Sensor Fusion

The foundational recursive estimator for linear systems, predicting a state and updating it with noisy measurements to minimize mean squared error. For nonlinear systems, the Extended Kalman Filter (EKF) linearizes about the current estimate using Jacobians, while the Unscented Kalman Filter (UKF) propagates sigma points through the true nonlinear function, avoiding linearization errors and capturing higher-order moments. These algorithms are the workhorses of real-time object tracking and navigation.

A nonparametric Bayesian filter that represents the posterior distribution using a set of weighted random samples called particles. Unlike Kalman filters, particle filters handle highly non-Gaussian and multimodal distributions, making them ideal for global localization (the kidnapped robot problem) and tracking in cluttered environments. The Sequential Importance Resampling (SIR) step prevents particle degeneracy by resampling particles based on their weights.

Represents the state estimation problem as a bipartite graph of variable nodes (robot poses, landmark positions) and factor nodes (probabilistic constraints from sensor measurements). Solving this graph via nonlinear least squares—commonly using Gauss-Newton or Levenberg-Marquardt algorithms—yields the maximum a posteriori (MAP) estimate. This is the dominant paradigm in modern Simultaneous Localization and Mapping (SLAM) systems, enabling batch optimization over a sliding window of historical states.

The critical process of determining which sensor measurement originated from which physical object. Joint Probabilistic Data Association (JPDA) computes soft assignment probabilities by evaluating all possible joint association hypotheses, avoiding hard, brittle decisions. Multiple Hypothesis Tracking (MHT) defers association decisions, propagating multiple competing track hypotheses over time until future measurements resolve the ambiguity. These algorithms are essential for tracking multiple objects in radar and LiDAR point clouds.

In decentralized sensor networks, fusing state estimates requires knowledge of their cross-correlation, which is often unknown. Covariance Intersection (CI) solves this by computing a convex combination of the estimates, producing a consistent fused covariance that is guaranteed not to be overconfident. This algorithm is fundamental to Track-to-Track Fusion architectures where local sensor nodes process data independently and share only their state estimates, not raw measurements.

Iterative Closest Point (ICP) aligns two point clouds by iteratively associating points via nearest-neighbor search and minimizing point-to-point or point-to-plane distances. Normal Distributions Transform (NDT) instead maps the target scan into a set of local Gaussian distributions, enabling efficient scan matching by maximizing the likelihood of the source points. Both are critical for LiDAR odometry, extrinsic calibration, and loop closure detection in SLAM.