INTRODUCTION

To write Simultaneous Localization and Mapping (SLAM) continues to be a fundamental ability in autonomous robotics, allowing mobile agents to traverse and comprehend unfamiliar environments without existing maps. Among the most examined frameworks, the Extended Kalman Filter-based SLAM (EKF-SLAM) formulation remains a dependable and computationally efficient method for state estimation, especially in structured or somewhat dynamic settings. By keeping a joint Gaussian distribution for both robot pose and landmark positions, EKF-SLAM successfully propagates uncertainty while integrating sensor feedback through a prediction-correction cycle [1]. Nonetheless, in spite of its theoretical elegance and practical success, classical EKF-SLAM faces several limitations that impede its application in more complex real-world scenarios. The primary considerations include the assumptions of Gaussian noise, static landmarks, and consistent, independent sensor observations. In settings characterized by perceptual aliasing, occlusions, dynamic objects, or non-stationary noise patterns, the performance of the filter diminishes because of inadequate data association and fragile update mechanisms. Most importantly, EKF-SLAM considers all observed features in the correction step, depending only on the current residual and previous covariance structure to modify the belief state [2]. Recent attempts to address these vulnerabilities have investigated the combination of learning-based perception, strong filtering, and information-theoretic planning. For example, deep learning has been utilized to improve loop closure detection and landmark recognition, thereby enhancing map consistency in settings with varying appearances [3] [4]. At the same time, strong SLAM algorithms have implemented gating mechanisms that utilize Mahalanobis distance or residual norm thresholds to remove outliers [5]. Simultaneously, entropy and mutual information have been utilized in active SLAM and exploration, where actions are selected to enhance expected information gain [6] [7]. Although these directions show potential, they either separate the sensing and filtering processes or utilize information-theoretic reasoning only at the planning layer, without modifying the internal estimation dynamics of EKF-SLAM. It is important to note that only a limited number of methods have tackled the issue of dynamically adjusting the impact of specific observations in the EKF update equation according to their long-term usefulness. Most SLAM frameworks operate under the assumption that an observation, when it is geometrically consistent and falls within noise limits, holds equal utility. This assumption fails in situations where certain landmarks yield unreliable or unclear measurements over time, like reflective surfaces, textureless walls, or recurring patterns. An adaptive strategy would assess the historical impact of each feature on the estimation process and adjust its influence as needed. We propose an innovative approach that integrates a lightweight but robust information-theoretic correction scheme into the traditional EKF framework. Our approach calculates rolling entropy profiles based on landmark measurements and employs them to adjust the innovation term during the correction phase. This entropy-aware gating mechanism allows the filter to prioritize features that reliably yield informative, low-entropy measurements, while diminishing the influence of those that display high uncertainty or perceptual ambiguity. In contrast to outlier rejection methods that depend on rigid thresholds, our approach offers a continuous trust score based on information theory, thereby maintaining essential weak signals and preventing filter degradation. This approach connects robust estimation with information-theoretic filtering, introducing a novel dimension of adaptivity to EKF-SLAM. By evaluating not only the accuracy of a measurement but also its historical significance, we improve the resilience and reliability of SLAM in practical applications. Our research aligns with contemporary trends in uncertainty-aware, learning-informed SLAM, while preserving compatibility with traditional filter logic and real-time requirements. This paper presents a new SLAM design that adds an information-based improvement to the traditional Extended Kalman Filter (EKF) system, with the goal of bettering how mobile robots navigate in unclear environments. Our principal contribution is the incorporation of an entropy-aware innovation gating mechanism that assesses the temporal consistency of landmark observations through rolling measurement entropy profiles. Unlike traditional methods that only rely on fixed noise models or immediate differences, our approach changes how much each observation affects the EKF update based on how useful it has been over time. This adaptive trust model allows the SLAM system to ignore noisy, confusing, or unreliable features while focusing on landmarks that have performed well over time. The outcome is a more robust estimation process that markedly diminishes drift and enhances resilience to visual aliasing and sensor deterioration. We execute and assess our system through simulation, utilizing a differential-drive robot functioning in a two-dimensional environment with numerous landmarks. The results show major improvements in position accuracy, landmark dependability, and overall map quality compared to traditional EKF-SLAM. This study highlights the potential of using information-theoretic observability in probabilistic filtering to create more flexible and dependable systems for autonomous navigation. The subsequent sections of this paper follow this structure: Section 2 looks at important research on improvements to EKF-SLAM, strong estimation methods, and navigation guided by entropy. Section 3 summarizes the traditional EKF-SLAM framework, encompassing its state and measurement models. Section 4 delineates our proposed Entropy-Gated Feature-Aware EKF-SLAM (EFG-EKF-SLAM), accompanied by comprehensive mathematical formulation and theoretical justification. Section 5 delineates the simulation configuration, implementation specifics, and evaluation criteria while also analyzing the experimental outcomes. Ultimately, Section 6 concludes the paper and delineates prospective avenues for future research.

