Where to put stabilising capacitor?
See my answer to your previous question here, specifically this image:
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You want the caps to be as close as possible to the components which are drawing current.  The voltage varies due to to trace/wire inductance, so it doesn't help to locate the cap before this inductance.  The caps absolutely must be on the sensor.  You should already have output caps on your power board and decoupling caps near every IC on your 'processing board'.