Current Measurement. 50Amps 0.5% error margin
Inductors and regular current transformers only work on AC. For measuring DC current your choices are a shunt resistor, Hall effect sensor, or DCCT (DC 'Current Transformer', which is really a magnetic flux balancing device). DCCT's are bulky and expensive. Hall effect has lower loss than a shunt resistor, but is less accurate. 

A shunt resistor must drop voltage to measure current, but that voltage doesn't have to be large. With Kelvin connections and a good 'zero-drift' op amp you should be able to get accurate readings with very low voltage drop and acceptable power dissipation.  

At 50A a 0.001&ohm; resistor dissipates 50A2*0.001&ohm; = 2.5W, with a voltage drop of 50mV. But if you put two 0.001&ohm; resistors in parallel then the voltage is halved and current splits between them, so they only dissipate 0.625W each (75% less) and total power dissipation is halved so heating is greatly reduced. Of course you now only have 25mV to work with instead of 50mV, but simply doubling the amplifier gain will get your signal back to its original level.  

You should also check that your PCB traces and connectors are large enough and not significantly contributing to heating (don't just assume - measure the voltage drop across them!).