BIM-Loc: BIM-integrated discrepancy-aware LiDAR-based indoor localization

2.1. LiDAR localization and mapping

LiDAR-based SLAM provides centimeter-level localization for autonomous vehicles and UAVs, a capability critical in GNSS-denied indoor environments. Typically, LiDAR SLAM systems comprise a front-end for odometry (via scan matching) and a back-end for map optimization that enforces consistency among scans (Cadena et al., 2016; Ebadi et al., 2024).

For robust scan matching, various geometric features are used within the Iterative Closest Point (ICP) paradigm. For example, KISS-ICP (Vizzo et al., 2023) uses point-to-point ICP with adaptive thresholds, while other works employ point-to-plane metrics (Ferrari et al., 2024) or combine them via covariance matrices (Koide et al., 2021). Feature-based methods like LOAM (Zhang and Singh, 2014) and Lego-LOAM (Shan and Englot, 2018) extract corner and planar features for improved performance. FAST-LIO2 (Xu et al., 2022) enables direct plane matching using an iKd-Tree for efficient search. NV-LIOM (Chung and Kim, 2024) incorporates surface normal vectors for better indoor performance. BIM-Loc is agnostic to the front-end odometry, allowing it to seamlessly integrate with various algorithms to bound their drift.

For consistency-oriented map optimization, Pose-Graph Optimization (PGO) and Bundle Adjustment (BA) are standard techniques. Factor graphs are widely used in PGO; for instance, LIO-SAM (Shan et al., 2020) formulates LiDAR-inertial odometry within a factor graph using GTSAM (Dellaert and Contributors, 2022). For multi-session SLAM, LAT-OM (Zou et al., 2024) uses STD (Yuan et al., 2023) loop detection for long-term mapping. In contrast, BA achieves finer feature-level consistency. Works like Zhou et al. (2021) and Liu et al. (2023b) proposed global plane adjustment to refine plane parameters and keyframe poses jointly, later extended to lines, cylinders, and curves (Li et al., 2024a; Zhou et al., 2022). The hierarchical framework HBA (Liu et al., 2023a) balances real-time performance and precision in large-scale tasks by combining the idea of PGO and BA. Following this paradigm, BIM-Loc designs novel graph factors to tightly integrate as-designed BIM models into a PGO framework, enforcing both inter-scan and scan-BIM consistency constraints from the front-end odometry.

2.2. Indoor localization with map priors

Prior maps serve as a reliable reference in localization. While high-definition maps with GNSS are well-established in autonomous driving, various map types are used indoors due to the absence of satellite signals. Schematic floor plans are a common choice for indoor localization. Wang et al. (2019) proposed a factor graph-based global localization method that utilizes wall intersections as features, incorporating robust data association through pairwise measurement consistency checks and a max-mixtures error model. FP-Loc (Gao and Kneip, 2022) uses a custom nearest-neighbor search for efficient wall and column lookup from floor plans, while AG-Loc (Xie and Schwertfeger, 2023) leverages area graphs extracted from floor plans for lifelong localization given a broad initial pose estimate. Compared to schematic floor plans, prior maps reconstructed from recorded point clouds provide more direct geometric information for map-based localization. 2D grid maps have been utilized for global localization and trajectory refinement (Hess et al., 2016). More recently, research has increasingly focused on pre-built 3D point cloud maps that offer rich geometric constraints for 6-DoF localization. For instance, Koide et al. (2024a) use reconstructed point clouds as reference maps for a range-inertial localization with a sliding-window factor graph. PALoc (Hu et al., 2024) utilizes point-cloud-based prior maps to generate ground-truth-level trajectories with uncertainty estimation in degraded indoor environments. Other works use representations like normal distributions (Einhorn and Gross, 2015) or meshes (Dreher et al., 2021; Mock et al., 2024) to reduce memory footprint of the prior maps.

In the AEC industry, several works have been proposed to integrate BIM into localization. Torres et al. (2023) project BIM into 2D occupancy grid maps for particle-filter-based robust localization. An extension, BIM-SLAM (Vega-Torres et al., 2024), supports multi-session tasks by exploiting loop detection, pose-graph optimization, and change detection. LIO-BIM (Stührenberg and Smarsly, 2025) couples LiDAR-inertial odometry with BIM through dual scan-to-BIM matching. The BIM/IFC files are processed to generate plain and corner features from point clouds. Another approach converts BIM into semantic-enhanced point clouds to keep both geometric and semantic information so that a coarse-to-fine semantic localization can align laser points to the map via ICP (Yin et al., 2023). While these works demonstrate feasibility of BIM-aided SLAM, they do not fully and directly integrate BIM into the SLAM framework. Instead, they rely on points sampled from BIM surfaces, which incurs significant memory overhead that hinders deployment on resource-constrained devices. More importantly, these methods largely overlook the substantial BIM-reality discrepancies prevalent in construction and renovation scenarios, limiting their practical applicability in real-world settings where design models diverge from as-built conditions. Recent efforts address such discrepancies through either continuous deviation estimation (Shaheer et al., 2025), which excels in structured environments via global graph matching and hierarchical semantic scene graphs, or probabilistic dynamic object removal (Jia et al., 2025).

2.3. Discrepancy-aware mapping

Identifying and managing discrepancies in sensor measurements across multiple sessions has been widely investigated. While several studies provide multi-modal datasets for change detection (Lambert and Hays, 2021; Park et al., 2021), applying these techniques to robot localization remains challenging. The primary sources of discrepancies include dynamic objects and environmental changes. To distinguish dynamic objects from static backgrounds, a popular solution is employing set difference operations through map-to-map complement extraction (Wellhausen et al., 2017). Visibility-based approaches prove more robust against localization errors. For example, Removert (Kim and Kim, 2020) uses multi-scale range images to reconstruct static maps. Extending this to multi-session mapping, LT-mapper (Kim and Kim, 2022) provides a modular framework for dynamic change detection and multi-layer map management without requiring perfect initial alignment. For highly dynamic environments, DynamicFilter (Fan et al., 2022) combines visibility-based and map-based approaches for dynamic object removal, with subsequent extensions enabling long-range open-world navigation in fully dynamic settings (Fan et al., 2025).

Recent research has also addressed map comparison challenges. Holoch et al. (2022) proposed creating, comparing, and merging new maps upon re-localization to handle lifelong localization failures in dynamic environments, by detecting invalid merges caused by perceptual aliasing. Rozsa et al. (2020) introduced a feature-based, comparison-free change detection method for SLAM maps that uses ICP-like frame matching and pose graph optimization to identify alterations through residual analysis. For dynamic environment modeling, Nobre et al. (2018) enhanced traditional sparse maps by incorporating feature persistence and spatio-temporal correlations. This probabilistic framework captures relationships between nearby features to compute joint posteriors over feature persistence, improving online data association for localization.