RELATED WORKS

The evolving landscape of SLAM research reflects a growing interest in bridging classical probabilistic estimation with modern machine learning and information-theoretic models. While the Extended Kalman Filter-based SLAM (EKF-SLAM) framework is still popular because it is efficient and well-supported by theory, it has ongoing challenges—especially with issues like confusing similar objects, dealing with moving scenes, and ensuring accurate measurements. A major line of enhancement has focused on integrating deep learning to support tasks like visual understanding and data association. CNN-based systems such as DeepVO [8] and DROID-SLAM [9] have demonstrated significant improvements in pose estimation accuracy through end-to-end learning. These systems often replace or augment parts of the SLAM pipeline with differentiable neural components. However, they are typically dataset-dependent and computationally intensive, limiting their applicability in real-time, resource-constrained platforms. Moreover, they decouple perception from state estimation, treating learned features as static inputs to a separate filtering or optimization layer. In response, hybrid SLAM architectures have emerged, combining learning-based perception with classical filters like EKF or particle filters. Some examples are neural modules that help with recognizing when a robot has returned to a previous location [10], understanding the environment [11], and estimating distances [12], while traditional probabilistic filters still handle the tracking of the robot's position. A notable case is CNN-enhanced EKF-SLAM [13], where deep visual features inform landmark observations. While promising, such systems typically treat learned features as fixed priors, lacking mechanisms for adaptive trust during the filtering process. Another research avenue has investigated information-theoretic methodologies in SLAM, particularly regarding active exploration. Methods utilizing entropy and mutual information have been employed to direct motion planning, allowing robots to traverse environments in a manner that optimizes comprehension of their surroundings [14] [15]. Nonetheless, these informational measures are typically implemented at the planning stage and do not directly influence the EKF's internal correction phase, rendering the estimation process susceptible to erroneous or ambiguous observations. To make sure the measurements are reliable, strong filtering methods like Mahalanobis gating, residual norm tests, and outlier rejection have been recommended to prevent the EKF from being affected by incorrect sensor data [16] [17]. These methods are generally binary and threshold-dependent, jeopardizing the acceptance of potentially valuable information. Significantly, they also lack memory, perceiving each observation as an isolated event without deriving insights from historical patterns. Recently, adaptive observation modeling has been introduced using methods such as heteroscedastic Gaussian processes and time-varying noise scaling [18]. Even though they can manage changing uncertainty, these methods often require a lot of computing power and may need the model to be updated or retrained regularly. Additionally, they continue to depend on Gaussian assumptions and do not clearly monitor or utilize long-term observation statistics for each landmark. In 2024, Chen and his team created an EKF-SLAM model that used special features to change the Kalman gain based on the current randomness of sensor data [19]. This method improved resilience to unpredictable data but failed to account for time-related patterns, rendering it susceptible to brief variations. In 2025, Li and Kumar presented Temporal Entropy SLAM, which employed rolling entropy profiles to reduce the influence of observations from unstable landmarks [20]. Although conceptually aligned with our work, their entropy computation functioned outside the EKF loop, necessitating post-processing and extra logic. They also failed to assess performance under landmark aliasing, which is a frequent failure point in real-world deployments. At the same time, Garcia and others developed a system for linking data using information theory, applying mutual information to improve loop closure and feature matching [21]. While successful in visually repetitive settings, the approach depended on pretrained descriptors and was unable to adaptively adjust measurement trust throughout the filtering process. These recent initiatives highlight the significance of incorporating information-aware mechanisms into SLAM pipelines. Nonetheless, many continue to regard entropy as an external factor, fail to model temporal consistency, or add computational complexity that is not appropriate for real-time applications.

