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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

Open the air-missile-defense pageair-missile-defense Proportional navigationguidancecontrol: Guidance law commanding acceleration proportional to line-of-sight rateClock synchronizationdistributed: 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 isolationrecoveryembedded: Monitor/response tables, fault isolation and safe-mode recovery hierarchies for autonomous systemsHot-standby redundancyembedded: 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.›Time triggered schedulingembedded: Static cyclic schedules where every task and message has a precomputed time slotHomogeneous transformsgeometry: 4x4 affine and projective matrices, homogeneous coordinates, view and projection, normal matricesQuaternion rotationsgeometry: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.›Assignment problem (Hungarian /Jonker–Volgenant)graphs: 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: 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: Predicting multi-modal future paths of agents from history and map contextTdl message translationnetworking: Translate between bit-packed tactical data link messages (Link 16 J-series, VMF) via field-level mapping, scaling and unit conversionDiscrete event simulationnumerics: Simulation driven by a time-ordered event queue with deterministic, reproducible replayMonte Carlo integrationnumerics: 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: The classic four-stage, fourth-order ODE step; error drops 16× when the step halves, with no derivatives or past steps needed.›Mixed-integer programming(branch and bound)optimization: Solves LPs with integer variables by solving the LP relaxation, branching on a fractional variable, and pruning subtrees whose LP bound cannot beat the incumbent.›Nonlinear resource assignmentoptimization: Assign resources to targets to maximise success probability under constraints (nonlinear assignment heuristics and exact)Simulated annealingoptimization: Stochastic local search with a cooling schedule for combinatorial optimizationExtended Kalman filterrobotics: 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.›Interacting multiple modelfilterrobotics: IMM filter mixing several motion models for maneuvering targetsKalman filterrobotics: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.›Sensor fusionrobotics: Combining IMU, GNSS, camera, lidar and radar estimates with Kalman-type filters and time alignmentBeamformingsignal-processing: Phased-array weights that steer radio energy toward a receiver; per-client steering vectorsCfar detectionsignal-processing: Constant false alarm rate detector: set the threshold from a noise estimate of neighbouring cells (CA, OS, GO/SO-CFAR)Pulse deinterleavingsignal-processing: Separate interleaved pulse trains by emitter using pulse repetition interval histograms and sequence search (CDIF, SDIF)Space time adaptive processingsignal-processing: Radar clutter suppression with 2D adaptive filter over antenna and pulse samples using covariance estimation and weight solvingPID controllerrobotics: 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: 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: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.›Redundancy votingembedded: N-modular redundancy and MooN voting (2oo3, TMR) with discrepancy detectionHierarchical state machinesystems: Nest states so a substate inherits its parent's reactions and only overrides what differs, with ordered entry and exit actions along the path.›Watchdog timerembedded: A hardware down-counter that resets the chip unless software proves, in time and in a plausible pattern, that it is still healthy.›Primary-backup replicationdistributed: One node orders all writes and ships them to standbys; the acknowledgement rule (none, one, all) sets what a crash loses, and an external arbiter decides who takes over.›Dijkstra's algorithmgraphs: Single-source shortest paths with non-negative edge weights by settling vertices in order of distance with a priority queue.›Non-maximum suppressionmachine-learning: Keep the best-scoring candidate in each neighbourhood and drop the rest; greedy NMS, Soft-NMS and 1-D peak picking share one loop.›Object detectionmachine-learning: A network turns an image into scored, classified boxes in one pass; anchor-based, anchor-free and set-prediction heads differ in how they assign labels and remove duplicates.›Loss functionsmachine-learning: The scalar a model minimizes: cross-entropy for classes and tokens, MSE or Huber for values, each with a stable form and simple gradient.›Recurrent networksmachine-learning: GRU and LSTM cells for streaming sequence models+ 13 moreLeasesdistributed: A lock that expires on its own: bounded-time ownership that survives crashes and partitions, given bounded clock drift and fencing tokens on writes.›Write-ahead logstorage: Append each change to a checksummed sequential log and fsync it before touching data pages; the basis of crash durability in nearly every database.›Health checkingsystems: Decide per backend whether to route to it using probes and real-traffic errors, with consecutive-count hysteresis, capped ejection and a panic fallback.›Data augmentationmachine-learning: Generate label-preserving variants of each training example on the fly to enlarge the effective dataset and bake in invariances.›Convolutional networksml-training: Layers that slide a small shared kernel over a grid, giving translation equivariance and few parameters; still the most compute-efficient choice for many vision tasks.›+ 12 moreFencing tokensdistributed: A number that grows with every lock grant and is checked by the protected resource, so a paused ex-holder's late write is rejected.›CRC32C checksumshardware-os: The Castagnoli CRC-32 with dedicated instructions on x86 (SSE4.2) and ARMv8. It is the standard fast integrity check for storage blocks, logs and network frames.›fsync, O_DSYNC and O_DIRECThardware-os: What fsync, fdatasync, O_DSYNC, O_DIRECT and F_FULLFSYNC really guarantee on Linux and macOS, and the exact call sequences for crash-safe files.›+ 1 moreSIMD programminghardware-os: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.›

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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