# Online Nodal Demand Estimation in Branched Water Distribution Systems Using an Array of Extended Kalman Filters

## TL;DR

This paper introduces a new method to estimate water demand at different points in a water distribution system using sensor data and advanced filtering techniques.

## Contribution

The novelty lies in using an array of extended Kalman filters in a cascade setup to estimate nodal demands with only pressure and flow measurements.

## Key findings

- The proposed method effectively estimates nodal demands using pressure and flow data.
- Simulation and experimental tests confirm the method's reliability under various conditions.
- The approach works for both steady-state and variable input scenarios.

## Abstract

This paper proposes a model-based methodology to estimate multiple nodal demands by using only pressure and flow rate measurements, which should be recorded at the inlet of the distribution system. The algorithm is based on an array of multiple extended Kalman filters (EKFs) in a cascade configuration. Each EKF functions as an unknown input observer and focuses on a section of the pipeline. The pipeline model used to design the filters is an adaptation of the well-known rigid water column model. Simulation and experimental tests on standardized pipeline systems are presented to demonstrate the proposed method’s effectiveness. Finally, for the case of the experimental validation, both steady-state and variable input conditions were considered.