Equivariant Filter
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4 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.
Latest papers 19
Geometric filters have recently been introduced to improve the accuracy and consistency of inertial-based integrated navigation systems. Error states were defined through specific group operations, introducing state correlations in error definition, which were lacked in the additive error used by a conventional indirect Kalman filter. The desirable consistent filtering models can be obtained based on specific geometric errors. For zero-velocity measurements expressed in the reference frame, this paper derives left-error process and measurement models from invariant filtering, two-frame-group filtering, and equivariant filtering. Importantly, a new group operation is introduced for the left tangent-group equivariant error. The analysis shows that the two-frame-group invariant extended Kalman filter (TFG-IEKF) and the tangent-group equivariant filter (TG-EqF) do not offer a significant consistency advantage over the invariant extended Kalman filter (IEKF). Experiments with an INS/ZUPT measurement system show that, under small initial attitude errors, the conventional indirect extended Kalman filter (EKF) achieves loop-closure position errors below of the traveled distance, while the three geometric filters achieve comparable positioning accuracy.
Equivariant Filter Design for Acoustic and Depth Aided Inertial Navigation Systems
Autonomous Underwater Vehicles (AUVs) navigating without GPS typically fuse inertial measurements with acoustic Doppler Velocity Log (DVL) velocities and pressure-derived depth. Posing the navigation state on a Lie group improves accuracy and consistency. However, state-of-the-art filters based on the Invariant Extended Kalman Filter (IEKF) append the Inertial Measurement Unit (IMU) biases as a Euclidean extension, which breaks the group-affine structure required for exact log-linear error dynamics, causing the reported covariance to degrade alongside the estimate. We apply the Tangent-Group (TG) symmetry, which carries the biases within the geometry of the state space, to derive an Equivariant Filter (EqF) for this system, leaving zero linearization error in the navigation states and second-order error only in the biases. We develop an equivariant output model for the DVL, whose update incurs only third-order linearization error, together with a direct pressure output. Monte Carlo simulations benchmark the TG-EqF against a Two-Frame-Group IEKF and a Multiplicative EKF. The TG-EqF reduces error by 18--25% against both alternatives in each of attitude, velocity, and position. The main benefit is in the covariance it estimates: its Average Normalized Estimation Error Squared (ANEES) stays closer to its nominal value of one than that of the others. Offline analysis on AUV field data corroborates the findings of the simulations, demonstrating reduced position drift.
Understanding User Preferences of a Slope-Aware Variable-Admittance Filter for a Robot Guide Dog
This letter investigates how the parameters of a slope-aware variable-admittance filter influence user preferences in force-based interaction with a robotic guide dog for visually impaired individuals. The proposed system consists of a quadruped robot equipped with a sensor-free rigid handle for physical guidance. The framework combines path following, momentum-based interaction-wrench estimation, and a variable-admittance filter whose stiffness and damping are adapted online from slope information extracted by the robot's depth camera. The adaptation policies are evaluated through high-fidelity simulations and a human-subject study involving blindfolded sighted participants. Multiple strategies are compared using a Taguchi L9 design of experiments. Preliminary main-effect results suggest that increasing stiffness uphill and decreasing it downhill improves both objective and subjective metrics, whereas damping shows no significant main effect.
The Iterative Equivariant Filter
This paper presents the iterative equivariant filter (IterEqF). The iterative extended Kalman filter (IterEKF) replaces the standard EKF correction step with an iterative correction step that is the Gauss-Newton solution to a nonlinear weighted least squares problem. The standard equivariant filter (EqF) exploits and respects the underlying symmetry of state estimation problems posed on homogeneous spaces and Lie groups. The motivation behind the IterEqF is to combine the features of both the IterEKF and the EqF, thus leading to a high-performance state estimation solution that is well suited to navigation problems. This paper derives the iteration procedure for the IterEqF update step and shows how the intrinsic nonlinearity of the approach naturally results in a `reset' of the filter's covariance into new coordinates. Monte-Carlo simulations of range-based localisation for a mobile robot demonstrate the improvement in performance relative to a standard EqF, especially during the transient convergence.
Input Shaping for Point-to-Point Motion with a Continuum Robot Arm
A cable-driven continuum robot arm is an underactuated mechanism and may suffer residual vibration at the end of a rest-to-rest maneuver. In this work, a time-delay filter is applied as an input shaper to the system to eliminate the excitation of vibratory modes. A non-robust and a robust time-delay filter are designed based on a linear system model and demonstrate improved response compared to a velocity-driven pulse input. Experimental results using the continuum robot validate the application of the input shaper, with reduced overshoot and settling time exemplifying the reduction in oscillation at the end of the maneuver. It is also shown that utilizing the robust shaper further improves the response of the arm in comparison to applying the non-robust shaper. These results are significant towards the precise and robust implementation of continuum robots in applications involving arbitrary end-effector trajectories.
