Measuring the Dynamic Soaring of Albatrosses by Time
Transcrição
Measuring the Dynamic Soaring of Albatrosses by Time
Lehrstuhl für Flugsystemdynamik Technische Universität München Colloquium Satellite Navigation 2009 Measuring the Dynamic Soaring of Albatrosses by Time-Differential Processing of Phase Measurements from Miniaturized L1 GPS Receivers Dipl.-Ing. Johannes Traugott Institute of Flight System Dynamics Technische Universität München [email protected] +49 (0)89 289-16066 June 15, 2009 Johannes Traugott 1 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München The Project Dynamic Soaring of the Wandering Albatross The Albatross – a perfect glider • Flight over thousands of kilometers over open seas (97% gliding without flapping) • Approx. 80% of lifetime airborne (sleeping while flying?) • High wingspan (max. 3.5m), wing loading (~13 kg/m2), aspect ratio (~18) and gliding ratio (~20) • Very weak flight muscles (< 6% of body mass only); tendon mechanism to lock wings while gliding Wandering Albatross (diomedea exulans) in the skies [Photo: Traugott] June 15, 2009 Johannes Traugott Track of a Wandering Albatross on migration [Tickell 2000] 2 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Dynamic Soaring • No thermal lift over open seas • Extraction of wind energy in boundary layer above sea surface tcyc = 7.3s DS trajectory and shear wind profile Energy neutral dynamic soaring cycle [Sachs 2004] [Sachs 2004] Controversy in community: • Wave-slope soaring? • Shear wind effect not sufficient for continuous flight? • Upper curve? June 15, 2009 Johannes Traugott Real measurements required… • …for finding answers to these questions • …for validating simulation & optimization results 3 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München GPS Measurement Campaign (Winter 2008/09) Sate of the art: • Measurement of global tracks for studies of migration and foraging behavior (e.g. BirdLife International 2004) • Low sampling rates / modest precision (ARGOS) Our objectives: • Measurement of individual flight cycles with high precision sufficient for flight mechanical analysis on maneuver scale • Global trajectories of secondary interest only. Cooperation with CNRS / Centre d’Ecologie Fonctionnelle et Evolutive (Montpellier) Expedition to Kerguelen Archipelago The distribution of Wandering Albatrosses. Prince Edward Is. (1), Is. Crozet (2), I. Amsterdam (3), Is. Kerguelen (4), Heard I. (5), Macquarie I. (6), Auckland Is. (10), Campbell I. (11), Antiposes Is. (12), South Georgia (18), Tristand da Cunha (19) and Gough Island (20) [Tickell 2000] June 15, 2009 Johannes Traugott 4 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Navigation Requirements and Constraints Precision in the decimeter range for individual maneuvers limited from 15 seconds up to a view minutes High sampling rate (10 Hz) due to high dynamics / short cycle times No baseline restriction due to far distances travelled • shadowing during bird equipment • shadowing during prey catching [Photo: Traugott] • loss-off-lock due to exceeding bank angles, … June 15, 2009 Johannes Traugott [Photo: National Oceanic and Atmospheric Administration/ Administration/DoC] No (static) initialization procedures due to practical constraints in the field: [Photo: Archive Traugott] 5 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Sensor Requirements and Constraints Form-factor < 100 x 50 x 15 mm Mass < 100 g Lifetime: Several days or triggering mechanism for high rate sampling • Memory no off-the-shelf solution • Battery limiting factor concerning weight No wiring on the bird! self-contained, sealed & rugged unit Approach Processing time differences of L1 phase observations from low cost, miniaturized GPS receiver modules Find & test suitable hardware Develop & implement algorithm Find & equip bird (and get receiver back) June 15, 2009 Johannes Traugott 6 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Hardware Receiver Module U-blox LEA-4T • Access to 10 Hz raw-data via binary UBX protocol (UBX-RAW) • 4 Hz online solution • Promising results in ZBL-tests • L1 only Zero-baseline test result of the TIM module (TIM-LL -TIM-LP, PRN 26-12, 07/08/07, DLR Oberpfaffenhofen,Germany) June 15, 2009 Johannes Traugott 7 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Integrated Logger B C 2 GB (Micro) SD Card as external memory (8 MB integrated flash not sufficient)) approx. 