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air-missile-defense

threat evaluation, weapon assignment and interceptor guidance: TEWA optimisation, impact-point prediction, fire-control loops within seconds

Patriot, Aegis BMD, Iron Dome, IBCS

SystemTechniques · 20Primitives · 52 air-missile-defense Clock synchronizationdistributed · medium: Estimate a clock's offset from four timestamps, filter out queueing noise, and steer the clock smoothly; NTP gets about a millisecond, PTP with hardware timestamps under a microsecond.›Fault detection isolation recoveryembedded · medium: Monitor/response tables, fault isolation and safe-mode recovery hierarchies for autonomous systemsHot-standby redundancyembedded · medium: A second, always-current controller shadows the primary and takes over within a few cycles of silence; epochs stop the old primary from fighting back.›Assignment problem (Hungarian / Jon…graphs · medium: Optimal one-to-one matching of rows to columns in O(n³) by growing a matching along shortest augmenting paths over dual potentials.›Multi-object trackingmachine-learning · medium: Turn per-frame detections (camera boxes or radar plots) into persistent IDs by predicting each track, gating, assigning and managing track births and deaths.›Trajectory predictionmachine-learning · medium: Predicting multi-modal future paths of agents from history and map contextDiscrete event simulationnumerics · medium: Simulation driven by a time-ordered event queue with deterministic, reproducible replayKalman filterrobotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.›Extended Kalman filterrobotics · low: Kalman filter for nonlinear motion and measurement models: linearize f and h with Jacobians at the current estimate each step. The default estimator in robot navigation.›Quaternion rotationsgeometry · low: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.›Proportional navigation guidancecontrol · low: Guidance law commanding acceleration proportional to line-of-sight rateTime triggered schedulingembedded · low: Static cyclic schedules where every task and message has a precomputed time slotHomogeneous transformsgeometry · low: 4x4 affine and projective matrices, homogeneous coordinates, view and projection, normal matricesTdl message translationnetworking · low: Translate between bit-packed tactical data link messages (Link 16 J-series, VMF) via field-level mapping, scaling and unit conversionMonte Carlo integrationnumerics · low: Estimate an expectation by averaging random samples; error falls as σ/√N in any dimension, and variance reduction (antithetic, control variates, importance sampling) shrinks σ.›Runge-Kutta 4numerics · low: The classic four-stage, fourth-order ODE step; error drops 16× when the step halves, with no derivatives or past steps needed.›Beamformingsignal-processing · low: Phased-array weights that steer radio energy toward a receiver; per-client steering vectorsCfar detectionsignal-processing · low: Constant false alarm rate detector: set the threshold from a noise estimate of neighbouring cells (CA, OS, GO/SO-CFAR)PID controllerrobotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.›Phase-locked loop (digital)signal-processing · low: Feedback loop that locks a local oscillator to the phase and frequency of an input tone; the core of carrier recovery, clock recovery and GNSS tracking.›Robust statisticsstatistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.›Redundancy votingembedded · low: N-modular redundancy and MooN voting (2oo3, TMR) with discrepancy detectionWatchdog timerembedded · low: A hardware down-counter that resets the chip unless software proves, in time and in a plausible pattern, that it is still healthy.›+ 13 more techniques+ 36 more primitives

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In-house systems

Named systems of this kind at large companies, with their paper or write-up.

IBCS (Integrated Battle Command System)Northrop Grumman