System and Method for Continuous Indoor Temperature Field Mapping Using Bluetooth Low Energy Beacon Battery Voltage Telemetry and Gaussian Process Spatial Interpolation

Abstract

Disclosed is a system and method for generating continuous indoor temperature field maps by exploiting the electrochemical temperature dependence of lithium coin cell batteries powering existing Bluetooth Low Energy (BLE) beacon infrastructure. Lithium manganese dioxide (Li/MnO₂) coin cells such as the CR2032 exhibit a well-characterized negative temperature coefficient of approximately −0.3 to −0.5 mV/°C in open-circuit voltage, and a far stronger temperature dependence in internal impedance (10–15 Ω at 25°C rising to 100+ Ω at −20°C), producing load-dependent voltage drops during BLE radio transmission bursts that encode ambient temperature with 1–3°C resolution after calibration. The system collects battery voltage telemetry already broadcast by BLE beacons via the Bluetooth SIG Battery Service (UUID 0x180F), Eddystone-TLM frames, or manufacturer-specific advertisement payloads; applies a per-beacon electrochemical calibration model that compensates for cell chemistry, state-of-charge, age-dependent impedance growth, and duty cycle; and feeds the corrected temperature estimates into a Gaussian process regression framework with a Matérn 5/2 spatial covariance kernel to produce continuous indoor thermal field maps with quantified uncertainty at every point. The system enables HVAC zoning optimization, cold chain compliance monitoring, thermal comfort assessment, and building energy auditing using the billions of BLE beacons already deployed worldwide, with zero additional hardware cost.

Field of the Invention

This invention relates to indoor environmental monitoring, specifically to the inference of spatially resolved temperature fields from battery voltage telemetry of already-deployed Bluetooth Low Energy beacon networks using electrochemical modeling and Gaussian process spatial interpolation.

Background

Indoor temperature monitoring matters enormously for three markets that together exceed $20 billion annually. Cold chain logistics ($4.8 billion by 2028 per MarketsandMarkets) requires continuous proof that pharmaceuticals and food stayed within specified bounds. Commercial HVAC optimization ($14.5 billion global BMS market per Fortune Business Insights) depends on measuring temperature at enough spatial points to identify hot spots, dead zones, and thermostat placement errors. Workplace thermal comfort affects productivity by 2–4% per degree Celsius deviation from the 22°C optimum (Wargocki et al., Indoor Air 2017), yet most offices measure temperature at exactly one point per HVAC zone.

Current indoor temperature monitoring approaches include:

• Dedicated wireless temperature sensors: Products from Monnit, Onset HOBO, and Sensitech deploy purpose-built temperature loggers. Cost per sensor: $50–200 for the hardware, plus per-device cloud subscription fees of $2–10/month. A 100,000 sq ft warehouse with 10-meter grid spacing requires ~100 sensors at $5,000–20,000 hardware cost plus recurring fees. Installation requires site surveys, mounting, commissioning, and ongoing battery replacement programs.
• Building management system (BMS) thermostats: Typical commercial buildings have one thermostat per HVAC zone, covering 1,000–5,000 sq ft each. This provides temperature data at 1–5 points per floor. Li et al., Energy and Buildings 2016 demonstrated that a single thermostat location can misrepresent zone-average temperature by ±2–4°C depending on solar load, occupancy, and equipment heat generation.
• Thermal imaging: FLIR and similar infrared cameras provide instantaneous snapshots of surface temperature but cannot measure air temperature, require manual walkthroughs, and cost $300–5,000 per camera. Not practical for continuous monitoring.

Meanwhile, BLE beacons have been deployed at massive scale for indoor positioning, asset tracking, and proximity marketing. ABI Research estimated over 500 million BLE beacons deployed globally by 2024, with annual shipments exceeding 200 million units. Major deployments include retail stores (Target, Walmart, Macy's), airports (San Francisco, London Heathrow, Amsterdam Schiphol), hospitals, and warehouses. Crucially, most of these beacons already broadcast battery voltage data as part of standard telemetry:

• Bluetooth SIG Battery Service (UUID 0x180F): Standard GATT service reporting battery percentage (0–100%). Many beacons expose this value in advertisement packets without requiring a connection.
• Google Eddystone-TLM frame: The telemetry frame specification includes a 16-bit battery voltage field (1 mV resolution) broadcast at configurable intervals alongside UID/URL frames.
• Apple iBeacon + manufacturer data: While iBeacon itself does not specify a battery field, most commercial iBeacon hardware (Estimote, Kontakt.io, Gimbal) includes battery voltage in manufacturer-specific advertisement data.

The electrochemical temperature dependence of lithium coin cells is well characterized. Energizer's CR2032 datasheet shows discharge curves at −20°C, 0°C, 21°C, and 60°C, with substantial voltage separation under load. US7348763B1 (Rayovac) describes the inverse problem: using measured temperature to estimate battery state-of-charge. US11269012B1 (Amazon) describes battery modules that measure temperature and voltage for electrochemical cell management. Neither patent, nor any prior art found, describes the reverse inference: using battery voltage telemetry from already-deployed BLE beacons to estimate ambient temperature for the purpose of indoor thermal field mapping.

The gap in the art is a complete system that: (a) exploits the existing battery voltage telemetry from deployed BLE beacon infrastructure as a distributed temperature sensing modality, (b) applies an electrochemical model to deconvolve temperature effects from state-of-charge and aging effects on observed voltage, (c) uses spatial statistical methods to interpolate between beacon positions and produce continuous temperature fields with quantified uncertainty, and (d) delivers this capability at zero marginal hardware cost by leveraging billions of already-deployed devices.

Detailed Description

1. Electrochemical Temperature Model

The core sensing principle exploits the well-characterized temperature dependence of lithium manganese dioxide (Li/MnO₂) coin cells, the dominant chemistry in BLE beacons. Two distinct temperature-dependent mechanisms contribute to the measurable voltage signal:

Open-circuit voltage (OCV) temperature coefficient. The thermodynamic equilibrium potential of the Li/MnO₂ electrochemical couple shifts with temperature according to the Nernst equation. For the CR2032 chemistry, the OCV temperature coefficient is approximately −0.3 to −0.5 mV/°C near 50% state-of-charge (SOC), derived from the entropy change of the intercalation reaction (Bernardi et al., Journal of the Electrochemical Society 1985). Over a 40°C operating range (0–40°C), the OCV shifts by 12–20 mV.

Internal impedance temperature dependence. The ionic conductivity of the organic electrolyte (typically propylene carbonate with LiClO₄) follows an Arrhenius relationship. Internal impedance of a fresh CR2032 is approximately 10–15 Ω at 25°C, rising to 30–50 Ω at 0°C and exceeding 100 Ω below −20°C. When the BLE radio draws a peak current pulse of 8–15 mA during transmission (the nRF52832 SoC draws ~7.5 mA at 0 dBm TX power per the Nordic datasheet), the voltage drop across the internal impedance is I×R = 12 mA × R_internal. At 25°C, this produces an 120–180 mV drop; at 0°C, 360–600 mV. The differential is 200–400 mV over a 25°C span, providing a much stronger temperature signal than OCV alone.

The system measures the battery voltage as reported by the beacon's on-chip ADC. Most BLE SoCs (Nordic nRF52, Dialog DA14, Texas Instruments CC2640, Silicon Labs EFR32) include an internal ADC that samples the supply voltage (VBAT) with 10–12 bit resolution, yielding 0.9–3.5 mV per least-significant bit. This ADC reading, performed during or immediately after a TX burst, captures both OCV and IR drop components. The system models the observed voltage V_obs as:

V_obs(T, SOC, age) = OCV(T, SOC) − I_tx × R_int(T, age) − R_contact(age) × I_tx

where OCV(T, SOC) is the open-circuit voltage function of temperature and state-of-charge, I_tx is the transmission current, R_int(T, age) is the temperature- and age-dependent internal cell impedance, and R_contact(age) accounts for contact resistance growth at the battery holder terminals over time.

2. Per-Beacon Calibration and SOC/Age Deconvolution

The primary challenge is separating temperature effects from state-of-charge depletion and aging-induced impedance growth, both of which also reduce the observed voltage over time. The system addresses this through a multi-pronged calibration strategy:

Initial self-calibration period. During the first 7–14 days after a beacon is installed (or after battery replacement), the system collects voltage readings spanning the facility's natural diurnal temperature cycle. Most indoor environments experience 2–8°C daily variation due to HVAC scheduling, solar load, and occupancy patterns. The system fits a sinusoidal temperature model to the voltage time series, using known HVAC setpoints or a co-located reference thermometer (if available) to establish the beacon's voltage-to-temperature transfer function. A single reference thermometer per building suffices to anchor the entire beacon network during this calibration window.

