Multipath propagation is still a major source of error in Global Navigation Satellite Systems (GNSSs), especially in urban areas. Here, satellite signals can be reflected by obstacles in the closer receiver environment, resulting in additional delayed signal replicas at the receiver. As a result, conventional GNSS receivers provide biased range estimates, leading to Position, Velocity, and Time (PVT) errors. The demand for high accuracy and fail-safe positioning is rising, especially for newly emerging safety-relevant applications like autonomous cars and unmanned aerial vehicles. GNSS positioning with deviations of several meters, as it may occur in multipath environments, would be insufficient. Besides multipath, the ionosphere, introducing a frequency-dependent delay to GNSS signals, is a second major source of error. Estimating and compensating for this effect with a state-of-the-art multi-frequency receiver using the ionosphere-free combination is the standard approach. However, the positioning accuracy suffers from multipath errors and amplified noise contributions. Therefore, a novel multi-frequency Extended Kalman Filter (EKF) based algorithm for multipath and ionosphere estimation and mitigation is proposed. The solution relies on a multi-correlator structure which replaces the conventional Delay Locked Loop (DLL) and no longer requires the ionosphere-free combination. The underlying signal model of the EKF accounts for multipath by considering the radio propagation channel between satellite and user. In addition to increased resilience against multipath propagation, an estimate of the Channel Impulse Response (CIR) is obtained. The performance gains achieved using the multifrequency EKF are demonstrated with simulations. A hardware GNSS constellation simulator was used to compare the proposed solution to a state-of-the-art dual-frequency receiver. The results were then verified by processing actual measurements. The proposed method proved to be very effective against multipath. Furthermore, good estimates for the ionospheric Total Electron Content (TEC) were obtained.