10 MB / h RXM-RAW @ 10 Hz, NAV-SOL @ 1Hz 8 MB flash only (30 min recording) 3 LS 1450 (C) lithium-thionyl chloride primary cells 2 LS 1450 cells sufficient for all applications Operated by reed contact Wireless data downloaded to base station Recording time: several days 3 axis MEMS accelerometer June 15, 2009 Triggering logic for high-rate raw-data recording Johannes Traugott C A&B A 8 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Casing (for B) • Custom-made casing milled by AKA-MODELL of TUM • Transparent for reading status LED when sealed • Material: Makrolon • Mass: approx 20 g • Sealing by SikaFlex 221 1st prototype June 15, 2009 Final design Johannes Traugott 9 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Power supply • Ilog = 65 mA; Ulog = 3.0 V; Plog = 195 mW • Ambient temperature 0°C – 13°C • Required lifetime corresponding to memory up to 6 days U [v] ? LS 17500 LS 14500 L 91 14.5 g 16.7 g 21.9 g 18 g Test results Li/FeS2 LiSoCl2 primary primary ? Datasheet Saft LS 14500 [manufacturer] LiPoLy rechargeable June 15, 2009 • Info from datasheets not sufficient to make proper decision Johannes Traugott • Tests under expected conditions for various candidates • Final choice: Lithium-thionyl chloride primary cells 10 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München 3D MEMS accelerometer (C only) Calibration line Calibration test results 8 4000 low sensitivity normal sensitity 3500 6 3000 digital output [-] acceleration [g] 4 2 0 • Determination of scale factor, bias, temperature sensitivity,… currently in progress for each axis of the tags applied in the field +1g 2500 2000 • One sample per GPS raw data set (10 Hz) 1500 -1g -2 1000 -4 -6 0 low sensitivity normal sensitity • No anti-aliasing filter in front of ADC 500 2000 digital output [-] June 15, 2009 4000 0 0 • σ = 0.1 m/s (experimental results @ room temperature) 2000 sample [-] 4000 Johannes Traugott • Adjustment of sensitivity settings in the field by flight data analysis 11 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Software / Algorithm Core Algorithm THE OBSERVABLE Individual carrier phase measurement [Montenbruck 2006] [Montenbruck 2006] ( ) Φ(t ) = ρ (t ) + cδ R (t ) + λ1 ϕ S (t0 ) − ϕ R (t0 ) + N = f (ξ i , X i , ti ) 144424443 June 15, 2009 N ' ≠ f (t ) Johannes Traugott 12 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Forming time-differences bi ∇x := x(ti ) − x(tb ) bi ∇Φ = bi ∇ρ + c bi ∇δ + λ1 ∇N ' bi provided continuous phase-lock in receiver PLL, unknown ambiguity cancels! June 15, 2009 Johannes Traugott 13 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München BASIC NAVIGATION TASK Geometry of the problem X bS X iS ρi ρb eb • Only relative solution of interest • Change of unit vectors due to elapsed time not neglected ei xb tb ∆xi bi b xi ti Receiver position and time (PT) at time ti x i = (xi , yi , zi ) T ξ i = (x i , cδti ) T June 15, 2009 Baseline between “virtual” base epoch at time tb and ti b bi = x i − x b β bi = ξ i − ξ b Johannes Traugott / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Equations of the problem • Models enhanced by atmospheric corrections (troposphere, ionosphere) ) ) R Φ i = ρ i + cδ i + λ1 N '+Tˆi − I i bi ( ) ( ˆ = (ρ − ρ ) + c(δ − δ ) + Tˆ − Tˆ + Iˆ − Iˆ ∇Φ i b i b i b i b ) bi bi bi bi = ∇ρ + c ∇δ + ∇Ti − ∇Iˆi ( = f ξ i , X i , ti , ξ b , X b , t b ) ) unknown • “Observed = Computed” for all satellites in view (m>=4) bi ~ bi ˆ ∇Φ = ∇Φ (Over-determined) set of nonlinear equations in receiver PT June 15, 2009 Johannes Traugott 15 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München • Numeric solution by linearization and iteration bi bi ˆ (ξ ˆ (ξ , ξ ,...) + H ∆ξ ∇Φ , ξ ,... ) = ∇Φ i , k +1 b i ,k b ξ i ,k i ξ i ,k +1 = ξ i ,k + ∆ξ i Updated in each iteration cycle / epoch H ξ i ,k ˆ d bi ∇Φ = = dξ i ξ i ,k bi ( ) ( ˆ = (ρ − ρ ) + c(δ − δ ) + Tˆ − Tˆ + Iˆ − Iˆ ∇Φ i b i b i b i b ) ˆ1 ∂ bi ∇Φ ∂xi ˆ2 ∂ bi ∇Φ ∂xi M bi ˆm ∂ ∇Φ ∂x i ˆ1 ∂ bi ∇Φ ∂yi ˆ2 ∂ bi ∇Φ ∂yi M bi ˆm ∂ ∇Φ ∂yi ˆ ∂ bi ∇Φ ≈ ∂ρˆ i / ∂x i = −e i ∂x i Only variation of bi ˆ T,I neglected ∂ ∇Φ ≈ 1 (compensated by iteration) ∂(cδ i ) June 15, 2009 ˆ1 ∂ bi ∇Φ ∂zi ˆ2 ∂ bi ∇Φ ∂zi M bi ˆm ∂ ∇Φ ∂zi H ξ i ,k Johannes Traugott ˆ1 ∂ bi ∇Φ ∂(cδ i ) ˆ 2 ∂ bi ∇Φ ∂(cδ i ) M bi m ˆ ∂ ∇Φ ∂(cδ i ) x − e1 T i ,k = M − e m T i ,k i ,k , yi ,k , z i ,k , cδ i ,k 1 M 1 16 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München − Solution by least squares ( ) −1 ∆ξi = H H H T ( T bi ) ~ bi ˆ ∇Φ − ∇Φ(ξi,k ,...) ξ i ,k +1 = ξ i ,k + ∆ξ i − Minimization of residuals between measured and computed (modeled) observations m ∑ res j2 = min j =1 ~ ˆj res j = bi ∇Φ j − bi ∇Φ − If measurement errors are uncorrelated, unbiased and have constant variance ∆ξ has minimum variance of all estimates that are linear combinations of the observations. June 15, 2009 Johannes Traugott 17 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München − Solution process similar to standard single point positioning − ξ calculated in each iteration cycle in order to update Jacobian / unit vectors − Note: β is “real” solution of the problem (relative positioning) xi,k bbik xb June 15, 2009 bbik−1 Johannes Traugott ∆x = ∆b xi,k −1 18 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Error considerations MEASUREMENT ERRORS bi ~ bi ˆ bi ∇Φ = ∇Φ + ∇χ bi ∇χ = − bi ∇δ S + bi ∇E + bi ∇T − bi ∇I + bi ∇noise + bi ∇mp satellite clocks non-modeled measurement troposphere noise ephemeris non-modeled multipath ionosphere Primary error remaining for time-differenced observables is error drift S d δ dE dT dI dT dI bi bi bi ∇χ = − + + − (ti − tb ) + − b + ∇noise + bi ∇mp dt dt dt t dx dx tb dt b Dependent of temporal autocorrelation of error contributions June 15, 2009 Present in any kind σ ∇noise = 2σ noise of differential Single differences only processing Johannes Traugott 19 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Error drift for “clean” static data with best corrections 0.2 0.2 0.15 Eph.: Sat.-Clk.: Iono.: Tropo.: igs15295.sp3 igs15295.clk_30s igsg1210.09i UNB3 3D position error [m] 0.1 C/A SPP with all corrections north [m] 0.15 0.1 0.05 0.05 High quality receiver from IGS reference network (BRUS) 1Hz, #SV 8, PDOP ~ 1.9 0 -0.05 June 15, 2009 0 east [m] 0.05 0 0 100 100 200 Johannes Traugott 300 400 500 tau [s] 600 700 800 20 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Error drift for “clean”, static data with best various corrections omitted 1.4 1.2 • Initial solution by C/A SPP • Solution variations typical compare [Traugott 2008b] 1 3D position error [m] • Same corrections for initial solution and time-relative solution best no hr clk no hr clk / brdc eph no ion no trop 0.8 0.6 0.4 0.2 0 0 June 15, 2009 100 100 200 Johannes Traugott 300 400 500 tau [s] 600 700 800 21 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München GEOMETRIC ERROR Offset in initial position causes “distortion” of base vector b x b ,estimated δb bi bi* x*i ~ ˆ (ξ , ξ ) + ∇Φ = bi ∇Φ i ,0 b,0 + H ξ i , 0 (∆ξ i − δξ b ) + δx b x b , true bi & (t − t )δξ + bi ∇χ +H i b i 1ξ4 4 24 4 3b b bi xi bi Effect can be interpreted as additional, “geometric” range error No relative