Edge Triggering in IoT Mesh Networks: A Comparative Monte Carlo Study of Seven Detection Algorithms

1. [1]

   Overview The Temporal Spectral Noise-Floor Adaptive (TSNFA) trigger is the detection method proposed by Makovetskii and Thomsen

2. [2]

   Defence 1: Spectral band selection

   It is built on three interlocking defences, each targeting a distinct failure mode observed in deployed IoT perimeter- security sensors. Defence 1: Spectral band selection. An L-point FFT decomposes each frame into frequency bins, and only the bins covering the event band [f low, fhigh] = [1, 5] Hz are retained. All energy from noise sources lik e electro...

   2026

3. [3]

   Pseudocode Algorithm 1: TSNFA Mean Variant Input: Sample frame x[0..N−1], noise floor Nƹ(m−1), filter buffer B(m) Params: γd = 3, γa = 64, ζ = 6.0, α = 1 − 1/γa Output: Trigger decision E[m], updated noise floor Nƹ(m) Stage 1: Spectral estimation (band selection)

4. [4]

   X ← |FFT(x)| // time → frequency domain, magnitude only, phase discarded

5. [5]

   X(m) ← max{ X[k] : k ∈ {1,…,6} } // select strongest event-band bin Stage 2: Digital noise filter (γd persistence)

6. [6]

   append X(m) to buffer B // sliding window of γd frames

7. [7]

   if |B| > γd then discard oldest // FIFO, keep exactly γd entries

8. [8]

   XNJ(m) ← mean(B) // X̄ (m) = (1/γd) × Σ B Stage 3: Threshold from last noise-floor update

9. [9]

   Θ(m) ← ζ × Nƹ(m−1) // Θ = 6.0 × previous noise floor Stage 4: Detection ratio and trigger decision

10. [10]

    R(m) ← XNJ(m) / Θ(m) // ratio of filtered energy to threshold

11. [11]

    if R(m) > 1.0 then E[m] ← 1 // trigger: in-band energy exceeds 6× noise floor Stage 5: Noise-floor adaptation (gated EMA)

12. [12]

    if R(m) < 0.8 then // Rgate = 0.8: update only during quiet frames

13. [13]

    Nƹ(m) ← α × Nƹ(m−1) + (1−α) × XNJ(m) // α = 0.984: blend 1.6% new, 98.4% old else Nƹ(m) ← Nƹ(m−1) // freeze: event energy must not leak into noise floor end if

14. [14]

    which bin has highest amplitude right now?

    Line-by-Line Annotation ALG1.Line 1: `X ← |FFT(x)|` Compute the 128-point Fast Fourier Transform of the current sample frame, then take the magnitude (absolute value) of each complex bin. The FFT converts 128 time-domain samples into 64 frequency bins (plus DC and Nyquist). Each bin represents energy at a specific frequency: bin k corresponds to frequency...

    2000

15. [15]

    Fits in STM32G071 SRAM (512 B real, 1 KB complex)

    Parameters TABLE I ALGORITHM 1 (TSNFA-MEAN) PARAMETERS Parameter Symbol Value Reasoning FFT size L 128 At fₛ = 100 Hz: Δf = 0.78 Hz. Fits in STM32G071 SRAM (512 B real, 1 KB complex). Frame duration Tᵦ = 1.28 s. Sample rate fₛ 100 Hz Nyquist for the 1-5 Hz event band. Higher rates waste power/memory; lower rates alias event content. Event band [flow, fhig...

16. [16]

    Overview The median variant of TSNFA is the form implemented in the deployed hardware. It differs from Algorithm 1 in four specific operations, each of which can be expressed as a direct formula substitution (the four differences are outlined in details in Figure 2): Difference 1 to Alg.1: Bin aggregation replaced by per-bin processing. Algorithm 1 collap...

17. [17]

    Pseudocode Algorithm 2: TSNFA Median Variant Input: Sample frame x[0..N−1], circular buffers Bd,k and Ba,k Params: γd ∈ [3, 5], γa ∈ [64, 128], ζk Output: Trigger decision, updated noise floors Nƹk[t] Spectral estimation (shared with Algorithm 1)

18. [18]

    X[k] ← FFT(x) for k ∈ 𝒦 // time → frequency, complex-valued

19. [19]

    |Xk| ← √(Re² + Im²) // magnitude only, phase discarded

20. [20]

    E[t] ← 0 // no event until a bin proves otherwise Per-bin processing loop

21. [21]

    for each bin k ∈ 𝒦 do // k = 1..6, each bin processed independently // Stage 1: Digital noise suppression (per-bin median)