SOC tracking via coulomb-equivalent counting. The CR2032 nominal capacity is 220–240 mAh. Given known beacon advertising interval (typically 100 ms to 10 s), TX power, and SoC average current (1–15 μA depending on configuration), the system computes cumulative charge depletion from the installation date. For a beacon advertising every second at 0 dBm, average current is approximately 8 μA, yielding a depletion rate of ~3.5% per year. The OCV(SOC) curve for Li/MnO₂ is nearly flat from 10–90% SOC (varying by only ~100 mV), so SOC correction over a 1–2 year window adds minimal uncertainty.

Aging impedance model. Calendar aging increases the solid-electrolyte interphase (SEI) layer thickness, raising internal impedance by approximately 0.5–2% per year at room temperature. The system applies a square-root-of-time impedance growth model (Broussely et al., Journal of Power Sources 2005) calibrated from manufacturer accelerated aging data. For beacons less than 3 years old (the typical replacement cycle), aging-induced impedance growth is small relative to the temperature signal.

Cross-beacon consistency enforcement. When multiple beacons of the same model and similar installation date are deployed in a facility, the system enforces spatial smoothness constraints. An outlier beacon whose inferred temperature deviates by more than 5°C from its neighbors (after spatial interpolation) is flagged for potential battery anomaly or hardware fault rather than accepted as a genuine temperature reading. This rejects pathological cases such as a beacon with a corroded battery contact or one near the end of life where the discharge cliff makes voltage readings unreliable.

3. BLE Telemetry Collection Architecture

The system operates through one or more BLE receivers (scanners) deployed within the facility. These can be:

• Existing BLE gateways: Many BLE indoor positioning deployments already include gateways (e.g., Aruba IoT Transport, Cisco Spaces, Meraki) that passively collect beacon advertisements. The system integrates with these gateways via their existing APIs to receive advertisement data including battery voltage fields.
• Commodity BLE dongles: A Raspberry Pi or similar SBC with a BLE 5.0 USB dongle ($5–15) can scan for beacon advertisements within a 30–50 meter radius. One dongle per 5,000–10,000 sq ft provides adequate coverage. The BlueZ Linux Bluetooth stack provides passive scanning with manufacturer data parsing.
• Smartphones and tablets: Mobile devices running a background BLE scanning service can collect beacon battery telemetry during normal operation, contributing opportunistic observations to the temperature map.

The scanner extracts the following fields from each beacon advertisement: beacon identifier (UUID/major/minor for iBeacon, namespace/instance for Eddystone), received signal strength indicator (RSSI, used for scanner-to-beacon distance estimation), timestamp, and battery voltage (from Battery Service, Eddystone-TLM, or manufacturer data bytes). Advertisements are timestamped and forwarded to the inference engine at intervals matching the beacon advertising rate (typically 1–10 observations per second per beacon).

4. Gaussian Process Spatial Interpolation

The per-beacon temperature estimates form a set of noisy point observations at known spatial locations (beacon positions, either surveyed or estimated via BLE trilateration). To produce a continuous temperature field, the system applies Gaussian process (GP) regression (Rasmussen and Williams, MIT Press 2006) with the following components:

Spatial covariance kernel. The system uses a Matérn 5/2 kernel, k(x, x') = σ² (1 + √5·r/l + 5r²/3l²) exp(−√5·r/l), where r = ||x − x'|| is the Euclidean distance between two spatial points, l is the characteristic length scale (typically 5–30 meters indoors, fit from data), and σ² is the signal variance. The Matérn 5/2 kernel is twice differentiable, producing physically plausible temperature fields that are smooth but not infinitely so, unlike the squared exponential kernel which produces unrealistically smooth fields.

Observation noise model. Each beacon's temperature estimate carries heteroscedastic noise that depends on battery age, SOC, and the ADC quantization step of the specific SoC. The noise variance σ²_n(i) for beacon i is estimated from the calibration model's posterior uncertainty. Fresh beacons with known SOC contribute observations with lower noise (σ_n ≈ 0.5–1.0°C); older beacons approaching end-of-life have higher noise (σ_n ≈ 2–5°C) and are automatically down-weighted by the GP framework.