error for ti-tb0 No error in initial position no error due to geometry variation ∇χ geo − e&1 T i ,0 & = M H ξi − e& m T i ,0 0 M 0 vsat ≈ 3.9km/s e& max ≈ 1.9e − 4 Derivation [Traugott 2008], [Ulmer 1995] June 15, 2009 Johannes Traugott 22 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Error drift for clean, static data caused by initial offset 7 • uBlox TIM-LP • 25x25 mm, active patch antenna 6 best off 12.5 m off 25 m off 50 m 6.45 • Location: Open fields • Typical results 5 #PRN 7 Compare [Traugott 2008] 1.2 3D position error [m] 1 3D position error [m] 1.4 Initial position as given by IGS for station BRUS (including Antenna phase center corrections) 0.8 4 PDOP ~ 2.1 3.1 3 0.6 2 0.4 1.43 0.2 0 0 1 100 200 300 400 500 tau [s] 600 700 800 • Offset in initial position may compensate for other errors June 15, 2009 0.252 0 0 100 Johannes Traugott 200 300 tau [s] 400 500 23 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Two Approaches to a Precise Trajectory OVER-ALL SOLUTION δξb SPP ξb tb βbi ξi ti Each epoch independent from previous epochs reduced computational load for static applications (if no outlier detection required) Easier & better estimation of error drift (r.t. later slides) Change of used constellation / drop-out of satellites steps in trajectory possible Same PRN subset at base and rover epoch less observations available June 15, 2009 Johannes Traugott 24 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München ACCUMULATED SOLUTION ξ n−1 tn−1 δξb SPP βn−1,n ξ n tn ξb tb ξi ti Accumulation of incremental solutions Max. number of PRN for processing available Incremental solution anyhow required for outlier detection Difficult estimation of error drift (see later slides) Accumulation of errors random walk effects? June 15, 2009 Johannes Traugott 25 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München COMPARISON ti tb ξ b over-all solution ˆ = const Φ b ~ ~ Φi − Φb i ∑ n =b +1 nonlinear ξ i , 0 = ξ i −1 678 ~ b ,i ~ n −1, n Φ = ∇Φ 1 42∇ 4 3 f (∑ n −1, n ) ∑f( ~ ∇Φ,... = n −1, n ~ ~ Φ n − Φ n −1 f nonlinear ˆ Φ n −1 Linearity : f (c1a + c2b ) = c1 f (a ) + c2 f (b ) ( ξ n =ˆ β n −1,n ) i ∑ β n −1,n β bi n =b +1 ξ n −1 t n t n −1 Johannes Traugott ) ) ~ ∇Φ,... exact ξ n, 0 = ξ n −1 June 15, 2009 ( ξ i =ˆ β bi f accumulated solution 26 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Equivalence of incremental and over-all time differences of observations i ∑ n −1, n ~ ∇Φ = n =1+1 i ∑ ~ ~ Φ n −Φ n −1 n =1+1 = i ∑ (Φ n =b +1 n + δΦ n ) −(Φ n −1 + δΦ n −1 ) = [(Φ 2 + δΦ 2 ) − (Φ1 + δΦ1 )] + [(Φ 3 + δΦ 3 ) − (Φ 2 + δΦ 2 )] + [(Φ 4 + δΦ 4 ) − (Φ 3 + δΦ 3 )] + ... + [(Φ i − 2 + δΦ i − 2 ) − (Φ i −3 + δΦ i −3 )] + [(Φ i −1 + δΦ i −1 ) − (Φ i − 2 + δΦ i − 2 )] + + [(Φ i + δΦ i ) − (Φ i −1 + δΦ i −1 )] = [(Φ i + δΦ i ) − (Φ1 + δΦ1 )] ~ 1,i = ∇Φ δΦ “usual suspects” in GPS-land systematic & stochastic component June 15, 2009 (IF this sum was computed Numeric error with double precision) for 10.000 epochs (~15 min @ 10 Hz) < 8e-6 m) Johannes Traugott 27 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Geometric evidence of equivalence of over-all and accumulated solution (“pinned” satellite geometry) k 1,5 ∇Φk = 5 ∑ n−1,n ∇Φk n =2 2,3 1, 2 1,5 ∇Φ k 3, 4 ∇Φk 4,5 ∇Φk ∇Φk ∇Φk June 15, 2009 x1=b Johannes Traugott 28 / 62 Lehrstuhl für Flugsystemdynamik tb=1 Technische Universität München t2 t3 t4 t5 k 1,5 ∇Φk = 5 ∑ n−1,n ∇Φk n =2 ρ3 ρ4 ρ5 2,3 1,5 ∇Φk ρ3 ∇Φ k ρ2 ρ2 1, 2 June 15, 2009 ∇Φk 3, 4 ∇Φk ρ 4 ρ5 4,5 ∇Φk ρ5 Geometric evidence of equivalence of over-all and accumulated solution (changing satellite geometry) Johannes Traugott 29 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München ρk ,1 = imported ( ( ) ) ~k ~k ρk ,2 = ρk ,1 + Φ2 − Φ1 ~k ~k ~k ~k ~k ~k ρk ,3 = ρk ,2 + Φ3 − Φ1 = ρk ,1 + Φ2 − Φ1 + Φ3 − Φ1 ρk ,1 = imported [( [ ( ( ) ] )] ) ( ) ~k ~k k ρ = ρk ,1 + Φ2 + δΦ2 − Φ1 ~k ~k ~k ~k ~k ~k ' ' k k ρk ,3 = ρk ,2 + Φ3 − Φ2 + δΦ2 = ρk ,1 + Φ2 + δΦ2 − Φ1 + Φ3 − Φ2 + δΦk2 ~k ~k = ρk ,1 + Φ3 − Φ1 ' k ,2 ( ) [( ) ][ ( = ρ k ,3 Error on range measurements does not cause difference btw. over-all and accumulated position June 15, 2009 Johannes Traugott 30 / 62 )] Lehrstuhl für Flugsystemdynamik Technische Universität München Comparison of accumulated and over-all solution (clean, static data) 3D position error over-all accumulated 0.25 0.06 0.05 0.2 0.04 0.15 [m] [m] Receiver: BRUS 3D position difference (over-all - accum.) 