Recent work on self-updating HD maps demonstrates the limitations of binary discrepancy detection, modeling changes instead as atomic operations, such as geometry edits (e.g., boundary vertex shifts) and marking edits, rather than simple existence checks (Wild et al., 2025). In the AEC industry, discrepancy checking is essential for construction progress monitoring (Huang et al., 2022; Meyer et al., 2022; Zhang et al., 2025). Existing methods for verifying discrepancies between BIM models and real scenes typically rely on dense 3D point clouds and spatial voxelization. For instance, Meyer et al. (2022) model laser range impacts on spatial occupancy using belief functions, while Huang et al. (2022) extend this framework by integrating semantic information with UAV-acquired photogrammetric point clouds. In contrast, our BIM-Loc method introduces a novel ray-casting strategy that performs discrepancy detection directly in surface texture space, which significantly reduces memory overhead compared to point cloud or 3D voxel representations.

3.1. Problem formulation

For a sensor suite containing a LiDAR sensor and an Inertial Measurement Unit (IMU), we define a sensor frame whose pose is iteratively estimated by front-end odometry. The sensor’s pose at time step k is denoted as x _k := [R _k | t _k ], where t k ∈ R 3 is the translation and R _k ∈ SO(3) is the orientation. The trajectory over K time steps is X : = x 1 , … , x K . Each observation at step k, denoted z k : = x ˜ k , P k ∈ Z , consists of the estimated sensor pose x ˜ k and the corresponding scan points P k .

As map priors, we use as-designed Building Information Modeling (BIM) models B , which contain structural components { b n ∣ b n ∈ B , n = 1 , … , N } like walls, columns, beams, and coverings. To account for discrepancies between the BIM model and reality, we introduce an indicator set L . Each element I n ∈ { 0,1 } in this set reflects the consistency of a BIM structure b _n with its sensor data. The subset of BIM structures that exist in reality can then be inferred as B real : = b n ∣ I n = 0 .

This paper tackles the challenge of localization when map discrepancies exist. Our approach simultaneously estimates the motion trajectory X ^ and the BIM-reality discrepancies L ^ from noisy sensor measurements Z and the BIM model B in an online fashion. We formulate this as a Maximum a Posteriori (MAP) estimation problem:

( X ^ , L ^ ) = arg max X , L p ( X , L ∣ Z , B ) = arg max X , L p ( X ) ⋅ p ( Z ∣ X , L , B ) ⋅ p ( L ∣ B ) .

(1)

p ( Z ∣ X , L , B ) = ∏ n = 1 N ∏ k = 1 K p ( z k ∣ x k , b n ) ( 1 − I n ) ,

(2)

Maximizing this likelihood is equivalent to minimizing the residual error E = E odom + E consistency , which balances the odometry prior P ( X ) against the BIM-consistency p ( Z ∣ X , B , L ) . The two residual components are:

E odom = r ( x 0 ) + ∑ k = 1 K r ( x k ∣ x k − 1 ) , E consistency = ∑ k = 1 K ∑ n = 1 N δ ( n , k ) ⏟ ( 1 ) ⋅ r ( P k , x k , b n ) ⏟ ( 2 ) ⋅ ( 1 − I n ) ⏟ ( 3 ) ,

(3)

As shown in Figure 2, the BIM-Loc framework computes the three components of E consistency through dedicated modules: (1) the association indicator δ(⋅) is determined by a novel multi-hit ray casting strategy (Section 3.2); (2) consistency residuals r ( P k , x k , b n ) are optimized within a BIM-aided trajectory module (Section 3.3) to estimate X ^ ; and (3) the discrepancy indicator I n is updated by a discrepancy detection module (Section 3.4) to estimate L ^ . The online localization is solved by iterating between trajectory estimation and discrepancy detection. The following sections detail each module. A summary of notations used in the algorithm details is provided in Table 6.

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Figure 2.

Framework of the proposed BIM-Loc method. The system processes as-designed BIM models and front-end odometry measurements through three core modules: (1) multi-hit ray casting for BIM-observation association, (2) BIM-aided trajectory optimization, and (3) BIM-observation discrepancy detection. Using an iterative strategy, the method outputs an optimized trajectory and discrepancy maps, relying solely on design-phase BIM models.

3.2. Multi-hit ray casting

The paths of casted rays reflect real-world surface conditions, making them ideal for associating sensor observations with BIM models. Building on this principle, we propose a novel multi-hit ray casting model, illustrated in Figure 3.OPEN IN VIEWER

For a given point cloud (omitting time subscript k), each point is treated as a ray defined by its origin, measured distance, and unit direction vector. We first transform these rays into the BIM coordinate system. A ray casting operation then simulates each ray’s path through the BIM model, starting from the sensor origin and terminating slightly behind the real-world measured endpoint with an extended length to deal with sensor noise. Under this setting, even the ray would normally stop slightly before the BIM surface, the designed extended length forces an intersection.

Unlike standard methods that stop at the first intersection, our strategy evaluates multiple intersections along the ray’s path until it reaches the neighborhood of the endpoint. This process is detailed in Algorithm 1. For each intersection with a BIM surface (facet), the StatusEvaluation function computes the point-to-surface distance d (see Figure 3, upper right). If the ray has not yet reached its endpoint neighborhood, the RayUpdate function sets the intersection point as a new origin and continues casting. This iterative process continues until all rays are processed, generating a set of synthetic counterpart points in the BIM coordinate system.

For each intersection, the RayCasting function returns the following information: (1) association: the indices of the struck BIM structure and its specific planar facet; (2) synthetic surface point: a hit point p ′ and its normal vector n ′ on the BIM surface; (3) projection data: barycentric coordinates (u, v) and a binary intersection status σ. The barycentric coordinates result from projecting the 3D intersection onto a 2D texture space using a pre-computed UV-mapping dictionary (generated by the xatlas library (Jonathan Young, 2025)). This projection strategy avoids storing numerous 3D points, significantly reducing memory consumption. The intersection status σ is 1 (hit) if the distance from the synthetic point to the real surface is below a threshold, and 0 (miss) otherwise. The collected data is then organized into a hit set H and a miss set M based on this status.

In summary, the multi-hit ray casting module contributes to the BIM-Loc framework in three critical ways. First, it establishes an efficient and accurate association between BIM structures and point clouds, which is comparable with traditional nearest-neighbor search. Second, the synthetic hit points with normals in H serve as local samples of BIM surfaces, which are crucial for the BIM-aligned trajectory estimation in Section 3.3. Finally, the barycentric coordinates enable the projection of 3D observations into a 2D texture space, which is fundamental to the discrepancy detection method in Section 3.4.

3.3. BIM-aided trajectory optimization

This section describes the trajectory optimization that maintains consistency between sensor observations and the BIM model. We formulate the residuals from equation (3) as a pose factor graph. This graph combines two components: (1) motion priors from front-end odometry E odom , derived from p ( X ) and (2) BIM-observation consistency E consistency , derived from the likelihood p ( Z ∣ X , B , L ) in equation (2).

For the trajectory optimization sub-problem, the association indicator δ(k, n) is provided by the multi-hit ray casting module (Section 3.2), while the discrepancy indicator I n is held fixed. This allows us to isolate the effective composite residual for independent analysis: ∑ δ ( k , n ) = 1 , I n = 0 r ( P k , x k , b n ) : = r ( Z , B ) .

