orientation of the RX frame w.r.t. the TX frame Then, the magnetic vector field described in the RX frame is ΩB 1,2,3 = µ TXN TX I TX A [ TX 3rr T ] 4πr 3 Ω r 2 I 3 (4) Unconventional Positioning Technology (University of Oxford) 49 / 56

57 Free-space Magnetic Channel Model for a pair of Triaxial Coils The voltages induced in the RX (x, y, z)-axes due to TX excitations (e 1, e 2, e 3 ) are decribed by the following channel matrix: S S x1 S x2 S x3 S y1 S y2 S y3 S z1 S z2 S z3 = 2πf µ RX N RX A RX ΩB 1,2,3 (5) where f is the frequency of the excitation µ RX is the magnetic permeability of the RX coil core N RX = number of turns of the RX coil A RX = the area of the RX coil Unconventional Positioning Technology (University of Oxford) 50 / 56

58 Free-space Magnetic Channel Model for a pair of Triaxial Coils Define the range-dependent scaling factor that also incorporates all the TX/RX coils specific constants Then, we can write: c = 1 r 3 0.5f µ TXµ RX N TX N RX I TX A TX A RX (6) [ 3rr T ] S = cω r 2 I 3. (7) Note that the channel matrix depends on the position vector r we are interested in, and the orientation Ω Unconventional Positioning Technology (University of Oxford) 51 / 56

59 Free-space Magnetic Channel Model Channel Matrix Estimation The channel matrix S containing the position information can be estimated at the RX using a known transmitted preamble The input-output relationship of the 3 3 channel is P RX = P TX S T + (Gaussian noise), (8) where P TX and P RX are the Nx3 transmitted and received preamble, respectively (tall matrices) Therefore, the LS estimate (which in this case is also Maximum Likelihood estimate) of the channel matrix is Ŝ = [P TX P RX] T, (9) where ( ) denotes the Moore-Penrose pseudoinverse Unconventional Positioning Technology (University of Oxford) 52 / 56

60 Free-space Magnetic Channel Model Range Estimation Let us analyze a bit the channel matrix and try to infer the range r: [ 3rr T ] S = cω r 2 I 3, (10) The scaling factor c r 3, and therefore contains the range information The latter factor depends only on the versor r/ r (i.e., only on the direction of the position vector, not on its magnitude) Therefore, in free-space, the Frobenius norm of S also decays with the cube of the range, and can be used for range estimation S F r 3, (11) Since orthogonal matrices preserve the Frobenius norm, the range estimate is invariant w.r.t. TX/RX relative orientation Unconventional Positioning Technology (University of Oxford) 53 / 56

61 Free-space Magnetic Channel Model Range Estimation Define the overall RSSI (Received Signal Strength Indicator) measured in db as ρ = 20 lg S F (12) Since S F r 3, the law describing the RSSI vs. distance in free-space is ρ = ρ 0 60 lg(r/r 0 ), (13) where ρ 0 is the RSSI measured at some reference distance r 0 Therefore, the range estimate in free-space is r = r 0 10 (ρ 0 ρ)/60 (14) When plotting the RSSI vs the log-distance lg(r/r 0 ), the slope of the line is 60dB/decade Unconventional Positioning Technology (University of Oxford) 54 / 56

62 Free-space Magnetic Channel Model Position estimation Our next goal is to determine the position vector r Its modulus (the range) r = r is known by now, we only need to determine its direction in 3D Recall that [ 3rr T ] S = cω r 2 I 3, (15) We first get rid of the arbitrary RX orientation Ω SO(3) as follows Define the channel inner product matrix C = S T S (16) From Eqs. (15) and (16), obtain [ ] C = c 2[ 3rr T ] T [ 3rr r 2 I 3 Ω }{{ T T ] 2 Ω } r 2 I 3 = c 2 3 r r T r r I 3 (17) I 3 Unconventional Positioning Technology (University of Oxford) 55 / 56

63 Free-space Magnetic Channel Model Position estimation Let C = UDU T be the eigendecomposition of C We get r r r = 1 3c r T C 1/2 }{{} UD 1/2 U T I 3 }{{} UU T [ 1 = U 3c D1/2 + 1 ] 3 I 3 U T (18) which is a rank-one matrix Consequently, the maximal eignevector u max of C is the position versor we are interested in: r r = u max (19) Finally the 3D position vector can be written as r = ru max (20) Unconventional Positioning Technology (University of Oxford) 56 / 56