0.07 0.03 0.1 0.02 0.05 0 0 0.01 200 400 600 tau[s] 800 0 0 200 400 600 tau [s] 800 • Very same constellation used within both solutions (8 PRN, PDOP ~1.9) • For the time spans of interest, both solutions virtually coincide (difference < 10%). • Difference stemming from second order effects • No random walk effects June 15, 2009 Johannes Traugott 31 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Comparison of accumulated and over-all solution (not so clean, static data) 1 1 0.8 0.8 0.4 0.6 PRN 31 manually excluded for obtaining same constellation for over-all all solution 3D pos. error [m] (over-all) 3D pos. error [m] (accum.) #SV × 0.1 (over-all) #SV × 0.1 (accum.) 0.6 3D pos. error (over-all) 3D pos. error (accum.) #SV × 0.1 (over-all) #SV × 0.1 (accum.) 0.4 Drop-out of PRN14 0.2 0.2 0 0 200 400 600 tau [s] 800 0 650 700 750 800 tau [s] 850 • LEA-4T / 1/4 lambda wire antenna • Data screened for outliers (see later slides, • Open fields June 15, 2009 dResRms < 0.005 m) Johannes Traugott 32 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München • Change of used PRN after long processing intervals can cause huge steps in over-all solution ( each solution independent from previous solutions) − Not relevant for time spans of interest − Not possible when using accumulated solution • Accumulated solution working with more PRN − continuously better geometry… − …but here: faster error drift than accumulated solution − PRN do not drop out “without reason”, poor measurement quality not compensated by better geometry Choice of processing method case dependent For very view satellites in view, accumulated solution often is the only feasible alternative June 15, 2009 Johannes Traugott 33 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Digression: Comparison of accumulated solution with speed calculation • Doppler (range-rate) measurements • Velocity equations − e1T M − e mT D = ρ& + cδ& R − Generated by receiver PLL or FLL? − Afflicted with (unknown)time-delay? 1 v M λ1δf 1 D1 − e1T V1 = M m T D − em V m [Montenbruck 2006] • Alternative strategy using raw phase ranges instead of receiver calculated Doppler measurement (outline): n −1, n ∇Φ n −1, n f β Vel. equs. vn ∑ β n −1,n β bi 1 / (t n − t n −1 ) D June 15, 2009 ∑ v (t n n Johannes Traugott − t n −1 ) β bi 34 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München • Calculating speed instead of position (increments) − Unit vectors need to be calculated (by SPP) for each epoch in a preprocessing step Increased noise on (base of) unit vectors Unit vectors not coherent with solution Additional problems? As no iteration is required when calculating speed, computational load might remain unchanged − Receiver clock drift calculated instead of receiver clock bias. Additional problems when differentiating and integrating? − Changed situation when reconstructing trajectory in case of phase outages x x v v t t t t − No over-all solution possible − Similar approach but not investigated in the scope of this work June 15, 2009 Johannes Traugott 35 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Quality Monitoring OUTLIER DETECTION RAIM based on RMS of residuals of incremental solution (tn-1,tn) RMSres = m ∑ j =1 2 j resn −1,n if RMSres > user defined threshold if m>4 (over-determined set