Respiratory-Amplification Semi-Static Occupancy

• RASSO is a framework that amplifies low-amplitude respiratory signals to detect and localize occupants in quasi-static settings.
• It integrates physical models, signal processing, and statistical inference from sensors like wireless RSS, CO₂, and radar for enhanced accuracy.
• Experimental findings demonstrate robust, privacy-preserving occupancy estimation across domains such as healthcare, building automation, and search-and-rescue.

Respiratory-Amplification Semi-Static Occupancy (RASSO) is a set of methodologies that leverage respiratory micro-motions for detecting, localizing, and quantifying human occupancy in environments where subjects remain quasi-static. This paradigm integrates physical models, advanced signal processing, and statistical inference to amplify and extract low-amplitude respiratory signatures from sensor data—including wireless, ambient CO₂, and low-resolution radar—enabling robust, privacy-preserving, and calibration-free occupancy estimation suitable for domains such as healthcare, building automation, and search-and-rescue (Patwari et al., 2013, Esmaieeli-Sikaroudi et al., 2024, Trinh et al., 25 Jan 2026).

1. Core Physical and Measurement Models

RASSO frameworks are grounded in the amplification and isolation of periodic, respiration-induced signal modulations. In wireless sensor networks, received signal strength (RSS) across static transceiver links is modeled as a superposition: $r_l[n] = p_l + s_l[n] + n_l[n]$ where $p_l$ is baseline path-loss, $s_l[n]$ is the respiration-induced periodic fluctuation, and $n_l[n]$ accounts for noise and interference. The fluctuation $s_l[n]$ models chest motion as a single-tone sinusoid: $s_l[n] = A_l \sin(2\pi f_b nT + \phi_l)$ with amplitude $A_l$, respiration frequency $f_b$, and phase $\phi_l$ (Patwari et al., 2013).

In the context of building CO₂ dynamics, occupancy directly modulates indoor gas concentrations. Conservation of mass yields: $$\frac{dx(t)}{dt} = -\frac{1}{\tau}(x(t) - x^{(0)}) + n(t) r$$ where $x(t)$ is the concentration, $x^{(0)}$ is ambient level, $n(t)$ is occupancy, $r$ is per-person emission rate, and $\tau$ is the air-exchange time constant (Esmaieeli-Sikaroudi et al., 2024).

Low-resolution radar applications employ Doppler-domain amplification: radar returns are warped via a nonlinear, invertible mapping that densifies near-zero Doppler bins, rendering micro-respiratory motions more separable from static clutter.

2. Signal Extraction and Preprocessing Techniques

RASSO employs specialized techniques to extract weak respiratory features:

• Mean Removal and Windowing (Wireless): Sliding windows of RSS samples undergo piecewise-constant mean subtraction, determined by breakpoints signaled by abrupt, non-respiratory motion detected using a T-score GLRT for mean-shifts. Band-pass filtering (0.1–0.4 Hz) targets typical breathing rates (Patwari et al., 2013).
• Switching AR(1) Modeling (CO₂ Sensing): Exact discretization of the physical CO₂ ODE produces a switching autoregressive process:

$$y_{t+1} = e^{-\Delta t/\tau} y_t + (1 - e^{-\Delta t/\tau}) r n_t$$

Innovations are modeled as Gaussian noise, and both occupancy and ventilation regimes are inferred via a Markov state model (Esmaieeli-Sikaroudi et al., 2024).

• Non-Linear Doppler Warping (Radar): Doppler frequencies are remapped:

$$D = \mathrm{sgn}(f) \frac{f_e}{\ln 2} \ln\bigl(1 + \frac{|f|}{f_e}\bigr)$$

with $f_e$ tuning density near $f = 0$, so micro-Doppler energy from respiration is concentrated, facilitating spatial beamforming (Trinh et al., 25 Jan 2026).

3. Statistical Inference and Occupancy Estimation

• Spectral Estimation and Localization (Wireless): The breathing rate is estimated via a multi-link periodogram. For localization, per-link breathing power measurements $v_l$ are input to a linear tomographic model over 2D spatial grids, regularized by a spatial prior covariance. Localization resolves the maximum breathing intensity pixel (Patwari et al., 2013).
• Markov-Regime Switching (CO₂ Sensing): The time series of excess CO₂ is modeled as a regime-switching AR(1) process, with hidden states encoding “vacant,” “occupied, low-ventilation,” etc. Inference employs EM combined with the Viterbi algorithm for joint estimation of occupancy levels and ventilation regimes. Parameters—including transition probabilities, AR coefficients, and drift terms—are updated via segmental K-means and ordinary least squares fit, with occupancy count estimated from model drift terms (Esmaieeli-Sikaroudi et al., 2024).
• Spatial Processing and Classification (Radar): Warped Doppler data enables robust Capon (MVDR) beamforming to generate range–azimuth maps. Occupancy is then detected via CA-CFAR (cell-averaging constant false alarm rate) thresholding or by leveraging discriminative machine learners (SimpleCNN, CNN-LSTM), which attain high cross-subject accuracy and macro-F1 uplift (Trinh et al., 25 Jan 2026).