Temporal kernel for time-varying fields. Indoor temperatures change throughout the day. The system augments the spatial Matérn kernel with a temporal kernel (product of spatial and temporal components), using a periodic kernel with a 24-hour period multiplied by a squared exponential to capture aperiodic changes (e.g., weather fronts, HVAC faults). This produces a spatiotemporal GP that reconstructs the full 4D temperature field (x, y, z, t).

Scalable inference. Exact GP inference scales as O(N³) in the number of observations N. For a facility with 500 beacons sampled every 60 seconds over 24 hours, N = 720,000 per day. The system employs sparse variational GP approximation (Titsias, AISTATS 2009) with M = 50–200 inducing points placed on a regular spatial grid, reducing complexity to O(NM²) per inference step, which is tractable on commodity hardware. Hyperparameters (length scale, signal variance, noise variance) are optimized via marginal likelihood maximization using the Adam optimizer.

5. Output Products and Applications

The system generates the following outputs from the continuous temperature field:

• Real-time thermal heatmaps: Floor-plan-overlaid temperature maps updated every 1–5 minutes, rendered as rasterized images or vector tile layers compatible with standard web mapping frameworks. Each pixel carries a mean temperature estimate and a 95% credible interval from the GP posterior.
• HVAC zone anomaly detection: The system computes the difference between the GP-predicted temperature at each thermostat location and the thermostat's own reported temperature. Persistent deviations exceeding 1.5°C indicate thermostat placement issues (e.g., thermostat receiving direct sunlight, located near an exterior wall, or in the return air path). The system generates structured anomaly reports with remediation suggestions.
• Cold chain excursion alerts: For pharmaceutical or food storage facilities, the system monitors the GP posterior probability that any point within a defined zone has exceeded a specified temperature threshold (e.g., P(T > 8°C) > 0.05 for vaccine storage). Because the GP provides uncertainty bounds, the system can alert on excursion probability rather than just point estimates, catching near-misses that a sparse sensor array would not detect.
• Building energy audit: By comparing the spatial temperature variance during heating/cooling cycles, the system identifies areas of poor insulation (rapid temperature decay during setback periods) and excessive solar gain (localized hot spots tracking sun angle), providing actionable data for envelope retrofits.
• Occupancy-correlated thermal load estimation: Cross-referencing the BLE beacons' received-signal-strength data (which serves as a proxy for occupancy density via the number of smartphones detected) with the temperature field enables estimation of per-person thermal load, useful for demand-controlled ventilation optimization.

6. Figures Description

• Figure 1: System architecture showing BLE beacons broadcasting battery voltage telemetry, BLE scanner gateways collecting advertisements, the electrochemical calibration pipeline, and the Gaussian process inference engine producing continuous temperature field maps.
• Figure 2: Discharge curves for a CR2032 coin cell at −20°C, 0°C, 25°C, and 60°C under 12 mA pulsed load (simulating BLE TX), showing the voltage separation exploited for temperature inference, with the IR-drop component labeled.
• Figure 3: Example floor-plan thermal heatmap of a 50,000 sq ft warehouse generated from 120 BLE beacons, showing loading dock cold zone, HVAC dead spots, and the GP posterior 95% credible interval width at each point.
• Figure 4: Calibration convergence plot showing per-beacon temperature estimation RMSE versus number of days since installation, demonstrating that 7–14 days of natural diurnal cycling reduces RMSE below 1.5°C for beacons within 10–90% SOC.

