## 1 Introduction  
The problem of monitoring objects via a real-time system is still a topical and important issue for the industry connected with ecological systems. The need to control the quality of surface water is primarily due to the necessity of protecting the natural environment. The increasing level of water pollutants is mainly associated with the rapid increase of social development. As a result of these transformations, the need for functioning wastewater treatment plants with much higher requirements in terms of quality and efficiency of operation has arisen. In addition to the impact of the treatment plant, weather conditions also have a big influence on the quality of water in rivers, which in turn leads to the need for continuous monitoring with a control and management function to ensure the possibility of managing water in a given region [1,2]. Real-time monitoring systems, which are additionally used for monitoring and control functions, also require fast and accurate determination of the desired signal values. This is achieved by applying various methods and techniques related to the necessity of carrying out the key computer calculations. The simplest monitoring solutions only use easily implementable online measurements, which are part of a full monitoring system, as no other signals of the object are taken into consideration [3]. The proposition for the estimation of water quality presented in [4] uses artificial neural networks and canonical correlation analysis to ensure the correctness of water quality assessment. Theseconsiderations include numerous water quality parameters but determine only their static parameters. With this approach, we were not able to observe the dynamic changes in water quality resulting from random extortions. A similar approach was presented in [5], in which the authors developed and proposed methods for assessing water quality for management purposes of local governments, with data obtained on a weekly or annual basis. However, this solution did not take into account the impact of anomalous pollution changes, which indicates the need for continuous online measurements. In [6], the authors proposed real-time monitoring based on online measurements using mobile measurement stations. This type of mobility does not ensure continuous comprehensive monitoring of water quality in a given water catchment. Other solutions concern the monitoring and control system involving interaction with the object. Such hybrid solutions lead to positive results but at the cost of larger computational effort associated with the current \"improvements\" of the characteristics of stochastic signals [7; 8; 9; 10]. In monitoring systems, soft sensors are often used to obtain information about certain parameters, which are produced on the basis of measurements of other signals. The principle of soft sensing technology is to build a mathematical model to estimate signals which are difficult to measure, based on the relationship between these signals and certain online signals measured directly. An approach implementing such a soft sensor was presented, among others, in [11; 12; 13]. The first study previously mentioned used genetic algorithms to control the value of dissolved oxygen (DO) in a wastewater treatment plant. The authors obtained the right quality of sewage and minimized the energy demand, which is a valuable achievement for an integrated global monitoring system with the control function. The second and third mentioned works considered a control system for which the controller's parameters were selected using an artificial neural network or extreme learning machine (ELM). Satisfactory results were obtained in the form of good real-time performance and high accuracy of soft sensor prediction. Solutions which are not based on artificial neural networks can also give positive results, even for nonlinear objects [14]. There has been research done on a soft sensor based on locally weighted regression which estimates the regression surface by multivariate smoothing.