Comprehensive comparison of TSNFA against four classical detection algorithms across 4 Monte Carlo configurations.
Four Monte Carlo configurations were run, factorial across two network sizes (10 and 50 nodes) and two SNR levels (12 dB and 18 dB). Each configuration was simulated for 24 hours of synthetic time and replicated five times with independent random seeds for variance estimation.
| Configuration | Origin | N nodes | SNR (dB) | Duration | MC Runs | Total Events | Preset |
|---|---|---|---|---|---|---|---|
| 10n / 18dB | 20260513_102615 | 10 | 18 | 24.0h | 5 | — | ACCURATE |
| 10n / 12dB | 20260513_091959 | 10 | 12 | 24.0h | 5 | — | ACCURATE |
| 50n / 18dB | current | 50 | 18 | 24.0h | 5 | — | ACCURATE |
| 50n / 12dB | 20260513_161751 | 50 | 12 | 24.0h | 5 | — | ACCURATE |
Five detection algorithms were evaluated. TSNFA is the proposed cascade. Lipski FFT, CA-CFAR, OS-CFAR, and CUSUM are classical baselines drawn from radar and statistical signal processing literature, used here at their canonical published settings to allow a fair comparison.
Two-stage cascade: spectral consistency (FFT-binned, Defence-1) followed by median-CFAR rank statistic (Defence-2). Designed for low-SNR seismic monitoring with strict bandwidth constraints.
Per-bin energy detector firing when bin power exceeds μ + kσ for a minimum number of consecutive bins. Canonical k = 3 (Lipski et al.).
Cell-averaging Constant False Alarm Rate detector using a sliding mean of N reference cells. Threshold multiplier α = 7.71 derived from P_fa = 10⁻³ via the Finn-Johnson formula.
Order-statistic CFAR using the 75th-percentile (k = 24 of N = 32) of the reference cells. Threshold multiplier α = 37.33 from P_fa = 10⁻³ (Rohling 1983).
Tartakovsky's bounded-memory cumulative-sum change detector with α_fa = 10⁻⁵ and a finite window K_end = 100 to prevent unbounded accumulation in stationary noise.
The canonical settings used across all four runs. These are fixed by-design parameters drawn from the published literature, not tuned to the data. Identical settings ensure detectors are compared at their published operating points rather than at empirically-optimized configurations.
| Detector | Parameter | Canonical Value |
|---|---|---|
| TSNFA | γ_d (Defence-1 threshold) | — |
| γ_a (Defence-2 threshold) | — | |
| ζ (CFAR multiplier) | — | |
| Lipski FFT | k (sigma multiplier) | — |
| N_bins_min (min consecutive bins) | 3 | |
| CA-CFAR | N_ref (reference cells) | 32 |
| P_fa (false-alarm prob) | — | |
| OS-CFAR | N_ref (reference cells) | 32 |
| k_rank (rank statistic) | — | |
| P_fa (false-alarm prob) | — | |
| CUSUM | α_fa (false-alarm rate) | — |
The central result table. Each detector evaluated across all four configurations on the four most diagnostic metrics: detection rate, event precision, false-positive cluster count, and per-node network load.
| Detector | 10n / 18dB | 10n / 12dB | 50n / 18dB | 50n / 12dB |
|---|---|---|---|---|
| Detection Rate (%) | ||||
| TSNFA | 100.00% | 100.00% | 100.00% | 99.97% |
| Lipski | 99.73% | 99.73% | 99.85% | 99.85% |
| CA-CFAR | 100.00% | 100.00% | 100.00% | 100.00% |
| OS-CFAR | 100.00% | 100.00% | 100.00% | 100.00% |
| CUSUM | 68.14% | 51.30% | 70.81% | 51.08% |
| Event Precision (%) | ||||
| TSNFA | 100.00% | 100.00% | 100.00% | 100.00% |
| Lipski | 1.65% | 1.66% | 1.72% | 1.69% |
| CA-CFAR | 2.25% | 2.25% | 2.29% | 2.29% |
| OS-CFAR | 2.59% | 2.59% | 2.65% | 2.65% |
| CUSUM | 1.70% | 1.28% | 1.78% | 1.26% |
| FP Clusters | ||||
| TSNFA | 0 | 0 | 0 | 0 |
| Lipski | 12574 | 12519 | 67501 | 68603 |
| CA-CFAR | 9194 | 9188 | 50303 | 50305 |
| OS-CFAR | 7952 | 7953 | 43286 | 43285 |
| CUSUM | 8437 | 8441 | 46029 | 47348 |
| Network Load (B/hr) | ||||
| TSNFA | 392 B/hr | 232 B/hr | 2.0 kB/hr | 1.2 kB/hr |
| Lipski | 241.3 kB/hr | 240.9 kB/hr | 1.19 MB/hr | 1.18 MB/hr |
| CA-CFAR | 145.8 kB/hr | 145.9 kB/hr | 715.9 kB/hr | 716.1 kB/hr |
| OS-CFAR | 150.0 kB/hr | 150.1 kB/hr | 737.0 kB/hr | 737.2 kB/hr |
| CUSUM | 12.2 kB/hr | 12.2 kB/hr | 55.1 kB/hr | 57.0 kB/hr |
For each detector, the simulator swept a threshold multiplier in post-processing (using the saved per-frame strengths) to trace out the ROC upper envelope. Hollow circles mark the canonical operating point — the threshold value that produces the headline metrics in Section 4.
