This open-access educational module presents the physical principles, sensor noise formulations, computer vision geometry, and recursive Bayesian state estimation techniques foundational to modern robotic perception.
Core Technical Topics
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Measurement & Noise Modeling: Linear and non-linear observation models (z = h(x) + v), zero-mean multivariate Gaussian noise covariance (R = E[vv^T]), and first-order Taylor series Jacobian linearization.
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Computer Vision Geometry: Pinhole camera perspective projection ([u, v]^T = (f/Z)[X, Y]^T), intrinsic calibration matrices (K), and stereoscopic disparity depth triangulation (Z = fB/d) with quadratic range error scaling.
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Time-of-Flight LiDAR Ranging: Laser pulse propagation (d = cDelta_t / 2) and pulse repetition frequency limits (d_max = c / (2f_rep)) governing maximum unambiguous distance.
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Recursive Bayesian State Estimation: Bayes' rule decomposition into motion prediction and measurement likelihood, and the discrete Kalman filter (prediction, innovation residual, and optimal Kalman gain update).
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Multi-Sensor Data Fusion: Minimum-variance sensor fusion weighting observations inversely proportional to individual measurement variances (x_hat = (sigma_2^2z_1 + sigma_1^2z_2) / (sigma_1^2 + sigma_2^2)).
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Modern Perception Pipelines: Multi-modal fusion across cameras, LiDAR, and radar, neuromorphic event-based sensing, and occupancy grid mapping for spatial awareness.
Pedagogical Assets
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12 fully worked numerical engineering problems with complete mathematical derivations and step-by-step solutions.
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Dedicated engineering challenges analysis addressing degraded visual environments (DVE), extrinsic coordinate calibration loss, edge neural inference bottlenecks, and dynamic occlusions.
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Interactive conceptual quick reviews and self-assessment checkpoints.
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Standardized cross-platform layout designed for university coursework adoption and permanent reference.
Target Audience & Level Designed for upper-division undergraduate engineering courses (Robotics, Computer Vision, Electrical Engineering, and Autonomous Systems), advanced university-preparatory STEM programs, and robotic perception software engineers.
