How can I size the 'supply noise filtering' capacitors at the load end for this scenario?
I guess the way caps are placed correct, but is there a way to size
  the capacitors here? I need to find a logical explanation why we
  should use the capacitors with particular capacitance. Telling "I have
  seen somewhere it is a rule of thumb" does not convince some people.
  What should be the approach?


There are a few ways to do this:

1) Put in a large cap and a small cap with feelings (or the force or whatever). I usually use 1-10uf for 10-100mA of digitally switching current and under 1uf for 10mA (depends on what it is, and how fast its switching). maybe 100uf+ for 1A switching loads. This is what I get a feel for after reading lot's of datasheets over the years. 
If the microprocessor has many GPIO's that are switching on and off at the same time, then this could also be a problem. If the part is switching more than 10's of Mhz I'll also add a 0.1uf or few nf cap in parallel (or use an EMI 4 pin cap) to minimize terminal and PCB inductance. This is the leas time consuming method.

2) You can calculate it. The first number you need to know is the acceptable ripple on the Vcc line (or the minimum acceptable lowest voltage, on a 3.3V bus perhaps 3.2V would be a worst case voltage, depends on the part and datasheets). Then you find the max and nominal load and currents/loads. You estimate and calculate the cable and PCB trace resistance (and inductance if you think it will make a difference. There are wire and PCB trace available all over, or you could measure it)

You then solve this circuit with filter below. You start with the nominal current (if it's 50mA nominal current with a 5V Vcc then that's a 100Ω load. If the max current is 200mA then that would be a 25Ω load). You solve the circuit below with the switch thrown (which is something I don't have time to do right now) and calculate the max voltage drop, if it's too much increase the capacitor size until it falls in the acceptable level, doesn't sound like too much fun does it?







simulate this circuit &ndash; Schematic created using CircuitLab

3) You load the same circuit as in 2) into a spice package and solve it in 1 minute, or you load up a .param statement and solve for 5 decades of capacitor values and solve in a few more minutes. Packages like LT spice make it easy to put in parasitic resistance and inductance to make sure ripple is acceptable across all frequencies, with an AC sweep.