The multi-hit ray casting operation establishes data association by assigning each point in the hit set H a tuple of indices (structure and facet). This allows points striking the same facet to be grouped into a point cluster. As shown in Figure 4, a point cluster with the index c (visualized as borderless circles of the same color) comprises all points from a single scan that hit the same BIM facet. This creates an explicit link between BIM surface facets and point clusters. Given their similar planar nature, both the BIM facets and the point clusters are modeled as planes. Let {π _f } be the set of analytically defined planes for the BIM facets, and {π _c } be the set of planes for the point clusters. A plane π _c for the point cluster is parameterized by the point cluster’s mean vector μ _c (which defines a point on the plane) and the covariance matrix Σ _c (which defines the plane’s normal).OPEN IN VIEWER

Given C point clusters and F facets from a sequence of K poses and N BIM structures, the number of association pairs equals the number of point clusters C. The number of clusters associated with a specific facet f is C _f , where C = ∑ f = 1 F C f . These associations create two distinct constraints for trajectory optimization: (1) inter-scan consistency: all point clusters from different scans that are associated with the same facet must be geometrically consistent with each other; (2) BIM-scan consistency: each point cluster must align with its corresponding BIM surface facet. Incorporating both constraints enhances the system’s robustness. Relying solely on constraints from often-simplified BIM structures can yield incomplete constraints and suboptimal results. The combination of inter-scan and BIM-scan constraints mitigates this issue and corrects accumulated drift by using the BIM model as a global reference. To balance these constraints, the composite residual is decomposed as follows (for clarity, δ(k, n) and I n are omitted):

r ( Z , B ) = ∑ f = 1 F r ( { π c } 1 : C f ) ⏞ ( 1 ) E scan : Inter - Scan + ∑ f = 1 F ∑ c = 1 C f r ( π c , π f ) . ⏞ ( 2 ) E bim : BIM - Scan

(4)

This formulation separates the residual into two components: (1) E scan that enforces inter-scan consistency by imposing a unified constraint on all point clusters { π c } 1 : C f associated with the same facet f. Because this is a single constraint involving multiple clusters, the residual cannot be separated per cluster. (2) E bim that enforces BIM-scan consistency by evaluating the alignment between each point cluster π _c and its corresponding BIM facet π _f . The following sections detail the residual formulations for these two constraints.

3.3.1. Inter-scan consistency

To formulate the constraints among the C _f point clusters associated with the same facet f, we design a multi-way factor, with the residual representation as illustrated in Figure 4. Inspired by Huang et al. (2021), we frame the bundle adjustment of point clusters as an eigenvalue minimization problem. For a point cluster c, the point distribution can be mostly captured by a mean vector μ _c and a covariance matrix Σ _c . The optimization objective E scan is:

E scan = ∑ c = 1 C f λ c 1 ‖ n g ⊤ ( R k Q c e x ) ‖ 2 + ∑ c = 1 C f λ c 2 ‖ n g ⊤ ( R k Q c e y ) ‖ 2 + ∑ c = 1 C f ‖ n g ⊤ ( R k μ c + t k − μ g ) ‖ 2 ,

(5)

where R _k is the rotation matrix at pose x _k . For each cluster c, the covariance matrix is decomposed via SVD as Σ c = Q c ⊤ Λ c Q c , where Λ c = diag ( λ c 1 , λ c 2 , λ c 3 ) , e _x = [1,0,0] ^⊤ , and e _y = [0,1,0] ^⊤ . The terms μ _g and n _g are derived from the aggregated distribution of all C _f point clusters. The global mean μ _g is the weighted sum of the individual cluster means μ _c . The global normal vector n _g comes from the SVD of the aggregated covariance matrix Σ _g that is calculated as: Σ g = ∑ c = 1 C f ( Σ c + Σ μ c ) , where Σ μ c = ( μ c − μ g ) ( μ c − μ g ) ⊤ .

Equation (5) is designed to reformulate inter-scan consistency problem into the thickness of the aggregated point distribution along n _g . This objective is achieved by iteratively evaluate the similarity between eigenvector related to λ c 3 of point clusters and n _g and update until they are almost the same. The optimization proceeds as two-fold iteratively: (1) hold μ _g and n _g fixed to update all cluster parameters μ _c and R _k and (2) use the updated cluster parameters to recompute μ _g and n _g . This process repeats until convergence, tightly coupling the point clusters from multiple scans through their associated BIM structures.

3.3.2. BIM-scan consistency

This factor enforces consistency between associated BIM structures and point clusters. Using the synthetic points sampled from BIM surfaces via multi-hit ray casting, the BIM-scan residual is defined by the point-to-surface distance between real-world scan points and the local BIM surfaces. This is illustrated on the right side of Figure 3. The residual is formulated as:

E bim = ∑ i = 1 ‖ n i ′ ⊤ ( R k p i + t k − p i ′ ) ‖ 2 .

(6)

Here, each point index by i in a point cluster is associated with a BIM facet. The variables p i ′ and n i ′ are the associated synthetic hit point and its normal vector, respectively. As shown in Figure 4, the distance for a real-world point p _i is calculated relative to the plane defined by the synthetic point p i ′ and its normal n i ′ .

3.4. Discrepancy detection

This section addresses the subproblem of detecting discrepancies in BIM structures. As shown in equation (3), the status of each structure is represented by a discrepancy indicator, denoted here as I S (the structure index n is omitted for clarity and we use subscript S to emphasize its affiliation within structure-level representation). This structure-level discrepancy indicator is a discrete random variable following a Bernoulli distribution: I S ∼ Bern ( p ; θ S ) = θ S p ( 1 − θ S ) 1 − p , where p ∈ {0, 1}. The hyper-parameter θ_S is the probability that a discrepancy exists ( I S = 1 ) when comparing the BIM structure against actual sensor observations, for example, I S = 1 when the discrepancy exists.

The goal of discrepancy detection is to estimate the posterior distribution p ( θ S ∣ Z ) . However, two challenges arise: sparse point cloud observations cannot be directly used for structure-level identification, and clear comparison criteria are lacking. To address these issues, we propose a hierarchical continuous mapping method in the surface texture spaces of BIM structures, as illustrated in Figure 7. This strategy converts sparse ray-casting observations into real-time estimates of the discrepancy status I S .OPEN IN VIEWER

3.4.1. Hierarchical discrepancy modeling

To bridge this representation gap, we design a probabilistic model based on the hierarchical architecture of BIM models: structure, facet, texture pixel, and observations Z . The prediction objective is decomposed as follows:

p ( θ S ∣ F , I , Z ) ∝ p ( θ S ∣ F ) ⋅ p ( F ∣ I ) ⋅ p ( I ∣ Z ) ,

(7)

where F ≔ { I F } and I ≔ { I I } are two sets of auxiliary discrete random variables. I F follows a Bernoulli distribution, I F ∼ Bern ( p ; θ F ) , with hyperparameter θ _F representing the probability that a BIM surface facet exhibits a discrepancy ( I F = 1 ) . I I is pixel-wise discrepancy indicator, which will be defined in equation (10). Equation (7) forms a three-layer hierarchical model with a chain structure from observations, texture pixels, facets to building structures: Z → { I I } → { I F } → I S . Two relationships are key in this chain: (1) the structure-facet relationship { I F } → I S and (2) the facet-pixel relationship { I I } → I F . These relationships are defined as follows:

Structure-facet relationship between the structure indicator I S and its facet indicators I F defined via the hyperparameter θ _S :

I S ∼ B e r n ( θ S ) , θ S = ⋃ F ( w F ⋅ I F ) ,

(8)

where θ_S is the weighted union of the facet discrepancy indicators in F . This formulation reflects the composition of a complete building structure from its facets. To prioritize larger facets, we define an area-based weight w F = A F 2 / ∑ A F 2 , where A _F is the area of a facet. This “larger-area, higher-weight” strategy focuses the model’s updates on more significant surfaces.

