Smooth a Simulated Particle Trajectory

Use a combination of BlockMap and TrimmedMean to smooth out data from a particle trajectory.

Simulate a stochastic path by adding noise to an exact trajectory.

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exact[u_] := {u Cos[u], u Sin[u]} noise[u_] := RandomReal[CauchyDistribution[0, 1], 2] data = Table[exact[u] + noise[u], {u, 0, 6 \[Pi], 1/100}];

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ListPlot[data, AspectRatio -> Automatic]

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Smooth the simulated trajectory with BlockMap using a moving TrimmedMean to eliminate possible outliers.

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smooth[r_] := BlockMap[TrimmedMean, data, r, 1]

Increase the window size to get a smoother trajectory.

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Table[ListPlot[smooth[r], AspectRatio -> Automatic], {r, {25, 50, 100, 200}}]

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