Beyond Gaussian-assumed EKF formulations, recent research has explored state estimation under non-Gaussian noise and highly uncertain sensing conditions. For instance, a nonlinear non-Gaussian filtering framework built on a Gaussian noise model with jump assumptions has demonstrated increased robustness against abrupt process and measurement disturbances, particularly useful in multipath-affected environments [22]. Similarly, a Gaussian mixture unscented Rauch–Tung–Striebel smoothing framework has been proposed to improve trajectory reconstruction accuracy in scenarios with significant nonlinearities and non-Gaussian uncertainties [23]. Furthermore, distributed maneuvering vehicle tracking using ultra-wideband observations has been shown to provide reliable positioning in convoluted indoor environments where vision-only SLAM can degrade [24]. These works address robustness at the uncertainty modeling level, whereas the proposed EFG-EKF-SLAM framework introduces complementary benefits by adaptively modulating measurement trust within the classical EKF structure using information-theoretic consistency. Integrating entropy-aware trust gating with mixture-based filters or smoothing approaches represents a promising direction for future research.

The EFG-EKF-SLAM we suggest adds a simple, per-landmark entropy profile right into the EKF innovation step, allowing the filter to adjust how much each measurement matters based on its long-term usefulness. This combination makes the system better at handling noise, confusion, and similar environments—without needing outside classifiers, learning models, or complicated preprocessing. Unlike nonlinear gating methods that rely on instantaneous residual thresholds (e.g., Mahalanobis gating), the proposed approach uses temporal information-theoretic consistency rather than geometric outlier detection. Therefore, it does not directly compete with residual-based gating but complements it by modeling long-term landmark reliability. To help clarify our contribution, Table 1 shows a comparison of recent SLAM methods, focusing on their main innovations, limitations, and how they differ from our proposed Entropy-Gated Feature-Aware EKF-SLAM (EFG-EKF-SLAM). This table highlights that, although numerous works have investigated learning-based perception, robust filtering, or information-theoretic reasoning, none have closely integrated long-term, entropy-based trust modulation directly into the EKF correction step, as we suggest.

EKF-SLAM FRAMEWORK

Simultaneous Localization and Mapping (SLAM) is the problem where a robot builds a map of an unknown environment while simultaneously estimating its pose within that map. The Extended Kalman Filter (EKF) SLAM provides a solution when assuming: Gaussian noise in motion and measurement, and small nonlinearities that can be approximated linearly.

State Representation

Let Define 𝐱t=[xt,yt,θt]T the robot pose at time t, 𝐦i=[mix,miy]T the Coordinates of landmark i, 𝐦=[𝐦1T,𝐦2T,…,𝐦NT]T the Full map, and 𝐲t=[𝐱tT,𝐦T]Tthe Complete system state with 𝐲t∈ℝ3+2N. The Differential drive robot motion is described by the equation (1).

where 𝐮t=[vt,ωt]T is the control input: translational and rotational velocities, and 𝐰t∼𝒩(0,𝐐t) is the process noise. A common motion model for differential drive robots can be given by equation (2).

In vector form, equation (2) becomes equation (3):

Since the map 𝐦 is static, so: is static, so:

Thus, the full motion model for 𝐲t is: is:

Measurement Model

Assuming range and bearing sensors, measurement to landmark i, is:

Thus:

where 𝐯i,t∼𝒩(0,𝐑t). Generalizing to multiple observations:. Generalizing to multiple observations:

EKF-SLAM Prediction Step

Using the motion model:

where 𝛍x and and 𝛍m denote the robot and map parts respectively. The Jacobian denote the robot and map parts respectively. The Jacobian 𝐆t of of g with respect to the with respect to 𝐱 is: is:

Explicitly:

Augment with map (since map is static):

Thus:

EKF-SLAM Correction Step

The Extended Kalman Filter (EKF) correction step in Simultaneous Localization and Mapping (SLAM) serves to refine the robot’s belief about its pose and the map using incoming sensor measurements. Mathematical development proceeds as follows: First, given a predicted mean 𝛍t|t−1 and predicted covariance 𝚺t|t−1 after the motion update, we use the sensor model to compute the expected measurement 𝐳̂t, which represents what the robot expects to observe, given its current predicted state. This expected measurement is evaluated by passing the predicted state through the observation function h(⋅):