Facet-pixel relationship leverages the surface texture projection from Section 3.2, where BIM facets are projected onto a texture image with pre-computed barycentric coordinates. The connection is established through a model averaging of pixels:

I F ∼ B e r n ( θ F ) , θ F = 1 N pixel ∑ I I ,

(9)

where N_pixel is the number of pixels in the facet and I I is the pixel-wise discrepancy indicator. With these definitions, the problem of detecting discrepancies in a BIM structure is equivalent to identifying the status of its corresponding texture pixels, which form the supporting set for each planar facet. The next section defines the pixel discrepancy indicator and its connection to point cloud observations.

3.4.2. Bayesian kernelized inference

Building on the hierarchical probabilistic model, this section describes a continuous texture mapping strategy using sparse point cloud observations to establish the relationship Z → I I between points and texture pixels. This mapping must fulfill two requirements: (1) model the pixel discrepancy indicator I I to determine discrepancies in each pixel’s local surface neighborhood; and (2) support incremental updates for online sequential measurements.

As noted in Section 3.2, laser rays are organized into hit ( H ) and miss ( M ) sets, with point positions defined by UV coordinates. However, unlike the uniform grid of a texture image, ray intersections occur at arbitrary coordinates and provide only sparse coverage of facet surfaces. To address this, we apply Bayesian kernelized inference, inspired by methods in occupancy voxel mapping (Doherty et al., 2019) and terrain traversability mapping (Shan et al., 2018). Specifically, we define a series of 2D continuous spaces covering the planar facets of each BIM structure; these spaces are proper subsets of the texture image space. Each pixel within a facet serves as an anchor, representing the local status of its neighborhood through the pixel discrepancy indicator:

I I ∼ B e t a ( α I , β I ) ,

(10)

where a Beta distribution models the accumulated status, parameterized by hyper-parameters α_I and β_I. For each ray intersection with status σ (0 for miss, 1 for hit) and barycentric coordinates (u, v), a texture-wrapping lookup table identifies the neighborhood pixels (Section 3.2). Given sequential observations, the hyper-parameters of affected anchor pixels are updated incrementally:

α I ← α I + ∑ x ′ ∈ N ( x ) k ( x , x ′ ) ⋅ ( 1 − σ ) , β I ← β I + ∑ x ′ ∈ N ( x ) k ( x , x ′ ) ⋅ σ ,

(11)

where each anchor pixel x is updated using all neighborhood measurements x ′ ∈ N ( x ) . The kernel function k(⋅, ⋅) weights the influence of each measurement. We directly adopt the sparse kernel from Doherty et al. (2019) to incorporate measurements from the spatial neighborhood with three reasons: (1) Computational tractability: its compact support restricts computation to local neighborhoods, avoiding the intractable cost of dense RBF kernels over all historical observations. (2) Physical locality: the hard cutoff ensures query points are evaluated only against locally adjacent surfaces, preventing false correspondences and physically implausible inference. (3) Online incremental update: only nearby pixels contribute and new measurements are incorporated through exact recursive Bayesian updates to local (α_I, β_I) without revisiting the full history.

3.4.3. Discrepancy status propagation

The hierarchical model and kernelized inference establish a complete chain for discrepancy propagation: Z → { I I } → { I F } → I S . At level of observations and texture images, laser rays update anchor pixels via equation (11). We characterize each pixel’s state using the mean and variance of its discrepancy indicator I I . Given its Beta distribution, these statistics are:

E [ I I ] = α I α I + β I , V a r [ I I ] = α I β I ( α I + β I ) 2 ( α I + β I + 1 ) .

(12)

These pixel-level estimates are then propagated upward. For the facet-level indicator I F , which also follows a Bernoulli distribution, the estimates are derived by model averaging over the facet’s pixels:

E [ I F ] = 1 N pixel ∑ E [ I I ] , V a r [ I F ] = E [ I F ] − 1 N pixel 2 ∑ V a r [ I I ] − ( E [ I F ] ) 2 .

(13)

Finally, the structure-level estimates are computed from the facet-level indicators using the weighted union from equation (8):

E [ I S ] = ∑ w F ⋅ E [ I F ] , V a r [ I S ] = E [ I S ] − ∑ w F 2 ⋅ V a r [ I F ] − ( E [ I S ] ) 2 .

(14)

The definitions in equations (13) and (14) enable the propagation of discrepancy estimates from point cloud observations across all levels, from individual pixels to entire BIM structures. The final discrepancy indicator I ^ for a facet or structure is determined by:

I ^ : = 1 , if E [ I ] ≥ γ μ + , V a r [ I ] ≤ γ σ ( consistent ) 0 , if E [ I ] ≤ γ μ − , V a r [ I ] ≤ γ σ ( discrepant ) 0 , otherwise ( unknown ) ,

(15)

where the hyper-parameters γ μ + , γ μ − , and γ _σ control the sensitivity of the detection.

For a BIM structure, I ^ S = 1 indicates it exists in the actual scene. When I ^ S = 0 , two scenarios are possible: (1) If the variance V a r ( I S ) is below γ _σ , the structure is discrepant (i.e., it differs from the BIM model). (2) Otherwise, it is classified as unknown, indicating insufficient data.

The effectiveness of this module is shown in Figure 8. For instance, in case (c), the module correctly distinguishes completed H-shape beams from nearby walls, while in case (d), a square beam is identified as completed, while the H-beam inside it is labeled “unknown” due to lack of observations.OPEN IN VIEWER

Figure 8.

Texture mapping visualization for discrepancy detection. Cases (a) and (b) show wrapped BIM models aligned with texture maps, highlighting discrepancies from elevator and roller doors. Cases (c) and (d) show H-shape beam detection behind unfinished and finished walls. Color coding indicates alignment status: blue for consistent, orange for discrepant, and gray for unknown regions.

Each indicator in the hierarchy serves a distinct purpose: I I manages fine-grained, pixel-level discrepancy checking, revealing surface details; I F facilitates data association for trajectory optimization (Section 3.3), and I S determines the existence of a BIM structure for high-level discrepancy reporting.