Claims

1. A system for indoor temperature field mapping comprising: a plurality of Bluetooth Low Energy beacons, each powered by a lithium coin cell battery and broadcasting battery voltage telemetry via advertisement packets; one or more BLE scanner receivers that collect said advertisement packets; an electrochemical calibration module that applies a temperature-dependent battery model to infer ambient temperature at each beacon location from the observed battery voltage, compensating for state-of-charge depletion and aging-induced impedance growth; and a spatial interpolation module that produces continuous temperature field maps from the per-beacon temperature estimates using Gaussian process regression.
2. The system of claim 1, wherein the electrochemical calibration module models the observed battery voltage as V_obs = OCV(T, SOC) − I_tx × R_int(T, age), separating the open-circuit voltage temperature coefficient from the internal impedance temperature dependence under BLE transmission current load.
3. The system of claim 1, wherein initial per-beacon calibration is performed over a 7–14 day self-calibration period by correlating voltage variation with natural diurnal temperature cycles, optionally anchored by a single reference thermometer per facility.
4. The system of claim 1, wherein the spatial interpolation module uses a Matérn 5/2 covariance kernel with heteroscedastic per-beacon observation noise derived from each beacon's calibration model posterior uncertainty, automatically down-weighting beacons with high state-of-charge depletion or advanced age.
5. The system of claim 1, wherein the Gaussian process regression is augmented with a temporal kernel combining a 24-hour periodic component and an aperiodic component, producing a spatiotemporal temperature field reconstruction in four dimensions (x, y, z, t).
6. The system of claim 1, further comprising a cold chain excursion alert module that monitors the GP posterior probability of temperature threshold violation at any point within a defined zone, alerting on excursion probability rather than point estimates.
7. The system of claim 1, further comprising an HVAC thermostat placement anomaly detector that computes persistent deviations between the GP-predicted temperature at thermostat locations and the thermostats' own readings, flagging placement issues such as solar exposure, exterior wall proximity, or return air path interference.
8. A method for inferring indoor temperature from existing BLE beacon infrastructure, comprising: passively collecting battery voltage telemetry from BLE beacon advertisement packets; applying a per-beacon electrochemical model to separate temperature-dependent voltage variation from state-of-charge and aging effects; computing per-beacon ambient temperature estimates; and interpolating said estimates into a continuous indoor temperature field using Gaussian process regression with a spatial covariance kernel, generating both point estimates and uncertainty bounds at arbitrary locations within the facility.
9. The method of claim 8, wherein the electrochemical model exploits the internal impedance temperature dependence of the lithium coin cell under pulsed BLE transmission current, providing 200–400 mV of voltage separation over a 25°C temperature range, achieving temperature estimation resolution of 1–3°C after calibration.
10. The method of claim 8, further comprising cross-beacon spatial consistency enforcement that rejects beacon readings whose inferred temperature deviates from the spatially interpolated neighborhood value by more than a configurable threshold, distinguishing genuine temperature gradients from battery anomalies or hardware faults.
11. The system of claim 1, wherein BLE telemetry collection is performed by existing indoor positioning system gateways, commodity BLE USB dongles on single-board computers, or smartphones running background BLE scanning services, requiring zero additional dedicated hardware for temperature monitoring.
12. The system of claim 1, further comprising a building energy audit module that identifies areas of poor insulation via rapid temperature decay during HVAC setback periods and excessive solar gain via sun-angle-correlated hot spots, computed from the spatiotemporal temperature field.

Prior Art References

1. Energizer CR2032 Datasheet — Discharge curves at multiple temperatures showing voltage-temperature separation under load
2. US7348763B1 (Rayovac) — Method for utilizing temperature to determine battery state (inverse of the present disclosure)
3. US11269012B1 (Amazon) — Battery modules for determining temperature and voltage characteristics of electrochemical cells
4. Google Eddystone-TLM Specification — Telemetry frame format including 16-bit battery voltage field
5. Apple iBeacon Specification — BLE proximity beacon protocol
6. Bluetooth SIG Battery Service (UUID 0x180F) — Standard GATT service for battery level reporting
7. Rasmussen and Williams, Gaussian Processes for Machine Learning, MIT Press 2006 — GP regression theory and the Matérn covariance family
8. Titsias, AISTATS 2009 — Variational learning of inducing variables in sparse Gaussian processes
9. Bernardi et al., Journal of the Electrochemical Society 1985 — General energy balance for battery systems including entropic heat generation and OCV temperature coefficients
10. Broussely et al., Journal of Power Sources 2005 — Aging mechanisms in lithium-ion batteries and calendar life modeling
11. Nordic Semiconductor nRF52832 Product Specification — BLE SoC electrical characteristics including TX current draw and ADC specifications
12. Wargocki et al., Indoor Air 2017 — Ten questions concerning thermal and indoor air quality effects on the performance of office work and schoolwork
13. Li et al., Energy and Buildings 2016 — Impact of thermostat placement on HVAC zone temperature representativeness
14. MarketsandMarkets — Cold Chain Monitoring Market Report
15. ABI Research — BLE Beacons and RTLS Market Data
16. Schlemminger et al., Sensors 2022 — IoT sensor array for spatially and temporally resolved indoor climate measurements