The next step involves computing the innovation, also known as the measurement residual, which quantifies the difference between the actual received measurement 𝐳t and the expected measurement:

This innovation vector captures the inconsistency between prediction and observation and will later be used to correct the state estimate. Since the observation function h(⋅) is generally nonlinear (for example, involving range and bearing calculations), we must linearize it to apply the Kalman update equations. This is achieved by computing the Jacobian matrix 𝐇t, which consists of partial derivatives of h with respect to the full state vector 𝐲. For a single landmark i, the Jacobian 𝐇i,t is given by:

where hi is the function predicting the observation of landmark i.

Explicitly, the form of 𝐇i,t for a 2D landmark and robot pose can be written as:

where (xt,yt) denote the robot’s predicted position, (mix,miy) are the predicted coordinates of landmark i, and ri is the expected range:

It is important to emphasize that 𝐇i,t is sparse: its nonzero entries correspond only to the robot’s pose components and the specific observed landmark i; the other landmarks are unaffected in the measurement model. When multiple landmarks are observed at once, the corresponding individual Jacobians 𝐇i,t are stacked vertically to form the overall measurement Jacobian 𝐇t:

where K denotes the total number of observed landmarks at time t. Having computed Jacobian, the next step is to determine the innovation covariance 𝐒t, which represents the uncertainty associated with the difference between expected and actual observations:

Here, Ri,teff=1γiRi,t,γi∈(0,1]. 𝐑𝐭 is the measurement noise covariance matrix, typically assumed known based on sensor characteristics. To preserve the statistical consistency of the EKF, entropy-based trust modulation is implemented as adaptive measurement noise inflation rather than direct innovation scaling. For each landmark i, the effective measurement covariance is defined by 𝐑𝐢,𝐭eff . The Kalman gain 𝐊t can now be computed, which balances trust between the predicted state and the new measurement.

It is given by:

A larger Kalman gain indicates that the filter gives more weight to the measurement, while a smaller gain indicates more reliance on the prediction. With the Kalman gain available, the corrected mean 𝛍t is obtained by adjusting the prior prediction by the innovation weighted by the Kalman gain:

This update incorporates new information from the measurements to refine the state estimate. Simultaneously, the corrected covariance 𝚺t is updated to reflect the reduced uncertainty after incorporating the measurement:

This ensures that the updated uncertainty is properly reduced based on the reliability of the measurements. To summarize the entire EKF-SLAM framework, at each time step, the filter proceeds through the following steps:

1. Prediction Step:

   • Predict the new state mean 𝛍t|t−1 using the motion model g(𝐱,𝐮),

   • Predict the new covariance 𝚺t|t−1 using the linearized motion model Jacobian 𝐆t.

2. Correction Step:

   • Use the sensor model to compute the expected measurement 𝐳̂t,

   • Compute the innovation 𝐫t=𝐳t−𝐳̂t,

   • Compute the measurement Jacobian 𝐇t by linearizing the sensor model,

   • Calculate the innovation covariance 𝐒t,

   • Compute the Kalman gain 𝐊t,

   • Update the mean and covariance with the correction terms.

PROPOSED METHOD

We begin our development from the standard correction step in EKF-SLAM. The EKF update equations for the state mean 𝛍t and covariance Σt after incorporating sensor observations are given by:

Here, 𝛍t|t−1 is the predicted state mean, and Σt|t−1 is the predicted covariance. The matrix 𝐇t is the Jacobian of the observation model with respect to the state, and 𝐊t is the Kalman gain computed as:

The term 𝐫t=𝐳t−𝐳̂t is the innovation or measurement residual, where 𝐳t is the actual observation, and 𝐳̂t=h(𝛍t|t−1) is the predicted observation based on the observation function h(⋅).

The core novelty of the proposed method lies in modulating the influence of each landmark observation according to its long-term reliability. Instead of directly scaling the innovation, which could lead to statistical inconsistency, we adjust the effective measurement uncertainty associated with each landmark. Specifically, a trust coefficient γi∈(0,1], computed from the temporal entropy of past innovations, is used to inflate the measurement noise covariance: Ri,teff=1γiRi,t,γi∈(0,1], where smaller trust values correspond to larger assumed measurement uncertainty. The innovation remains defined in the standard EKF form.

