The Kalman filter is the recursive estimator that turns noisy predictions and noisy sensors into a single best guess of where something is and how fast it is moving. We walk the predict-update loop, the actual equations, the gain as a trust dial, the EKF and UKF extensions, and the honest pain of tuning Q and R on real hardware.
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Kalman Filters Explained -
How GPS Computes Your Position GPS is one of the few consumer technologies that would fail within minutes if Einstein had been wrong. We walk the physics of fixing your position from four orbiting atomic clocks, why four and not three, the special- and general-relativistic corrections baked into every receiver, how the C/A code lets a phone hear a signal weaker than thermal noise, and why your first fix is slow and the next one is instant.