4D Radar-assisted Gaussian Initialization

• 4D radar-assisted Gaussian initialization converts sparse 4D radar measurements into Gaussian scene representations, providing compact priors for mapping and detection.
• It employs radar cues such as Doppler and radar cross section (RCS) to filter dynamics and enrich geometric accuracy during scan matching and odometry.
• The approach underpins diverse pipelines—including radar-only SLAM, inertial odometry, and BEV-based detection—boosting precision and computational efficiency.

4D Radar-assisted Gaussian Initialization denotes a family of methods that use 4D millimeter-wave radar measurements to seed, parameterize, or regularize Gaussian scene representations before downstream optimization. Across mapping, odometry, reconstruction, and detection, the common operation is to convert sparse radar returns into Gaussian means, covariances, and auxiliary attributes such as view-dependent Radar Cross Section (RCS), Doppler-informed motion cues, image-conditioned features, or object-level box distributions. In the literature, this initialization appears as clustered 3D Gaussian maps for scan matching, per-point Gaussian splats for map optimization, radar-guided partition of static and dynamic Gaussians, and Gaussianized point or box representations for 3D object detection (Amodeo et al., 16 Apr 2026, Amodeo et al., 2024, Tang et al., 16 Sep 2025).

1. Definition and representational scope

In radar literature, “4D” usually refers to measurements comprising range, azimuth, elevation, and Doppler. Several works convert these observations into Cartesian point clouds with associated radar attributes. One explicit sensing model writes a radar point as

$$\mathbf{z}= \begin{bmatrix} x\ y\ z\ v_\mathrm{doppler}\ \rho \end{bmatrix},$$

where $\rho$ is the raw RCS value (Amodeo et al., 16 Apr 2026). Other works retain the polar interpretation and emphasize $(r,\theta,\phi,v)$ before transforming points into 3D coordinates (Amodeo et al., 2024, Xiao et al., 20 Nov 2025).

A recurrent misconception is that radar-assisted Gaussian initialization necessarily means fitting a full Gaussian over position, Doppler, and RCS. In the RCS-aware scan-matching formulation, the Gaussian model remains purely 3D over point positions $\mathbf{p}=[x,y,z]^T$; Doppler is used upstream for dynamic filtering, and RCS is attached as a view-dependent attribute rather than folded into a 5D covariance (Amodeo et al., 16 Apr 2026). By contrast, detection-oriented methods often use one Gaussian primitive per radar point and let learned features determine scale and rotation, while reconstruction-oriented systems may initialize one Gaussian per point or per pixel and then optimize the set with photometric or geometric losses (Li et al., 10 Dec 2025, Xiong et al., 19 Sep 2025).

The term therefore spans several distinct but related constructions. In map-based odometry, it usually denotes initialization of a compact Gaussian map or keyframe prior. In 3D Gaussian Splatting pipelines, it denotes the first conversion from radar-supported geometry into Gaussian ellipsoids. In detector design, it denotes the conversion of sparse radar points or boxes into Gaussian primitives or Gaussian distributions before BEV rendering or box regression (Amodeo et al., 2024, Bai et al., 26 Jul 2025, Xiong et al., 20 May 2026).

2. Core Gaussian formulations

A canonical map-based form summarizes a radar point cloud as

$$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$

with

$$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$

This form is used to construct a 3D Gaussian map from clustered radar points, yielding initial means and covariances that act as a compact prior map or NDT-like grid for registration (Amodeo et al., 16 Apr 2026).

A more explicit geometric parameterization appears in radar-inertial odometry, where each Gaussian is represented by a center $\boldsymbol{\mu}_j$, log-scale vector $\mathbf{s}_j$, and quaternion $\mathbf{q}_j$. The paper defines

$$\mathbf{S}_j=\operatorname{diag}\big(\exp_\circ(\mathbf{s}_j)\big),\qquad \mathbf{M}_j=\mathbf{R}_j\mathbf{S}_j,\qquad \boldsymbol{\Sigma}_j=\mathbf{M}_j\mathbf{M}_j^T.$$

Initialization is obtained from Bisecting K-Means cluster centers, with isotropic unit-scale Gaussians that are later refined by gradient descent (Amodeo et al., 2024).

