# Novel Gain-Optimized Two-Step Fusion Filtering Method for Ranging-Based Localization Using Predicted Residuals

## TL;DR

A new two-step filtering method improves positioning accuracy in wireless sensor networks by reducing errors from disturbances and initial estimates.

## Contribution

A novel two-step fusion filtering method using predicted residuals and gain adaptation for improved localization accuracy.

## Key findings

- The proposed algorithm improves average positioning accuracy by 28.57% compared to other initial positioning algorithms.
- The method achieves performance close to the Cramér–Rao lower bound using weighted least squares for initial estimation.
- Reconstructed Gaussian white noise and Kalman filtering enhance the final position estimation.

## Abstract

A two-stage fusion filtering positioning algorithm based on prediction residuals and gain adaptation is proposed to address the problems of disturbance and modeling errors in the application of distance-based positioning algorithms in wireless sensor networks, as well as inaccurate initial filtering values leading to large estimation errors or even divergence. Firstly, based on parameterization methods, a pseudo linear equation is constructed from the time of arrival (TOA) and multipath delay. The weighted least squares (WLS) method is applied to obtain the initial value of target position resolution, and its performance approaches the Cramér–Rao lower bound (CRLB). Secondly, the exact position of the target is obtained using the reconstructed Gaussian white noise statistics and the Kalman filtering algorithm. The simulation results show that compared with other initial positioning algorithms, the average positioning accuracy of the proposed algorithm is improved by 28.57%, and it has a better filtering performance.