POOLING ESTIMATORS OF THE LOGNORMAL MEAN BASED ON INDEPENDENT SAMPLES

An imaging compensation or transformation method for signals detected by a sensor which is placed arbitrarily away from its ideal location into signals which would result if the sensor were in the ideal location. This method links movement of the on-screen cursor to the movement of the ball by a user. The actual location of the sensor in the device can be at any necessary location relative to the other components of the device within the housing, and the necessary transformation functions can be calculated and applied to the signals. Enabling placement of the sensor at a location which is displaced from the ideal location provides degrees of design freedom to optimize ergonomic and aesthetic factors. The compensation or conversion method is a transformation which simulates the sensor being disposed at the ideal location regardless of where it is actually placed. This is done by defining a user vector space, a sensor vector space and a reported vector space. The actuation of the ball occurs in the user vector space which corresponds a detected movement in the sensor vector space. The motion detected in the sensor vector space is transformed to movement in the reported vector space which simulates the movement of the ball as if the sensor were located in the ideal location.