Its impact on the state update is naturally reduced through the Kalman gain computed using the inflated covariance. γi represents the normalized information content of the observation, and it dynamically adapts based on the entropy history of the corresponding landmark. When a landmark is observed for the first time, no observation history is available to compute a reliable entropy estimate. To address this cold-start situation, the trust coefficient is initialized progressively according to the number of observations accumulated for that landmark. Specifically, the trust value increases gradually from a conservative initial level and reaches full entropy-based evaluation once a minimum history length is obtained. This prevents newly initialized landmarks—whose positions are still highly uncertain—from exerting excessive influence on the state update, while ensuring that they are not permanently suppressed. After sufficient observations are collected, the standard entropy-based trust modulation is applied. We compute the rolling entropy of the measurement stream for landmark i over a recent time window. Let 𝒵i={𝐳t−ki,…,𝐳ti} denote the sequence of past range-bearing observations to landmark i. We construct a histogram of these measurements over pre-defined bins to estimate the empirical probability distribution Pi={p1,p2,…,pn}. The Shannon entropy is then calculated as:

where ϵ is a small positive constant added for numerical stability.

The entropy estimation depends on two parameters: the rolling window length kand the number of histogram bins n. The window length controls the trade-off between responsiveness and statistical stability. In practice, kis chosen to include sufficient samples for reliable distribution estimation (typically 10–20 observations per landmark). The number of bins is determined using the Freedman–Diaconis rule to balance resolution and sampling noise. Sensitivity analysis showed that moderate variations of these parameters affect only the smoothness of trust adaptation while preserving the relative performance trends of the proposed method.

Although raw range and bearing measurements naturally vary as the robot moves, such deterministic geometric changes remain structured and consistent with the motion and observation models. Over a short temporal window, these variations produce a concentrated empirical distribution. In contrast, unreliable observations arising from occlusion, aliasing, or sensing disturbances lead to irregular fluctuations that broaden the distribution and increase entropy. Therefore, the entropy measure primarily captures temporal observation consistency rather than deterministic motion-induced variation.

The size of the rolling entropy window W governs the trade-off between responsiveness and stability of the trust coefficient γi. A shorter window allows the entropy estimate to react quickly to sudden changes in landmark observability (e.g., temporary occlusion or sensor degradation), resulting in faster trust adaptation. However, this may introduce higher variance and sensitivity to transient noise. Conversely, a longer window smooths short-term fluctuations and provides a more stable estimate of landmark reliability, at the cost of slower adaptation to abrupt environmental changes. In our implementation, Wwas chosen to balance these effects, ensuring both temporal stability and reactivity.

The entropy estimation relies on histogram binning of recent measurements. The number of bins nwas selected to provide sufficient resolution while maintaining statistical stability, avoiding over-fragmentation of sparse data. A moderate bin count ensures that entropy reflects genuine measurement variability rather than discretization artifacts. Empirically, we found that results are robust to moderate variations in n, provided that bins adequately cover the measurement range. To normalize the entropy into the interval [0,1], we divide it by the maximum possible entropy Hmax=log(n), yielding the trust weight:

This means that landmarks with low entropy (i.e., consistent and reliable observations) are assigned γi≈1, while those with highly uncertain or noisy measurements receive γi≈0.

Let K denote the number of landmarks observed at time t. We stack all residuals 𝐫ti to form the total innovation vector 𝐫t, and organize the γi values into a block-diagonal matrix:

Here, each 𝐈2 corresponds to the dimensionality (e.g., range and bearing) of a single landmark measurement. We then define the entropy-aware residual vector as:

The Kalman gain and the Jacobian remain unchanged and are computed as in standard EKF-SLAM, but the measurement residual now carries an embedded notion of temporal feature trustworthiness.

