Problem How to compute expected distance for any given(, y,6) Ray-tra Cached expected distances for all(x, y, 8) Approximation Assume a symmetric sensor model depending only on Ad absolute difference between expected and measured ranges Compute expected distance only for(x, y) Much faster to compute this sensor model Only useful for highly-accurate range sensors (e.g, laser range sensors, but not sonar) Computing Importance Weights(Approximate Method) Off-line, for each empty grid-cell(x, y) Compute d(x, y) the distance to nearest filled cell from(x, y) Store this"expected distance" map At run-time for a particle(x, y and observation z=(r, Compute end-point (X (x+rcos(e), y+rsin(e)) Retrieve d(x, y), error in measurement Compute probability of error, p(d), from Gaussian sensor model of specific g2Problem ● How to compute expected distance for any given (x, y, θ)? ● Ray-tracing ● Cached expected distances for all (x, y, θ). ● Approximation: ● ∆d: ● Compute expected distance only for (x, y) ● ● Only useful for highly-accurate range sensors (e.g., laser range sensors, but not sonar) Computing Importance Weights (Approximate Method) ● Off-line, for each empty grid-cell (x, y) ● Compute d(x, y) the distance to nearest filled cell from (x, y) ● Store this “expected distance” map ● At run-time, for a particle (x, y) and observation zi =(r, θ) ● Compute end-point (x’, y’) = (x+rcos(θ),y+rsin(θ)) ● Retrieve d(x’, y’) ● Compute probability of error, p(d), from Gaussian sensor model of σ2 Assume a symmetric sensor model depending only on absolute difference between expected and measured ranges Much faster to compute this sensor model , error in measurement specific