Grid-Based Fusion

The foundational paradigm where the environment is tessellated into a discrete grid of cells, each storing a probability of occupancy. A Bayesian Occupancy Filter recursively updates each cell's belief state by fusing sequential, noisy measurements from sensors like LiDAR and sonar. This elegantly handles the inverse sensor model problem, converting raw range returns into probabilistic evidence of free, occupied, or unknown space, making it a cornerstone of robotic mapping and autonomous navigation.

An extension beyond Bayesian probability that explicitly models epistemic uncertainty—the ignorance arising from sensor occlusion or conflicting returns. Each grid cell maintains a belief mass and a plausibility value, not just a single probability. This framework is powerful for fusing highly heterogeneous sensors (e.g., radar and camera) because it can represent the state of 'I don't know' distinctly from 'equal evidence for occupied and free,' preventing premature, overconfident classification in ambiguous zones.

For moving objects, static occupancy grids are insufficient. Bayesian Occupancy Filters (BOFs) extend the concept by estimating both occupancy and dynamic state (velocity) for each cell using a 4D grid. Alternatively, a particle filter can be run on a grid representation, where each particle represents a hypothesis about the state of a dynamic entity. This hybrid approach fuses raw sensor data to track multiple moving objects directly on the grid without requiring a hard, error-prone object segmentation step first.

A specialized grid form where each cell stores a 2.5D elevation value and a reflectivity intensity instead of a binary occupancy probability. This is the standard output for fusing dense LiDAR point clouds into a compact, traversable map. By projecting points onto a horizontal plane grid and computing statistics (mean height, variance, max intensity) per cell, the system creates a rich terrain model. This representation is critical for off-road autonomous vehicles to assess traversability cost and detect negative obstacles.

A robust grid-based fusion system must model sensor degradation and temporal decay. A cell's occupancy probability should not remain static if it's unobserved; a forgetting factor or a dynamic decay rate is applied. This is often implemented by transitioning a cell's state toward 'unknown' over time. This mechanism is essential for handling dynamic environments where objects move away, preventing 'ghost tracks' from stale sensor data and ensuring the fused map reflects the current, not historical, state of the world.

To balance computational load with representational fidelity, advanced frameworks use multi-resolution grids like octrees or adaptive quadtrees. A sparse region of empty space is represented by a single large cell, while a cluttered area with dense sensor returns is subdivided into many fine cells. This allows for efficient memory usage and fast ray-casting for sensor model updates. The fusion logic must seamlessly aggregate evidence across different scales, a technique vital for large-scale, long-term SLAM systems.

A probabilistic framework that recursively estimates the likelihood of each cell being occupied or free. It uses Bayesian inference to fuse sequential, noisy sensor observations, providing a mathematically rigorous method for updating grid cell probabilities over time. This filter is the core update mechanism for most modern occupancy grids.

• Handles sensor noise and false positives
• Recursively updates P(occupied | measurements)
• Foundational for dynamic environment modeling

A mathematical theory of evidence that extends Bayesian probability by explicitly representing epistemic uncertainty and ignorance. Unlike Bayesian methods, it assigns belief and plausibility to propositions, allowing a grid cell to represent conflicting evidence (e.g., from a LiDAR return and a radar return) without forcing a false commitment.

• Models 'unknown' as distinct from 'equal probability'
• Handles conflicting sensor modalities gracefully
• Used in advanced occupancy grid frameworks

A mathematical function that maps a raw sensor measurement directly to a probability of occupancy for each grid cell in its field of view. This model encapsulates the physical characteristics of a specific sensor—such as a LiDAR beam's Gaussian range error or a radar's angular uncertainty—to generate evidence for the grid.

• Converts raw data to P(occupied | measurement)
• Sensor-specific calibration required
• Critical for sensor-agnostic grid frameworks

A graphical model framework that represents the state estimation problem as a bipartite graph of variable nodes (robot poses, landmark positions) and factor nodes (probabilistic constraints from sensor measurements). It solves for the maximum a posteriori estimate via nonlinear least squares, enabling globally consistent grid maps by optimizing over historical poses.

• Eliminates drift in SLAM-generated grids
• Supports loop closure constraints
• Used in GTSAM, g2o, and Ceres solvers

A sequential Monte Carlo method that represents the posterior distribution of a system's state using a set of weighted random samples called particles. In grid-based fusion, particle filters are often used to track the robot's pose while building the map, enabling robust localization in highly non-Gaussian and multimodal environments.

• Handles non-linear, non-Gaussian motion models
• Each particle represents a possible robot trajectory
• Foundation for FastSLAM and grid-based SLAM variants

The computational process of determining which sensor measurements originate from which physical objects or grid cells. In dynamic occupancy grids, data association resolves whether a new LiDAR point corresponds to a static obstacle, a moving vehicle, or sensor noise before updating cell states.

• Critical for multi-target tracking in grids
• Uses techniques like Joint Probabilistic Data Association (JPDA)
• Prevents ghost objects and missed detections