In radar-centric 3D Gaussian Splatting, each Gaussian is an anisotropic ellipsoid with mean $\rho$0, scale $\rho$1, rotation $\rho$2, opacity $\rho$3, and spherical-harmonic color parameters $\rho$4, with covariance

$\rho$5

Super4DR initializes $\rho$6 from the radar point coordinate, $\rho$7 from nearest-neighbor distances, and $\rho$8 by projecting the point onto images and sampling RGB or thermal values (Li et al., 10 Dec 2025).

Detection work generalizes the same idea in BEV. RadarGaussianDet3D converts each radar point into a Gaussian primitive $\rho$9, fixes $(r,\theta,\phi,v)$0 and $(r,\theta,\phi,v)$1, predicts scales and rotations, and splats the resulting 3D Gaussians into a dense BEV feature map (Xiong et al., 19 Sep 2025). SMURF uses a different but related construction: kernel density estimation over $(r,\theta,\phi,v)$2 yields “density features of a multi-dimensional Gaussian mixture distribution,” which serve as Gaussian-initialized input features rather than explicit 3DGS primitives (Liu et al., 2023).

3. Radar cues used during initialization

Doppler is the most common upstream cue. In RCS-aware scan matching, Doppler is used for dynamic filtering rather than for the Gaussian state itself (Amodeo et al., 16 Apr 2026). In radar-vision SLAM, a point is classified as dynamic if

$(r,\theta,\phi,v)$3

after estimating platform velocity $(r,\theta,\phi,v)$4 by least squares from raw detections. Dynamic-labeled raw detections are removed from map construction, and only static detections contribute to Gaussian initialization and refinement (Xiao et al., 20 Nov 2025). Radar-inertial odometry similarly uses Doppler with RANSAC-LSQ to estimate egovelocity before scan matching (Amodeo et al., 2024).

RCS can be used as a Gaussian attribute with explicit physical structure. One method defines the incidence vector

$(r,\theta,\phi,v)$5

enforces a consistent radar-facing direction, and models predicted RCS as

$(r,\theta,\phi,v)$6

using spherical harmonics of degrees $(r,\theta,\phi,v)$7 through $(r,\theta,\phi,v)$8, hence $(r,\theta,\phi,v)$9 coefficients per Gaussian. Per-Gaussian normalization uses the median $\mathbf{p}=[x,y,z]^T$0, the scale

$\mathbf{p}=[x,y,z]^T$1

and normalized inliers

$\mathbf{p}=[x,y,z]^T$2

This inserts a view-dependent RCS signature into initialization without changing the 3D geometric state of the Gaussian map (Amodeo et al., 16 Apr 2026).

Several reconstruction pipelines use radar for metric depth and dynamic/static separation. In 4DRadar-GS, radar ego-motion compensation identifies dynamic points, a radar-camera network assembles a global dynamic mask

$\mathbf{p}=[x,y,z]^T$3

and static radar points calibrate monocular depth scale. Using three nearest visual neighbors $\mathbf{p}=[x,y,z]^T$4 on the unit sphere, the local plane normal is

$\mathbf{p}=[x,y,z]^T$5

and the local scale estimate is

$\mathbf{p}=[x,y,z]^T$6

The resulting metric depth and dynamic mask determine which initial Gaussians belong to $\mathbf{p}=[x,y,z]^T$7 and which belong to $\mathbf{p}=[x,y,z]^T$8 (Tang et al., 16 Sep 2025).

A detection-oriented variant appears in RaGS. Its Frustum-based Localization Initiation first estimates depth from image features concatenated with a sparse radar depth map, back-projects foreground pixels via

$\mathbf{p}=[x,y,z]^T$9

and then augments the seed set with radar candidate voxel centers projected into the image frustum and sampled by Furthest Point Sampling. Final Gaussian positions are assembled as

$$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$0

so radar contributes both sparse depth and direct 3D seeds (Bai et al., 26 Jul 2025).

4. Initialization pipelines across tasks

For map-based odometry and SLAM, initialization usually begins with a short accumulation window. One formulation explicitly recommends collecting an initial batch of radar scans using known or approximate poses, applying Doppler filtering, merging scans into a common frame, clustering points into cells or regions, and computing $$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$1 for each cluster. RCS statistics $$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$2 and spherical-harmonic coefficients $$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$3 are then estimated per Gaussian, yielding the initialized set

$$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$4

This map is used for RCS-aware NDT-style registration or Gaussian mixture-based SLAM (Amodeo et al., 16 Apr 2026).

