Sensor Fusion Latency & Sampling Rate Alignment Calculator
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Sensor Fusion Latency & Sampling Rate Alignment Calculator
Calculate the effective fusion latency, least common sampling period, synchronization buffer size, and phase alignment error for multi-sensor fusion systems.
### Sensor A
Sampling Rate A (Hz)
Processing Latency A (ms)
### Sensor B
Sampling Rate B (Hz)
Processing Latency B (ms)
### Sensor C (optional)
Sampling Rate C (Hz)
Processing Latency C (ms)
### Fusion Parameters
Fusion Algorithm Latency (ms)
Network/Transport Delay (ms)
Clock Jitter / Sync Error (ms)
Calculate
### Results
function senGcd(a, b) { // Euclidean GCD for floats via integer scaling a = Math.round(a); b = Math.round(b); while (b) { var t = b; b = a % b; a = t; } return a; } function senLcm(a, b) { return (a / senGcd(a, b)) * b; } function senGcdFloat(a, b) { // Scale to integers (up to 6 decimal places) then compute GCD var scale = 1e6; var ai = Math.round(a * scale); var bi = Math.round(b * scale); return senGcd(ai, bi) / scale; } function senLcmFloat(a, b) { var g = senGcdFloat(a, b); return (a / g) * b; } function senRow(label, value, unit, note) { return '' + '' + label + '' + '' + value + ' ' + unit + '' + '' + (note||'') + '' + ''; } function senCalc() { var err = document.getElementById('sen-error'); var res = document.getElementById('sen-result'); err.textContent = ''; res.style.display = 'none';
var rA = parseFloat(document.getElementById('sen-rate-a').value); var lA = parseFloat(document.getElementById('sen-latency-a').value); var rB = parseFloat(document.getElementById('sen-rate-b').value); var lB = parseFloat(document.getElementById('sen-latency-b').value); var rCv = document.getElementById('sen-rate-c').value.trim(); var lCv = document.getElementById('sen-latency-c').value.trim(); var lF = parseFloat(document.getElementById('sen-fusion-latency').value); var lT = parseFloat(document.getElementById('sen-transport-delay').value); var jitter = parseFloat(document.getElementById('sen-jitter').value);
// Validate required if (isNaN(rA) || rA = 0.'; return; } if (isNaN(rB) || rB = 0.'; return; } if (isNaN(lF) || lF = 0.'; return; } if (isNaN(lT) || lT = 0.'; return; } if (isNaN(jitter) || jitter = 0.'; return; }
var useC = false; var rC, lC; if (rCv !== '' || lCv !== '') { rC = parseFloat(rCv); lC = parseFloat(lCv); if (isNaN(rC) || rC = 0 if provided.'; return; } useC = true; }
// Sampling periods in ms var TA = 1000.0 / rA; // ms var TB = 1000.0 / rB; // ms
// LCM of sampling periods => common alignment period var lcmPeriod = senLcmFloat(TA, TB); if (useC) { var TC = 1000.0 / rC; lcmPeriod = senLcmFloat(lcmPeriod, TC); }
// Fusion output rate = 1 / LCM period var fusionRate = 1000.0 / lcmPeriod; // Hz
// Effective fusion latency = max sensor latency + fusion algo latency + transport delay // L_eff = max(L_i) + L_fusion + L_transport var maxSensorLatency = Math.max(lA, lB); if (useC) maxSensorLatency = Math.max(maxSensorLatency, lC); var effectiveLatency = maxSensorLatency + lF + lT;
// Worst-case latency includes jitter var worstCaseLatency = effectiveLatency + jitter;
// Phase alignment error: max difference between sensor periods // When sensors are not synchronized, the max temporal misalignment // is bounded by the largest sampling period among sensors var maxPeriod = Math.max(TA, TB); if (useC) maxPeriod = Math.max(maxPeriod, 1000.0 / rC); var phaseError = maxPeriod / 2.0; // worst-case half-period misalignment
// Buffer size needed per sensor to hold samples during LCM window // Buffer_i = ceil(f_i * T_lcm / 1000) var bufA = Math.ceil(rA * lcmPeriod / 1000.0); var bufB = Math.ceil(rB * lcmPeriod / 1000.0); var bufTotal = bufA + bufB; if (useC) { var bufC = Math.ceil(rC * lcmPeriod / 1000.0); bufTotal += bufC; }
