Enhancing Automotive Child Presence Detection Using PCA-Based Spatial Descriptors on FMCW Radar Point Clouds

Let the point cloud detected in frame i be: P_i = {p_i,j = (x_i,j, y_i,j, z_i,j) ∈ ℝ³; j = 1, …, N_i} where each point encodes the estimated Cartesian position derived from the range–azimuth–elevation measurement. The cabin is partitioned into K disjoint cuboid regions: $$ {\left\{Z_k\right\}}_{k=1}^K$$ = [x_min,k, x_max,k] × [y_min,k, y_max,k] × [z_min,k, z_max,k]. A point p_i,j is assigned to zone k if it lies within the boundaries of Z_k; points that are not associated with any zone are discarded. For each zone and frame, we collect the set of assigned points: P_i,k = {p_i,j ∈ P_i : p_i,j ∈ Z_k} and their corresponding signal-to-noise ratios s_i,j . The cardinality |P_i,k| and average SNR: $$ {\stackrel{-}{s}}_{i,k}=\frac{1}{\left|P_{i,k}\right|}\sum {}_{p_{i,j}\in P_{i,k}}{}^{}s_{i,j}$$ are the primary inputs to the subsequent state machine.

Fig. 3

Principal Component Analysis (PCA) applied to radar point clouds for each frame for target shape analysis

The CPD documentation recommends a two-stage thresholding procedure. To enter the occupied state, zone k must exceed a minimum point count T_pts,1 if this criterion is met, the average SNR is compared against a threshold T_SNR,1. Remaining in the occupied state uses possibly different thresholds T_pts,2 and T_SNR,2 to incorporate hysteresis. When a certain points and SNR value are exceeded, the state for the occupied state is counted, and if this count exceeds a threshold, the zone is considered occupied. Fig. 4 shows how to divide the area for the actual seat into cuboids and distinguish the incoming points within the area as detected objects.

Fig. 4

Zone mapping for in-cabin occupant detection. The seat area is partitioned into predefined three-dimensional cuboids (zones). Points outside the zones (gray) are excluded, and only points inside the zones (blue) are used

Traditional CPD pipelines often rely on point count and average SNR as indicators of occupancy. While these metrics are effective for detecting large, highly reflective occupants such as adults, they are less reliable for children or infants whose movements are small in both amplitude and spatial extent. In such cases, the generated point clouds are sparse and exhibit limited motion cues, making it difficult to distinguish a child from background clutter or inanimate objects.

This limitation is particularly problematic in CPD contexts, where the system must detect not only the presence of a small body, but also infer its dynamic state awake, asleep, or absent under diverse conditions. Large objects with broad spatial profiles naturally generate many radar reflections, thereby exceeding the point-count thresholds easily. In contrast, small and irregular motions from a sleeping or quietly awake infant may yield only a handful of points, often insufficient to surpass the static detection thresholds. Moreover, certain reflective inanimate objects, such as water bottles or metallic containers, may falsely trigger detection by producing dense point clouds with high SNR, despite being non-living.

To overcome these challenges, we incorporate a geometric analysis of the spatial structure of the detected points within each zone. Specifically, we apply three-dimensional Principal Component Analysis (PCA) to characterize the shape and dispersion of the point cloud. For zone k in frame i, the points P_i,k are centred by their centroid:

The sample covariance matrix is then computed as:

