08-EFT.WP.Core.Sea v1.0 | Appendix B — Calibration Workflow Templates

Home ／ Docs-Technical WhitePaper ／ 08-EFT.WP.Core.Sea v1.0

Appendix B — Calibration Workflow Templates

I. Scope and Versioning

• Applies to
  Calibration of amplitude, frequency response, sampling/timebase, environmental correction, and path/arrival-time for sensor.class ∈ {"accel","mic","rf","imu","temp","pressure"}.
• Version anchors
  sensor.cal_id (calibration version); filt.H_rev (filter-chain revision); path.toa_model_rev (arrival-time model); io.manifest_rev (manifest revision).
• Common conventions
  Linear calibration: x_corr = A_gain * ( x_raw - B_bias ) + C_offset.
  Timebase model: ts_i(t) = alpha_i * tau_mono + beta_i.
  Arrival-time dual forms:
  T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell ) and T_arr = ( ∫ ( n_eff / c_ref ) d ell ); discrepancy
  delta_form = | ( 1 / c_ref ) * ( ∫ n_eff d ell ) - ( ∫ ( n_eff / c_ref ) d ell ) |.
  Uncertainty: U = k * u_c.

II. Common Preparation and Record Template (CAL-0)

• Prepare
  Traceable reference certificates and validity; env.RefCond and control ranges; sampling config acq.fs, acq.window, filt.chain.
  Timebase & sync: time.sync_ref ∈ {"ptp","gps","ntp"}, record alpha, beta, J, and uncertainties u_alpha, u_beta.
• Record
  Metadata: sensor.sid, sensor.model, sensor.serial, sensor.cal_id_prev.
  Data blocks: time.ts_start, time.ts_end, acq.fs_hat, env.temp, env.hum, env.press.
  Results: coefficients, residuals, coverage, quality.q_score, U, acceptance decision.

III. Linear Amplitude Calibration (Mx-C1)

1. Objective
   Estimate A_gain, B_bias, C_offset; verify linear region and saturation; cover target DR.
2. Procedure
   • Under env.RefCond, apply N step or evenly spaced references x_ref[k], acquire x_raw[k], k=1..N.
   • Fit x_corr = A_gain * ( x_raw - B_bias ) + C_offset, compute residuals r[k] = x_corr[k] - x_ref[k].
   • Assess linearity NL = max_k | r[k] | / range(x_ref) and R2.
   • Compute expanded uncertainty U = k * u_c, with u_c combining repeatability and reference uncertainty.
3. Acceptance
   NL <= eps_lin; R2 >= 1 - eps_r2; saturation threshold above target top by margin_db; U <= U_max.
4. Persist
   sensor.A_gain, sensor.B_bias, sensor.C_offset, quality.q_score, env.RefCond, U, sample coverage.

IV. Frequency Response & Anti-Aliasing Calibration (Mx-C2)

1. Objective
   Identify system transfer H(f) and group delay tau_g(H); set anti-alias parameters f_c, BW, stop-band attenuation.
2. Procedure
   • Use sweep or multitone; capture X_in(f) and X_out(f); estimate H_meas(f) = X_out(f) / X_in(f).
   • Compute phase phi(f) and group delay tau_g(H) = - d phi / d omega (numeric derivative, omega = 2 * pi * f).
   • Design/validate filt.chain; set f_c in [0.4, 0.45] * fs; meet passband ripple and stopband goals.
   • Bound residual alias energy E_alias approx ∑_{k ≠ 0} ∫ | X_in(f - k * fs ) | * | H(f) | d f.
3. Acceptance
   Passband ripple ≤ r_pb_db; stopband ≥ A_s_db (with BW_alias ≥ 0.55 * fs); max |tau_g(H)| within window below tau_g_max.
4. Persist
   filt.H_rev, filt.f_c, filt.BW, filt.tau_g, spec.window, spec.method, E_alias.

