arXiv subjects

Sifeddine Benahmed

Publications and source records attributed to Sifeddine Benahmed.

6 recordsLinked to original sources

arXiv2026

Scalar-Measurement Attitude Estimation on $\mathbf{SO}(3)$ with Bias Compensation

Attitude estimation methods typically rely on full vector measurements from inertial sensors such as accelerometers and magnetometers. This paper shows that reliable estimation can also be achieved using only scalar measurements, which naturally arise either as components of vector readings or as independent constraints from other sensing modalities. We propose nonlinear deterministic observers on $\mathbf{SO}(3)$ that incorporate gyroscope bias compensation and guarantee uniform local exponential stability under suitable observability conditions. A key feature of the framework is its robustness to partial sensing: accurate estimation is maintained even when only a subset of vector components is available. Experimental validation on the BROAD dataset confirms consistent performance across progressively reduced measurement configurations, with estimation errors remaining small even under severe information loss. To the best of our knowledge, this is the first work to establish fundamental observability results showing that two scalar measurements under suitable excitation suffice for attitude estimation, and that three are enough in the static case. These results position scalar-measurement-based observers as a practical and reliable alternative to conventional vector-based approaches.

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arXiv2026

A General Nonlinear Observer Design for Inertial Navigation Systems with Almost Global Stability Guarantees

This paper studies nonlinear observer design for rigid-body extended pose estimation using inertial measurements and generic exteroceptive sensing. The estimation problem is formulated as a cascade architecture that separates translational dynamics from rotational kinematics while preserving the geometric constraint of attitude evolution on $SO(3)$. By embedding the inertial navigation model into a Linear Time-Varying (LTV) representation, we construct an observer composed of a Kalman-Bucy-type estimator for translational states and an auxiliary unconstrained attitude variable, coupled with a nonlinear geometric reconstruction filter evolving on $SO(3)$. The cascade interconnection is analyzed within a nonlinear systems framework. We prove that uniform observability of the LTV subsystem guarantees almost global asymptotic stability of the overall nonlinear observer. For a benchmark GPS landmark aided configuration, explicit sufficient conditions on admissible trajectories are derived to ensure uniform observability. Simulation results illustrate the effectiveness of the proposed estimation framework.

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arXiv2025

Attitude Estimation Using Scalar Measurements

This paper revisits the problem of orientation estimation for rigid bodies through a novel framework based on scalar measurements. Unlike traditional vector-based methods, the proposed approach enables selective utilization of only the reliable axes of vector measurements while seamlessly incorporating alternative scalar modalities such as Pitot tubes, barometers with range sensors, and landmark-based constraints. The estimation problem is reformulated within a linear time-varying (LTV) framework, allowing the application of a deterministic linear Kalman filter. This design guarantees Global Uniform Exponential Stability (GES) under the Uniform Observability (UO) condition. Simulation results demonstrate the effectiveness of the proposed approach in achieving robust and accurate attitude estimation, even with partial vector measurements that simulate sensor axis failure.

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arXiv2025

A Geometric Approach For Pose and Velocity Estimation Using IMU and Inertial/Body-Frame Measurements

This paper addresses accurate pose estimation (position, velocity, and orientation) for a rigid body using a combination of generic inertial-frame and/or body-frame measurements along with an Inertial Measurement Unit (IMU). By embedding the original state space, $\so \times \R^3 \times \R^3$, within the higher-dimensional Lie group $\sefive$, we reformulate the vehicle dynamics and outputs within a structured, geometric framework. In particular, this embedding enables a decoupling of the resulting geometric error dynamics: the translational error dynamics follow a structure similar to the error dynamics of a continuous-time Kalman filter, which allows for a time-varying gain design using the Riccati equation. Under the condition of uniform observability, we establish that the proposed observer design on $\sefive$ guarantees almost global asymptotic stability. We validate the approach in simulations for two practical scenarios: stereo-aided inertial navigation systems (INS) and GPS-aided INS. The proposed method significantly simplifies the design of nonlinear geometric observers for INS, providing a generalized and robust approach to state estimation.

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arXiv2024

State Estimation Using Single Body-Frame Bearing Measurements

This paper addresses the problem of simultaneous estimation of the position, linear velocity and orientation of a rigid body using single bearing measurements. We introduce a Riccati observer-based estimator that fuses measurements from a 3-axis accelerometer, a 3-axis gyroscope, a single body-frame vector observation (e.g., magnetometer), and a single bearing-to-landmark measurement to obtain the full vehicle's state (position, velocity, orientation). The proposed observer guarantees global exponential convergence under some persistency of excitation (PE) condition on the vehicle's motion. Simulation results are presented to show the effectiveness of the proposed approach.

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arXiv2023

Stability analysis of optimal control problems with time-dependent costs

We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general attractors are established. This work covers and generalizes the related results on discounted optimal control problems to more general systems and cost functions.

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