of equations) / (m − 1) resnj−1,n Outlier detected = n −1, n ~ j n −1,n ˆ j ∇Φ − ∇Φ if m>5 Search afflicted measurement by iterative exclusion Error drift virtually cancels for incremental solution very low residual level Cycle slip - outlier (multipath) discrimination possible by analysis of resulting residual of excluded observation (difficult) Discrimination not necessary for accumulated solution June 15, 2009 Johannes Traugott 36 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Outlier detection: Flight data • Dynamic (but not acrobatic) maneuvers • RTK reference solution (DEOS, TU Delft) available 200 0 -200 north [m] -400 -600 -800 -1000 • LEA-4T with 25x25 mm passive patch antenna -1200 • 10 Hz sampled data -1400 -1600 June 15, 2009 Johannes Traugott 0 500 east [m] 1000 1500 37 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München • Comparison with outlier corrected RTK solution 0.4 0.4 3D pos. difference [m] # PRN × 0.01 [-] 0.3 0.3 0.2 0.2 0.1 0.1 20 40 60 80 0.02 0.01 0 0 June 15, 2009 0 0 100 RMSres [m] 0 0 RMSres [m] Tight outlier detection Loose outlier detection 20 40 60 tau [s] 80 3D pos. difference [m] # PRN × 0.01 [-] 20 40 60 80 100 20 40 60 tau [s] 80 100 0.02 0.01 100 Johannes Traugott 0 0 38 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München ERROR (DRIFT) ESTIMATION Estimation of measurement noise (Least squares rule) 1. Unbiased obs. σ 2. Uncorrelated obs. 2 ~ ∇Φ 3. Obs. with constant variance ∑ = m j =1 res m 2 m−4 Error propagation to position domain (DOP) Cβ = σ 2 ∇Φ D ( D= H H T ) −1 Assumptions (1,(2),3) true for incremental solution (tn-1, tn) Estimation of stochastic component of position error June 15, 2009 Assumption 1 violated for over-all solution (tb, ti) Application of …for the lack of stochastic concept to systematic errors… better knowledge. “Confirmed” by experimental results. Estimation of systematic / drift component of position error Johannes Traugott 39 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Noise estimation / estimation of stochastic error component 0.25 3D position error 3D estimate of stochastic error component [m] 0.2 0.15 0.1 0.05 0 0 100 • Clean, static data 200 300 tau [s] 500 3D estimate = σ ∇Φ~ × PDOP • TIM-LL / active patch antenna June 15, 2009 400 Incremental solution Johannes Traugott 40 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Error drift estimation: Accumulated solution • Problem: increasing over-all residuals (tb, ti) not available • Observation from analysis of test data: resij,b = i ∑ resnj−1,n n =b +1 • Proposed solution: Reconstruction of over-all RMS of residuals: RMSres = 2 j resn −1,n / (m − 1) j =1 n =b +1 m i ∑ ∑ − Accumulated position solution shows no steps (e.g. in case of PRN dropout) − Error estimate must be smooth as well − Reset of accumulated residuals required in case of changing number of satellites • Remaining problem: Resulting error estimate too pessimistic June 15, 2009 Johannes Traugott 41 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Error drift estimation: Accumulation of incremental residuals 0.03 11 resPRN i,b 0.025 11 resPRN n-1,n 11 SUM(resPRN ) n-1,n 0.02 [m] 0.015 0.01 0.005 0 -0.005 -0.01 0 June 15, 2009 50 100 tau [s] Johannes Traugott 150 200 42 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Error drift estimation for clean static data Over-all solution 0.25 Accum. solution RMSres RMSres (reconstructed) σ σ ∇Φ 3D error estimate (PDOP × σ∇Φ) 0.25 3D error [m] [m] 0.2 0.15 0.15 0.1 0.1 0.05 0.05 June 15, 2009 3D error estimate (PDOP × σ∇Φ ) 3D error 0.2 0 0 ∇Φ 100 200 300 tau [s] 400 500 0 0 Johannes Traugott 100 200 300 tau [s] 400 500 43 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Error drift estimation for not so clean, static data Accum. TD solution 0.4 RMSres (reconstructed) 3D error estimate 3D error [m] 0.3 0.2 0.1 [-] 0 June 15, 