V. Sampling Rate & Timebase Calibration (Mx-C3)

1. Objective
   Calibrate fs and fs_hat; estimate alpha, beta, J to ensure cross-device consistency.
2. Procedure
   • From a reference pulse train (or known-period signal) compute fs_hat = ( N - 1 ) / ( tau_{N-1} - tau_0 ).
   • Align to external reference; fit ts_i(t) = alpha_i * tau_mono + beta_i to obtain alpha_i, beta_i.
   • Estimate RMS jitter J and uncertainties u_alpha, u_beta.
3. Acceptance
   Relative rate error |fs_hat - fs_nom| / fs_nom <= eps_fs; |alpha_i - 1| <= eps_alpha; |beta_i| <= eps_beta; J <= J_max.
4. Persist
   acq.fs_hat, time.alpha, time.beta, time.J, time.u_alpha, time.u_beta.

VI. ADC Quantization & Noise Calibration (Mx-C4)

1. Objective
   Evaluate ENOB, quantization noise, spurs; verify DR.
2. Procedure
   • Inject a pure tone; choose window and fft_len per Chapter 5; estimate SNR_dB via sine-fit or FFT.
   • Compute ENOB = ( SNR_dB - 1.76 ) / 6.02; separate SFDR and noise floor.
   • Verify clipping probability and AGC settings (if used).
3. Acceptance
   ENOB >= ENOB_min; SFDR >= SFDR_min; clip_rate <= clip_max.
4. Persist
   sensor.ENOB, sensor.DR, quality.clip_rate, spec.S_xx_units, tone frequency & amplitude.

VII. Environmental Correction Model Calibration (Mx-C5)

1. Objective
   Build corr_env(x; RefCond) to regress readings under varying conditions back to env.RefCond.
2. Model shapes (examples)
   Additive: x_env = x_raw + k_T * ( temp - RefCond.temp ) + k_H * ( hum - RefCond.hum ) + k_P * ( press - RefCond.press ).
   Multiplicative: x_env = x_raw * ( 1 + a_T * Delta_T + a_H * Delta_H + a_P * Delta_P ).
3. Procedure
   • Design a matrix covering temp/hum/press; collect paired {x_raw, x_ref, env}.
   • Fit coefficients; compute residuals r_env and cross-validation error.
   • Combine uncertainties to report U = k * u_c.
4. Acceptance
   In-domain max residual <= eps_env_abs; extrapolation slopes bounded; U <= U_max.
5. Persist
   env.RefCond, env.correction_applied, model coefficients and valid domain, U.

VIII. Arrival Time & Path Calibration (Mx-C6)

1. Objective
   Calibrate T_arr and n_eff conventions on a known gamma(ell); report delta_form.
2. Procedure
   • Build a path with known geometry; record L_gamma = ( ∫ 1 d ell ), c_ref, and environmental settings affecting n_eff.
   • Estimate measured arrival time T_arr_meas = estimate_toa( sig, method="xcorr" ).
   • Compute modelled arrival time:
     • Form 1: T_arr_1 = ( 1 / c_ref ) * ( ∫ n_eff d ell ).
     • Form 2: T_arr_2 = ( ∫ ( n_eff / c_ref ) d ell ).
   • Report delta_form = | T_arr_1 - T_arr_2 | and bias | T_arr_meas - T_arr_model |.
3. Acceptance
   delta_form <= eps_form; | T_arr_meas - T_arr_model | <= eps_toa.
4. I80 binding
   path_integral(n_eff, gamma, c_ref); enforce_arrival_time_convention(trace); estimate_toa(sig,"xcorr").
5. Persist
   path.gamma_desc, path.L_gamma, path.c_ref, path.n_eff_model, path.T_arr_meas, path.T_arr_model, path.delta_form.

IX. Uncertainty Evaluation & Combination (Mx-C7)

1. Objective
   Provide combined standard uncertainty u_c and expanded uncertainty U for y = f( x_1, ..., x_m ).
2. Conventions
   Linear propagation: u_c^2 approx J Σ J^T, with J = ( ∂f/∂x_1, ..., ∂f/∂x_m ), and Σ the input covariance.
   With correlations: u_c^2 = ∑ c_i^2 * u_i^2 + 2 * ∑_{i<j} ρ_{ij} * c_i * c_j * u_i * u_j.
   Expanded uncertainty: U = k * u_c (typ. k=2).
3. Procedure
   • Classify sources (Type A repeatability; Type B spec/model/resolution).
   • Estimate u_i and correlation ρ_{ij}, assemble Σ.
   • Compute u_c, choose coverage k, obtain U.
4. Persist
   env.u_c, env.k, env.U, and a source contribution breakdown.

