Mixed integer–real least squares (MIRLS) estimation still has two open scientific problems, i.e., the validation of results and computational efficiency for a large number of satellites. This paper presents and discusses a non-conventional approach to MIRLS estimation, which belongs to the ambiguity function method (AFM) class. Because the solution is searched for in the constant three-dimensional coordinate domain instead of the n-dimensional ambiguity domain, the computational efficiency does not depend as much on the number of satellites as it does in conventional MIRLS estimation. Simple numerical pretests have shown that the reliability and precision of results from the presented approach and the conventional MIRLS estimation are exactly the same. Hence, the presented approach, contrary to AFM, may be treated as MIRLS estimation. Furthermore, the presented approach is a few hundred times faster than AFM and may be considered in (near) real-time GNSS positioning. In light of the above, the new field of research on MIRLS estimation may be opened.

The paper presents a new method of searching for a fixed solution in precise positioning based on carrier phase data. The main idea is to search for a fixed solution in the coordinate domain instead of in an ambiguity domain. The dimension of the ambiguity domain depends on the number of satellites. The dimension of the coordinate domain is always three, and it does not depend on the number of satellites. It considerably reduces computational load.

The subject of the paper is the range–based indoor positioning method, based on the ZigBee physical layer. Some computational problems are also investigated. A proposition for overcoming these problems is presented involving an experiment on the convergence of the computational process. In order to investigate the details of computational process an experiment was planned and carried out. A case study was performed on the basis of this experiment. The behavior of the Least Squares objective function was investigated on the basis of its graphic representation. The graphic representation was formed for both linearized and non-linearized versions of this function. Different methods of minimizing this function were tested. The analysis of the results allowed the best method to be selected for assuring the convergence of the computational process to correct solution.