# Closed-Form Error Analysis on RSS-based Indoor Localization Method

## TL;DR

This paper provides a theoretical analysis of RSS-based indoor localization, deriving a closed-form error expression for the NLS method and establishing its optimality and limitations in accuracy.

## Contribution

It introduces a closed-form error expression for the NLS localization method and analyzes its fundamental accuracy limits, guiding future improvements.

## Key findings

- NLS method minimizes localization error theoretically
- Derived a closed-form expression revealing key accuracy factors
- Established a lower bound for localization error

## Abstract

Received Signal Strength (RSS) is considered as a promising measurement for indoor positioning. Lots of RSS-based localization methods have been proposed by its convenience and low cost. This paper focuses on two challenging issues in RSS-based localization schemes: finding optimal localization algorithms and knowing what affects the accuracy of these algorithms. Through theoretical and experimental analysis, we present three important results: 1) we prove that the Non-linear Least Square (NLS) method is efficient to solve the RSS-based localization problem, i.e., its localization error is minimal in theory; 2) we provide a closed-form expression of the localization error for the NLS method. Such an expression reveals the key factors that affect the accuracy of the NLS method; 3) we further conduct a new lower bound of localization error, i.e., the best accuracy achieved possibly. The study of this paper shows the inherent limitation of RSS-based localization schemes and provides guidance for achieving optimal accuracy.

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Source: https://tomesphere.com/paper/1702.03980