4. Time-of-flight and radar sensing for occupant presence, position, and vital sign detection.

Camera-based occupant sensing delivers rich spatial information, but it struggles in darkness, behind occluding objects, and under strict privacy constraints. Time-of-flight (ToF) and millimeter-wave (mmWave) radar fill these gaps. Both measure distance by timing electromagnetic or optical signals, yet they operate in different frequency bands and exploit different physical phenomena. This chapter explains how each modality detects occupant presence, estimates position, and extracts vital signs, and how to integrate them into a smart restraint system.

4.1 Time-of-Flight Ranging: Principles and Sensor Types

ToF sensing measures the round-trip time of emitted light or radio waves. Two implementation families dominate automotive cabins:

• Direct ToF (dToF): A short laser pulse is emitted, and a single-photon avalanche diode (SPAD) array records the return time. dToF excels at long range and low ambient-light interference, making it suitable for detecting a child seat in the rear row.
• Indirect ToF (iToF): A modulated continuous-wave signal is emitted, and the phase shift between emitted and received signals yields depth. iToF provides higher lateral resolution at short range, ideal for hand-on-wheel or seat-occupancy classification.

For a dToF sensor, the distance d is computed as:

d = (c × Δt) / 2

where c ≈ 3 × 10⁸ m/s and Δt is the measured round-trip time. A typical cabin dToF sensor with 1 cm resolution requires timing accuracy of about 67 ps. In practice, a histogram of photon arrivals is built over many pulses, and the peak bin determines Δt. The figure below illustrates the signal chain from emission to depth map generation.

The histogram peak position directly encodes distance. A key practical concern is ambient light rejection: bright sunlight can saturate the SPAD, so most automotive dToF sensors use narrowband optical filters and time-gating to suppress background photons.

4.2 mmWave Radar: FMCW Operation and Range-Doppler Processing

Millimeter-wave radar operates at 60 GHz or 77–79 GHz. Unlike ToF, it transmits a frequency-modulated continuous wave (FMCW) and mixes the received echo with a replica of the transmitted signal. The resulting intermediate frequency (IF) is proportional to range:

f_IF = (2 × B × d) / (c × T_chirp)

where B is the sweep bandwidth, T_chirp is the chirp duration, and d is the target range. For a 77 GHz radar with B = 4 GHz and T_chirp = 50 µs, a target at 1 m produces f_IF ≈ 533 kHz. Range resolution is:

ΔR = c / (2 × B) = 3.75 cm

Velocity is extracted from the phase shift across consecutive chirps, forming a range-Doppler map. This allows the system to distinguish a stationary child seat from a moving adult. Angular position is obtained via multiple receive antennas and digital beamforming.

4.3 Vital Sign Detection: Breathing and Heartbeat

Radar can detect vital signs by measuring subtle chest-wall displacement. The phase of the received signal at a given range bin varies with displacement Δd:

Δφ = (4π × Δd) / λ

At 77 GHz, λ ≈ 3.9 mm. A breathing displacement of 5 mm produces a phase change of about 16.1 rad, easily detectable. Heartbeat displacement (0.1–0.5 mm) is smaller but still resolvable with phase unwrapping and bandpass filtering.

Typical processing chain:

1. Range-FFT to isolate the occupant's range bin.
2. Phase extraction and unwrapping across slow-time samples.
3. Bandpass filter: 0.1–0.5 Hz for breathing, 0.8–2.0 Hz for heartbeat.
4. FFT or peak detection to estimate rates.

In a representative bench setup, a 77 GHz radar placed 0.8 m from a seated subject, with a frame rate of 20 Hz and 128 chirps per frame, can resolve breathing rates from 6 to 30 breaths/min. Heartbeat extraction typically requires 15–30 s of data for stable estimation. These figures are illustrative and depend on subject motion, distance, and antenna gain.

4.4 Sensor Fusion and Restraint Decision Logic

Neither ToF nor radar alone is sufficient for all occupancy states. A robust architecture fuses them with weight sensors and seatbelt buckle switches. The table below summarizes complementary strengths:

A practical fusion rule for airbag suppression might be: if radar detects a breathing rate between 10 and 40 breaths/min AND ToF depth map indicates a rear-facing child seat profile AND weight sensor reads below 30 kg, suppress the passenger frontal airbag and enable the rear-seat reminder. Each condition is evaluated with hysteresis to avoid chattering.

4.5 Practical Integration Checklist

The following checklist captures key engineering steps when integrating ToF and radar into an occupant sensing module. It is intended as a starting point, not a rigid procedure.

• Mounting: Place radar behind the headliner or B-pillar trim with a clear aperture; avoid metalized coatings. Mount ToF at the overhead console, angled toward the rear seat.
• Calibration: Perform empty-cabin background subtraction for both sensors. Record a baseline range-Doppler map and depth map with no occupant.
• Threshold setting: Set CFAR threshold to achieve <1 false alarm per hour in a static cabin. For ToF, set confidence threshold to reject <10% of valid pixels.
• Vital sign validation: Compare radar-derived breathing rate against a reference chest strap during development. Acceptable error is typically ±2 breaths/min.
• Fusion logic: Implement a state machine with states: EMPTY, OCCUPIED_STATIC, OCCUPIED_MOVING, CHILD_SEAT, REAR_FACING. Transitions require two consecutive frames of evidence.
• Diagnostics: Monitor signal-to-noise ratio (SNR) per range bin. If SNR drops below 10 dB for more than 5 s, flag sensor degradation.

By combining ToF's spatial resolution with radar's penetration and vital-sign capability, the restraint system can make more reliable decisions across the full range of real-world cabin conditions — from an empty seat to a sleeping infant — without compromising privacy or requiring visible light.