2009 8 6 4 2 0 0 # PRN PDOP 100 200 300 400 500 tau[s] Johannes Traugott 600 700 800 900 44 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Error drift estimation for clean dynamic data north [m] 0 -50 -100 -300 -250 -200 -150 -100 east [m] -50 0 50 • Car driving on open fields • RTK solution from DEOS available • TIM-LL with 25 x 25 mm active patch mounted on rooftop • 10 Hz sampling rate • Good data quality (7 PRN, DOP 2.15) June 15, 2009 Johannes Traugott 45 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München • Position difference between accumulated time-difference solution and fixed ambiguity RTK solution • Error estimate matches real offset well 0.1 3D position differene (RTK - accum. TD) 3D error estimate 0.09 0.08 0.07 [m] 0.06 0.05 0.04 0.03 0.02 0.01 0 0 June 15, 2009 20 40 60 80 100 tau [s] Johannes Traugott 120 140 160 / 62 46 Lehrstuhl für Flugsystemdynamik Technische Universität München Error drift estimation for flight test data Over-all solution Accum. solution 0.5 0.45 0.4 0.5 3D position difference (RTK - TD) [m] 3D error estimate [m] # PRN × 0.01 [-] PDOP × 0.01 [-] 0.45 0.4 0.35 0.35 0.3 0.3 0.25 0.25 0.2 0.2 0.15 0.15 0.1 0.1 0.05 0.05 0 0 20 40 60 tau [s] 80 100 0 0 3D position difference (RTK - TD) [m] 3D error estimate [m] # PRN × 0.01 [-] PDOP × 0.01 [-] 20 40 60 tau [s] 80 100 • Accumulated solution drifts faster from RTK as over-all solution • Error estimate of accumulated solution too pessimistic. Problem observed with frequently changing geometry June 15, 2009 Johannes Traugott 47 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Albatross Data Equipment of 20 birds during breeding season June 15, 2009 20 receivers recovered 16 valid flights = 80% success rate Johannes Traugott 48 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Five 30 min trajectories with 3D acceleration data Albatross colony (breeding site) June 15, 2009 Johannes Traugott 49 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München 11 one to six day trajectories June 15, 2009 Johannes Traugott 50 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München First 6 days out of 30 day trip (approx. 3.500 km) Kerguelen June 15, 2009 Johannes Traugott 51 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Objective: Analysis of individual dynamic soaring cycles June 15, 2009 Johannes Traugott 52 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München 3D trajectory of exemplary cycle up × 3 [m] 20 10 0 200 100 north [m] 0 0 20 40 60 80 100 east [m] June 15, 2009 Johannes Traugott 53 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Time history in vertical direction 10 8 up [m] 6 4 2 0 -2 -4 0 5 10 15 tau [m] June 15, 2009 Johannes Traugott 54 / 62 Lehrstuhl für Flugsystemdynamik 1.4 1.2 Technische Universität München Data analysis 0 3D error estimate [m] # PRN × 0.1 PDOP × 0.1 EXC BC 5 NO 1 10 CS PRN 0.8 BM 15 LE 0.6 20 MD 0.4 REP 25 OK 0.2 30 0 0 5 10 15 20 tau [m] • Frequently changing geometry • Multiple outliers (RMSres limit set to 5 mm ) June 15, 2009 NA 40 60 80 100 tau × 10 [s] 120 140 • Estimate of 3D position drift 1.1 m (probably too pessimistic) • Cycle with relatively good data quality! Johannes Traugott 55 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Data interpolation (here: vertical direction) 10 original data smoothing spline fit up [m] 5 0 resid. [m] noise est. [m] -5 0 5 10 15 5 10 15 5 10 15 x 0.02 0.01 0 0 0.02 0 -0.02 0 tau [m] • Cubic smoothing spline (first shot only) June 15, 2009 • Residuals correlated with 3D noise estimate Johannes Traugott 56 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Speed and acceleration 30 [m/s] 25 20 sog (fit dot) sog (Doppler SPP) sog (pos. data diff) 15 10 0 5 10 15 accel (fit ddot) accel (accelerometer) accel (pos. data ddiff) 20 • Speed from differentiation less noisy than speed calculated using