41-EFT.WP.Comms.Navigation v1.0 | Chapter 9: Robustness — NLOS/Multipath/Occlusion Detection & Mitigation

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Chapter 9: Robustness — NLOS/Multipath/Occlusion Detection & Mitigation

I. Objectives & Applicability

• Provide minimal usable threat–detection–mitigation schemes for NLOS/multipath/occlusion, covering channels TOA/TDOA/AOA/FOA/RSS/CarrierPhase, and the interfaces to Chapter 7 dynamics priors and Chapter 8 filtering/graph fusion.
• All formulas/symbols/definitions are in English and wrapped in backticks. Whenever arrival-time terms are present, use the selected T_arr convention and explicitly declare the path gamma(ell) and measure d ell.

II. Problem Modeling & Equivalent Forms

• S90-1 (Equivalent bias/variance model)
  For any observation y, under NLOS/multipath write
  y = h(x) + b_NLOS + ε, with ε ~ 𝒟(0, Σ_y). The term b_NLOS can be zero-mean random or a deterministic bias (map/ray-based).
• S90-2 (Mixture likelihood)
  Robust modeling as
  p(y|x) = π_LOS 𝒩( h(x), Σ_LOS ) + (1−π_LOS) 𝒩( h(x)+μ_NLOS, Σ_NLOS ), with π_LOS ∈ [0,1] provided by a detector.
• S90-3 (Occlusion & visibility)
  Use visibility 𝒱(r,anchor) ∈ {0,1} or probability p_vis ∈ [0,1]. If 𝒱=0, disable or downweight the channel.
• S90-4 (Nonstationarity & drift)
  Track environment changes via sliding-window statistics stats_t or drift detectors (CUSUM/ADWIN) to refresh thresholds/params.

III. Channel Features & Detectors (Dual Track: Feature–Threshold / Learning)

• S90-5 (TOA/TDOA features)
  Excess delay τ_ex = y_TOA − h_TOA(x̂), RMS delay spread τ_rms, CIR peak ratios, and the deviation τ_g − T_arr.
• S90-6 (AOA features)
  Beam/space-spectrum main-lobe width, inter-peak ratio, angular residuals Δθ, Δφ vs. geometric prediction n̂(x̂).
• S90-7 (FOA features)
  Short-window frequency variance, residual between f_D and −(f_c/c_ref)(v_rel·n̂), ridge sharpness.
• S90-8 (RSS features)
  Rician K-factor, log-domain variance, fast-fading correlation length, mean collapse due to occlusion.
• S90-9 (Carrier-phase features)
  Phase-jump rate, cycle-slip tests (narrow-lane/dual-frequency), residual periodicity.
• S90-10 (Vision/odometry occlusion)
  Track ratio, reprojection-error tails, optical-flow consistency; wheel-speed gaps and ground-constraint violations.
• M9-1 (Feature→score→flags)
  Input raw/intermediate channel data → compute feature vector ϕ → produce score ∈ [0,1] and NLOS_flag/occlusion_flag.

IV. Statistical Thresholds & Learning-Based Discrimination

• S90-11 (Statistical)
  Mahalanobis gating d^2 = r^T S^{-1} r > τ (set τ by χ^2_{k,α}).
• S90-12 (Supervised / semi-supervised)
  score = σ( w^T ϕ ) or g(ϕ) (GBDT/lightweight DL). Semi-supervised self-training with consistency and temperature warm-start to reduce domain shift.
• S90-13 (Calibration & interpretability)
  Calibrate score to probability via temperature scaling/Platt; log AUC/ECE and the threshold τ_score.
• M9-2 (Detector training/update)
  Offline labels or weak supervision → cross-validate → export compact weights & thresholds; online drift triggers recalibration.

V. Mitigation Strategies (Reweight, Correct, Reconstruct, Censor)

• S90-14 (Reweight/deflate)
  For suspicious observations set w = π_LOS, update Σ_y ← Σ_y / w + (1−w)Σ_NLOS or use Dynamic Covariance Scaling (DCS).
• S90-15 (Bias correction)
  Ray-trace/map-based μ_NLOS = f(map,ray); mapless regression μ̂_NLOS(ϕ) when maps are absent.
• S90-16 (Censoring & soft gating)
  If w < τ_drop or 𝒱=0, drop the factor/measurement; otherwise apply robust kernels Huber/Cauchy/Tukey.
• S90-17 (Path reconstruction)
  For multipath, attempt multi-peak decomposition (CIR/space spectrum) and insert discrete hypotheses (MHT/switchable constraints) in the factor graph.
• M9-3 (Mitigation pipeline)
  detect → score → reweight/deflate → (correct bias) → robust-solve → audit.

