Static/Dynamic Interval Detection and Measurement Generation

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Classes: com.irurueta.navigation.inertial.calibration.intervals (detection, 9 classes), com.irurueta.navigation.inertial.calibration.generators (measurement building, 13 classes), plus the root-level BodyKinematicsGenerator, BodyMagneticFluxDensityGenerator, TimeIntervalEstimator, and TimeIntervalEstimatorListener.

This is the preprocessing step behind the calibrators in Accelerometer Calibration and Gyroscope Calibration that don’t need a turntable or precisely known frames — most directly, [imu-tk]'s "Easy" gyroscope calibrator and the accelerometer’s gravity-norm family. Both need the raw sensor stream split into static periods (device held still, mean specific force reveals the local gravity direction) and dynamic periods (device being moved between orientations) — without any external ground truth telling them which is which.

flowchart LR A["Raw BodyKinematics stream"] --> B["intervals package:\nTriadStaticIntervalDetector"] B --> C["generators package:\nMeasurementsGenerator"] C --> D["StandardDeviationBodyKinematics\n(one per static interval)"] C --> E["BodyKinematicsSequence\n(one per dynamic interval)"] D --> F["Accelerometer calibrator\n(gravity-norm family)"] E --> G["Gyroscope calibrator\n(Easy family)"]

TriadStaticIntervalDetector: classifying static vs. dynamic

The core class, TriadStaticIntervalDetector (specialized as AccelerationTriadStaticIntervalDetector, AngularSpeedTriadStaticIntervalDetector, MagneticFluxDensityTriadStaticIntervalDetector), runs a simple state machine per incoming sample:

stateDiagram-v2 [*] --> IDLE IDLE --> INITIALIZING : first sample INITIALIZING --> INITIALIZATION_COMPLETED : initialStaticSamples reached\n(baseNoiseLevel established) INITIALIZING --> FAILED : sudden excessive movement,\nor noise level too high INITIALIZATION_COMPLETED --> STATIC_INTERVAL STATIC_INTERVAL --> DYNAMIC_INTERVAL : windowed std-norm exceeds threshold DYNAMIC_INTERVAL --> STATIC_INTERVAL : windowed std-norm drops back below threshold FAILED --> [*]

Initialization. For the first initialStaticSamples samples (default 5,000, assumed static), the detector feeds both an accumulated noise estimator (a running mean/std over all samples so far) and a windowed noise estimator (a moving-window mean/std, default window ~101 samples — see Noise and Approximate-Bias Estimators) from the sibling noise package. If the windowed-to-accumulated standard-deviation ratio ever exceeds instantaneousNoiseLevelFactor (default 2.0), initialization fails (SUDDEN_EXCESSIVE_MOVEMENT_DETECTED) — the device was disturbed before a stable noise baseline could be established.

Threshold. Once initialization completes, the accumulated standard-deviation norm becomes the baseNoiseLevel, and the classification threshold is

Steady-state classification. For every subsequent sample, the detector recomputes the windowed standard-deviation norm and classifies:

While STATIC_INTERVAL, samples accumulate into a fresh noise estimator; on transitioning to DYNAMIC_INTERVAL, the accumulated mean and standard deviation for that completed static period are reported to the listener (onStaticIntervalDetected) and the accumulator resets for the next one. This moving-window-variance-versus-noise-floor test is the same static/dynamic classification idea used by [imu-tk].

AccelerationTriadStaticIntervalDetector detector = new AccelerationTriadStaticIntervalDetector(
        new AccelerationTriadStaticIntervalDetectorListener() {
            @Override
            public void onStaticIntervalDetected(
                    AccelerationTriadStaticIntervalDetector detector, double instantaneousAvgX,
                    double instantaneousAvgY, double instantaneousAvgZ, double instantaneousStdX,
                    double instantaneousStdY, double instantaneousStdZ) {
                // a static interval just ended - these are its accumulated mean/std values
            }
            // ...other TriadStaticIntervalDetectorListener callbacks
        });

// feed raw accelerometer samples (m/s^2) as they arrive
detector.process(fx, fy, fz);

MeasurementsGenerator: building calibration inputs from intervals

MeasurementsGenerator wraps a TriadStaticIntervalDetector and reacts to its state transitions to build the actual measurement objects calibrators consume — discarding static intervals shorter than 2 x windowSize samples and dynamic intervals longer than 30 x windowSize samples as unreliable:

Class Produces Consumed by

AccelerometerMeasurementsGenerator

One StandardDeviationBodyKinematics per static interval (mean specific force + noise-derived std dev)

Gravity-norm / position accelerometer calibrators

GyroscopeMeasurementsGenerator

One BodyKinematicsSequence per dynamic interval, bracketed by the mean specific force of the static intervals immediately before and after

EasyGyroscopeCalibrator / KnownBiasEasyGyroscopeCalibrator

MagnetometerMeasurementsGenerator

One StandardDeviationBodyMagneticFluxDensity per static interval

Norm/position magnetometer calibrators

AccelerometerAndGyroscopeMeasurementsGenerator

Both of the above, from a single interval-detection pass

Calibration pipelines needing both sensors from one recording

AccelerometerGyroscopeAndMagnetometerMeasurementsGenerator

All three measurement types, from a single pass

Full tri-sensor calibration pipelines

 
List<StandardDeviationBodyKinematics> measurements = new ArrayList<>();

AccelerometerMeasurementsGenerator generator = new AccelerometerMeasurementsGenerator(
        (gen, measurement) -> measurements.add(measurement));

// feed raw BodyKinematics samples as they arrive from the IMU
for (BodyKinematics sample : rawKinematicsStream) {
    generator.process(sample);
}
// 'measurements' now holds one StandardDeviationBodyKinematics per detected static
// interval, ready for calibration/accelerometer.adoc's gravity-norm calibrators

TimeIntervalEstimator

A small, separate utility: estimates the actual average sampling period (and its variance) of an incoming timestamp stream using an online recursive mean/variance update (the same recursive form used throughout the noise estimators):



The resulting average time interval feeds the timeInterval used throughout the noise/interval/PSD computations above.

TimeIntervalEstimator estimator = new TimeIntervalEstimator();

for (double timestampSeconds : rawTimestamps) {
    estimator.addTimestamp(timestampSeconds);
}

double timeInterval = estimator.getAverageTimeInterval(); // seconds, e.g. ~0.02 for a 50 Hz IMU
double timeIntervalStd = estimator.getTimeIntervalStandardDeviation();

Root-level generators: synthetic test data (a different purpose)

BodyKinematicsGenerator and BodyMagneticFluxDensityGenerator are unrelated to interval detection — they go the other direction, synthesizing noisy, uncalibrated measurements from known-true kinematics/field plus a known IMUErrors model, for testing calibrators and fixers against ground truth. They follow [book-groves] and its companion IMU_model.m script rather than the Tedaldi et al. method.

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