Nonlinear Bias-Compensated Adaptive Filter and Its Application for Time-Series Prediction
Most existing nonlinear adaptive filtering algorithms only account for output noise, neglecting the fact that input noise is also prevalent in practice. Although the recently proposed bias-compensated kernel least mean square (BCKLMS) algorithm addresses input noise in the nonlinear errors-in-variables (EIV) model, it still suffers from two major limitations. First, the use of a fixed-size dictionary restricts network growth but also prevents it from fully capturing the characteristics of the input signal. Second, as an least mean square (LMS) based algorithm, it exhibits poor robustness in the presence of non-Gaussian noise in the output signal. To overcome these issues, this paper proposes the random Fourier bias-compensated filter under general adaptive function (RFFBCGA) algorithm. Within the random Fourier feature based bias-compensated (RFFBC) framework, the proposed algorithm not only maintains a fixed network structure and effectively mitigates input noise interference through the BC term, but also achieves improved characterization of the input signal. Moreover, by leveraging the flexible form of the general adaptive (GA) function, the algorithm's robustness across various noise scenarios is further enhanced. Extensive simulations, including real-world time series prediction tasks, demonstrate the superiority of the proposed method.
Flexible-Region Based Adaptive In-Loop Filter for Video Coding
Adaptive loop filter (ALF) for video coding, which is designed to minimize the mean square error between original and reconstructed samples by using Wiener-based filter, has attracted increasing attention for its significant capability in improving coding efficiency. In the second and third Audio Video Coding Standard, i.e., AVS2 and AVS3, ALF is adopted as one of the in-loop filters. In current design, each frame is divided into 16 regions at most and corresponding filter coefficients are then derived and utilized to reconstruct each region. In this paper, a flexible-region based ALF (FRALF) scheme is proposed to improve the adaptability of existing ALF in AVS3, which introduces multiple region partition templates, such as , , and . We subsequently propose the filter coefficients merging algorithm to further improve coding efficiency by estimating the distortion level of different partition regions. The proposed FRALF can fully consider the local texture characteristics as well as non-local similarities synthetically. The experimental results show that FRALF outperforms the existing region-based ALF in AVS3 with relatively low complexity increasing.
Overview of Cross-Component In-loop Filters in Video Coding Standards
In-loop filters have been comprehensively explored during the development of video coding standards due to their remarkable noise-reduction capability. In the early stage of video coding, in-loop filters, such as Deblocking Filter, Sample Adaptive Offset, and Adaptive Loop Filter, were performed separately for each component. Recently, cross-component filters were studied to improve the chroma fidelity by exploiting correlations between the luma and chroma channels. This paper summarizes the cross-component filters used in the state-of-the-art video coding standard. Specifically, it includes the Cross-Component Adaptive Loop Filter and Cross-Component Sample Adaptive Offset. Cross-component filters aim to reduce compression artifacts based on the correlation between different components and provide more accurate pixel reconstruction values. In this paper, we introduce the origin, development, and status of cross-component filters in the current video coding standards. Finally, we had some discussions on the further evolutions of cross-component filters.
Equivariant Filter for High Performance Image Tracking using an Event Camera
Image tracking is the problem of estimating the transformation that relates a moving image of a scene to an original reference image. The problem is important in control of autonomous vehicles or robots, where the image encodes information about the motion of the camera or environment, as well as in pure computer vision applications. In this paper, we present an equivariant filter design for high performance tracking of planar image transformations using an event camera. The design exploits the Asynchronous Event Blob (AEB) tracker (Wang et al., 2024) to extract feature-position measurements from the raw event stream, and an equivariant filter to compute an affine image translation and rotation using the special Euclidean group symmetry. The equivariant filter incorporates an equivalent-measurement update step that de-correlates the (highly temporally correlated) feature-position measurements provided by the AEB tracker. We evaluate the design experimentally using two datasets involving general and fast rotational motion. We benchmark results against direct optimisation (estimating the relative transformation from the raw blob tracks), and a covariance intersection approach for overcoming data correlation. Our design provides smooth image tracking for features moving up to 7000 pixels per second on the image plane.
Optimized Adaptive Loop Filter in Versatile Video Coding
In the Versatile Video Coding~(VVC) standard, adaptive loop filter~(ALF), including Geometry transformation-based Adaptive Loop Filter~(GALF) and Cross Component Adaptive Loop Filter~(CCALF), plays an essential role in reducing compression artifacts. However, it also has high coding complexity and requires many picture buffer accesses in the encoder that will increase external memory access and is unfriendly to the software and hardware design. Therefore, we propose an optimized ALF framework, including the parallel design of GALF and CCALF, the adaptive parameter decision of GALF, and one-pass CCALF scheme by effectively estimating the CCALF filtering distortion without conducting filter operation. Compared to VTM-8.0, the proposed method can reduce the picture buffer access from 152 to 1 and achieve roughly 25% time-savings of the ALF module with negligible coding performance change under RA configuration. Some of the proposed methods have been adopted in the VVC reference software.
