RepILN: Reparameterized Inertial Localization

• The paper introduces a reparameterized inertial localization framework that converts a multi-branch training block into a single-path inference model without loss in accuracy.
• It employs a temporal-scale sparse attention mechanism and gated convolution to fuse long-range dependencies with local feature variations for robust trajectory reconstruction.
• Empirical evaluations demonstrate reduced ATE and RTE across multiple datasets, validating the design's efficiency and hardware-friendly deployment.

Searching arXiv for the focal paper and closely related inertial localization work to ground the article in current literature. Reparameterized Inertial Localization Network, or RepILN, is a data-driven inertial localization model proposed for consumer-grade IoT devices, where inertial localization is attractive because IMUs are cheap, low-power, and ubiquitous, yet must operate under severe compute, memory, and power constraints. In "RepILN: Reparameterized Inertial Localization Network" (Zhang et al., 21 Jul 2025), the model addresses two coupled problems: the computational cost of increasingly complex inertial networks and the need to model long-term dependencies in inertial measurements for accurate trajectory reconstruction. Its central design combines a multi-branch structure during training with an equivalent single-path architecture at inference, and complements that structural reparameterization with a temporal-scale sparse attention mechanism and a sparse attention gated convolutional unit.

1. Conceptual setting and research lineage

RepILN belongs to a line of inertial localization methods that reformulate the estimation problem so that learning is carried by more stable intermediate variables or architectural priors. Earlier work already showed several such reformulations: IONet breaks continuous integration and estimates a window-level polar motion increment $(\Delta l,\Delta \psi)$ over fixed-length windows (Chen et al., 2018); IDOL uses a two-stage pipeline that first estimates device orientations and then estimates device position (Sun et al., 2021); NILoc uses RoNIN to turn inertial sensor history to a sequence of velocity vectors and then employs a transformer-based neural architecture to find device location from the sequence of velocities (Herath et al., 2022); and RIOT applies the traditional state estimation recursive methodology in the deep learning domain by feeding inertial measurements and prior positions into a Transformer (Brotchie et al., 2023).

Within that lineage, RepILN is distinguished by a specific interpretation of reparameterization. Rather than reparameterizing the target into step length and heading, or separating orientation and translation, it reparameterizes the network itself: a training-time multi-branch block is converted into an inference-time single-path block, while temporal attention is sparsified so that long-range dependencies are retained without attending densely to every temporal interaction (Zhang et al., 21 Jul 2025). This places RepILN at the intersection of inertial odometry, efficient deployment, and long-horizon temporal modeling.

2. Input, output, and learning objective

RepILN takes an inertial sequence

$\mathbf{IMU} \in \mathbb{R}^{C \times L},$

with $C=6$, corresponding to 3-axis accelerometer and 3-axis gyroscope measurements. The input is therefore a windowed IMU sequence rather than a sample-wise state estimate. The network outputs velocity through an MLP head, and trajectory is obtained by integrating predicted velocity (Zhang et al., 21 Jul 2025).

The supervision signal is mean squared error on velocity. If $\hat{v}_t$ is the predicted velocity at time $t$ and $v_t$ is the ground truth, the loss is

$$\mathcal{L}_{\text{vel}} = \frac{1}{T} \sum_{t=1}^T \left\| \hat{v}_t - v_t \right\|_2^2.$$

This keeps the training target in velocity space rather than direct position space. A plausible implication is that RepILN inherits the practical advantages of velocity-centered inertial learning already seen in RoNIN-style systems, while shifting most of the methodological novelty into its backbone and temporal modeling.

3. Network organization

The architecture is built around RepBlocks and SA-GCU modules. It begins with a RepBlock for channel alignment, uses a backbone of 8 RepILN Blocks arranged into 4 stages, performs downsampling in the last RepILN Block of each stage, and finishes with an MLP head that outputs predicted velocity (Zhang et al., 21 Jul 2025).

Each RepILN Block has a residual form:

$$X' = \text{RepBlock}(X),\quad X'' = X' + \text{SA\text{-}GCU}(X').$$

This means that RepBlock first transforms the input feature map, after which SA-GCU provides a residual refinement that mixes long-range temporal structure and local fine-grained features.

Component	Function
RepBlock	Reparameterizable conv module
SA-GCU	Fuses global long-range dependencies with local fine-grained features
TSSA	Builds a sparse $L \times L$ temporal dependency matrix
MLP head	Outputs predicted velocity

This organization is explicitly aimed at inertial sequences rather than generic time series. The paper describes additional skip connections between intermediate feature maps to stabilize training. The overall design is therefore not only compact in deployment form, but also strongly biased toward residual temporal feature refinement.

4. Training-time multi-branch design and inference-time single-path conversion

The defining reparameterization in RepILN is the transformation of a multi-branch training block into a single-path inference block. During training, RepBlock uses three parallel branches,

$y = x + \phi(x) + \psi(x),$

where $\mathbf{IMU} \in \mathbb{R}^{C \times L},$0 is the identity branch, $\mathbf{IMU} \in \mathbb{R}^{C \times L},$1 is a 1D convolution with kernel size 3, and $\mathbf{IMU} \in \mathbb{R}^{C \times L},$2 is a 1D convolution with kernel size 1 (Zhang et al., 21 Jul 2025). This multi-branch form improves representational capacity and optimization during training.

