Filter-based SLAM Algorithms

Updated 22 December 2025

Filter-based SLAM is a recursive estimation framework that jointly propagates the robot’s pose and map using methods like EKF, UKF, and particle filters.
It enables real-time, constant-complexity updates by approximating state distributions with Gaussian or multi-Gaussian models for scalable performance.
Innovations include invariance-preserving filters, deep learning hybrids, and random finite set methods, extending applications in autonomous driving and visual-inertial navigation.

Filter-based SLAM is a class of algorithms for Simultaneous Localization and Mapping in which the robot’s joint belief over its own state and the map (landmarks or grid) is represented and propagated recursively by an explicit filtering framework. This paradigm contrasts with batch-optimization (windowed or graph-based) SLAM, which estimates all states through a global nonlinear least-squares, and excels in providing real-time constant-complexity updates at the cost of approximating the distribution—typically assuming Gaussian or multi-Gaussian forms. Filter-based approaches encompass the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), invariant and geometric extensions, particle filters (FastSLAM and variants), random finite set (RFS) filters (PMBM/PMB), model-based deep learning hybrids, and differentiable, end-to-end learned architectures. Theoretical and empirical advances have established precise boundaries of scalability, consistency, and numerical efficiency for these methods across a range of real-world sensing modalities and data association regimes.

1. Classical Formulation and Algorithmic Structure

Filter-based SLAM algorithms maintain a recursive belief over a (potentially high-dimensional) state vector $\mathbf{x}_k$ , which typically includes the robot’s pose and a set of static (sometimes dynamic) landmark positions. The standard filtering loop consists of

Prediction: Based on the motion model $f(\mathbf{x}_{k-1}, u_k)$ and process noise $Q$ , propagate the mean and covariance (EKF/UKF) or sample set (particle filter).
Correction: For each measurement $z_k$ (e.g., range, bearing, scan), compute the innovation and update the belief using the measurement model $h(\mathbf{x}_k)$ and measurement noise $R$ .

In the EKF-SLAM framework, the state is augmented as $\mathbf{x}_k = [x_k^{\mathrm{R}}, y_k^{\mathrm{R}}, \theta_k^{\mathrm{R}}, x_1^{\mathrm{L}}, y_1^{\mathrm{L}}, \dots]^\top$ with nonlinear time and measurement updates, using appropriate Jacobians $F_k$ , $H_k$ for linearization (Choi et al., 2022). The filter’s recursion is defined by: $\begin{aligned} & \text{Prediction:}\quad \hat{\mathbf{x}}_{k|k-1} = f(\hat{\mathbf{x}}_{k-1|k-1}, u_k), \ & P_{k|k-1} = F_k P_{k-1|k-1} F_k^\top + Q, \ & \text{Update:}\quad K_k = P_{k|k-1} H_k^\top (H_k P_{k|k-1} H_k^\top + R)^{-1}, \ & \hat{\mathbf{x}}_{k|k} = \hat{\mathbf{x}}_{k|k-1} + K_k (y_k - h(\hat{\mathbf{x}}_{k|k-1})), \ & P_{k|k} = (I - K_k H_k) P_{k|k-1}. \end{aligned}$ Particle-filter-based SLAM executes prediction, importance weighting (via sensor likelihood), and resampling, maintaining per-particle map hypotheses (Liu et al., 12 Feb 2024, Karkus et al., 2021, Li et al., 17 Feb 2025).

2. Distinct Filtering Methodologies and Innovations

2.1. Gaussian-based Filters

The EKF, as well as adaptive and split-architecture versions integrating learned uncertainty models (Choi et al., 2022), is widely deployed for moderate map sizes. High-dimensional cases favor information-form or marginalization strategies (e.g., MSCKF) (Saxena et al., 2021). Further, invariance-preserving (IEKF) approaches (Barczyk et al., 2014, Bonnabel, 2011) define errors and corrections directly on Lie groups (e.g., SE(3)), decoupling linearization from the specific state trajectory and improving global consistency.

UKF-based SLAM utilizes sigma-point representations to capture higher-order moments of nonlinear transitions. Recent work includes dynamic landmark handling through distance-consistency checks, improving robustness in nonstationary scenes (Dorvash et al., 2023).

2.2. Particle Filters

Particle Filter SLAM maintains $N$ pose hypotheses, each paired with a map (typically occupancy grid or landmark ensemble), as in FastSLAM and its derivatives (Liu et al., 12 Feb 2024, Karkus et al., 2021). Importance weighting is computed using scan–map correlation or learned observation models (SLAM-net, see below), and resampling ensures the survival of the most likely trajectory–map associations. Particle degeneracy in featureless or ambiguous environments can be detected and mitigated by deep learning–driven adaptive resampling, as in anti-degeneracy schemes (Li et al., 17 Feb 2025).

2.3. Random Finite Set (RFS) SLAM

Multi-object filtering has led to SLAM formulations over sets of landmarks modeled as Poisson–Multi-Bernoulli Mixtures (PMBM), which naturally accommodate map birth, death, and ambiguous data associations. Rao–Blackwellized PMBM (Kim et al., 2022), as well as low-complexity EK-PMB and CKF-PMB reductions (Ge et al., 2021, Ge et al., 2021), enable real-time operation under challenging multipath and clutter, especially for 5G mmWave vehicular applications.

