Combination of feature-based and geometric methods for positioning

Transcription

1 Combination of feature-based and geometric methods for positioning Stefan Niedermayr, Andreas Wieser Institute of Geodesy and Geophysics 3 rd International Conference on Machine Control & Guidance, March 27-29, 2012, Stuttgart, Germany

2 2 Classical approaches to positioning

3 3 Reduction to geometric content Peripheral and integral models reduce the observation to its geometric content Example: Φ () t = ρ () t + c δt () t c δt ( t T ) k k k k il, i i i k + δtr () t δion () t i k il, k il, k il, k + δmp () t + δorb () t k k k + δ reli ( t) + λ φi( t0) + δφi ( α) φ ( t0) λn + ε k i () t i geometric content

4 4 Line-of-sight Reduction is feasible if the signal propagates only along the line-of-sight LOS Established geodetic methods for positioning use EM-radiation with short wavelengths (e.g. light, optical radiation) i.e. only signal propagation in direct LOS High resolution/high accuracy Limited availability

5 5 Positioning ourselves We capture a representation of our environment using the sensory organs We estimate our position by minimizing the difference between observed features and the ones stored in our memory

6 6 Feature-Based positioning Position can also be derived by Measuring a spatially varying feature Locating the measured value within a database of georeferenced values (reference values) Rover measured value reference values

7 7 Feature-based positioning (2) Each spatially varying feature (e.g. WLAN signal strength of an AP) is mathematically a field F( x) ξ A measurement of such a feature contains information about the position of the sensor y = F( x ) + e i i i η y i Determination of position by means of inversion Method: Minimization of distance between measured feature-vector and given field xˆ : F( xˆ ) y F( x) y x i i i i

8 8 Appropriate features Any feature which is observable spatially varying stable over time or predictable Simulierte Signallaufzeit Ultraschall com_content&view=article&id=52&itemid=805 Examples: EM-signal strength Time-of-flight of signals Ambient light (color, intensity) Optical/geometrical structure bergeography/atlas/wireless.html

9 9 Deterministic Fingerprinting Position determined by minimization of distance between measured feature-vector and given field Let the field be given by georeferenced fingerprints y y j = j Rover d= Distance calculated between the observed feature-vector and N candidate fingerprints stored in the database: y = d : = y y j = 1,, N j j

10 10 Deterministic Fingerprinting (2) Actual position is usually calculated as a weighted mean of the reference positions, e.g. as nearest neighbour or k-nearest neighbour Open issues: Missing implementation of stochastics (reference data and measurements) Poor separability for vectors with high dimension (many features) Rover y = 68 d= y j = Missing tools for quality assessment

11 11 Probabilistic Fingerprinting Unknown position is treated as stochastic property Estimation using the related probability density function Posterior probability based on Bayes-theorem: + E{} x = x p() x dx ˆx P( x y) = P( y x) P( x) P( y) Numeric evaluation by: P( x y) Calculation of for M discrete positions x l (candidates) Estimation calculated from P( x 1 y),, P( x M y) Selection of x l : grid points or random samples

12 12 Project SESAAM Geo-Spatially Enhanced Situational Awareness for Airport Management Duration: 3/2010 8/2012 Funding: FFG Partners:

13 13 Complete Operational Picture (COP)

14 14 SESAAM positioning system Deep integration of GPS, WLAN-fingerprinting and RFID cell-of-origin in order to locate vehicles and objects with m-level accuracy MLAT- Server VOS- Server COP-Server

15 15 WLAN signal strengths - real situation at Salzburg airport

16 16 Exemplary result of probabilistic fingerprinting 3 access points used Assumption: Std of signal strength measurement is 2.5 dbm (simulated observation based on true map) MAP estimation using numerical evaluation of posterior density at 1x1 m 2 grid true estimated 95%-confidence region Error of estimate: 6 m 95%-confidence region: diameter >100 m, non-coherent

17 17 Attainable accuracy F( x) Gradient represents attainable accuracy : 1 dy δx δy dx ( f x ) 1 σmin = grad ( ) σ y y uncertainty ˆx ˆx x Depending on number and structure of fields, there may be non-uniqueness issues.

18 18 Gradient of WLAN signal strength Experimental data, Salzburg airport 10 dbm/m D Assuming a standard deviation of the measurments of 2.5 dbm we may thus expect a standard deviation of the position of about 0.25 D WLAN signal strengths will only be useful for positioning in the vicinity of the access point

19 19 Combination of feature-based and geometric positioning Measured features may be processed simultaneously with (individual) geometric observations to obtain better solutions Bayesian estimation provides a useful framework for seamless integration P( x y) = P( y x) P( x) P( y) SP 1 SP 2 Required: probability density function of the observations as a function of the true position likelihood P( y x)

20 20 Illustrating example Pre-defined feature-field Two distance observations with σ 1 =0.3 m und σ 2 =0.2 m SP 1 SP 2 Observation of feature with σ f1 =1 dbm Simulated observation-vector at unknown rover position: 7,8 m y = 5,0 m 54,3dBm Assumption: observations are normally distributed

21 21 Example: likelihood functions Py ( x) 1 Py ( x) 2 Py ( x) 3

22 22 Example: distance resection combined with stochastic fingerprinting SP 1 SP 2

23 23 SEAAM: GPS and WLAN fingerprinting Tight coupling of GPS and WLAN fingerprinting Particle filter in order to include dynamic model of moving vehicles Example trajectory: reference: RTK GPS + IMU position estimated from real C/A code observations and simulated WLAN observations (σ=3 dbm) 2D Mean Radial Error (MRE): GPS ok: 1.21 m no GPS: 8.31 m

24 24 Conclusions Any spatially varying feature can be used for positioning ( feature-based positioning ) Suitable fields may be readily available (e.g. magnetic field) or may be created artificially (e.g. signal strength of radio wave transmitters) Attainable accuracy depends on gradient of the field temporal stability (or modelling of temporal variation) accuracy of measurement Probabilistic processing is particularly suitable and allows combining features and geometric observations

25 25 This presentation contains results and figures of the publicly funded project SESAAM (FFG/519427) carried out with the following partners: Dipl.-Ing. Stefan Niedermayr Prof. Dr. Andreas Wieser Vienna University of Technology Institute of Geodesy and Geophysics Gußhausstraße 27-29/E Vienna Austria