Methods and systems are provided for diagnosing an in-range error of a pressure sensor arranged downstream of a lift pump in a fuel system of a vehicle. In one example, a method may include performing feedback control of the lift pump based on output of the pressure sensor, monitoring the pressure sensor output for flattening during the application of the voltage pulses, and adjusting operation of the fuel system depending on whether the pressure sensor output flattens for at least a threshold duration, which is indicative of an in-range error. The method may further include dynamically learning a setpoint pressure of a pressure relief valve of the fuel system and a fuel vapor pressure within the fuel system by monitoring pressure sensor output while adjusting the duty cycle of voltage pulses applied to the lift pump.