## 1 Introduction  
Aircraft with LSR configuration constitute a class of flying vehicles with large portions of their mass concentrated along the centerline. The LSR configuration is widely used in high-speed aircraft design because of its reduced drag, particularly for hypersonic vehicles, which have become a popular topic in recent years [1]. However, the coupling dynamics [2] related to its LSR configuration often lead to undesired stability and control characteristics, which have been a long-standing problem for aircraft designers. In the past, catastrophic accidents resulting from the control of LSR aircraft have occurred [3, 4]. As most LSR aircraft have a symmetric structure, the longitudinal and lateral-directional dynamics can be discussed separately. The lateral-directional dynamics are more complex, and designing control systems for them is a more challenging task. To enhance flight safety, many studies have focused on lateral-directional decoupling control. For multiple-input-multiple-output (MIMO) control methods, eigenstructure assignment (EA) has demonstrated great performance in lateral-directional control by simultaneously assigning eigenvalues and eigenvectors [5]. The linear quadratic integral (LQI) controller [6] possesses the advantage of simplicity of design for MIMO systems, particularly with regard to control effort allocation. The EA method is widely used in tailless aircraft control [7; 8], but because it is based on the linearized model, it can be challenging to address nonlinear dynamics. Nonlinear dynamic inversion (NDI) is a control method that has demonstrated effectiveness in controlling nonlinear systems. NDI control was utilized to achieve lateral-directional decoupling control for high-angle-of-attack flight in the F-18 [9]. However, an accurate nonlinear dynamics model is required for NDI, which can be challenging to obtain [10]. Reference [11] introduces the use of H-inf control to achieve precise control of lateral-directional motion during the landing approach phase. To reduce dependence on model information under these circumstances, INDI control has been proposed [12]. The core of INDI control involves using angular acceleration estimation to compensate for nonlinearities or disturbances, making it a sensor-based control method [13]. The differential method, coupled with a washout filter, is a widely used technique for estimating angular acceleration for INDI control. This is because most aircraft come equipped with a gyroscope, which can provide easy access to angular rate information. However, the method suffers from poor estimation performance due to the amplification of noise [14]. Furthermore, the availability and high cost of angular acceleration sensors present additional challenges [15]. To address these issues, researchers have explored alternative approaches, such as distributed MEMS IMUs based on the extended Kalman filter (EKF) [16] and non-delay differentiators based on sampling information [17]. Furthermore, the real-time observer based on the Kalman filter exhibits insensitivity to Gaussian white noise [18], rendering it suitable for online aircraft identification purposes. While these methods offer better estimation performance, they also require significant computational resources and algorithmic complexities. Complementary filters (CF) are another popular method for attitude estimation, as they combine gyroscope and linear accelerometer measurements with high computational efficiency and a simple structure. This paper proposes a hybrid INDI control structure that employs an ESO-based angular acceleration estimator [19]. The paper's main contributions can be summarized as follows: (1) The ESO-based estimator is empirically validated to surpass CF in noise suppression performance without introducing additional computational complexity. This improvement is substantiated through rigorous simulations. (2) The proposed control structure, incorporating the ESO-based estimator, enables the execution of supersonic roll maneuvers for the LSR aircraft.