VI. Multi-Sensor Consistency & Robust Graph/Filter Layers

• S90-18 (Cross-channel consistency)
  Joint residual checks between FOA and TOA/geometry; cross-validate AOA with occlusion maps.
• S90-19 (Robust factor graphs)
  Switchable constraints, heteroscedastic modeling (GNC/Geman–McClure), Student-t factors.
• S90-20 (Robust filtering)
  ES-EKF residual gating & IRLS; UKF Bernoulli/mixture measurement updates; PF hypothesis weight rescaling.
• M9-4 (Unified robust adapter)
  Plug score→weight→cov adapters at build_factors/update for graphs/filters alike.

VII. Adaptive to Nonstationary Environments

• S90-21 (Drift detection)
  CUSUM/ADWIN on the distributions of score/r, alarming and refreshing thresholds/models.
• S90-22 (Online learning)
  Sliding-window ERM + regularization with small steps; keep rule-based fallbacks for auditability.
• S90-23 (Scene tagging)
  Record scene_tag ∈ {indoor, urban, highway, forest, factory,...} in the dataset to select config sets.

VIII. Data Contract (Required/Recommended Fields for This Chapter)

unit_system: "SI"

robust:

nlos_flag: "<bool>"

occlusion_flag: "<bool>"

score: "<0..1>" # calibrated LOS probability

features:

toa: {tau_ex: "<s>", tau_rms: "<s>", cir_peaks: "<list>"}

aoa: {beamwidth: "<rad>", peak_ratio: "<dB>", dtheta: "<rad>", dphi: "<rad>"}

foa: {var_f: "<Hz^2>", ridge_sharpness: "<unitless>"}

rss: {K_rician: "<dB>", logvar: "<dB^2>"}

cp: {cycle_slip_rate: "<1/s>", phase_jump: "<rad>"}

weights:

w_channel: {"TOA": "<0..1>", "TDOA": "<0..1>", "AOA": "<0..1>", "FOA": "<0..1>", "RSS": "<0..1>", "CP": "<0..1>"}

bias_correction:

model: "map-ray|learned|none"

mu_nlos: "<s|rad|Hz|dB>" # per-channel units

arrival_time:

convention: "pulled_const|integrand"

delta_form: "c_ref^-1 * ∫ n_eff dℓ" # or "∫ (n_eff/c_ref) dℓ"

gamma: "piecewise: free|fixture|substrate|device|environment"

d_ell: "m"

covariance:

Σ_y: "<block-diagonal or sparse>" # after robust deflation

logging:

auc: "<0..1>", ece: "<0..1>", drift_alarms: "<count>"

references:

- "EFT.WP.Comms.Navigation v1.0:Ch.3 S30-*"

- "EFT.WP.Comms.Navigation v1.0:Ch.4 S40-*"

- "EFT.WP.Comms.Navigation v1.0:Ch.5 S50-*"

- "EFT.WP.Comms.Navigation v1.0:Ch.8 S80-*"

IX. Implementation Bindings (Interface Prototypes)

• I9-1 extract_robust_features(raw, meta) -> {ϕ, stats}
• I9-2 score_nlos(ϕ, model) -> {score, nlos_flag, ci}
• I9-3 robust_reweight(y, score, cfg) -> {w, Σ_y_updated}
• I9-4 correct_bias(y, map_or_net) -> {y_corr, μ̂_NLOS}
• I9-5 switchable_factor(y, score, cfg) -> {factor, switch_var}
• I9-6 drift_monitor(scores, residuals) -> {alarms, new_thresholds}

X. Quality Gates (This Chapter)

• Q1 Convention consistency: any channel involving T_arr must include convention/delta_form/gamma(ell)/d_ell in the dataset.
• Q2 Units/dimensions: s/rad/Hz/dB present (SI/engineering); all expressions pass check_dim.
• Q3 Covariance consistency: after reweight/deflation, update the corresponding blocks of Σ_y; censoring/gating must be reflected in the graph/filter structure.
• Q4 Auditable detectors: output AUC/ECE/thresholds/drift alarms; calibrated score matches actual FPR/TPR.
• Q5 Robust solving: switchable-constraint variables converge stably; avoid ill-conditioned priors or sparsity destruction.

XI. Cross-Volume References & Anchors (This Chapter)

1. Cross-volume (fixed style): this volume Ch. 3 (path/arrival/frequency), Ch. 4 (observation models), Ch. 5 (geometry & DOP), Ch. 7 (dynamics), Ch. 8 (fusion estimation).
2. Anchors in this chapter:
   • Minimal statements: S90-1—S90-23
   • Workflows: M9-1—M9-4
   • Interfaces: I9-1—I9-6

XII. Summary
Using equivalent bias/variance and mixture likelihoods, this chapter unifies the treatment of NLOS/multipath/occlusion, delivering an executable loop of features → detection → reweighting → correction → robust solving, and writing scores/flags and covariance updates into data contracts and interfaces—ensuring coherent, auditable coupling with geometry, synchronization, dynamics, and fusion estimation.