We propose a means of omni-directional contact detection using accelerometers instead of tactile sensors for object shape estimation using touch. Unlike tactile sensors, our contact-based detection method tends to induce a degree of uncertainty with false-positive contact data because the sensors may react not only to actual contact but also to the unstable behavior of the robot. Therefore, it is crucial to consider a robust shape estimation method capable of handling such false-positive contact data. To realize this, we introduce the concept of heteroscedasticity into the contact data and propose a robust shape estimation algorithm based on Gaussian process implicit surfaces (GPIS). We confirmed that our algorithm not only reduces shape estimation errors caused by false-positive contact data but also distinguishes false-positive contact data more clearly than the GPIS through simulations and actual experiments using a quadcopter.