4.1. Simulation platform

The initial evaluation targets indoor environments that are free of temporary objects not captured in the BIM models. To facilitate this, we developed a BIM-robot simulation platform built upon an autonomous exploration framework (Cao et al., 2022). As illustrated in Figure 9, BIM models are converted into .stl format and imported into the Gazebo simulator (Aguero et al., 2015). A mobile robot equipped with a Velodyne VLP-16 LiDAR sensor navigates through the virtual building along trajectories generated by an exploration algorithm (Cao et al., 2021), producing synthetic LiDAR scans. The resulting synthetic data sequences, along with the BIM models, serve as inputs for all evaluated algorithms.OPEN IN VIEWER

4.1.4. Result analysis

The simulation benchmark results are presented below according to the evaluation metrics. First, as shown in Table 1, our BIM-Loc method achieves the best performance across all 20 sequences, with the best RMSE values of 0.007 m for translation, 0.115° for rotation, and 0.007 m for scan-to-BIM distances. These lowest ATE RMSE values confirm BIM-Loc’s superior localization accuracy, while the minimal scan-to-BIM distances indicate optimal alignment between scans and the BIM model. Among the other evaluated algorithms, both the online map-based method (HDL) and offline BA-based methods outperform the DLO front-end, demonstrating that pose graph optimization and map priors can enhance raw odometry results. However, these methods cannot fully eliminate accumulated drift errors due to their reliance on voxelized point clouds for data association. HBA ranks second best in the CaseStudy, Office-02, and CityU-02 sequences, while HDL performs second best in CityU-01. This variation stems from the voxel-based association mechanisms in HBA and BALM2, which are misled by the narrow double sides of thin walls, as noted by Zhou et al. (2021) and visualized in Figure 6. The complex layout of CityU-01, with its numerous thin decorative walls, exacerbates this issue. In contrast, BIM-Loc’s multi-hit ray casting module clearly distinguishes both sides of thin walls, enabling their effective incorporation into the optimization. Consequently, BIM-Loc demonstrates better localization performance and greater robustness across all building structure experiments. Additionally, due to the fact that the experiments in CaseStudy and CityU-01 are conducted in BIM-consistent regions, that is, without BIM-reality discrepancies. It can prove that the performance gains in above settings are mostly owning to optimizations with BIM priors.

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Table 1.

Simulation benchmark results for ATE and scan-to-BIM distances. Column subscripts: t = ATE translation [m], θ = ATE rotation [deg], d = scan-to-BIM distance [m]. Lower values indicate better performance. Optimal results are in bold.

Sequence	BIM-Loc			DLO			HBA			BALM2			HDL			SC-PGO
	t	θ	d	t	θ	d	t	θ	d	t	θ	d	t	θ	d	t	θ	d
CaseStudy-01	0.011	0.147	0.009	0.174	0.847	0.158	0.181	0.766	0.163	0.237	1.595	0.222	0 . 157	2.469	0 . 142	0.203	1.916	0.189
CaseStudy-02-1	0.029	0.719	0.015	0.188	1.098	0.168	0 . 173	0 . 900	0 . 155	0.193	1.210	0.160	0.231	7.253	0.241	0.193	1.836	0.182
CaseStudy-02-2	0.034	0.187	0.011	0.260	1.326	0.219	0.240	1.228	0.205	0.209	0 . 915	0 . 166	0.208	3.654	0.199	0 . 183	2.130	0.183
CaseStudy-03	0.009	0.080	0.008	0.056	0.257	0.053	0 . 039	0 . 223	0 . 037	0.052	0.504	0.051	0.055	1.962	0.108	0.111	1.302	0.123
CaseStudy-04	0.007	0.093	0.008	0.023	0.143	0.022	0 . 016	0 . 123	0 . 016	0.031	0.193	0.030	1.180	1.676	0.862	0.145	0.682	0.116
CaseStudy-05	0.008	0.124	0.008	0.008	0.179	0 . 009	0.010	0 . 175	0.011	0.017	0.864	0.027	0.301	17.13	0.381	0.287	1.969	0.285
CaseStudy-06	0.043	0.323	0.023	0 . 065	0 . 921	0 . 057	0.087	1.409	0.075	0.074	1.046	0.068	0.194	3.436	0.232	0.161	2.058	0.171
CityU-01-F06	0.052	0.930	0.014	0.354	3.762	0.314	0.334	3.558	0.292	1.161	6.357	0.363	0 . 241	2 . 118	0 . 175	1.821	4.530	1.740
CityU-01-F07	0.008	0.151	0.006	0.471	1 . 566	0.394	0 . 448	3.084	0 . 389	0.486	1.723	0.411	0.574	4.066	0.508	0.726	2.079	0.700
CityU-01-F08	0.203	0.622	0.153	1 . 320	1 . 701	0 . 932	1.340	2.296	0.948	1.329	2.249	0.952	8.689	72.29	6.967	1.333	3.380	1.059
CityU-01-F09	0.012	0.281	0.007	0.443	1.628	0.403	0 . 413	1.945	0.372	0.597	2.366	0.466	0 . 185	2.192	0 . 145	1.314	2.385	1.204
CityU-01-F10	0.014	0.133	0.007	0.386	1.554	0.327	0.291	1 . 133	0.253	0.396	1.742	0.340	0 . 103	2.014	0 . 127	0.497	3.182	0.498
CityU-01-F11	0.013	0.233	0.007	0.356	1 . 222	0.331	0.292	1.232	0.271	0.373	1.431	0.336	0 . 111	2.000	0 . 119	0.666	3.266	0.616
CityU-01-F12	0.021	0.188	0.008	0 . 129	0 . 975	0 . 128	0.132	1.072	0.131	0.522	1.140	0.200	0.403	3.256	0.272	2.669	10.71	1.652
Office-01	0.018	0.245	0.009	0.265	1 . 418	0.237	0.231	1.615	0.207	0.292	1.558	0.269	0 . 155	3.823	0 . 167	0.552	3.640	0.535
Office-02	0.037	0.115	0.007	0.383	1.072	0.356	0 . 298	0 . 480	0 . 250	0.420	2.432	0.370	35.10	168.9	30.35	1.029	3.502	0.967
CityU-02-F07	0.018	0.177	0.010	0.078	0.496	0.071	0 . 070	0 . 446	0 . 064	0.263	0.872	0.099	0.215	1.808	0.182	0.206	1.115	0.195
CityU-02-F08	0.011	0.295	0.024	0.100	0.660	0.098	0 . 057	0 . 640	0 . 053	0.094	0.702	0.077	21.94	61.81	17.24	4.628	6.862	4.399
CityU-02-F10	0.009	0.121	0.009	0.095	0.424	0.090	0 . 041	0 . 285	0 . 035	0.078	0.364	0.066	15.81	67.47	13.56	0.171	0.775	0.170
CityU-02-F12	0.008	0.177	0.008	0.107	0.418	0.100	0.075	0.376	0.069	0.198	0.487	0.117	18.73	100.5	19.36	0.282	1.422	0.272

In Figure 10, the MME ratios are divided into three performance tiers. BIM-Loc alone occupies the top tier with a ratio of 95.73 ± 0.99%, significantly outperforming the DLO odometry (91.79 ± 1.17%) in the second tier. HBA and BALM2 also fall into the second tier (90.71 ± 1.03% and 91.03 ± 1.37%, respectively). The substantial gap between the first and second tiers underscores the impact of incorrect data association in HBA and BALM2, reducing their performance to the level of DLO odometry. SC-PGO and HDL belong to the third tier. BIM-Loc’s superior MME ratios reflect excellent local spatial consistency in the aggregated map and, according to Kornilova and Ferrer (2021), indicate the lowest relative pose errors among all methods, confirming its overall advantage.OPEN IN VIEWER

Figure 10.