4. Performance Benchmarks and Experimental Findings

RASSO methodologies demonstrate high accuracy in challenging, semi-static settings:

Modality	Metric	Conventional (Baseline)	RASSO/Enhanced
Wireless RSS	Breathing-rate error	1.69 bpm (basic)	1.00 bpm (breakpoint method)
Wireless RSS	Localization error	2.1 m (basic)	2.4 m (breakpoint mean removal)
Radar	CA-CFAR recall @ 1% FAR	0.643	0.920
Radar	AUC	0.920	0.981
Radar	CNN-LSTM accuracy	95.6–97.7%	98.4–99.6%
CO₂ Sensing	Occupancy detection acc.	69.8–67.4% (simple HMM)	97.3–94.7% (RASSO switching AR-HMM)

Wireless experiments on a 56 m² apartment achieved mean-localization errors of ~1–2 m and breathing-rate estimation within ±3 bpm over 81% of 30 s windows with breakpoint-based mean removal (Patwari et al., 2013). Radar-based RASSO attained AUC=0.981 and session-level macro-F1 gains up to 3.6 points over non-warped baselines, with subject-independent CNN-LSTM accuracy above 99% (Trinh et al., 25 Jan 2026). CO₂-driven RASSO offered ~97% overall accuracy, halved detection delay, and robustness to both occupancy and ventilation regime changes (Esmaieeli-Sikaroudi et al., 2024).

5. Limitations, Extensions, and Open Research Directions

Limitations of RASSO frameworks include:

• Multi-person separation: Overlapping respiratory tones pose inversion and fusion challenges. Sparse reconstruction and independent component analysis are likely necessities (Patwari et al., 2013).
• Fixed segmentation thresholds: Static parameters for breakpoint detection (wireless) or markov transitions (CO₂) may be suboptimal; adaptive or learning-based segmentation can potentially reduce bias and error.
• Node/Channel Placement: Strategic placement and frequency diversity are empirically shown to reduce variance; protocol-level adaptivity and radio sleep modes may improve resource efficiency (Patwari et al., 2013).
• Sensor Modality Extensions: Through-wall and cluttered scenarios require new propagation models; ultra-wideband radar or Wi-Fi channel state information could supplement or replace RSS measurements (Patwari et al., 2013).
• Security/Privacy: The passive nature of respiratory occupancy detection creates new adversarial vectors; MAC and protocol safeguards are indicated to prevent surreptitious monitoring (Patwari et al., 2013).
• Generalized State Models: Physics-informed state-space models (CO₂) are extensible to multi-room scenarios and additional observables (temperature, humidity), supporting vectorized AR or multivariate emissions (Esmaieeli-Sikaroudi et al., 2024).

This suggests that RASSO approaches may be further enhanced by integrating multimodal sensor fusion, online learning, and robust segmentation algorithms attuned to statistical or physical constraints of the indoor environment.

6. Application Domains and Significance

RASSO systems are deployed for contact-free monitoring in:

• Long-term care and medical settings: Privacy-preserving radar-based RASSO detectors support non-contact vital monitoring for quasi-static patients, including high-accuracy posture and presence detection without video or wearable devices (Trinh et al., 25 Jan 2026).
• Building management and automation: CO₂-driven RASSO enables continuous, physics-informed inference of occupancy states and ventilation regimes, supporting energy optimization and infection risk mitigation in smart buildings (Esmaieeli-Sikaroudi et al., 2024).
• Search-and-rescue and security: Wireless RSS-based RASSO frameworks can locate otherwise stationary breathing subjects in cluttered or obstructed environments (e.g., behind walls or rubble), relevant for rescue and security operations (Patwari et al., 2013).

A plausible implication is that the underlying respiratory-amplification principle may generalize to other modalities where micro-motions are indicative of presence, offering a coherent methodology for semi-static, privacy-sensitive occupancy detection across environments.