Engine runs well & has Crank Pos. Sens. P0335 & Cam. Pos. Sens. P0340 alarms in.

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I installed a used Japanese long block and the Crank. Pos. Sensor and its tone/ reflector? ring installed weren't new and were without warranty. I have been driving it for 18 months with the P0335- Crankshaft Position Sensor A Ckt & P0340-Camshaft Position Sensor A Ckt & Service Engine alarms in yet the engine is not only running, it is performing well. I would occasionally clear the alarms but they would quickly come back in. A new Crank. Pos. Sensor and its tone/ reflector? Ring have been installed and the same alarms quickly come in again and the engine is still running well. Where the big problem comes is that with the Service Engine alarm in that is an automatic failure of the Bi-Annual CA Smog Test even if the tail pipe emissions were OK. I beginning to wonder if it's possible that the ECU could have a glitch that causes the alarms to trigger when they aren't real and yet keep the engine running fine. Also is the Powertrain Control Module (PCM) something different from the ECU?