MME ratios for evaluated methods across data sequences in the simulation benchmark. Performance is grouped into three tiers, with BIM-Loc consistently ranking first.

Figure 11 presents box plots of Wasserstein Distance (WD) errors, evaluating global consistency between the aggregated and BIM maps. BIM-Loc achieves the lowest WD errors by effectively integrating BIM models. As with the ATE and MME evaluations, the complex layouts of CityU-01 degrade the performance of offline BA-based methods (HBA, BALM2) compared to CityU-02. Conversely, HDL benefits from map priors and performs better in CityU-01, confirming that map priors can enhance indoor localization accuracy. Overall, BIM-Loc maintains strong performance across all sequences by deeply integrating BIM models into a pose graph optimization framework, effectively bounding localization errors and ensuring tight consistency within the BIM coordinate system.OPEN IN VIEWER

Figure 11.

Wasserstein distance errors for evaluated algorithms in the simulation benchmark. Box plots show median WD values (logarithmic y-axis). Results for unmodified BIM models (left of dashed line) and synthetic BIM models (right) are grouped separately.

Table 2 evaluates the discrepancy detection performance on four CityU-02 sequences. BIM-Loc substantially outperforms the BIM-Reg algorithm, with an average F1-score of 0.913 versus 0.700. Notably, BIM-Loc achieves a higher recall (0.972) than precision (0.861), indicating that its discrepancy detection module (Section 3.4) prioritizes identifying all potential discrepancies to support localization tasks. This conservative approach may occasionally misclassify a finished structure as incomplete, but ensures that only verified completed structures contribute to optimization, safeguarding localization accuracy within the BIM coordinate system.

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Table 2.

Precision, recall, and F1-score values of discrepancy detection performance in four CityU-02 sequences in simulation benchmark.

Algorithm	Sequence	Recall	Precision	F1-score
BIM-Loc	CityU-02-F07	0.981	0.877	0.926
	CityU-02-F08	1.000	0.873	0.932
	CityU-02-F10	0.992	0.852	0.917
	CityU-02-F12	0.915	0.844	0.878
​	Average	0.972	0.861	0.913
BIM-Reg	CityU-02-F07	0.819	0.546	0.655
	CityU-02-F08	0.911	0.661	0.766
	CityU-02-F10	0.789	0.647	0.711
	CityU-02-F12	0.718	0.624	0.668
​	Average	0.809	0.619	0.700

Such conservative estimates have minimal negative impact in practice, as shown by the visualization of discrepancy detection results for the four CityU-02 sequences in Figure 12. The wrapped texture maps (first row) demonstrate the performance of BIM surface mapping via Bayesian kernelized inference. As described in Section 3.2, hit and miss statuses from multi-hit ray casting are recorded on the texture maps. The pixel-level details in these texture images clearly distinguish decorative walls from surrounding structures, corroborating the high recall values in Table 2. Using the hierarchical probabilistic model (Section 3.4.1), discrepancy predictions for each structure are generated and displayed as discrepancy maps (second row). These maps use a three-color scheme: blue for finished structures, orange for unfinished structures, and gray for unknown regions due to insufficient observation.OPEN IN VIEWER

Figure 12.

Discrepancy detection results for CityU-02 data group. Top row: texture maps for Floors 07, 08, 10, and 12. Bottom row: corresponding discrepancy maps showing built (blue) and unbuilt (orange) structures.

4.2. Real-world application

To complement the simulation benchmark, we conducted a series of real-world experiments. A key distinction from simulation is that real-world scans often contain significant occlusions from objects not represented in the BIM models. These occlusions can mislead algorithms, leading to incorrect data association and degraded localization performance. Additionally, similar to the CityU-02 simulation scenario, unfinished building structures further challenge localization accuracy. To fully evaluate the impact of BIM-reality inconsistencies throughout the building lifecycle, we selected two distinct environmental settings with corresponding BIM models: one representing the construction phase and another representing the usage phase.

The first set of experiments utilizes the SLABIM dataset (Huang et al., 2025), which includes BIM models of a multi-floor office building at the Hong Kong University of Science and Technology (HKUST). Data were collected using a handheld sensor suite featuring a Livox Mid-360 LiDAR sensor with a built-in IMU. This dataset captures typical office environments including corridors, rooms, lobbies, and lounges. As shown in the upper part of Figure 13, discrepancies between the BIM and reality primarily stem from interior decorations, furnishings, and other office elements not modeled in the BIM, which contains only structural components (walls, floors, columns, doors). This setup provides a realistic testbed for evaluating localization adaptability in operational settings and assessing potential for service robot applications.OPEN IN VIEWER

The second set of experiments focuses on the construction phase, using the same CityU BIM models from the CityU-01 and CityU-02 simulation benchmarks. Unlike the synthetic data, these sequences were recorded directly at active construction sites using two different LiDAR sensors (Ouster OS0-128 and Livox Mid-360) to enhance data diversity. Each data sequence includes LiDAR scans and synchronized IMU measurements. As illustrated in the bottom part of Figure 13, the CityU construction sites exhibit significant BIM-reality discrepancies arising from unfinished structures, construction materials, and temporary equipment (e.g., ladders, pipes, trolleys). This scenario validates localization performance under challenging conditions and demonstrates the method’s potential for construction inspection tasks.

4.2.4. Result analysis

The experimental results from the two benchmarks are organized and presented below according to the evaluation metrics. We first describe the results from the office benchmark, followed by those from the construction benchmark.

Office Benchmark provides ground truth trajectories from the SLABIM dataset. In terms of ATE in Table 3, BIM-Loc outperforms other map-based localization methods, having the RMSE values of 0.147 m in translation and 2.911° in rotation in the worst case. In contrast, Fast-Loc exhibits severe drift, with the worst RMSE values as high as 27.36 m (translation) and 138.9° (rotation). PALoc ranks second, showing relatively stable performance with the worst translation and rotation RMSE values of 1.121 m and 12.99°, respectively. While these values are notably higher than BIM-Loc’s worst results, they are much lower than those of Fast-Loc. This performance gap indicates that PALoc heavily relies on map priors from actual scenes to achieve high localization accuracy, and drift errors cannot be fully mitigated using BIM models alone due to BIM-reality discrepancies. In contrast, BIM-Loc demonstrates greater robustness by deeply integrating BIM models.

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Table 3.

RMSE of ATE values for the HKUST office benchmark. Each cell reports RMSE values for translation error [m] ∣ rotation error [degree]. Lower values indicate better performance. Optimal results are in bold.