This entropy-aware innovation scaling introduces several key advantages:

Thus, the proposed EFG-EKF-SLAM framework improves estimation robustness by embedding information-theoretic observability directly into the filtering process, leveraging entropy as a dynamic, interpretable, and computationally efficient confidence measure. The computational overhead of the proposed entropy-gated mechanism is minimal. For each observed landmark, the method requires only a histogram update and a scalar entropy computation over a fixed window. These operations scale linearly with the number of observations per landmark and do not alter the matrix dimensions involved in the EKF update. Consequently, the runtime complexity remains dominated by the EKF covariance update, preserving real-time feasibility comparable to standard EKF-SLAM. At the beginning of the mission, when insufficient measurement history is available, each new landmark is assigned a neutral trust value γi=1. As more observations accumulate, the entropy profile gradually refines this trust estimate. This ensures stable early behavior without prematurely suppressing new features. The step-by-step implementation of the proposed entropy-gated innovation mechanism within the EKF-SLAM correction stage is outlined in Algorithm 1 for clarity and reproducibility.

Algorithm 1. Entropy-Gated EKF-SLAM Correction.

For each observed landmark 𝐢:

Stack residuals and apply standard EKF update.

EXPERIMENTAL RESULTS

To evaluate the effectiveness of the proposed Entropy-Gated Feature-aware EKF-SLAM (EFG-EKF-SLAM) framework compared to the classical EKF-SLAM, four experimental scenarios were designed, each representing different real-world challenges. The robot motion and observation models were kept consistent across all experiments, while environmental conditions such as measurement noise and landmark distribution were varied to simulate different complexities. For each scenario, both EKF-SLAM and EFG-EKF-SLAM algorithms were run in parallel. For each case, a figure comprising four subplots is presented: robot trajectory comparison (top-left), landmark mapping and confidence ellipses (top-right), entropy dynamics (bottom-left), and pose estimation error over time (bottom-right). The motion noise covariance was set to Qt=diag(0.022,0.022,0.012), and the nominal measurement noise covariance was Rt=diag(0.12,(2∘)2). In noisy scenarios, measurement noise variance was increased up to threefold to simulate degraded sensing conditions. The experiments are detailed below, and a quantitative comparison across all cases is summarized in Table 2.

CONCLUSION

In this work, we introduced Entropy-Gated Feature-Aware EKF-SLAM (EFG-EKF-SLAM), an adaptive enhancement of the classical EKF-SLAM framework that incorporates information-theoretic trust modulation directly into the Kalman update. By monitoring the historical entropy profiles of landmark observations, our approach dynamically adjusts the influence of each measurement based on its long-term consistency, enabling the SLAM system to suppress ambiguous or unreliable features without requiring external classifiers or additional sensing modalities. Extensive simulations across four distinct scenarios — clean environments, high-noise sensing, perceptual aliasing, and dynamically changing noise conditions — confirmed the effectiveness of the proposed method. Compared to standard EKF-SLAM, EFG-EKF-SLAM consistently demonstrated improved trajectory accuracy, reduced landmark uncertainty, and increased resilience against both measurement noise and perceptual ambiguity. In particular, the entropy-adaptive gating mechanism proved crucial in environments characterized by non-stationary sensor reliability and spatial aliasing, where traditional static noise assumptions fail to maintain map fidelity. Moreover, EFG-EKF-SLAM maintains the lightweight computational footprint inherent to EKF architectures, ensuring real-time applicability for resource-constrained robotic platforms. Overall, the results validate that embedding long-term observability cues into the filtering process substantially enhances SLAM robustness, offering a promising pathway for next-generation autonomous navigation systems operating in uncertain and dynamic environments. While the proposed EFG-EKF-SLAM framework introduces an effective information-theoretic mechanism to modulate measurement influence based on entropy, further extensions could improve adaptability in more complex or non-Gaussian environments. For instance, future work could explore incorporating intelligent clustering algorithms similar to those used in radar detection under k-distributed sea clutter [25], enabling the SLAM system to dynamically group and reclassify landmarks based on uncertainty structure or spatial ambiguity. Such clustering could help disambiguate features in environments with dense or repeating visual patterns. Additionally, methods inspired by deep learning-based signal estimation [26] [27] could be leveraged to enhance landmark observability under perceptual noise. Specifically, neural networks trained to mitigate environmental clutter or to denoise weak signals may be adapted to improve feature detection confidence before entropy computation. These strategies may enable EFG-EKF-SLAM to better handle sensor drift, occlusions, or poor lighting conditions by learning contextual patterns beyond purely geometric cues. Integrating such techniques would allow the filter to operate more robustly in real-world, perceptually challenging scenarios, further strengthening the system’s reliability and extending its applicability to autonomous navigation in degraded sensing conditions.