## 1 Introduction
In [14], authors studied, tested and compared multiple weighing schemes for GNSS positioning relying upon the elevation angle and signal to noise ratio. In [15], two GNSS observation weighing models, sigma-elevation and CN0-elevation, are studied and compared by [PERSON]. For the WLSE algorithms, satellite elevation angle and SNR (signal to noise ratio) are the primary focus of the researchers to compute the observation weights. However, relying on the elevation angle is not always useful because it is possible for the signal, from high elevation satellite, to be disrupted from the multipath and radio interferences especially in urban canyons. The concept of non-linear statistics (or robust statistics) has been also studied in literature by several researchers to improve the GNSS positioning accuracy. In [16], neural networks are used to improve the performance of least absolute and least-squares estimators for robust GNSS positioning. However, the primary disadvantage is the computational cost in addition to the outfitting problem. In [17], the concept of robust M-estimator is used to improve the performance for the GNSS positioning by calculating and adding the weight matrix during the innovation step. In [18] multiple robust statistical estimation techniques have been discussed including M-estimators, L1 estimators and genetic algorithm. The proposed estimation process in [18] determines a set of all possible solutions by using the minimum required number of satellites (e.g., in case of GPS, four satellites are required for positioning) using LSE. The median of remaining estimates is considered as the user position after removing possible wrong estimates and a genetic algorithm is used to minimize the estimation error. The fundamental problem for this scheme is the number of possible solutions. The addition of new constellations increases the number of available satellites for positioning in a single epoch and the number of solutions as well with the increase in computational cost. Secondly, the positioning process starts with an unknown random initial estimate such as a least-squares estimate and the iterative reweighting scheme can ignore perfectly good measurements resulting to a wrong convergence point with a bad initial estimate. Some researchers focused on the development of techniques to minimize the effect of noise parameters, such as ionospheric, multipath etc. In [19], authors introduced the concept of the adaptive carrier smoothing to attain an optimal carrier smoothing time to minimize the cost functions related to white noise multipath and correlated multipath errors. In [20], authors studied the application of DGNSS (differential GNSS) in smartphones for enhancement of the GNSS positioning accuracy in challenged environments. However the primary drawback for DGNSS-aided navigation is that a base station must be required for transmission of useful information and without this information host system is not able to maintain the required accuracy. In this paper, we present a novel efficient estimation process for the GNSS positioning using signal data from multiple constellations. The proposed idea is based on the nonlinear statistical estimation theory. The proposed estimator is derived from the robust MM class estimators, proposed and named by [PERSON] [21]. The MM estimator is a class of robust statistics for more efficient statistical data analysis with a high breakdown point. Breakdown point is the proportion measure of the outliers that can be treated efficiently without spoiling the results, and for the MM estimator, the breakdown point is 50%. For a reliable initial estimate, a weighing scheme is provided using prior knowledge of signal-to-noise ratio and satellite geometry of all visible satellites. A set of available pseudorange observations is divided into small subsets with adaptive subset size. A three-step IRWLS estimation process is applied to the individual subsample to minimize the effect of observation errors on the positioning accuracy.