Network load per detector, expressed as bytes per hour each sensor node transmits. Total mesh load is per-node × (N − 1), where N − 1 is the number of sensor nodes (one node is the sink). The "vs TSNFA" column shows the bandwidth ratio, revealing how much more traffic each comparator generates at the same operating point.
| Detector | 10n / 18dB | 10n / 12dB | 50n / 18dB | 50n / 12dB | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Per-node | Total mesh | vs TSNFA | Per-node | Total mesh | vs TSNFA | Per-node | Total mesh | vs TSNFA | Per-node | Total mesh | vs TSNFA | |
| TSNFA | 392 B/hr | 3.5 kB/hr | 1.0× | 232 B/hr | 2.1 kB/hr | 1.0× | 2.0 kB/hr | 96.4 kB/hr | 1.0× | 1.2 kB/hr | 57.0 kB/hr | 1.0× |
| Lipski | 241.3 kB/hr | 2,171.5 kB/hr | 614.8× | 240.9 kB/hr | 2,168.5 kB/hr | 1,039.4× | 1.19 MB/hr | 58,157.7 kB/hr | 603.3× | 1.18 MB/hr | 57,988.5 kB/hr | 1,017.8× |
| CA-CFAR | 145.8 kB/hr | 1,312.4 kB/hr | 371.6× | 145.9 kB/hr | 1,312.8 kB/hr | 629.3× | 715.9 kB/hr | 35,081.3 kB/hr | 363.9× | 716.1 kB/hr | 35,089.5 kB/hr | 615.9× |
| OS-CFAR | 150.0 kB/hr | 1,350.3 kB/hr | 382.3× | 150.1 kB/hr | 1,350.7 kB/hr | 647.4× | 737.0 kB/hr | 36,113.7 kB/hr | 374.6× | 737.2 kB/hr | 36,124.1 kB/hr | 634.0× |
| CUSUM | 12.2 kB/hr | 109.9 kB/hr | 31.1× | 12.2 kB/hr | 109.9 kB/hr | 52.7× | 55.1 kB/hr | 2,699.7 kB/hr | 28.0× | 57.0 kB/hr | 2,790.9 kB/hr | 49.0× |
How much each detector's detection rate degrades when SNR drops from 18 dB to 12 dB. Robust detectors show ≈ 0 percentage-point drop; brittle detectors collapse. Cells highlighted: red for severe brittleness (>30 pp drop), amber for moderate (10–30 pp), green for stability (< 1 pp).
| Detector | N = 10 | N = 50 | ||||
|---|---|---|---|---|---|---|
| 18 dB | 12 dB | Δ% | 18 dB | 12 dB | Δ% | |
| TSNFA | 100.00% | 100.00% | ≈0 | 100.00% | 99.97% | +0.03 |
| Lipski | 99.73% | 99.73% | ≈0 | 99.85% | 99.85% | ≈0 |
| CA-CFAR | 100.00% | 100.00% | ≈0 | 100.00% | 100.00% | ≈0 |
| OS-CFAR | 100.00% | 100.00% | ≈0 | 100.00% | 100.00% | ≈0 |
| CUSUM | 68.14% | 51.30% | +16.84 | 70.81% | 51.08% | +19.73 |
Behaviour of each metric as network size grows from 10 to 50 nodes. Detection-quality metrics (DR, precision) are per-node algorithmic properties and should be invariant in N. Cost metrics (FP cluster count, network load) scale linearly because each node operates independently.
Each detector × configuration plotted as a single point in 2D (network load, event precision) space. The upper-left corner is ideal: high precision and low bandwidth. Marker size encodes network size.
Each detector × configuration as a bubble in three dimensions (FAR × network load × detection rate). Bubble size encodes event precision (big = useful triggers, small = noise). A "good" detector is a big bubble in the front-left-top corner: low FAR, low load, high DR, high precision.