Radar-inertial odometry uses a different initialization path. A new keyframe scan is Gaussianized by Bisecting K-Means, then refined by minimizing

$$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$5

where $$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$6. The pose prior used to align a new scan is itself initialized as a Gaussian over hypotheses,

$$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$7

and the best optimized hypothesis becomes the scan-matching observation (Amodeo et al., 2024).

Radar-centric reconstruction often initializes one Gaussian per point rather than one per cluster. Super4DR accumulates radar frames using odometry poses, sets each Gaussian center to the radar point, initializes scale from local neighbor distances, rotation by a default or local structure, opacity by a default, and spherical harmonics from synchronized RGB or thermal images. The map is then expanded by depth-assisted ground completion, geometry-aware densification, selective separation of sky floaters, and multi-view regularization (Li et al., 10 Dec 2025). Rad-GS similarly seeds the initial Gaussian map from static enhanced radar points after Doppler-based dynamic filtering and then inserts new Gaussians in previously empty octree cells as additional static points appear (Xiao et al., 20 Nov 2025).

Dynamic-scene initialization is denser. In 4DRadar-GS, every non-sky pixel is back-projected with radar-calibrated metric depth,

$$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$8

and Gaussians are partitioned immediately by the radar-guided dynamic mask into $$\mathcal{G}=\left\{\mathcal{N}(\boldsymbol{\mu}_k,\mathbf{\Sigma}_k)\right\}_{k=1}^K,$$9 and $$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$0. This creates a metric, dense, and dynamically partitioned initialization before deformation-field learning (Tang et al., 16 Sep 2025).

In detection, initialization is usually point-centric rather than map-centric. RadarGaussianDet3D turns every radar point into a Gaussian primitive, whereas RCGDet3D redefines the primitive in a ray-aligned local frame. For a radar point $$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$1, RCGDet3D constructs a ray-centric coordinate system whose $$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$2 axis follows the radar ray, predicts $$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$3, $$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$4, and $$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$5 in that frame, and transforms them analytically back to ego coordinates before BEV splatting. This decouples coordinate transformation from representation learning and makes Gaussian initialization explicitly ray-aligned (Xiong et al., 20 May 2026).

5. Optimization after initialization

Once initialized, Gaussian representations are typically optimized by registration, rendering, or detection losses. In RCS-aware radar scan matching, the total cost combines geometry and view-dependent RCS: $$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$6 with geometric alignment expressed through Mahalanobis distance to Gaussian means and the RCS term robustified by a Cauchy loss. The RCS Hessian is restricted to rotation because the signal is weakly sensitive to pure translation (Amodeo et al., 16 Apr 2026).

The multi-hypothesis radar-inertial formulation uses a different registration objective. For each pose hypothesis $$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$7, a transformed point cloud is scored against the Gaussian model by

$$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$8

and the best hypothesis after gradient descent is selected. The resulting residual is then constrained to reliable radar degrees of freedom, namely X, Y, and yaw, before the EKF update (Amodeo et al., 2024).

In map optimization with 3D Gaussian Splatting, radar-derived Gaussians are refined by differentiable rendering. Super4DR renders color, depth, and normals from Gaussian parameters and optimizes

$$\boldsymbol{\mu}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}\mathbf{p}_i,\qquad \mathbf{\Sigma}_k=\frac{1}{|\mathcal{I}_k|}\sum_{i\in\mathcal{I}_k}(\mathbf{p}_i-\boldsymbol{\mu}_k)(\mathbf{p}_i-\boldsymbol{\mu}_k)^\top.$$9

where $\boldsymbol{\mu}_j$0 is a multi-view photometric and SSIM loss, $\boldsymbol{\mu}_j$1 compares rendered depth to DepthAnythingV2 depth, and $\boldsymbol{\mu}_j$2 compares normals to Metric3D normals (Li et al., 10 Dec 2025). Rad-GS instead combines photometric, geometric, and roughness terms,

$\boldsymbol{\mu}_j$3

so radar-initialized Gaussians remain anchored to radar geometry while being refined by synchronized and unsynchronized images (Xiao et al., 20 Nov 2025).