3. Robustness, Consistency, and Theoretical Guarantees

Invariant filtering on matrix Lie groups (Barczyk et al., 2014, Bonnabel, 2011, Hashim et al., 2021, Hashim, 2021) ensures estimation error dynamics that are autonomous or depend only on invariant inputs, sidestepping the highly nonstationary linearizations of classical EKF. This enables global or almost-global exponential convergence for the robot and landmarks, subject to weak observability constraints (e.g., three non-collinear landmarks ensure full-rank observability in 3D (Aghili, 2022)).

Self-tuning approaches incorporate online IMU miscalibration estimation and adaptive whitening of the measurement covariance via innovation-window statistics for real-time correction in dynamic or poorly-modeled environments. Explicit bias adaptation and stochastic noise bounding are integrated in geometric nonlinear stochastic filters (Hashim, 2021).

4. Handling High-Dimensional or Feature-Rich Maps

As map size increases, EKF and UKF approaches are challenged by $O(n^3)$ covariance complexity. FastSLAM/particle filter variants scale linearly in the number of particles but require independent maps per particle—impractically memory-intensive in dense grid scenarios (Liu et al., 12 Feb 2024). Feature filtering routines, like PFilter (Duan et al., 2022), actively prune transient or nonpersistent features from the active map by discounted observation count (p-Index), achieving substantial reductions in per-frame computational time and increased mapping accuracy (e.g., 20.9% runtime improvement, 9.4% ATE reduction on KITTI data).

Batch-marginalization and structure-preserving nullspace projection (as in MSCKF (Saxena et al., 2021)) enable efficient handling of high-rate vision/inertial data for state-of-the-art visual-inertial navigation.

5. Deep Learning and Differentiable Filter-based SLAM

Recent research has highlighted the role of learning in filter-based SLAM. SLAM-net (Karkus et al., 2021) formulates a fully differentiable computation graph corresponding to a particle filter, with all modules (mapping, transition, and observation models) parameterized as neural networks and trained end-to-end through backpropagation. This approach demonstrates high robustness to visual noise and reduced dependency on handcrafted data association. Model-based deep learning hybrids (Split-KalmanNet (Choi et al., 2022)) integrate neural networks to estimate filter parameters (e.g., gain, covariance) to compensate for model-mismatch, outperforming both traditional EKF and previous learning-based alternatives.

6. Data Association, Dynamic Environments, and Real-world Deployment

Efficient data association is essential for robust SLAM under ambiguous, dynamic, or cluttered conditions. Advances include:

Geometric and appearance-based dynamic landmark rejection (Dorvash et al., 2023).
Hypothesis management and factor graph inference in RFS-PMB(M) methods (Kim et al., 2022, Ge et al., 2021, Ge et al., 2021).
Deep anti-degeneracy diagnostics enabling context-adaptive sensor trust reweighting, fusion, and hierarchical pose search in particle-SLAM (Li et al., 17 Feb 2025).

Filter-based SLAM methods have demonstrated real-time capabilities across autonomous driving (Lidar+IMU EKF (Aghili, 2022)), mmWave radio localization (PMBM/PMB/CKF (Kim et al., 2022, Ge et al., 2021, Ge et al., 2021)), and visual-inertial navigation (MSCKF, SLAM-net (Saxena et al., 2021, Karkus et al., 2021)). Limitations include scalability for very large maps, performance under severe nonlinearity or large initial uncertainty, and consistency loss for filters improperly tuned or operated outside their observability regimes.

7. Comparative Performance and Practical Considerations

Empirical studies show that filter-based algorithms are computationally efficient—capable of updates in the 1–10 ms range per step on modern CPUs for typical scene sizes—while batch-optimization/graph-based methods deliver slightly higher mapping accuracy at much higher or variable computational cost (Saxena et al., 2021, Aghili, 2022). Filter-based RFS/PMB approaches nearly match the accuracy of full joint RBPF-PMBM filters with <1% of their computational overhead (Ge et al., 2021). Learned and geometric nonlinear filters offer robustness against bias, model-mismatch, and initialization errors that are challenging for classical EKF/UKF (Hashim, 2021, Choi et al., 2022).

The selection of filter class and its algorithmic instantiation must balance map scale, real-time update constraints, hardware limitations, sensor modality, and specific operational challenges such as data association ambiguity or environmental nonstationarity (Dorvash et al., 2023, Duan et al., 2022, Li et al., 17 Feb 2025). The evolving landscape of differentiable, symmetry-preserving, and hybrid deep learning–filter architectures continues to expand the operational domain of filter-based SLAM.

Key references: (Barczyk et al., 2014, Bonnabel, 2011, Aghili, 2022, Choi et al., 2022, Dorvash et al., 2023, Ge et al., 2021, Karkus et al., 2021, Saxena et al., 2021, Hashim et al., 2021, Hashim, 2021, Kim et al., 2022, Li et al., 17 Feb 2025, Liu et al., 12 Feb 2024, Duan et al., 2022, Ge et al., 2021).