We present decentralized collision avoidance algorithms for quadrotor swarms\noperating under uncertain state estimation. Our approach exploits the\ndifferential flatness property and feedforward linearization to approximate the\nquadrotor dynamics and performs reciprocal collision avoidance. We account for\nthe uncertainty in position and velocity by formulating the collision\nconstraints as chance constraints, which describe a set of velocities that\navoid collisions with a specified confidence level. We present two different\nmethods for formulating and solving the chance constraints: our first method\nassumes a Gaussian noise distribution. Our second method is its extension to\nthe non-Gaussian case by using a Gaussian Mixture Model (GMM). We reformulate\nthe linear chance constraints into equivalent deterministic constraints, which\nare used with an MPC framework to compute a local collision-free trajectory for\neach quadrotor. We evaluate the proposed algorithm in simulations on benchmark\nscenarios and highlight its benefits over prior methods. We observe that both\nthe Gaussian and non-Gaussian methods provide improved collision avoidance\nperformance over the deterministic method. On average, the Gaussian method\nrequires ~5ms to compute a local collision-free trajectory, while our\nnon-Gaussian method is computationally more expensive and requires ~9ms on\naverage in scenarios with 4 agents.\n