Doppler measurements (&x& ) A EE E 15 = M ES ((a Accel )S − (g )S ) (&x& ) 2 [m/s ] A EE 10 = 1g xS 0 0 gravity = 1g 2g 5 5 10 tau [s] 15 zS • Absolute values of acceleration measured by accelerometers and derived from GPS position plausible June 15, 2009 Johannes Traugott 57 / 62 Lehrstuhl für Flugsystemdynamik Total energy Technische Universität München E= 1 2 mv + mgh 2 30 E 1 2 = v +h mg 2 g 10 total energy [m] 10 0 0 5 10 15 -10 40 40 total energy [m] 250 200 north [m] 20 300 height [m] speed [m/s] 20 150 100 30 50 20 0 10 0 5 10 15 tau [s] 0 50 100 east [m] • Already at this point investigation of bird’s total energy management possible June 15, 2009 Johannes Traugott 58 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Outlook • Evaluation of individual cycles under different (environmental) conditions − Wind strength − Relative heading w.r.t. wind direction − Sex / size • Starting with wind information from global models (QuickSCAT L3) and boundary models • Reconstruction of flight state using additional field measurements (wing geometry) [http://manati.orbit.nesdis.noaa.gov/quikscat] • … up × 3 [m] • (Reconstructing local wind from trajectories) 500 400 40 300 20 200 0 Confirmation of 0 dynamic soaring theory and gain of new insights June 15, 2009 600 100 50 100 0 north [m] east [m] Johannes Traugott C:\DATEN_JT\FSD\02_GPS_Tests\06_Kerguelen\090114_ #10f_Rec7\Processing\1514_347135_347171 clean cycles 59 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Conclusion Relative accuracy is an absolute value! Many applications • Motion analysis − …for (aircraft) performance and parameter identification e.g. gliding ratio of gilder planes − …for sport applications (without antenna shadowing) −… • Static measurement of relative position − …for avalanche rescue − …for azimuth determination −… Time-differences of L1 receiver phase ranges are proposed as a means to achieve relative precision whilest… • ….keeping costs really low • ….keeping field procedures really simple • ….using miniaturized equipment June 15, 2009 Johannes Traugott 60 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Thank you for your attention! [Photo: Traugott] June 15, 2009 Johannes Traugott 61 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München Acknowledgements Oliver Montenbruck Anna Nesterova, Francesco Bonadonna Alexei Vyssotsky, Giocomo Dell’Omo Franz Kümmeth, Wolfgang Heidrich Jan Wendel Dennis Odijk, Christian Tiberius AKAModell, TU München IDAFlieg, AKAFlieg, TU München … June 15, 2009 Johannes Traugott 62 / 62 Lehrstuhl für Flugsystemdynamik Technische Universität München References BirdLife International (2004). Tracking ocean wanderers: the global distribution of albatrosses and petrels. Results from the Global Procellariiform Tracking Workshop, 1–5 September, 2003, Gordon’s Bay, South Africa. Cambridge, UK: BirdLife International. Montenbruck, o. (2006). Lectures on Satellite Navigation. Technische Universität München, 2006 Sachs, G (2004). Minimum shear wind strength required for dynamic soaring of albatrosses. Ibis. Tickell, W.L.N. (2000). Albatrosses. Yale University Press. New Haven and London. Traugott, J., G. Dell'Omo, A.L. Vyssotski, D. Odijk, and G. Sachs (2008). A time-relative approach for precise positioning with a miniaturized L1 GPS logger. In Proceedings of ION GNSS 21th International Technical Meeting of the Satellite Division, GA, 16 – 19 September 2008. The Institute of Navigation. Traugott, J., D. Odijk, O. Montenbruck, G. Sachs, and C.C.J.M.Tiberius (2008b). Making a dierence with GPS. GPS World, 19(5):48 - 57, May 2008. Ulmer, K., P. Hwang, B. Disselkoen and M. Wagner (1995). Accurate azimuth from a single PLGR+GLS DoD GPS receiver using time relative positioning. Proc. of ION GPS-95, Palm Springs, CA, 12-15 September 1995, pp. 17331741. June 15, 2009 Johannes Traugott 63 / 62