Among other things, the disclosure features a system comprising a sensor, a DC magnetic field source, an AC magnetic field source, and a receiver. The sensor has an aspect ratio of 10:1 or higher and comprises a ferromagnetic material. The ferromagnetic material has a non-linear magnetization response, and the response contains a maximum point of non-linearity. The DC magnetic field source is adjustable for providing a magnetic excitation field to excite a magnetic field within the sensor. The provided magnetic excitation field has a range such that the excited magnetic field within the sensor is near the maximum point of non-linearity. The AC magnetic field source is configured to generate an AC magnetic field to cause the sensor to generate even harmonics. The receiver is configured to receive the even harmonics from the sensor for determining a position of the sensor.