Quaternion-Averaging-Based Adaptive Complementary Filter for Pedestrian Dead Reckoning With a Foot-Mounted AHRS
Pedestrian Dead Reckoning (PDR) can be applied to indoor navigation systems. GPS suffers from signal degradation due to roofs and high-rise buildings, whereas PDR can estimate positions without being affected by such signal degradation. The accuracy of a foot-mounted AHRS(Attitude and Heading Reference System)-based PDR depends on the accuracy of the attitude estimation algorithm used in the AHRS. In this article, a Quaternion-Averaging-Based Adaptive Complementary Filter (QAACF) for PDR with a foot-mounted AHRS is proposed to improve estimation accuracy while reducing computational cost. QAACF fuses a quaternion derived from angular velocity with quaternions derived from acceleration and magnetic field measurements using Markley's quaternion averaging, which combines two quaternions more rigorously than linear interpolation. In addition, QAACF adaptively adjusts the weights of angular velocity, acceleration, and magnetic field measurements according to gait phases and the level of magnetic disturbances. Experimental results showed that the proposed QAACF achieves low Root Mean Square Errors (RMSEs) compared to existing attitude estimation filters while requiring lower computational cost than Kalman filters.
A DDSP Framework for Adaptive Room Equalization
Adaptive room equalization remains challenging under time-varying acoustic conditions and complex excitation signals, such as music. In these scenarios, classical filtered-x least mean squares (Fx-LMS) methods falter due to their rigid formulation. We present a modular differentiable digital signal processing (DDSP) framework for closed-loop adaptive room equalization that recovers Fx-LMS as a special case through automatic differentiation. The framework supports interchangeable EQ structures, response estimation methods, loss functions, and optimizers. Experiments with time-varying measured room impulse responses show that frequency-domain objectives provide more stable adaptation than time-domain objectives in the considered scenarios. Relative to the non-equalized response, system distance is reduced by 70% and mel-spectral distance by 13% (worst-case scenario). We further examine how online room response estimation accuracy and frame length affect the trade-off between responsiveness and convergence stability. Overall, the framework provides a unified open-source basis for exploring synergies between classical adaptive filtering and DDSP-based optimization.
Training-free sparse attention based on cumulative energy filtering
Sparse attention accelerates Diffusion Transformers (DiTs) for video generation by computing only the important tokens while skipping the rest. The token selection strategy is key to balancing sparsity and accuracy. We formulate the token filtering process as a dual-goal optimization problem: maximizing sparsity and minimizing accuracy degradation. Existing algorithms cannot fulfill both objectives simultaneously. For example, Top-p only considers the accuracy constraint, while Top-k maintains a fixed computational budget but loosens the accuracy constraint. This paper demonstrates that maintaining a fixed recall rate is sufficient for ensuring accuracy, whereas a fixed threshold is suboptimal for reducing computational cost. Therefore, we propose a dynamic thresholding scheme to improve sparsity while maintaining the same level of accuracy. Furthermore, our algorithm is deeply integrated with Flash Attention (FA), eliminating the need for any additional masking computation overhead. Experimental results on Wan 2.2 validate that, compared to the BLASST algorithm which is also integrated with FA, our dynamic thresholding strategy enhances sparsity from 61.42% to 82% with a VBench metric drop of less than 5%. This results in an approximate 15% in attention computation and a increase in computational efficiency, which is 1.18x higher than that of BLASST.
Relative Pose-Velocity Estimation Using Dual IMU Measurements and Relative Position Sensing
This paper addresses the problem of estimating the relative pose (position and orientation) and velocity of a vehicle with respect to a moving target, where both are equipped with Inertial Measurement Units (IMUs), assuming the availability of relative position or bearing measurements. The body-target relative dynamics are formulated on and recast into a linear time-varying (LTV) model in the ambient space , on which a deterministic Riccati observer is designed. We analyze the uniform observability (UO) conditions required to guarantee global exponential convergence of the estimation error in the ambient space for both measurement cases. In the case of relative position measurements, UO requires only a persistence-of-excitation condition on the target acceleration, whereas for bearing measurements, additional conditions are required. Building on this, a nonlinear complementary filter on is designed to provide a smooth estimate of the orientation component of the state with almost global asymptotic stability. Finally, simulation results are provided to validate the proposed solution.
