Moving Grid Filter in Hybrid Local Positioning

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Presentation transcript:

Moving Grid Filter in Hybrid Local Positioning Niilo Sirola & Simo Ali-Löytty Institute of Mathematics Tampere University of Technology Finland European Navigation Conference ENC 2006 9.11.2018

European Navigation Conference ENC 2006 Local positioning Use measurements from near-by sources → strong nonlinearities, multimodality non-normal noise structure – multipath, quantization, etc. position filter: use all current and past data European Navigation Conference ENC 2006 9.11.2018

Nonlinear position filtering problem User state: position (2D or 3D), velocities, heading, acceleration, biases, drifts, ... Solve and propagate the state distribution instead of just point estimates Using initial distribution of the state measurement model motion model European Navigation Conference ENC 2006 9.11.2018

European Navigation Conference ENC 2006 Moving grid filter 1. Initial distribution 2. Apply motion model to get the prior distribution 3. Approximate measurement likelihood on the grid 4. Multiply prior and likelihood to get the posterior 5. Repeat from 2 European Navigation Conference ENC 2006 9.11.2018

European Navigation Conference ENC 2006 Example run Range measurements to one or two cellular base stations Reference solution is particle filter with 2 million particles European Navigation Conference ENC 2006 9.11.2018

20000 particles vs. 200 grid elements European Navigation Conference ENC 2006 9.11.2018

Comparing accuracy of position filters We want to compare the full pdf’s and not just the point estimates. Two separate problems: what is the optimal (Bayesian) solution? how to compare an approximate solution to the optimal (or near-optimal) one? Both questions still largely open European Navigation Conference ENC 2006 9.11.2018

European Navigation Conference ENC 2006 Example run (cont) Grid error is less than the element radius: European Navigation Conference ENC 2006 9.11.2018

European Navigation Conference ENC 2006 Conclusions Grid filter gives rough but reliable results. Fair and expressive comparison of nonlinear filters still an open problem. Questions? European Navigation Conference ENC 2006 9.11.2018