Dynamic reconstruction adds motion supervision. 4DRadar-GS trains a deformation field on top of the initialized static and dynamic Gaussian sets using photometric, SSIM, inverse-depth, object-mask, and sky losses, together with optical-flow and radar radial-velocity supervision. The radar term constrains the radial projection of predicted scene flow,

$\boldsymbol{\mu}_j$4

which directly preserves Doppler consistency in the learned motion field (Tang et al., 16 Sep 2025).

In detection, optimization can also be Gaussianized. RadarGaussianDet3D uses a Point Gaussian Encoder to rasterize a dense BEV map and a Box Gaussian Loss that converts 3D boxes into Gaussian distributions with

$\boldsymbol{\mu}_j$5

then measures their discrepancy by KL divergence. RCGDet3D inherits this Gaussian encoder and improves it with ray-centric prediction and semantic injection from image features prior to BEV fusion (Xiong et al., 19 Sep 2025, Xiong et al., 20 May 2026).

6. Empirical behavior, limitations, and directions

Across tasks, initialized Gaussians help primarily by compensating for radar sparsity and by injecting radar-specific structure into subsequent optimization. In RCS-aware scan matching, preliminary experiments on the Snail-Radar dataset with perturbation up to $\boldsymbol{\mu}_j$6 and $\boldsymbol{\mu}_j$7 report the best results at $\boldsymbol{\mu}_j$8, clear improvement over geometry-only, and degradation at $\boldsymbol{\mu}_j$9. This establishes an important boundary condition: RCS can regularize rotation, but RCS alone is insufficient because pure rotation optimization cannot correct translation (Amodeo et al., 16 Apr 2026).

In radar-centric mapping, Super4DR reports a 67% performance gain over prior self-supervised methods, nearly matches supervised odometry, and narrows the map quality disparity with LiDAR while enabling multi-modal image rendering (Li et al., 10 Dec 2025). In radar-vision SLAM, Doppler-driven removal of dynamic regions before Gaussian creation reduces rendering artifacts; integrating Doppler-based masks into 3DGS improves PSNR by $\mathbf{s}_j$0 dB, SSIM by $\mathbf{s}_j$1, and LPIPS by $\mathbf{s}_j$2 on average (Xiao et al., 20 Nov 2025). In dynamic reconstruction, 4DRadar-GS reports PSNR $\mathbf{s}_j$3, SSIM $\mathbf{s}_j$4, LPIPS $\mathbf{s}_j$5, and shows that 4D radar-based initialization is competitive with LiDAR-based initialization within the same PVG framework, with PSNR $\mathbf{s}_j$6 for radar and $\mathbf{s}_j$7 for LiDAR (Tang et al., 16 Sep 2025).

Detection work exhibits the same pattern. RadarGaussianDet3D improves a CenterPoint-pillar baseline from $\mathbf{s}_j$8 to $\mathbf{s}_j$9 mAP$\mathbf{q}_j$0 on TJ4DRadSet when Point Gaussian Encoder and Box Gaussian Loss are added, while maintaining $\mathbf{q}_j$1 FPS on Tesla V100 (Xiong et al., 19 Sep 2025). RCGDet3D further shows that ray-centric Gaussian prediction improves over ego-centric Gaussian prediction, and that adding positional offsets and Semantic Injection yields the best configuration on VoD, reaching EAA mAP $\mathbf{q}_j$2, ROI mAP $\mathbf{q}_j$3, and $\mathbf{q}_j$4 FPS on V100 (Xiong et al., 20 May 2026).

Several limitations recur. Radar point clouds remain sparse and noisy; map quality and initialization quality are sensitive to calibration; scale recovery methods may rely on local planarity assumptions; and some odometry pipelines still build Gaussians per keyframe rather than maintaining a global Gaussian map (Amodeo et al., 2024, Tang et al., 16 Sep 2025). A broader implication is that “Gaussian initialization” in 4D radar is not a single algorithm but an organizing principle: radar can initialize Gaussian geometry, radar can initialize Gaussian attributes, and radar can initialize Gaussian priors for downstream learning. Adjacent work on latent diffusion for 4D radar point cloud generation makes this explicit by imposing a Gaussian latent prior $\mathbf{q}_j$5 and learning conditional radar distributions in latent space, suggesting a route toward synthetic or prior-driven Gaussian initialization when real radar supervision is limited (Kwok et al., 16 Dec 2025).