22. [22]

    insert |Xk| into Bd,k // FIFO, keeps last γd values for this bin

23. [23]

    Ñk ← median(Bd,k) // middle value of γd frames; 1 outlier ignored // Stage 2: Noise-floor tracking (per-bin median, no gate)

24. [24]

    insert Ñk into Ba,k // FIFO, keeps last γa cleaned values

25. [25]

    Nƹk[t] ← median(Ba,k) // noise floor = middle of 64 values; 31 outliers tolerated // Trigger: raw magnitude vs per-bin threshold

26. [26]

    if |Xk| > ζk × Nƹk[t] then // raw |Xk|, not filtered Ñk

27. [27]

    E[t] ← 1 // any single bin exceeding triggers (OR logic) end if end for

28. [28]

    return E[t], { Nƹk[t] } // event flag + 6 updated noise-floor estimates

29. [29]

    no event

    Line-by-Line Annotation ALG2.Line 1: `X[k] ← FFT(x) for k ∈ K` Same 128-point FFT as Algorithm 1, but here we retain the complex-valued output for each monitored bin. K = {1, 2,…,6} covers the event band. On the STM32G071 (Arm Cortex-M0+, 64 MHz, no hardware FPU), the fixed-point FFT using CMSIS- DSP arm_cfft_q31 completes in ~0.4 ms. ALG2.Line 2: `|Xₖ| ←...

30. [30]

    The time constant is comparable to Algorithm 1’s EMA (82 s), but with much stronger outlier rejection

    With γₐ = 64, the median of 64 values tolerates up to 31 anomalous entries and even if an event lasts 31 consecutive frames (39.7 s), the noise-floor estimate is unaffected. The time constant is comparable to Algorithm 1’s EMA (82 s), but with much stronger outlier rejection. Computation: partial sort to position 32 requires ~64 × 32 = 2,048 comparisons p...

31. [31]

    Median of 3–5 values rejects up to ⌊(γᴅ − 1)/2⌋ outliers

    Parameters TABLE II ALGORITHM 2 (TSNFA-MEDIAN) PARAMETERS Parameter Symbol Value Reasoning Digital filter γᴅ 3–5 Per-bin circular buffer. Median of 3–5 values rejects up to ⌊(γᴅ − 1)/2⌋ outliers. Analog tracker γₐ 64–128 Per-bin circular buffer. Median of 64– 128 values tracks slow drift while rejecting up to 31–63 anomalous frames. Time constant ≈82–164 ...

    2023

32. [32]

    Overview The Zhang method is a time-domain adaptive threshold detector that operates on the peak amplitude of each sample frame without any spectral decomposition. It represents the class of energy-based detectors that assu me the detection statistic can be computed directly from time-domain signal levels, relying on an adaptive threshold to track changin...

33. [33]

    2023) Input: Sample frame x[0..N−1], noise floor NZ(m−1) Params: β = 0.95, ζ = 6.0 Output: Trigger decision E[m] Time-domain frame statistic (no FFT, no band selection)

    Pseudocode Algorithm 3: Time-Domain Adaptive Thresholding (Zhang et al. 2023) Input: Sample frame x[0..N−1], noise floor NZ(m−1) Params: β = 0.95, ζ = 6.0 Output: Trigger decision E[m] Time-domain frame statistic (no FFT, no band selection)

    2023

34. [34]

    XZ(m) ← maxn |x[n]| // peak sample in frame; includes EMI, digital, thermal Trigger decision

35. [35]

    R ← XZ(m) / NZ(m−1) // ratio of peak amplitude to noise floor

36. [36]

    if XZ(m) > ζ × NZ(m−1) then E[m] ← 1 // trigger if peak > 6× noise floor Noise-floor update (gated EMA, faster than TSNFA)

37. [37]

    if R < 0.8 then // same gate logic as Algorithm 1

38. [38]

    NZ(m) ← β × NZ(m−1) + (1−β) × XZ(m) // β = 0.95: 5% new, 95% old; τ ≈ 26 s else NZ(m) ← NZ(m−1) // freeze during events end if

39. [39]

    return E[m] // NZ tracks composite noise, not in-band only

40. [40]

    This is the time-domain peak detector with no frequency analysis

    Line-by-Line Annotation ALG3.Line 1: `Xᴵ(m) ← maxₙ |x[n]|` Scan all 128 samples in the frame and find the maximum absolute value. This is the time-domain peak detector with no frequency analysis. The peak amplitude captures whichever signal component has the highest instantaneous value at any moment within the 1.28-second frame. In the simulation noise en...

