Hi Phil,
Since the sensor output is ratiometric with the supply voltage, any variation in supply voltage will also proportionally appear at the output of the sensor. However, it should continue working when the battery voltage decreases, but the accuracy and linearity spects mentioned in the datasheet would change with a supply voltage below 2.7V (operating the device at a different range may induce additional error).
You can use the MP3V5050V without the need of a voltage regulator between the battery and the sensor, but, you need to take in mind if the ratiometric nature of the sensor would not affect your application.
From the noise point of view, it is preferable to use a linear regulator rather than a relatively more noisy switching power supply, but since one of your key factors is efficiency, then I would definitely recommend you to use a switching regulator, just try to adequate de-coupling to reduce noise. A 0.33 µF to 1.0 µF ceramic capacitor in parallel with a 0.01 µF ceramic capacitor should work well for this purpose.
In case you need extra filtering, then you can use a low-pass RC filter with a cutoff frequency (650 Hz is recommended). A 750 ohm resistor and a 0.33 µF capacitor have been determined to give the best results since the 750 ohm series impedance is low enough for most A/D converters.
We do not have any recommendation for a switching regulator or a linear regulator.
Have a great day,
Jose
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