An Information-Based Micro-Kalman Filter for Satellite Tracking: A Comparative Study

Jul 16, 2026

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Satellite dynamics and tracking pose persistent difficulties for space exploration and communication systems, making accurate state estimation essential for reliable orbit maintenance and system performance. The study develops a mathematical framework for satellite state estimation using a linearized radial–angular model. Two measurement-noise sources, tied to range and scaled angular deviations, are modeled as mutually independent with known covariances. Kalman filtering with the Algebraic Riccati Equation yields time-varying and steady-state solutions, while a micro-Kalman filter is compared against KF, EKF, UKF, and an adaptive KF, showing nearly identical accuracy and low bounded mean square estimation error in linear Gaussian settings.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

Abstract

Introduction

Filtering Module on Satellite Tracking

Problem Formulation

Mathematical Model

State-Space Representation

arXiv :2304 .04111v3 [ ee ss . SY] 19 Jun 2026 AN INFORMATION-BASED MICRO-KALMAN FILTER FOR SATELLITE TRACKING: A COMPARATIVE STUDY Moh Kamalul Waﬁ Department of Engineering Physics Institut Teknologi Sepuluh Nopember (ITS) Surabaya, Indonesia {[kamalul.wafi}@its.ac.id](kamalul.wafi}@its.ac.id) ABSTRACT Satellite dynamics and tracking remain important challenges in the context of space exploration and communication systems. Accurate state estimation is essential to maintain reliable orbital motion and system performance. This paper presents a mathematical framework for satellite state estimation based on a linearized model described by radial and angular states. The model incorporates two types of measurement noise corresponding to range and scaled angular deviations, which are assumed to be mutually independent with known covariance structures. The estimation problem is formulated using the Kalman ﬁlter, together with the associated Algebraic Riccati Equation (ARE), leading to both time-varying and steady-state solutions. In addition, a micro-Kalman ﬁlter (µKF) formulation is considered and compared with the classical Kalman ﬁlter, as well as with the extended Kalman ﬁlter (EKF), unscented Kalman ﬁlter (UKF), and an adaptive Kalman ﬁlter under a uniﬁed simulation setup. The results demonstrate that the proposed µKF achieves estimation performance nearly identical to that of the classical Kalman ﬁlter and its variants, with small and bounded estimation errors. The mean square estimation error (MSEE) remains low for all state variables under both noise conﬁgurations, conﬁrming the effectiveness of the proposed approach for linear Gaussian systems. Keywords State Estimation · Kalman Filtering · Information Filter · Satellite Dynamics · Adaptive Covariance · Linear Gaussian Systems 1 Introduction Tracking an object is becoming more challenging and it has been studying to get the precise position while tracking it. The object refers to the satellite and it has increasingly attained as one of the most challenging topics due to the attraction of elaborating the outer space. The proposed concept of doing it is to use Kalman ﬁlter as conducted by [1] and [2] which presented the reduced order of the Riccati differential equation, the tractable of the object in terms of mathematical model, and the the ease in the real implementation in turn. This also stimulates to upgrade the classic Kalman ﬁlter in order to obtain another best estimation method as done by [3], comprising the upgrade of gradient decent in terms of error covariance. The classic Kalman ﬁlter [4] is emerged so as to compare the method in [5] in terms of the mean square estimation error (MSEE) along with its average over certain iterations. The basic concept of the classic Kalman is set from [4] while the elaborating of the basic is well-presented in [6] saying the various possibility of any engineering and non-engineering being perturbed by any noises including tracking a moving object. The initial foundation has been inspired by [7], [4] along with [8] for the concept of ﬁltering. The classic is matched with the Micro-Kalman Filter developed by [5] which then was upgraded in the following paper presented in [9] . This algorithm is the beginning of the possibility of Distributed Kalman Filter (DKF) . This paper proposes the algorithm compared to the classic in terms of the mean square error and overall performance of the states. Filtering Module on Satellite Tracking 2 Problem Formulation This paper considers the problem of satellite state estimation based on a mathematical model of orbital motion, as illustrated in Fig. 1. The objective is to accurately estimate the system states under the presence of measurement uncertainties. The formulation begins with the derivation of a suitable state-space representation corresponding to a nominally circular orbit. Small deviations from this nominal motion are introduced and used to deﬁne the state

FAQs

What satellite model does the proposed estimation framework use?

It uses a linearized satellite orbital model based on radial and angular states around a nominally circular orbit, with small deviations expressed in state-space form.

How are measurement noises modeled in the paper?

Two independent noise types are included: range deviation noise and scaled angular deviation noise, each with known covariance structures.

How does the micro-Kalman filter performance compare with classical Kalman filtering methods?

Under a unified simulation setup, the micro-Kalman filter achieves estimation performance nearly identical to the classical Kalman filter and its variants, with small and bounded estimation errors and low MSEE for all state variables.

Jul 16, 2026

Upload by Jiven