Sequence	BIM-Loc	Fast-Loc	PALoc
3F-Region1	0.147|0.748	10.75|40.61	0 . 359 | 4 . 036
3F-Region2	0.144|0.565	1 . 271 | 9 . 468	1 . 121 | 12 . 99
3F-Region3	0.055|0.470	3.958|115.4	0 . 170 | 3 . 144
4F-Region1	0.098|0.668	17.46|105.7	0 . 353 | 2 . 581
4F-Region2	0.053|0.558	21.13|123.9	0 . 374 | 2 . 510
4F-Region3	0.033|0.397	1.624|16.48	0 . 231 | 4 . 181
5F-Region1	0.076|2.911	14.04|75.21	0 . 455 | 4 . 046
5F-Region2	0.043|0.402	27.36|138.9	0 . 126 | 2 . 952
5F-Region3	0.055|0.632	19.34|36.50	0 . 836 | 4 . 286

As shown in Figure 14(a), a significant gap in MME ratios exists between BIM-Loc (93.13 ± 2.94%) and the other two methods (Fast-Loc: 84.82 ± 0.94%, PALoc: 85.10 ± 2.55%). This gap is consistent across all test sequences. Although Fast-Loc and PALoc alternate in securing the second place across individual sequences, their average MME ratios are nearly identical (84.82% vs 85.10%).OPEN IN VIEWER

Figure 14.

MME ratios for evaluated methods in two real-world benchmarks. BIM-Loc achieves the highest ratios, with a substantial performance gap in the HKUST office benchmark and a smaller but consistent lead in CityU construction benchmark.

The scan-to-BIM distance evaluation (Table 4) further confirms BIM-Loc’s superiority, with an average RMSE of 0.046 m, outperforming Fast-Loc (0.074 m) and PALoc (0.069 m). BIM-Loc consistently achieves the lowest RMSE values in every sequence, ranging from 0.037 m (3F-Region2) to 0.054 m (5F-Region1). This underscores its ability to maintain strong consistency between LiDAR scans and the BIM model. In comparison, Fast-Loc and PALoc exhibit higher RMSE values, indicating weaker BIM-observation consistency. Note that because the scan-to-BIM distance is truncated, Fast-Loc’s results are only reliable when drift errors are minimal.

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Table 4.

RMSE of scan-to-BIM distance errors [m] on HKUST Office benchmark. Lower values indicate better performance. Optimal results are in bold.

Sequence	BIM-Loc	Fast-Loc	PALoc
3F-Region1	0.052	0.067	0.077
3F-Region2	0.037	0.062	0.065
3F-Region3	0.044	0.067	0.061
4F-Region1	0.044	0.102	0.073
4F-Region2	0.047	0.063	0.068
4F-Region3	0.045	0.068	0.061
5F-Region1	0.054	0.085	0.067
5F-Region2	0.039	0.065	0.066
5F-Region3	0.045	0.082	0.081

Similar trends are observed in the WD errors (Figure 15). BIM-Loc consistently shows the lowest first quartile (Q1) values and maintains smaller error magnitudes, reflecting its stable performance when using BIM as a reference. The median error values (represented by the red line in the box plots) also highlight BIM-Loc’s advantage across regions. Additionally, BIM-Loc’s error spread is narrower in most sequences, with no extreme high-error outliers that may appear in Fast-Loc or PALoc, further proving its resilience to environmental variations across different floors and regions in complex office scenarios.OPEN IN VIEWER

Figure 15.

Wasserstein distance errors for evaluated methods in the HKUST office benchmark. Red lines indicate median WD errors within each box plot.

Construction benchmark evaluates performance in construction sites, where ground truth trajectories are unavailable. Thus, localization accuracy is assessed using MME ratios, scan-to-BIM distances, and WD errors. Compared to the simulation and office benchmarks, BIM-Loc’s MME ratios show a slight decrease, reflecting the challenging nature of construction environments. Nonetheless, BIM-Loc still outperforms Fast-Loc and PALoc across all floors and sensor types. As illustrated in Figure 14(b), with the Ouster OS0-128 sensor, BIM-Loc’s MME ratios range from 80.25% to 84.57%, demonstrating high and stable performance. PALoc ranks second, with ratios between 80.83% and 83.80%, always lower than BIM-Loc. The gap widens to 0.72%–2.54% when comparing the same sequences. With the Livox Mid-360 sensor, BIM-Loc achieves exceptional MME ratios of 90.32% (Floor-06) and 88.98% (Floor-08), exceeding its performance with the Ouster sensor (max. 84.57%). This highlights BIM-Loc’s compatibility with the Mid-360 sensor, likely due to its high-ranging accuracy. The other methods struggle to match this performance: PALoc reaches 85.69% (Floor-06) and 85.80% (Floor-08), while Fast-Loc achieves only 85.28% (Floor-06) and 83.65% (Floor-08). The gaps between BIM-Loc and the others expand to 4.63%–5.33% (vs PALoc) and 3.64%–6.67% (vs Fast-Loc), underscoring BIM-Loc’s adaptability to diverse sensors.

BIM-Loc’s advantages are further validated by scan-to-BIM distances and WD errors. In Table 5, BIM-Loc achieves the lowest RMSE values across all sequences. For Livox-captured data, it records 0.036 m (Floor-06) and 0.038 m (Floor-08), outperforming both baselines. Even PALoc’s best result (0.057 m on Floor-08) is 0.019 m higher. For Ouster-captured sequences (Floors 06–12), BIM-Loc maintains consistently low RMSE values (0.041 to 0.046 m), significantly lower than Fast-Loc (0.071 to 0.078 m) and PALoc (0.060 to 0.073 m). The two structured-map baselines, LIO-BIM and CAD-Mesher, evaluated on the same Ouster sequences, also fall short of BIM-Loc: LIO-BIM attains 0.056 to 0.061 m (second-best per sequence in the table) and CAD-Mesher 0.060 to 0.065 m, both clearly higher than BIM-Loc’s 0.041 to 0.046 m. These consistent gaps demonstrate BIM-Loc’s ability to ensure precise scan-to-BIM alignment in construction scenarios, which is critical for progress monitoring and quality inspection.

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Table 5.

RMSE of scan-to-BIM distance errors [m] on CityU Construction benchmark. Lower values indicate better performance. Optimal results are in bold.

Sequence	BIM-Loc	Fast-Loc	PALoc	LIO-BIM	CAD-Mesher
Floor-06 (Mid-360)	0.036	0.080	0.087	–	–
Floor-08 (Mid-360)	0.038	0.070	0.057	–	–
Floor-06 (Ouster)	0.045	0.078	0.073	0.061	0.062
Floor-07 (Ouster)	0.046	0.076	0.068	0.059	0.064
Floor-08 (Ouster)	0.041	0.072	0.064	0.056	0.065
Floor-09 (Ouster)	0.044	0.073	0.060	0.059	0.065
Floor-10 (Ouster)	0.042	0.074	0.064	0.056	0.062
Floor-11 (Ouster)	0.044	0.076	0.067	0.059	0.062
Floor-12 (Ouster)	0.042	0.071	0.062	0.060	0.060

WD errors (Figure 16) show that BIM-Loc maintains the best overall performance in terms of global consistency between aggregated maps and BIM models. For Ouster sequences, its errors cluster tightly between 0.119 and 0.150 (e.g., 0.119 on Floor-09 vs PALoc’s 0.126). For Livox sequences, it retains an edge with values of 0.145 (Floor-06) and 0.128 (Floor-08). The narrow data range of BIM-Loc’s errors further confirms the consistency between BIM and accumulated scans.OPEN IN VIEWER

Figure 16.

Wasserstein distance errors for evaluated methods in the CityU construction benchmark. Results left of the dashed line correspond to Ouster OS0-128 sensor data; right side corresponds to Livox Mid-360 sensor data. Red lines indicate median WD errors.

