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. 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

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

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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
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Example run
Range measurements to one or two cellular base stations
Reference solution is particle filter with 2 million particles
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6. 20000 particles vs. 200 grid elements
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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
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Example run (cont)
Grid error is less than the element radius:
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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