41. [41]

    Dominated by 60 Hz EMI peak, not event

    Parameters TABLE III ALGORITHM 3 (ZHANG) PARAMETERS Parameter Symbol Value Reasoning Frame statistic maxₙ|x[n]| - Peak absolute amplitude over 128 samples. Dominated by 60 Hz EMI peak, not event. Smoothing β 0.95 EMA coefficient. Time constant = 25.6 s. Faster than TSNFA but tracks EMI amplitude, not event- band noise. Threshold ζ 6.0 Set equal to TSNFA f...

    2022

42. [42]

    There is no noise-floor adaptation and no temporal persistence filter

    Overview The STFT method applies the same spectral decomposition as TSNFA—an L-point FFT with band selection over K = {1,…,6}—but compares the in-band magnitude against a fixed noise threshold Θ₀ set once during an initial calibration period. There is no noise-floor adaptation and no temporal persistence filter. It represents the class of fixed-threshold ...

43. [43]

    2022) Input: Sample frame x[0..N−1], calibration threshold Θ0 Output: Trigger decision E[m] Spectral estimation (identical to Algorithm 1)

    Pseudocode Algorithm 4: Fixed Spectral Mask: STFT (Bhoi et al. 2022) Input: Sample frame x[0..N−1], calibration threshold Θ0 Output: Trigger decision E[m] Spectral estimation (identical to Algorithm 1)

    2022

44. [44]

    X[k] ← |FFT(x)| for k ∈ {1,…,6} // time → frequency, event band only, rejects EMI

45. [45]

    Xmax ← maxk{ X[k] } // strongest bin magnitude, same as Algorithm 1 Fixed-threshold comparison (set at deployment, never updated)

46. [46]

    if Xmax > Θ0 then E[m] ← 1 // no persistence filter, single frame can trigger

47. [47]

    return E[m] // Θ₀ frozen, cannot follow noise drift

48. [48]

    This correctly isolat es the event band and rejects EMI, digital noise, and out-of-band thermal energy

    Line-by-Line Annotation ALG4.Line 1: `X[k] ← |FFT(x)| for k ∈ {1,…,6}` Identical FFT and band selection as TSNFA (Algorithm 1, Lines 1–2). This correctly isolat es the event band and rejects EMI, digital noise, and out-of-band thermal energy. STFT shares this critical advantage with TSNFA and the frequency- domain processing is a robust approach. ALG4.Lin...

49. [49]

    Typically mean + 3σ of calibration-period band magnitude

    Parameters TABLE IV ALGORITHM 4 (STFT) PARAMETERS Parameter Symbol Value Reasoning Threshold Θ₀ Fixed at calibration Set once by measuring noise spectrum. Typically mean + 3σ of calibration-period band magnitude. Never updated. Band selection k ∈ {1,…,6} Same as TSNFA Correctly isolates 1–5 Hz event band. This is why STFT achieves 100% DR. No adaptation -...

    2022

50. [50]

    It computes the total energy in each sample frame across all frequencies and compares it against a smoothed long- term energy baseline

    Overview DEDaR (Dual-Energy Dynamic-Range) is a broadband energy- ratio detector. It computes the total energy in each sample frame across all frequencies and compares it against a smoothed long- term energy baseline. The method triggers when the short-term energy exceeds a fixed multiple of the long-term energy, which is when a transient energy sp ike oc...

51. [51]

    Pseudocode Algorithm 5: Energy-Ratio Triggering: DEDaR (Hussein et al. 2022) Input: Sample frame x[0..N−1], long-term energy Elong(m−1) Params: ζ = 6.0, βE = 0.95 Output: Trigger decision E[m] Compute short-term and long-term energy (broadband, no FFT)

    2022

52. [52]

    Eshort(m) ← Σn |x[n]|² // total energy across ALL frequencies in one frame

53. [53]

    Elong(m) ← βE × Elong(m−1) + (1−βE) × Eshort(m) // β = 0.95: 5% new, 95% old; always updates, even during events Energy-ratio trigger

54. [54]

    R ← Eshort(m) / Elong(m) // R ≈ 1.0 during steady noise; spikes on any transient

55. [55]

    if R > ζ then E[m] ← 1 // trigger on 6× energy spike from any source at any frequency

56. [56]

    return E[m] // no band selection, no persistence, no gated update

57. [57]

    expected

    Line-by-Line Annotation ALG5.Line 1: `Eshort(m) ← Σₙ |x[n]|²` Compute the total energy in the current frame by summing the squared amplitude of all 128 samples. Unlike TSNFA which isolates 6 frequency bins, this sum includes everything: thermal noise across the full bandwidth, EMI at 60 Hz and its harmonics, digital switching burs ts, and the event signal...

