1. These slides augment the FootSLAM ION GNSS 2009 and InsideGNSS (“SLAM Dance”) papers – we have made some minor improvements/corrections to notation Source: See www.kn-s.dlr.de/indoornav The next slides are animated! It is suggested you use animations in order to better follow the step-by-step arrangement of the coordinate systems The first illustration slide represents the coordinate systems and and pose changes that are involved in processing pedestrian step- estimation in a FootSLAM system Shown are the pose change during two subsequent steps (position and pose of the foot of the pedestrian equipped with the IMU) as well as the pose change of the person (body axis). The next slide shows the processing at a per-particle level by the likelihood particle filter as far as the errors and states of the step U are concerned.

2. Coordinate Systems IMU local reference system with respect to the beginning of step measurements (i.e., INS calculation) at the lower filtering level Coordinate system aligned to the heading of the IMU at the last step rest phase at the lower filtering level (called IMU zero heading) Coordinate system at the higher level filter aligned to the heading of the person’s body at the last step rest phase (called person zero heading) Global navigation coordinate system at the higher level filter in which the position estimate and orientation are computed (as well as the map)

3. Z U k ={Z r k + n r k ; Z ψ k + n ψ k }= {(Z rx k + n x k, Z ry k + n y k ) ; Z ψ k + n ψ k } U represents the true step vector r k (red); and the true person heading change ψ k φ k-1 ε : misalignment between person heading and IMU heading (“duck angle”); @ time k-1 Step measurement: Z U k = Z r k + noise vector n r k ; and heading change Z ψ k + noise n ψ k y x φ k-1 ε ψkψk rxkrxk rykryk x IMU zero heading coordinate system y Z ry k Z rx k Person zero heading coordinate system (i.e. w.r.t. person heading at time k-1) ZψkZψk φ k-1 ε - γ k rkrk k k-1 Navigation frame coordinate system Person walked, facing to then facing γ k : odometry heading drift γ k = Z ψ k - ψ k ; i.e. the noise free part of the angular error φ k-1 ε k-1 k ψkψk Actual (unknown) step U : U k ={r k ; ψ k }={(r x k, r y k ) ; ψ k } ; with ||r k ||= ||Z r k || k-1 k Scaled down view of the measured step (i.e. measured pose change) in IMU zero heading coords. (i.e. w.r.t. IMU heading at time k-1) ZψkZψk ZrkZrk rkrk Pose change (step) in person zero heading coordinate system For simplicity the illustration is for the noise free case ZψkZψk

4. k-1 k Measured step in IMU zero heading coords. k-1 k ψ /i k Z ψ k + n ψ k Z r k + n r k r /i k Lower Level EKF Raw IMU data Conversion to IMU zero heading coordinates (rotation) Randomly draw particle specific additive noises; compute Z ψ/i k & Z r/i k ; Particle index /i k-1 k Particle i drawn step in IMU zero heading coords. Z ψ/i k = Z ψ k + n ψ k - n ψ/i k Z r/i k = Z r k + n r k - n r/i k Randomly update particle specific φ k ε/I. Use this to compute the new person zero heading coord-sys. in which r /i k+1 will be defined φ k ε/i Relative person pose change in person zero heading coords. drawn for particle i Randomly update particle specific odometry heading drift γ /i k. Compute new person heading change ψ /i k =Z ψ/i k – γ /i k ; translate particle i by step vector r /i k = Z r/i k rotated by φ k-1 ε/I Performed per particle i True, unknown white measurement noise Particle white noiseParticle heading offset Performed once at lower layer Performed per detected step ψ /i k r /i k and drift states Noises are randomly drawn from zero mean, white Gaussian processes Random update of φ k ε/i : follows a bounded first order random walk process Random update of γ /i k : follows a first order random walk process