Near-Policy: Accelerating On-Policy Distillation via Asynchronous Generation and Selective Packing
Standard knowledge distillation for autoregressive models often suffers from distribution mismatch. While on-policy methods mitigate this by leveraging student-generated outputs, they rely on computationally expensive Reinforcement Learning (RL) frameworks. To improve efficiency, we propose Near-Policy Distillation (NPD), an asynchronous approach that decouples student generation from training. This reformulation enables Supervised Fine-Tuning (SFT) with sequence packing. However, asynchronous updates inevitably introduce policy lag and sample noise, which can cause the behavior to drift from near-policy toward off-policy. To counteract this without sacrificing efficiency, NPD integrates sparse student updates and the -IFD filtering mechanism, a heuristic sample selection mechanism that empirically stabilizes the optimization trajectory. By filtering extreme out-of-distribution samples, -IFD prevents noise from dominating the gradients, ensuring updates remain within a safe proximal learning zone. Empirically, the NPD framework achieves a 8.1x speedup over on-policy baselines and outperforms SFT by 8.09%. Crucially, by effectively narrowing the exploration space for subsequent RL, our method enables openPangu-Embedded-1B to reach a state-of-the-art score of 68.73%, outperforming the substantially larger Qwen3-1.7B. Codes will be released soon.
Equivariant Filter for Radar-Inertial Odometry
Radar-Inertial Odometry (RIO) based on the Extended Kalman Filter (EKF) relies on accurate extrinsic calibration between the radar and the Inertial Measurement Unit (IMU) and is sensitive to disturbances, as large linearization errors can degrade performance or even cause divergence. To address these limitations, this letter proposes an Equivariant Filter (EqF) for RIO based on a Lie group symmetry that geometrically couples navigation states and IMU biases, extending it to incorporate radar-IMU extrinsic calibration and multi-state constraint updates. This equivariant formulation inherently preserves consistency and enhances robustness, enabling reliable state estimation even under poor or completely wrong initialization of calibration states. Real-world experiments on two different Uncrewed Aerial Vehicles (UAVs) show that the proposed EqF-RIO achieves state-of-the-art accuracy under correct extrinsic calibration and offers improved convergence under large calibration errors, where the conventional EKF-RIO fails. Evaluation code is open-sourced.
Complementary Filtering on SO(3) for Attitude Estimation with Scalar Measurements
This paper proposes a complementary filter on SO(3) for attitude estimation from scalar measurements corresponding to projections of known inertial vectors onto body-frame sensing directions. The observer evolves directly on SO(3) and employs a constant-gain innovation tailored to the scalar-output structure. Under suitable persistence-of-excitation conditions, almost-global asymptotic stability is established when at least three inertial vectors are measured along a common body-frame direction. For configurations involving only two scalar measurements, sufficient conditions for asymptotic convergence are derived together with an explicit characterization of the region of attraction. Numerical simulations illustrate the proposed results.
An Interpretable, Controllable Time-Varying IIR Denoiser for On-Device Assistive Hearing
We present TVBC (Time-Varying Biquad Cascade), an interpretable, low-latency speech enhancement model for real-time, on-device assistive hearing. A lightweight neural controller predicts, in real time, the coefficients of a differentiable cascade of 35 second-order IIR filters (biquads), so the model tracks non-stationary noise while keeping a fully interpretable processing chain: every spectral modification is an explicit, adjustable equalizer curve rather than an opaque `black-box' transform. Because the biquad cascade carries the signal processing, the controller can be made very small, driving the cascade with only 24k parameters at a 10.7ms algorithmic latency, within hearing-aid budgets, and running entirely on-device so that audio never leaves the device. We also expose the suppression-versus-preservation trade-off as an explicit control: it can be set during training through the loss weighting, and adjusted at inference, with no retraining, by mixing the noisy input with the denoised output. On hearing-aid metrics (HASPI/HASQI) the 24k model stays within about 0.02 of DFNet3 (2.3M parameters, almost two orders of magnitude larger) while using about 29X fewer multiply-accumulates, although larger black-box models still lead on reference metrics such as PESQ. We present TVBC as a proof of concept for a compact, interpretable, and controllable denoiser for on-device assistive hearing.
Provable Filter for Real-world Graph Clustering
Graph clustering, an important unsupervised problem, has been shown to be more resistant to advances in Graph Neural Networks (GNNs). In addition, almost all clustering methods focus on homophilic graphs and ignore heterophily. This significantly limits their applicability in practice, since real-world graphs exhibit a structural disparity and cannot simply be classified as homophily and heterophily. Thus, a principled way to handle practical graphs is urgently needed. To fill this gap, we provide a novel solution with theoretical support. Interestingly, we find that most homophilic and heterophilic edges can be correctly identified on the basis of neighbor information. Motivated by this finding, we construct two graphs that are highly homophilic and heterophilic, respectively. They are used to build low-pass and high-pass filters to capture holistic information. Important features are further enhanced by the squeeze-and-excitation block. We validate our approach through extensive experiments on both homophilic and heterophilic graphs. Empirical results demonstrate the superiority of our method compared to state-of-the-art clustering methods.