X. Drift Monitoring & Re-Calibration Triggers (Mx-C8)

1. Metrics
   Drift D = || mu_x - mu_ref || / sigma_ref; quality q_score ∈ [0,1]; missing mask m ∈ {0,1}.
2. Triggers
   D >= D_warn → observe; D >= D_recal → re-calibrate; q_score <= q_min or clip_rate >= clip_max → troubleshoot.
3. Actions
   • monitor_drift(baseline, current, fields);
   • When triggered, run the relevant Mx-C1..C5 flows;
   • Update sensor.cal_id and version anchors; raise_alert(kind="recal", payload=...).

XI. Data Commit and Manifest Template (CAL-IO)

• Minimum required (aligned with Appendix A)
  Include sensor.* identity/coefficients, acq.*, time.*, filt.*, spec.*, env.*, path.*, quality.*, io.*.
• Version locking
  In io.manifest_rev record filt.H_rev, spec.window, spec.method, path.toa_model_rev, env.RefCond.

XII. Audit Checklist (CAL-QA)

• Metrology & conventions
  fs >= 2 * f_max; H(f) and tau_g(H) reported; delta_form computed; U = k * u_c reported.
• Consistency
  All delays/jitter in tau_mono; ts for release/audit; naming conflict rule enforced (T_fil vs T_trans).
• Traceability
  Data, scripts, coefficients, versions, and report mutually referenced and replayable.

XIII. Reference Script Skeleton (I80 Binding)

# register and load calibration

sns = register_sensor(model="ADX-1234", serial="SN-A1B2C3", meta={"class":"accel"})

cal = load_calibration(sid=sns, cal_id="CAL-2025-01")

# sampling & sync

configure_sampling(sid=sns, fs=20000.0, gain=None)

sync = sync_clocks(sids=[sns], method="ptp", ref="lab-ptp-1")

sync_stats = measure_skew_offset(sids=[sns], window=60.0)

# filter & response

fref = design_filter(kind="lp", params={"order":6, "f_c":9000.0, "ripple_db":0.1, "stop_db":80.0})

sig_f = filter_apply(sig=raw_block, filt=fref)

# FFT/PSD & ENOB

S = psd(sig=sig_f, method="welch", seg=16, overlap=0.5)

F = feature_extract(sig=sig_f, feats=["SNR_dB","THD","kurtosis"])

# environment correction

data_corr = apply_env_correction(data=sig_f, ref={"temp":23.0,"hum":45.0,"press":101325.0})

# time-of-arrival & path

toa = estimate_toa(sig=data_corr, method="xcorr")

tarr = path_integral(n_eff="n_air_std_v1", gamma="bench-straight-1m", c_ref=343.0)

enforce_arrival_time_convention(trace={"T_arr_meas":toa,"T_arr_model":tarr})

XIV. Exceptions and Rollback Template (CAL-RB)

• Input anomalies
  If references are unstable/out-of-range: pause, set quality.alert={kind:"ref_unstable"}, discard current block.
• Model non-convergence
  Switch to a secondary model (e.g., multiplicative → additive); record rationale and affected span.
• Convention conflict
  If delta_form > eps_form, lock c_ref and n_eff sources first, then re-run path or replace gamma(ell) description.

XV. Report Structure Template (CAL-REP)

• Overview: device, purpose, scenario, env.RefCond.
• Methods: H(f), fs_hat, alpha, beta, model(s), windowing.
• Results: coefficients & ranges, E_alias, ENOB, U, delta_form.
• Acceptance: thresholds vs results; pass/fix list.
• Versions: sensor.cal_id, filt.H_rev, path.toa_model_rev, io.manifest_rev.

XVI. Reuse and Cross-Volume Anchors

• Arrival time & path: c_ref, gamma(ell), d ell, L_gamma, n_eff(x,t), T_arr (see Chapter 8 and the Energy Filaments companion).
• Concurrency & lake: chan, cap, q_len, bp, W_q (see Core.Threads); serialization & manifests (see Chapter 7 and Appendix A).

XVII. Conclusions — Execution Highlights