GNSS signals in urban environments suffer from reflections and blockage. This causes erroneous measurements and leads to positioning accuracy degradation. Conventional positioning algorithms find the position that minimizes the errors in all the measurements, which results in positioning errors if some measurements are erroneous. This paper proposes an algorithm that identifies and discards erroneous measurements. The algorithm manipulates the measurement equation to express it as a plane in the position estimation errors and performs a search process to find the planes that share an intersection point. Those planes correspond to the error‐free measurements, and the shared intersection point corresponds to the estimated position. The algorithm is optimized to reduce the computations. Real GPS and GLONASS data, collected in a multipath urban environment, are used to test the algorithm. The resultant accuracy is 2–3 m, which approaches a standard GNSS receiver accuracy, using legacy GNSS signals and operating in an open‐sky environment. © 2018 Institute of Navigation.