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# Simultaneous localization and mapping

## 1 Introduction

Simultaneous localization and mapping (SLAM) is a fundamental computational problem in robotics and autonomous systems wherein a moving agent must construct a map of an unknown environment while simultaneously keeping track of its own location within that map. The core difficulty arises from a circular dependency: accurate localization requires a consistent map, but building the map depends on knowing the agent’s pose. SLAM algorithms typically employ sensor data—such as lidar, cameras, or inertial measurement units (IMUs)—alongside probabilistic estimation methods to jointly solve for both unknowns. Since its formalization in the 1980s, SLAM has become a foundational technology in autonomous navigation, augmented reality, and drone guidance, enabling real‑time, self‑contained spatial reasoning.

### 1.1 Historical background

The origins of SLAM trace to early work on probabilistic robotics in the 1980s. Researchers such as Hugh Durrant‑Whyte and John J. Leonard formulated the problem as a stochastic estimation task, initially using Kalman filters to manage uncertainty. In the 1990s, the introduction of the extended Kalman filter (EKF) provided a practical framework for real‑time SLAM with range sensors. A landmark achievement was the 1999 publication of “A solution to the simultaneous localization and map building problem” by Dissanayake et al., which proved theoretical convergence conditions. The 2000s saw the rise of particle‑filter‑based methods (FastSLAM) and graph‑based optimization, dramatically improving scalability and accuracy. The convergence of affordable sensors and increased computing power in the 2010s propelled SLAM into consumer applications.

### 1.2 Motivation and importance

SLAM is motivated by the need for autonomous agents to operate in unknown, unstructured environments without relying on external positioning infrastructure (e.g., GPS). Importance spans multi
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