Solutions:

1. Increase the sampling rate of the ADC. This allows the antialiasing filter to have a higher cutoff frequency and still eliminate aliasing. This enables the following:
   1. The filter rolloff can be more shallow - allowing a better time response
   2. The frequency response of the filter does not attenuate the lower sensor frequencies of interest
   3. Phase distortion is strongest around the cutoff frequency of the filter so if this is pushed higher, it will not affect the sensor frequencies this cutoff
2. Have linear phase filters. This, of course, will reduce the phase distortion problems.