Let $$ {𝜆}_{i,k}^{\left(1\right)}$$ ≥ $$ {𝜆}_{i,k}^{\left(2\right)}$$ ≥ $$ {𝜆}_{i,k}^{\left(3\right)}$$ ≥ 0 denote the eigenvalues of C_i,k. These eigenvalues summarise the shape of the point cluster: a static occupant seated in a seat typically produces an elongated cluster with a dominant first eigenvalue and two small eigenvalues, whereas irregular motion or the presence of multiple scatterers increases $$ {𝜆}_{i,k}^{\left(2\right)}$$. Physically, the second eigenvalue $$ {𝜆}_{i,k}^{\left(2\right)}$$ represents the spatial spread of the radar point cloud along the direction orthogonal to the dominant principal axis. When the target motion is mostly confined to a single direction, such as regular breathing or damped unidirectional oscillation of a water bottle, the point distribution remains elongated mainly along one axis, so $$ {𝜆}_{i,k}^{\left(2\right)}$$ stays small. In contrast, irregular infant motion involves asynchronous movement of multiple body parts, which broadens the point cloud not only along the dominant axis but also in an orthogonal direction. As a result, $$ {𝜆}_{i,k}^{\left(2\right)}$$ and its temporal variance become more sensitive indicators of irregular multi-directional motion. In the CPD context, this geometric encoding is particularly advantageous because it enables discrimination between living occupants and reflective inanimate objects without relying solely on motion periodicity. Moreover, the PCA computation comprising centroid estimation, covariance calculation, and eigen-decomposition is lightweight enough to run in real time on low-power embedded processors, making it suitable as a complementary module alongside conventional respiration-based detection pipelines.

Fig. 5 illustrates PCA eigenvalue characteristics. Blue dots indicate detected 3D scatter points visualized in 2D projection plane, while the shaded ellipses represent the spatial extent defined by the principal components. Red and green arrows depict the first and second principal eigenvectors, respectively, with lengths proportional to the square roots of their corresponding eigenvalues. Between frames, the second eigenvector undergoes a notable change in orientation and magnitude, reflecting irregular, multi-directional motion.

Fig. 5

Comparison of PCA results for two consecutive frames of an awake infant’s radar point cloud

In this work, PCA is not intended to fully represent the kinematics of highly complex nonlinear body motion. Rather, it is used as a lightweight geometric descriptor that captures changes in the spatial dispersion of the radar point cloud. This makes it suitable as a complementary module to respiration-based periodicity analysis, particularly when irregular motion weakens or obscures the periodic breathing pattern.

To detect breathing or sporadic movement, the PCA descriptors are tracked across frames using a sliding window of length N. For zone k at frame i, the variance of each eigenvalue over the window i - N + 1, ..., i is computed as:

where d ∈ {1,2,3} indexes the eigenvalues. When a zone contains a stationary occupant, the largest eigenvalue remains approximately constant and the variances $$ {𝜎}_k^{2,\left(1\right)}$$(i), $$ {𝜎}_k^{2,\left(2\right)}$$(i), $$ {𝜎}_k^{2,\left(3\right)}$$(i) are small. Breathing causes low-amplitude oscillations in λ⁽¹⁾, while irregular or limb movements induce larger fluctuations in λ⁽²⁾.

The variance of the second components is used within a multi-stage CPD state machine to refine occupant classification. First, coarse occupancy is determined from the mean SNR and point count in each zone. If the zone is classified as Occupied and corresponds to the seat-center cuboid without head-region points, the occupant is provisionally labeled as an Infant Candidate. For Infant Candidates, two analyses are performed:

Respiration-based periodicity analysis: If the SNR time series exhibits stable oscillations within the respiration frequency band, the occupant is classified as a Regular Breathing Infant (Deep Sleep).

PCA variance analysis: If the periodicity criterion is not met, the temporal variance of λ⁽²⁾ is evaluated over a sliding window. High variance primarily in the second eigenvalue component indicates multi-directional irregular motion consistent with an Awake Infant, whereas low variance across all components suggests a Non-living Object (e.g., reflective water bottle).

Additionally, detection of sufficient points in the head cuboid triggers classification as Adult, bypassing PCA analysis.

The analysis shows that mean SNR time series are effective for detecting deep sleep states but insufficient for separating awake infants from vibrating inanimate objects. Fig. 8 presents both the frame-by-frame mean SNR signals (left column) and the corresponding PCA eigenvalue trajectories (right column) for three scenarios: awake infant (top row), deeply sleeping infant (middle row), and a 20-liter water bottle (bottom row).

