## 1 Introduction, Positioning  
In the field of engineering sciences, state estimation (SE) is widely used for observation and control of multivariable systems. [PERSON] was the first to develop a method for the SE of power systems in 1969 [1], which was useful for high-voltage (HV) transmission networks. However, in the last decade, DSSE has been the focus of many scientific papers due to several trends in the 21 st century, such as the proliferation of electric cars and the growing popularity of small household-sized power plants, which pose several problems for distribution networks. [PERSON] and [PERSON] [2] group the different DSSE methods in terms of the algorithms applied, and they also provide an extensive literature review. [PERSON] et al. [3] also collect the state-of-the-art DSSE techniques complemented by evolutionary algorithms to solve nonlinear optimization problems. In the paper of [PERSON] et al., SE is compared to DSSE from the aspects of observability, network topology, metering system design, impacts of renewable penetration and cybersecurity [4]. [PERSON] et al. 's review concentrates on DSSE as an enabler function for smart grid features [5], and [PERSON] et al. [6] outline DSSE with its current challenges as well. Different algorithm implementations can be found in the literature for DSSE in terms of the number of phases, the load model, topology, the type of modeled elements and platform usage [7]. [PERSON] and [PERSON] [8] apply the widely used weighted least squares (WLS) algorithm for estimating the state of a distribution system, which is assumed to be balanced and represented by a single-phase model. The implementation was performed in MATLAB using a Fortran subroutine. The impact of the accuracy of real and pseudo measurements on the estimated bus voltages was tested in this distribution network, including distributed generation. [PERSON] and [PERSON] [9] also employed a single-phase DSSE method with a nonlinear WLS algorithm in MATLAB/Simulink, and they reached a reasonable accuracy in near real time, using smart meter measurements from few locations. To provide additional inputs to the DSSE, it is proposed to measure voltages close to the far end nodes using the smart metering infrastructure. [PERSON] et al. [10] also estimated single-phase voltage magnitudes at all non-monitored LV buses, but this estimation was performed using random forests, a supervised machine-learning algorithm implemented in Python. This learning-aided LV estimation applies untapped but readily available and widely distributed sensors from cable television networks. [PERSON] and [PERSON] [11] carried out a single-phase SE on a certainly unbalanced distribution grid as well because the geographic information system (GIS) model provided by the DSO of the city of Basel was correct by phase. With the help of the statistical tool R, their research examined the impact of data availability, which is important in LV DSSE. In Ref. [12], a three-phase DSSE model is implemented and tested through simulation studies on a real-life LV distribution grid using measured smart meter data. The study aims to estimate cable loading, power losses and node voltages by the offline analysis of the mentioned smart meter data. [PERSON] et al. [13] also use three-phase SE with WLS method for distribution systems. The algorithms for the simulated networks were implemented in the C++ programing language, and the OpenDSS software package was used as the load flow simulation tool to generate pseudo measurements for the state estimator module. There is another method for three-phase LV SE: [PERSON] et al. [14] compare the typical SE algorithm that implements the WLS method with an algorithm based on an iterated Kalman filter. SE is also an efficient tool for estimating daily load profiles, identifying major harmonic sources and determining their contributions in distribution systems [15]. However, when it comes to DSSE, consumer models and load profiles must be used as an input of the SE approach. For example, Ref.