At inference, the block is converted into one equivalent 3×1 1D convolution,

$\mathbf{IMU} \in \mathbb{R}^{C \times L},$3

The conversion is exact under kernel fusion. Let $\mathbf{IMU} \in \mathbb{R}^{C \times L},$4 and $\mathbf{IMU} \in \mathbb{R}^{C \times L},$5. The $\mathbf{IMU} \in \mathbb{R}^{C \times L},$6 kernel is padded to a centered $\mathbf{IMU} \in \mathbb{R}^{C \times L},$7 kernel, the identity branch is written as a conv kernel $\mathbf{IMU} \in \mathbb{R}^{C \times L},$8, and the merged kernel and bias become

$\mathbf{IMU} \in \mathbb{R}^{C \times L},$9

Thus,

$C=6$0

This reparameterization is nearly lossless in the reported experiments. On RNIN-VIO, RepILN in training form has 4.456M parameters, while RepILN_deploy has 3.809M parameters; ATE changes from 1.875 to 1.876 and RTE from 1.731 to 1.732 (Zhang et al., 21 Jul 2025). This suggests that RepILN treats architectural redundancy as a training aid rather than a deployment requirement.

5. Temporal-scale sparse attention and gated feature fusion

RepILN models long-range dependencies with Temporal-Scale Sparse Attention, or TSSA. Given feature input $C=6$1, the model projects to $C=6$2, $C=6$3, and $C=6$4 using a 1D convolution with kernel size 1 followed by a depthwise 1D convolution with kernel size 3. It then computes the temporal dependency matrix

$C=6$5

so attention is applied along time rather than channels (Zhang et al., 21 Jul 2025).

RepILN does not keep this matrix dense. Instead, it applies a max-$C=6$6 strategy: for each row, only the top $C=6$7 largest elements are retained, and the rest are masked. The TSSA output is

$C=6$8

The stated purpose is to focus on key time segments and suppress noise. Because attention is only along time, complexity is described as $C=6$9, which is significantly cheaper than channel-wise attention $\hat{v}_t$0 when channel count grows (Zhang et al., 21 Jul 2025).

SA-GCU then fuses this global branch with a local gating branch. TSSA serves as the value branch, capturing long-term trajectory dependencies, while the gating branch uses depthwise convolution followed by an activation function to capture local motion variations. The two outputs are fused through a gating mechanism. Factually, the paper frames SA-GCU as the mechanism that integrates global, long-range dependencies and local, fine-grained features; contextually, this means RepILN does not treat sparse attention as a complete substitute for local temporal modeling, but as one component in a structured global-local mixer.

6. Empirical performance, deployment profile, and limitations

RepILN is evaluated on RoNIN, RIDI, RNIN-VIO, and TLIO, with an 8:1:1 train:val:test split, using Absolute Trajectory Error and Relative Trajectory Error as the principal metrics (Zhang et al., 21 Jul 2025). Across all four datasets, RepILN yields the lowest ATE and usually the lowest RTE among the reported baselines.

Dataset	RoNIN-ResNet ATE / RTE	RepILN ATE / RTE
RoNIN	4.043 / 3.123	3.939 / 2.857
RIDI	1.987 / 2.125	1.718 / 1.927
RNIN-VIO	2.089 / 1.819	1.875 / 1.731
TLIO	1.601 / 3.968	1.459 / 3.637

On RoNIN, the reported improvement over RoNIN-ResNet is a 2.59% reduction in ATE and an 8.50% reduction in RTE. On RIDI, the reductions are 13.54% and 9.33%; on RNIN-VIO, 10.25% and 4.82%; and on TLIO, 8.85% and 8.33% (Zhang et al., 21 Jul 2025). The ablation study further shows that RepBlock alone is comparable to or better than RoNIN-ResNet on three of four datasets, while adding SA-GCU yields the large accuracy gains.

The efficiency profile is central to the method’s identity. On RNIN-VIO, RoNIN-ResNet has 4.635M parameters and 38.252M FLOPs; RepILN has 4.456M parameters and 60.968M FLOPs; and RepILN_deploy has 3.809M parameters and 76.784M FLOPs (Zhang et al., 21 Jul 2025). The paper emphasizes that, despite slightly higher FLOPs, the single-path structure is more hardware-friendly because it has better cache locality, fewer branches and conditionals, and a simpler topology for deployment.

The main stated limitation is accumulated heading drift. The paper notes that both RepILN and RepILN_deploy show minor residual heading drift in some segments, and that long-term heading errors are not fully eliminated in pure inertial systems without external corrections (Zhang et al., 21 Jul 2025). This places RepILN in a broader pattern already visible across inertial localization research: IONet reduces drift by replacing continuous integration with window-level motion primitives (Chen et al., 2018), IDOL isolates orientation as a major source of final position error (Sun et al., 2021), NILoc turns inertial history into velocity and then into location likelihood maps (Herath et al., 2022), and RIOT uses recursive position priors to stabilize transformer-based inertial odometry (Brotchie et al., 2023). RepILN’s contribution within that pattern is architectural: it shows that reparameterization can be applied not only to states and outputs, but also to the training/inference form of the network itself.