Fig. 8

Mean SNR and PCA eigenvalue trajectories across frames: (a) awake infant, (b) deep sleep infant, (c) water (20 L)

In the awake infant case, irregular multi-limb movements produce an SNR waveform that is highly erratic, with large amplitude fluctuations and little discernible periodicity. The corresponding PCA plot shows that the second eigenvalue λ⁽²⁾ is consistently elevated with large temporal variation, reflecting multi-directional irregular motion. The deeply sleeping infant exhibits stable, repetitive amplitude modulations aligned with respiratory cycles, yielding a clear periodic pattern in the SNR signal. The PCA eigenvalues remain low and stable, especially λ⁽²⁾ and λ⁽³⁾, indicating constrained motion along a single axis consistent with breathing. In contrast, the water bottle, a strong reflector undergoing damped unidirectional oscillation shows a gradual attenuation in SNR as internal fluid motion stabilizes. The PCA plot reveals that λ⁽²⁾remains low, consistent with damped unidirectional oscillation typical of sloshing fluid in a container. These observations indicate that while SNR-based analysis is effective for detecting regular breathing (e.g., deep sleep), it lacks sufficient discriminative power for distinguishing awake infants from vibrating inanimate objects. In contrast, the second eigenvalue λ⁽²⁾ demonstrates the strongest class-separating potential among the PCA components, particularly in identifying irregular motion patterns.

Fig. 9 illustrates the temporal variance profiles of the three PCA eigenvalues (λ⁽¹⁾, λ⁽²⁾, λ⁽³⁾) computed over a sliding window of 60 frames for the awake infant, deep-sleep infant, and water-bottle scenarios. For intuitive comparison of scale differences across components, all eigenvalues were multiplied by 1000 prior to variance computation.

Fig. 9

Sliding-window variance analysis of PCA eigenvalues: (a) awake infant, (b) deep sleep infant, (c) water (20 L)

For σ^2,(1) (principal-axis extent), both awake and deep sleep infants maintain moderate, stable variance values (~36–38), reflecting consistent body geometry with minor fluctuations from breathing or movement. In contrast, the water bottle exhibits substantially higher σ^2,(1) variance (~125) during the initial frames, followed by a gradual decline as internal water motion dissipates. This suggests that σ^2,(1) variance captures large-scale oscillations typical of rigid bodies with internal fluid movement, providing a useful auxiliary cue for distinguishing inanimate objects from sleeping infants.

For σ^2,(2) (orthogonal spatial spread), the awake infant shows markedly elevated and stable variance (~21.7) compared to the deep sleep infant (~1.7) and the water bottle (~4.5). This variance pattern reflects the presence of multi-directional, irregular motion in the awake state, which significantly increases the orthogonal dispersion of scattering points. In contrast, both deep sleep and water scenarios yield low σ^2,(2) variance due to motion constrained to a single axis or minimal breathing movement. σ^2,(2) variance thus emerges as the primary discriminative metric for identifying awake infants.

For σ^2,(3)(minor-axis spread), all three scenarios present very small variance values (<1), indicating that the third component contributes minimally to overall shape dynamics and offers limited discriminatory power. To further provide quantitative evidence beyond the qualitative trends in Fig. 9, Table 2 summarizes the scenario-wise mean, standard deviation, and range of the sliding-window variance features. The awake infant shows the highest σ^2,(2) value (20.10 ± 2.28), whereas the deep-sleep infant and the water bottle exhibit substantially lower values (5.31 ± 4.51 and 4.29 ± 0.29, respectively). In contrast, the water-bottle case yields the largest σ^2,(1) value (92.03 ± 46.02), reflecting large-amplitude but predominantly one-axis oscillation. Overall, these results confirm that σ^2,(2) is the most reliable descriptor for differentiating awake infants from non-living objects, while σ^2,(1) provides a secondary cue for separating deep-sleep infants from large reflective objects.

Table 2

Statistical summary of sliding-window variance features for each test scenario group.