Smart spaces and ambient intelligence (occupancy, non-camera sensing, placement)

"A camera in the ceiling knows what you look like. A CO2 sensor only knows that you are breathing. In a bedroom, that difference is the whole product."

A Tactful AI Agent

This section assumes you are comfortable with sensor measurement models and noise (Chapter 2), with change detection on streams (Chapter 12), and with the building-sensor context introduced in Chapter 39. Where we lean on radio and radar physics we point to the dedicated chapters rather than re-deriving them.

Occupancy is the atom of a smart space

Almost every smart-space behavior reduces to a question about people: is anyone here (presence), how many (count), where are they (localization), and what are they doing (activity). Presence is binary and cheap; count is a positive integer and much harder; localization and activity are progressively richer and progressively more invasive. The design discipline is to demand the weakest quantity that satisfies the use case. A corridor light needs presence. Demand-controlled ventilation needs count. A fall-response system for assisted living needs coarse localization plus an activity label, but deliberately not identity.

Why does this matter beyond privacy? Because each rung up the ladder costs sensing bandwidth, compute, and calibration effort, and each rung introduces new failure modes. A presence detector that mistakes a fluttering curtain for a person wastes a few watts. A count estimator that is off by two people can over-ventilate a room by fifty percent, or under-ventilate it into a stuffy, high-CO2 state that measurably degrades cognitive performance. The stakes rise with the richness of the claim, so you climb the ladder only as far as the application forces you.

The non-camera sensing menu

Each non-camera modality trades cost, coverage, and the richness of what it can infer. Knowing their failure modes is more useful than knowing their datasheets, because the failures are what your model has to survive in deployment.

• Passive infrared (PIR). Detects moving heat gradients across a segmented lens. Pennies per unit, microwatts of power, and the workhorse of occupancy lighting. Its fatal flaw is that it senses motion, not presence: a person reading quietly at a desk vanishes from PIR within a minute, which is why conference-room lights infamously switch off on still occupants.
• CO2 and air-quality. Exhaled carbon dioxide accumulates in proportion to how many people breathe in a room. Slow (minutes of lag) but uniquely good at counting, and immune to the stillness problem. We build a count estimator from CO2 below.
• mmWave radar. A 60 GHz FMCW chip resolves range, velocity, and angle, giving presence-through-stillness (it sees the micro-motion of breathing) plus coarse localization, with no image. It has become the default for privacy-sensitive presence in premium thermostats and elder-care sensors. See Chapter 44 for the signal processing.
• RF and WiFi sensing. Channel state information from existing WiFi access points shifts as bodies move through the multipath field, enabling device-free presence and crude motion mapping with hardware already on the ceiling. The physics and its brittleness under furniture changes are covered in Chapter 47.
• Thermopile arrays. Low-resolution (8x8 to 32x24) thermal grids see warm bodies as blobs. Enough to count and localize seated people, coarse enough that the vendor can honestly say it is not a camera. Contrast with full thermal imaging in Chapter 45.
• Acoustic, capacitive, and door counters. Microphones (event detection, not recording), capacitive floor and seat sensors, and infrared beam-break counters at doorways each answer a narrow question cheaply, and shine as corroborating evidence in a fusion stack.

Counting people from the air they breathe

CO2-based counting rests on a mass balance. At steady state, the CO2 an occupied room accumulates above outdoor levels is set by how many people exhale versus how fast fresh air dilutes them. If \(C_\text{in}\) and \(C_\text{out}\) are indoor and outdoor concentrations, \(G\) is the CO2 generation rate per person, and \(Q\) is the volumetric ventilation rate, then the steady-state occupant count is

The transient before steady state follows a first-order response with time constant \(\tau = V/Q\) for room volume \(V\), which is why CO2 lags occupancy by several minutes. The estimator below inverts the steady-state relation and is the kind of physics-grounded baseline you should always build before reaching for a neural model.

import numpy as np

# Physical constants (SI-ish, tuned for a small meeting room)
G_PER_PERSON = 0.0052    # m^3/s of CO2 exhaled by a seated adult (~5.2e-3 L/s)
C_OUTDOOR    = 420e-6    # outdoor CO2 mole fraction (420 ppm)

def occupancy_from_co2(co2_ppm, ventilation_m3s):
    """Steady-state occupant count from indoor CO2 and known ventilation."""
    c_in = np.asarray(co2_ppm) * 1e-6            # ppm -> mole fraction
    excess = np.clip(c_in - C_OUTDOOR, 0, None)  # never negative
    n = ventilation_m3s * excess / G_PER_PERSON
    return np.round(n).astype(int)

# A room ventilated at 40 L/s, sampled every few minutes as it fills up
co2_trace = [430, 512, 640, 815, 980, 1120, 1090]  # ppm
counts = occupancy_from_co2(co2_trace, ventilation_m3s=0.040)
print(counts)   # -> [ 0  1  2  4  5  6  6 ]

Notice what the baseline exposes: the estimate is only as good as your knowledge of \(Q\). In a variable-air-volume building the ventilation rate is itself a controlled, changing quantity, so a robust system co-estimates \(Q\) from damper positions or treats it as a latent state. This is exactly the kind of coupled-unknowns problem that pushes teams from a closed-form inverse toward the Bayesian filtering of Chapter 9.

Placement: the design decision that dwarfs the model

You can pick the perfect modality and the perfect model and still fail, because a sensor measures only the volume it can physically reach. PIR needs line of sight and is blinded by cubicle partitions; radar reflects off metal and floods small rooms with multipath; CO2 sensors near a doorway read the corridor, not the room. Placement is a coverage-optimization problem, and it usually matters more than a few points of model accuracy.

Formally, given candidate mounting locations and a set of zones that must be covered, choosing the fewest sensors that cover every zone is a set-cover problem: NP-hard in general, but its objective is submodular, so a greedy algorithm (repeatedly add the sensor that covers the most still-uncovered zones) is guaranteed to land within a factor of \((1 - 1/e)\), about 63 percent, of the optimum. That guarantee, plus its trivial implementation, makes greedy the default placement planner. For dense sensor networks whose readings are spatially correlated, the same submodular framing extends to placing sensors where they most reduce predictive variance, which connects to the graph and spatial models of Chapter 54.

Two placement rules earn their keep in practice. First, place the corroborating sensor and the anchor sensor to have independent failure modes: putting the CO2 sensor in the return duct (integrating the whole room) while the radar watches the seating zone means a curtain fooling the radar does not also fool the CO2. Second, mount for the physics, not for convenience: a thermopile array wants a top-down view of chairs, a PIR wants to look across the traffic it must catch, and neither belongs where the electrician finds it easiest to run conduit.

Ambient intelligence, on the edge and private by construction

The payoff of this modality discipline is that smart-space inference runs comfortably at the edge. PIR, CO2, thermopile, and even radar occupancy models are small enough for a microcontroller (Chapter 61), so the raw stream never leaves the room. When you do need to improve a model across a fleet of buildings, federated learning lets each site contribute gradients without shipping occupancy traces to a server, keeping the privacy promise intact end to end (Chapter 64). Ambient intelligence, done well, is a system that perceives just enough to act and forgets everything else by design.

What's Next

In Section 71.5, we step outdoors and scale up: environmental and climate sensing, where the room becomes a watershed or a city. We will trade the placement problem for spatial interpolation across sparse stations, add early-warning detection for floods and air-quality events, and confront the messy, wonderful world of citizen-sensing networks where the sensors are cheap, plentiful, and only sometimes trustworthy.