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Moving Grid Filter in Hybrid Local Positioning

This paper discusses the use of a moving grid filter for hybrid local positioning, which utilizes measurements from nearby sources to overcome nonlinearities and noise issues. The filter propagates the state distribution instead of just point estimates, allowing for a more accurate positioning solution. An example run comparing the accuracy of position filters is presented.

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Moving Grid Filter in Hybrid Local Positioning

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 20000 particles vs. 200 grid elements European Navigation Conference ENC 2006

  7. 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

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

  9. 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

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