Cascaded Estimation Architecture for Integration of Foot-Mounted Inertial Sensors
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1 Cascaded Estimation Architecture for Integration of Foot-Mounted Inertial Sensors Bernhard Krach and Patrick Robertson German Aerospace Center (DLR) Institute of Communications and Navigation Folie 1
2 Sensor Fusion for Pedestrian Applications Long term accuracy GNSS: 3D-PVT; Long term stability, Short term errors Optimal Sensor Fusion Algorithm Pedestrian Movement Model: Some short term aiding Maps and Movement INS measurement RFID: 3D-P; Long term stability, Short term errors Step counter INS: Estimation of step sequence and length; Long term stable Foot mounted INS: With Zero Update (ZUPT). Velocity: Long term stable, Position error linear in time INS: Orientation change (3D), Velocity change (3D); Very short term stability, Long term errors Barometer: Altitude change; Short-Mid term stability, Long term errors 3D 3D Maps (Map matching): Long and short term aiding in buildings Magnetometer: Orientation (2D or 3D); Long term stability, Short term errors Attitude/ Orientation Folie 2
3 Sensor Fusion for Pedestrian Applications Long term accuracy GNSS: 3D-PVT; Long term stability, Short term errors Optimal Sensor Fusion Algorithm Pedestrian Movement Model: Some short term aiding Maps and Movement INS measurement RFID: 3D-P; Long term stability, Short term errors Step counter INS: Estimation of step sequence and length; Long term stable Foot mounted INS: With Zero Update (ZUPT). Velocity: Long term stable, Position error linear in time INS: Orientation change (3D), Velocity change (3D); Very short term stability, Long term errors Barometer: Altitude change; Short-Mid term stability, Long term errors 3D 3D Maps (Map matching): Long and short term aiding in buildings Magnetometer: Orientation (2D or 3D); Long term stability, Short term errors Attitude/ Orientation Folie 3
4 Motivation Soft-Location: Sequential Bayesian estimation for localization Current state depends on the previous state and some noise v only x k = fk k ( xk 1, v 1) Transition Model Prediction Hidden Markov Model Measurements depend on the current state and some noise n only Measurements z z = h k k Likelihood ( xk, nk ) Prior Update k=k+1 TOA * Posterior Multi-sector Antenna Independent errors: Factorization of Likelihood Estimation of the state x: Posterior PDF contains inferable knowledge about the state Folie 4
5 Implementation via Particle Filter Particle filter is a technique for implementing recursive Bayesian filter by Monte Carlo sampling The idea: represent the posterior density by a set of random samples (particles) with associated weights. p ( x k z N s i i 1 : k ) w k δ ( x k x k ) i = 1 higher density more particles more weight where, Ns : number of samples(particles) { x i k { w, i = 0,..., N i k s }: set of sampled states, i = 0,..., Ns}: weights of sampled states For large numbers of samples the Random (Monte Carlo) Sampling approximation converges to the true PDF and is an optimal estimate. Folie 5
6 Bayesian Location Estimation Framework GNSS Pseudoranges & Carriers Altimeter Outputs RFID Detections Compass Outputs Likelihood Functions: GNSS, Altimeter, RFID Compass Fusion Filter (PF, RBPF) Particles ~1 Hz Particles, PVT, Sensor errors Pedestrian Movement Model PVT Output 3D Map Database Sensors Real-time sensor fusion framework (JAVA) Fusion via Bayesian filtering: Particle filter Measurements are incorporated via likelihood functions Movement model takes dynamic constraints into account Idea: Extend framework towards inertial sensors Folie 6
7 Foot Mounted Inertial Sensors Walk signatures, several steps Classical INS integration scheme: Accelerometers, Gyros, INS computer, Kalman filter Drift compensation via regular zerovelocity updates (ZUPT) Good performance even with low-cost MEMS Foot at rest 24,8 % 20,5 % 38,0 % 16,7 % Step Folie 7
8 Experimental Results Meeting Room Stride Rest, ZUPT IKN Building TE02 Folie 8