Furthermore, localization performance is visually validated through camera imagery. Using the sensor suite from Figure 13, we compare real-world footage from CityU construction sites with BIM-rendered images from the same camera poses. As shown in Figure 17 (rows 2–5), six image pairs (A–F) are presented for each floor. Each pair includes a real scene image (A, C, E) and a blended image overlaying the BIM rendering (B, D, F). For clarity, only structures present in the real scenes are included in the BIM renderings, with color coding for different types (e.g., walls: olive green, floors: red, H-shape beams: purple). In Floors 06 and 08, the purple H-shape beams in the BIM renderings show perfect overlap with their real-world counterparts throughout the localization tasks.OPEN IN VIEWER

Figure 17.

Localization and discrepancy detection results of BIM-Loc in the CityU construction benchmark. Top row: estimated trajectories in BIM coordinates for Floors 06 and 08. Middle rows: real construction site images (A, C, E) and corresponding BIM-rendered overlays (B, D, F). Bottom row: texture maps and discrepancy maps generated during localization.

The final row of Figure 17 illustrates the wrapped texture and discrepancy maps. Due to incomplete scan coverage, the texture maps use three colors to represent status: miss (orange), hit (blue), and unknown (white). These maps reflect data coverage during inspection. Decoration walls are accurately recorded and labeled in both texture and discrepancy maps. For example, in Floor 06, an H-shape beam embedded in a concrete column is not observed during inspection but is correctly labeled as unknown. Additionally, triangular H-shape beams behind tightly covered decoration walls are clearly distinguishable.

5.1. Computational scalability

In design, BIM-Loc is computationally scalable despite the seemingly intensive components (multi-hit ray casting, facet-based clustering, and hierarchical Bayesian updates). BIM-aided trajectory optimization uses iSAM2 in GTSAM for incremental inference with partial relinearization and variable reordering, so the per-step cost grows only with the locally affected region rather than the full trajectory. Second, multi-hit ray casting relies on a BVH built once offline with O(N log  N) complexity in the number of BIM triangles; at runtime, the cost is dominated by the number of rays and their maximum range and is effectively decoupled from global mesh size. Third, facet-based clustering exploits a precomputed dictionary from (Geometric ID, Primitive ID) to facet IDs, allowing O(1) lookups. Hierarchical Bayesian updates are also applied incrementally on this sparse factor graph, supporting deployment in large, complex buildings. For details of runtime analysis, please refer to Appendix D.

5.2. BIM map for localization tasks

BIM models play a pivotal role in our BIM-Loc method. Their technical characteristics align deeply with the requirements of practical indoor localization, offering significant advantages over traditional 3D representations like point clouds and voxels.

First, the lightweight nature of BIM effectively addresses storage and computational challenges. While point clouds accurately capture spatial morphology, their massive data volumes impose high memory and computational burdens during data loading. In contrast, BIM employs structured geometric topology and parametric attribute information (e.g., for walls and beams) to compress data volume, making it more suitable for mobile or embedded devices with limited computing resources. For example, in the construction benchmark, the BIM models for Floors 06 and 08 consume approximately 12.0 MB and 10.8 MB, respectively, whereas point clouds sampled from the same surfaces require 168.4 MB and 152.7 MB.

Second, BIM provides more stable geometric benchmarks for positioning. Point clouds are susceptible to scanning noise and occlusions, leading to uneven density and feature loss that can compromise the accuracy of normal vectors and other reference features. BIM, however, is built on design specifications or reconstructed structured models, ensuring clear topological relationships and consistent surface normals and corner features. This results in a more reliable positioning reference. Furthermore, BIM’s practicality extends across the entire building lifecycle. For new constructions, BIM is inherently available from planning and design phases, eliminating the need for additional modeling costs. For existing buildings, although laser scanning is required for reconstruction, the resulting BIM model supports long-term reuse, significantly reducing the storage and update overhead for spatial data in localization systems.

5.3. Texture map for discrepancy mapping

We selected texture mapping as the foundation for discrepancy detection due to its advantages in representation directness, storage efficiency, and resolution adaptability, which are superior to voxel-based association methods.

For information representation, texture maps directly encode the physical coverage status of building surfaces without requiring complex data association or feature mapping. Point clouds need interpolation to form continuous surfaces, a process prone to errors, while voxel methods rely on 3D grid discretization and filling rates, which struggle to accurately capture local surface discrepancies.

In terms of storage efficiency, the difference between 2D texture maps and 3D voxel data is substantial. For a 4000 m² space like Floor 06 of the CityU construction benchmark, a texture map consumes approximately 5.0 MB, whereas a Truncated Signed Distance Function (TSDF) voxel representation requires about 823.4 MB. This demonstrates that texture maps significantly reduce the storage and transmission costs of discrepancy detection systems.

Additionally, texture maps support adaptive resolution automatically, enhancing both flexibility and accuracy. Under this setting, the texel size (physical area per pixel in real world) is inversely proportional to the geometric surface area of the structural element. For High-curvature, small-area structures (e.g., H-shape beams), each pixel represents approximately 0.01 m² of surface area, allowing fine-grained detail capture for narrow structural elements. For Large planar surfaces (e.g., floor slabs), each pixel may represent approximately 1.0 m² of surface area, maintaining sufficient semantic information while preventing excessive memory consumption. Large-scale flat structures can be efficiently processed with low-resolution textures (e.g., 512 × 512 pixels for a 4000 m² slab), while small details like beams and columns can be captured with high-resolution textures (e.g., 2048 × 2048 pixels) to preserve subtle discrepancies. This structure-oriented resolution strategy avoids the detail loss of fixed low resolutions and the computational waste of fixed high resolutions, achieving an optimal balance between efficiency and accuracy.

5.4. Impacts of real-world BIM imperfections

The practical deployment of BIM-Loc must account for imperfections commonly present in real-world BIM models. A primary category is as-designed versus as-built discrepancies, where the constructed facility deviates from the design model. These represent the core challenge that BIM-Loc is specifically designed to address. By explicitly modeling which BIM surfaces are confirmed as built versus un-built through the discrepancy detection module, BIM-Loc treats these deviations as structured priors rather than sensor noise. This capability has been validated on the real-world CityU dataset, which contains real as-built conditions. These considerations demonstrate the practical boundaries within which BIM-Loc is expected to perform reliably.

Beyond as-built deviations, LOD also governs localization performance. BIM-Loc defaults to LOD 300 because this level provides sufficient geometric accuracy for primary structural elements and their topological relationships. Higher LODs ( > 300) do not substantially improve structural geometric fidelity. After removing non-structural IFC entities, models above LOD 300 remain compatible. Lower LODs (<300) degrade performance predictably. At LOD 200, dimensional tolerances and simplified geometry introduce misalignment into data association and trajectory optimization, which can be partially mitigated by relaxing the scan-to-BIM distance threshold at the cost of reduced accuracy. At LOD 100, the BIM models in city-level scenes lack requisite surface geometry and topological structure, rendering it unsuitable. We recommend at least LOD 300 for standard operation, with LOD 200 applicable via tuned parameters but with anticipated lower fidelity.