58. [58]

    Long energy Elong EMA (β E = 0.95) Smoothed baseline

    Parameters TABLE V ALGORITHM 5 (DEDAR) PARAMETERS Parameter Symbol Value Reasoning Short energy Eshort Σ|x|² Total energy in current frame across ALL frequencies. Long energy Elong EMA (β E = 0.95) Smoothed baseline. Time constant ~26 s. Always updates, even during events. Ratio threshold ζ 6.0 Trigger when Eshort/Elong > 6, i.e., 6 × energy spike (7.8 dB...

    2019

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    It transmits a sample only when the current value deviates from the last transmitted value by more than a fixed threshold Δ

    Overview Send-on-Delta (SoD) is a data-reduction protocol originally designed for slowly varying process-control signals (temperature, tank level, pressure). It transmits a sample only when the current value deviates from the last transmitted value by more than a fixed threshold Δ. In process-control applications where the signal of interest changes on th...

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    2019) Input: Current sample x[n], last transmitted value xref Params: Δ (fixed delta threshold) Output: Transmit decision, updated xref Sample-by-sample comparison

    Pseudocode Algorithm 6: Send-on-Delta Triggering: SoD (Correa et al. 2019) Input: Current sample x[n], last transmitted value xref Params: Δ (fixed delta threshold) Output: Transmit decision, updated xref Sample-by-sample comparison

    2019

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    if |x[n] − xref| > Δ then // deviation from last sent value exceeds threshold

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    transmit x[n] // send current sample to sink

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    xref ← x[n] // update reference, includes noise component end if // Failure mode: noise updates xref → reference random-walks // Result: events become indistinguishable from noise deviations

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    return transmit decision

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    event detection

    Line-by-Line Annotation ALG6.Line 1: `if |x[n] − xref | > Δ then` Compare the current individual sample against the last transmitted value. Note: SoD operates sample-by-sample at 100 Hz, not frame-by-frame at 0.78 Hz. There is no temporal aggregation, no spectral analysis, and no noise-floor estimation. The core assumption is that x ref represents the “tr...

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    If Δ > event amplitude: events missed

    Parameters TABLE VI ALGORITHM 6 (SOD) PARAMETERS Parameter Symbol Value Reasoning Delta Δ Design choice If Δ < noise amplitude: every fluctuation triggers, xᴿₑᶠ random- walks. If Δ > event amplitude: events missed. No viable Δ exists. Reference x ref Dynamic Updated every transmission. In noisy environments, random-walks with noise, destroying baseline st...

    2023

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    Overview TinyML takes a fundamentally different approach from all previous algorithms. Instead of designing explicit signal- processing rules (FFT, thresholds, noise-floor tracking), it trains a neural network to learn what “normal” sensor data looks like, and flags anything that deviates as an anomaly. How it works. An autoencoder is a neural network tha...

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    2023) Input: Sample frame x[0..N−1], trained autoencoder Aθ Params: ΘML (learned anomaly threshold) Output: Trigger decision E[m] Autoencoder inference

    Pseudocode Algorithm 7: Autoencoder Anomaly Detection: TinyML (Hammad et al. 2023) Input: Sample frame x[0..N−1], trained autoencoder Aθ Params: ΘML (learned anomaly threshold) Output: Trigger decision E[m] Autoencoder inference

    2023

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    x̂ ← Aθ(x) // compress 128 → 8 → 128, reconstruct input Reconstruction error as anomaly score

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    e(m) ← ǁx − x̂ǁ² // MSE over frame: low = noise, high = anomaly Trigger if error exceeds learned threshold

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    if e(m) > ΘML then E[m] ← 1 // ΘML frozen at training time, cannot adapt to noise drift

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    return E[m] // neither network weights nor threshold update during deployment

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    Line 1: `x̂ ← Aθ(x)` Feed the current 128-sample frame through the autoencoder to produce a reconstructed output

    Line-by-Line Annotation ALG7. Line 1: `x̂ ← Aθ(x)` Feed the current 128-sample frame through the autoencoder to produce a reconstructed output. The bottleneck forces the network to represent each 128-sample frame using only 8 numbers. During training on noise-only data, the encoder learns which 8 numbers best summarise the structure of noise: its energy l...

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    Trained on noise-only frames at P₀ = 1.0

    Parameters TABLE VII ALGORITHM 7 (TINYML) PARAMETERS Parameter Symbol Value Reasoning Autoencoder Aθ Trained 128→32→8→32→128, ReLU, ~5K params. Trained on noise-only frames at P₀ = 1.0. Threshold ΘML Learned 99th percentile of training-set reconstruction errors. Frozen at deployment. Training data - Fixed P₀ Trained at base noise power P₀ = 1.0. Does not ...

    2026

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