9 Conventional Integration of Inertial Sensors Gyroscope Triad Outputs Accelerometer Triad Outputs Strapdown Inertial Computer INS PVA Calibration Feedback ~ Hz PVA Output + - INS Errors PDF Sensors Foot still Detector Triggers ZUPT Extended Kalman Filter (INS Error Space) Fusion via Bayesian filtering: Extended Kalman filter Measurements are not incorporated via likelihood functions Movement model doesn t take dynamic constraints into account Problem: How to get things together? Folie 9
10 Solution 1 GNSS Pseudoranges & Carriers Altimeter Outputs RFID Detections Compass Outputs Likelihood Functions: GNSS, Altimeter, RFID Compass Fusion Filter (PF, RBPF) Particles ~1 Hz Particles, PVT, Sensor errors Pedestrian Movement Model PVT Output 3D Map Database Sensors ~ Hz Inertial Sensors Drawback: Increases filter rate, requires extension of state space to foot accelerations and turn rates, movement models become complex Folie 10
11 Solution 2 Gyroscope Triad Outputs Accelerometer Triad Outputs Sensors Strapdown Inertial Computer INS PVA Calibration Feedback ~ Hz Foot still Detector Triggers ZUPT Extended Kalman Filter (INS Error Space) PVA Output + - INS Errors PDF Drawback: Use of highly nonlinear movement models and sensors not possible (e.g. maps) Further Sensors: GNSS, Altimeter, RFID Compass ~1 Hz Folie 11
12 Solution 3: Our Approach GNSS Pseudoranges & Carriers Altimeter Outputs RFID Detections Compass Outputs Likelihood Functions: GNSS, Altimeter, RFID Compass, Step/INS Fusion Filter (PF, RBPF) Particles ~1 Hz Particles, PVT, Sensor errors Pedestrian Movement Model PVT Output 3D Map Database delta P PDF (Gaussian) Fusion Trigger Step Displacement (delta P) Computer INS PVA PDF Gyroscope Triad Outputs Accelerometer Triad Outputs Sensors Strapdown Inertial Computer INS PVA Calibration Feedback ~ Hz Foot still Detector Triggers ZUPT Extended Kalman Filter (INS Error Space) + - INS Errors PDF Use the lower filter to provide stepmeasurements to the upper filter Folie 12
13 The Step-Measurement Navigation coordinate system Pedestrian body coordinate system Inertial sensors coordinate system Strapdown calculations coordinate system Inertial sensor platform Strapdown calculations coordinate system Folie 13
14 The Step-Measurement Transformation from the strapdown to the pedestrian body coordinate system by a rotation via: α: Current heading according to strapdown calculations β: Misalignment of sensor axes with respect to the pedestrian body axes β α The step is sensed with respect to the coordinate system of the strapdown calculations Strapdown calculations coordinate system Folie 14
15 The Step-Measurement : Distance travelled during step (with respect to pedestrian body coordinate system) : Change of heading during step Folie 15
16 The Step-Measurement Measurement reports movement in the body coordinate system. Movement with respect to the navigation coordinate system is given by a rotation via γ. γ : Heading of pedestrian with respect to navigation coordinate system γ 1 γ 2 Folie 16
17 Dynamic Bayesian Network Measurements (Gaussian noise) States Temporal index k k+1 k+2 Movement: Position Heading Probabilistic movement model (including walls) Folie 17
18 Integration of a Pair of Platforms Left foot Body center Pedestrian body model: Body centered on connecting line of foot centers Right foot Folie 18
19 Integration of a Pair of Platforms Left foot Foot movement is 2x body movement: Body center Right foot Folie 19
20 Performance Analysis Simulation: Particle filter, 2000 particles, linear Gaussian movement model Error Analysis: Covariance analysis based on Kalman filter framework Folie 20
21 Experimental Results Scenario: Office building layout, initial position and heading unknown Location hypotheses Location hypotheses having crossed a wall during the recent step (forbidden by movement model) True track Folie 21
22 Conclusions Kalman filter for foot-mounted inertial sensors Low-cost MEMS inertial sensors become highly valuable Computational efficient for high rate INS ( ~ 100 Hz ) Main fusion algorithm based on Particle filtering Makes use of the provided step-measurements Low rate fusion (~ 1 Hz) takes nonlinearities into account Integration of a pair of platforms (right & left foot equipped) based on pedestrian model doubles PDR performance Folie 22
23 Thank you & questions Folie 23
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