// Interpolation requirement: if rates differ, interpolation needed var rateRatio = Math.max(rA, rB) / Math.min(rA, rB); if (useC) { var allRates = [rA, rB, rC]; rateRatio = Math.max(...allRates) / Math.min(...allRates); }
// Nyquist-limited fusion bandwidth // The fusion output cannot exceed the Nyquist frequency of the slowest sensor var minRate = Math.min(rA, rB); if (useC) minRate = Math.min(minRate, rC); var nyquistBW = minRate / 2.0;
// Synchronization window (tolerance): typically Sampling Alignment'; rows += senRow('Sensor A Period', TA.toFixed(4), 'ms', 'T_A = 1000 / f_A'); rows += senRow('Sensor B Period', TB.toFixed(4), 'ms', 'T_B = 1000 / f_B'); if (useC) rows += senRow('Sensor C Period', (1000.0/rC).toFixed(4), 'ms', 'T_C = 1000 / f_C'); rows += senRow('LCM Alignment Period', lcmPeriod.toFixed(4), 'ms', 'T_lcm = LCM(T_A, T_B' + (useC?', T_C':'') + ')'); rows += senRow('Fusion Output Rate', fusionRate.toFixed(4), 'Hz', 'f_fusion = 1000 / T_lcm'); rows += senRow('Sampling Rate Ratio', rateRatio.toFixed(3), '×', 'f_max / f_min');
rows += 'Latency Analysis'; rows += senRow('Max Sensor Latency', maxSensorLatency.toFixed(3), 'ms', 'max(L_A, L_B' + (useC?', L_C':'') + ')'); rows += senRow('Effective Fusion Latency', effectiveLatency.toFixed(3), 'ms', 'L_eff = max(L_i) + L_fusion + L_transport'); rows += senRow('Worst-Case Latency', worstCaseLatency.toFixed(3), 'ms', 'L_worst = L_eff + jitter');
rows += 'Synchronization'; rows += senRow('Phase Alignment Error', phaseError.toFixed(4), 'ms', 'T_max / 2 (worst-case half-period)'); rows += senRow('Sync Tolerance Window', syncWindow.toFixed(4), 'ms', 'T_min / 2'); rows += senRow('Nyquist Fusion BW', nyquistBW.toFixed(4), 'Hz', 'f_min / 2 (max observable frequency)');
rows += 'Buffer Requirements'; rows += senRow('Buffer Size (Sensor A)', bufA, 'samples', 'ceil(f_A × T_lcm / 1000)'); rows += senRow('Buffer Size (Sensor B)', bufB, 'samples', 'ceil(f_B × T_lcm / 1000)'); if (useC) rows += senRow('Buffer Size (Sensor C)', Math.ceil(rC * lcmPeriod / 1000.0), 'samples', 'ceil(f_C × T_lcm / 1000)'); rows += senRow('Total Buffer Size', bufTotal, 'samples', 'Sum of all sensor buffers');
document.getElementById('sen-tbody').innerHTML = rows; res.style.display = 'block'; }
#### Formulas Used
Sampling Period: Ti = 1000 / fi (ms)
LCM Alignment Period: Tlcm = LCM(TA, TB, ...) — the smallest window in which all sensors produce an integer number of samples, computed via the Euclidean GCD algorithm.
Fusion Output Rate: ffusion = 1000 / Tlcm (Hz)
Effective Fusion Latency: Leff = max(Li) + Lfusion + Ltransport
Worst-Case Latency: Lworst = Leff + σjitter
Phase Alignment Error: εphase = Tmax / 2 — worst-case temporal misalignment between unsynchronized sensors equals half the longest sampling period.
Nyquist Fusion Bandwidth: BWNyquist = fmin / 2 — the fused output cannot faithfully represent signals above half the slowest sensor's rate.
Buffer Size per Sensor: Ni = ⌈fi × Tlcm / 1000⌉ (samples)
#### Assumptions & References
- Effective latency uses the maximum sensor latency because the fusion algorithm must wait for the slowest sensor's data before producing an output.
- Phase alignment error of Tmax/2 is the worst-case bound for unsynchronized sensors; hardware timestamping or PTP/IEEE 1588 can reduce this to sub-millisecond levels.
- Fusion algorithm latency (Lfusion) covers Kalman filter, complementary filter, or other fusion computation time and must be measured empirically for the target hardware.
- Reference: Liggins, Hall & Llinas, Handbook of Multisensor Data Fusion, 2nd ed., CRC Press, 2008.
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