# Adaptive Satellite Navigation Anti-Interference Algorithm Based on Inverse Cosine Function
## 1 Introduction  
Satellite navigation signals need to travel a long distance to reach the ground to be received, and the ground reception signal power is weak, making it susceptible to many sorts of interference, whether deliberate or accidental [1; 2; 3; 4; 5]. For systems that rely on the global navigation satellite system (GNSS), even a small amount of interference might have disastrous results [6; 7; 8]. Satellite navigation system adopts spread spectrum communication technology and has certain anti-interference ability [9], but the receiver will malfunction if the interfering signal is too powerful and exceeds the system's tolerance limitations [10]. Narrowband interference is a common form of interference signal utilized by a variety of interference equipment because it is simple to produce, cheap, and has a strong interference impact [11]. The three basic processing domains used for narrowband interference suppression are time, frequency, and combined domain [12; 13; 14; 15]. One of the most popular methods for reducing narrowband interference in navigation receivers is time-domain anti-interference processing [16]. The time-domain anti-interference technology is now the more appropriate option for the future development trend in the BeiDou RDSS system, which has miniaturization and low power consumption as its aims [17]. Adaptive filters are primarily used in the time domain for interference suppression [18; 19; 20]. Adaptive algorithms modify their processes and parameters based on data traits, without full upfront information [21]. This ensures optimal convergence and maintains low error levels [22]. An algorithm with a good performance can ensure that the interference suppression effect is optimal, and the LMS algorithm is the classical algorithm [23]. Because the conventional LMS algorithm cannot accurately select the appropriate step size value accordingto the situation, the steady-state error and convergence speed cannot be optimized simultaneously. The problem of low applicability of a fixed step size LMS algorithm in many scenarios needs to be solved urgently. [PERSON] et al. [24] proposed a filtering algorithm with a variable step size that can be automatically adjusted. The convergence and tracking effects are improved in the algorithm, but the error cannot be controlled in a small range. [PERSON] et al. [25] obtained a new function model by improving the Sigmoid function, which greatly shorten the convergence time without losing accuracy. [PERSON] et al. [26] improved the LMS algorithm by using the hyperbolic secant cost function, which reinforces the system's ability to cope with harsh environments and reduces the oscillation amplitude. [PERSON] et al. [27] proposed an improved LMS filtering algorithm with higher stability based on the hyperbolic tangent function. [PERSON] et al. [28] introduced a step size compensation factor according to the normalized sigmoid function. The algorithm automatically adjusts the step size value without changing the parameters, and the calculation is simple, but the convergence time of this method is too long, and the error value is large. [PERSON] et al. [29] employed the inverse hyperbolic tangent function to construct a new formula, and achieved good results in system identification, noise removal, and other applications. The above algorithm reduces the waiting time during the convergence period and maintains a low steady-state error value, but there are still problems, such as that both factors cannot be balanced, the computation is large, and the tracking performance is poor. To obtain a reasonable algorithm that can solve the existing problems, a novel LMS algorithm leveraging the inverse cosine function is proposed to enhance convergence speed and achieve a reduced error level. This algorithm demonstrates its efficacy in effectively suppressing narrow-band interference in satellite navigation signals. The paper is structured into the following chapters: Section II explains the principle of suppressing interference using an LMS algorithm.