Smartphone sensor based orientation determination for indoor navigation

Transcription

1 Smartphone sensor based orientation determination for indoor naviation LBS Conference Andreas Ettliner Research Group Enineerin Geodesy Contact:

2 Outline Motivation and Methodoloical approach Orientation and Smartphone Measurement Data Kalman Filter for Orientation Determination Test Measurements and Results Conclusion and Outloo 2

3 Motivation and Methodoloical approach Indoor naviation Applications are aumented by 2D-PDR ( Pedestrian Dead Reconin ) - Distance d i and yaw ψ i à Position P i Critical part à calculation of users movin direction respectively yaw Methodoloical approach Calculate yaw with Kalman filter Detect turns of the user Smooth trajectory when user is walin straiht Reduce systematics of the smartphone sensors ψ 2 ψ 3 ψ 1 d 1 d 2 P 2 P 1 d 3 P 4 ψ 4 d4 P 0 P 3 3

4 Orientation and Smartphone Measurement Data Orientation Rotation of Sensor-Coordinate System x y z accordin to a superordinate Coordinate System X Y Z Different representations of orientation Elements of the Direction-Cosine-Matrix Euler anles Quaternions Euler anles pitch θ roll φ and yaw ψ Disadvantae: imbal loc 4

5 Orientation and Smartphone Measurement Data Pitch and Roll Part of the orientation Used to level measurement data Necessary for calculation of yaw Accelerometer: a x a y a z Calculation of roll and pitch directly ϕ = ( a ) ( ) y z θ = f a f a a a x y z Gravity à low-pass filter tan( ϕ ) = tan ( θ ) = a a a y z y sin a x ( ϕ) + a cos( ϕ) z Gyroscope: ω x ω y ω z Calculation of the anular chanes of roll and pitch ( 1 1) ( 1) ϕ = f ω ω ω ϕ θ x y z θ = f ωy ωz ϕ Initial values are necessary ( sin( 1) cos( 1) ) tan( 1) ϕ = ω ϕ + ω ϕ θ + ω y z x ( ) sin( ) θ = ω cos ϕ ω ϕ y 1 z 1 ϕ = ϕ +Δt ϕ 1 θ = θ +Δt θ 1 5

6 Orientation and Smartphone Measurement Data Yaw Manetometer: m x m y m z Calculation of yaw directly ψ Gyroscope: ω x ω y ω z Calculation of anular chane of yaw = ( x y z ϕ θ) f m m m ( ) ψ = f ωy ωz ϕ 1 θ 1 Initial value necessary mx cosθ sinθsinφ sinθcosφ mx m Y 0 cosφ sinφ m = y m Z sinθ cosθsinφ cosθcosφ m z tan ( ψ ) m = m X Y ( sin( ) ( )) ( ) 1 1 cos 1 cos 1 ψ = ωy ϕ + ωz ϕ θ ψ = ψ +Δt ψ 1 Systematic effects Manetic disturbance Gyro drift 6

7 Kalman Filter for Orientation Determination System equations State vector contains φ θ and ψ Control inputs: yro measurements ω y and ω z Disturbance: w φ w θ and w ψ Random wal model f :ϕ =ϕ + w ϕ f2 :θ =θ 1+ w 1 θ f3:ψ =ψ 1+ w 1 ψ User is turnin User wals straiht Δt f :ψ =ψ + sin ϕ ω + cosϕ ω + w ψ y 1 z 1 cosθ 1 Propaation of covariance = T T + B B + C C T T T xx xx $$ 1 uu ww T B C = δ f3 δ f 3 1 δϕ δθ = δ f3 δ f3 0 δωy δω z =Δt T Transition Control Disturbance 7

8 Kalman Filter for Orientation Determination Indicators for chanin system equation Statistical test on innovations d Yaw-rate H : ( ) 0 0 E d = HA: E( d) 0 d 2 P{ χ1;1 α H0} = 1 α σ 2 ψ 2 d ψ Innovation test responds > 0.3s Yaw-rate > 30 /s 8

9 Kalman Filter for Orientation Determination $ $ 1 ay a z ϕ $ $ $ l = θ 2 ( x y z = a a a ) ψ $ $ $ 3 ( mx my mz ax ay az ) Separate Kalman filter for acceleration measurements à a$ $ $ x ay az Observations Pitch roll and yaw are introduced as directly observed aa $$ ( ) Adaptive covariance matrix of the observations aa $$ 33 T ll F F σ m * I 33 = 0 F 1 1 K $ a x mz 2 3 = K a $ x mz 3 3 K a$ x m z ( m ) 2 2 m = m +Δ 1 σ σ uv uv Δ = m 1 m m 1 9

10 Test Measurements and Results 3 scenarios One smartphone à Samsun Galaxy S4 Ground truth from indoors mobile toolit Evaluation Inner and outer accuracy Comparison to results from orientation sensor of android Scenario 2 Scenario 1 Scenario 3 10

11 Test Measurements and Results Scenario 1 Roll Random wal model Smooth filter result Time shift ~2s No reference values Smartphone was held in textin mode Results are reasonable Pitch 11

12 Test Measurements and Results Scenario 1 Yaw filter result No drift Minimized influence of manetic disturbance Constant offset Outer accuracy: 16.2 Mean deviation from round truth Inner accuracy: 5.4 Mean standard deviation of deviations Error in round truth 12

13 Test Measurements and Results Scenario 2 Reduced influence of manetic disturbance Outer accuracy 8.9 Inner accuracy

14 Test Measurements and Results Scenario 3 Outer accuracy 12.2 Inner accuracy 3.6 Properties of deviations Varyin most of the time 14

15 Results Comparison of Scenario 1 and Scenario 2 Offset and residuals differ 15

16 Conclusion and Outloo Conclusions Systematic effects of the sensors are minimized Turns are detected correctly Residuals are rarely reproducible and not normally distributed Filter result ~20% better than android solution Inner accuracy ~60% better than outer accuracy Scenario Outer accuracy Inner accuracy Orienta(on filter Android Orienta(on filter 1 (straiht) (straiht with turns) (polyonal repeatedly) Outloo Tests on different smartphones Improvin round truth Additional orientation information to overcome remainin systematic effects Adaption of test statistics 16

17 Andreas Ettliner Research Group Enineerin Geodesy Contact: LBS Conference