## 1 Introduction
In [15], an improved Particle Swarm Optimization (PSO) algorithm with an adaptive search space and elite reservation strategy was proposed for real-time estimation of the fractional part of the inter-system phase bias. Additionally, ref. [16] introduced a PSO-backpropagation neural network to model variations in GNSS broadcast ephemeris orbit errors. In recent years, numerous new SI algorithms have been widely adopted, including the Grey Wolf Optimization (GWO) algorithm [17], the Harris Hawks Optimization (HHO) algorithm [18], the Sparrow Search Algorithm (SSA) [19], and the Parrot Optimization (PO) algorithm [20]. Among these, the Dung Beetle Optimization (DBO) algorithm [21] is a novel optimization algorithm inspired by the ball-rolling, spawning, foraging, and stealing behaviors of dung beetles [22]. It stands out for its parallelized approach, offering faster convergence, enhanced accuracy, and robustness when dealing with complex scenarios [23; 24; 25]. While diverse behaviors endow DBO with flexibility, certain limitations remain. In particular, the fixed population ratios and search range settings restrict its ability to adaptively leverage these diverse behaviors in more challenging scenarios. Furthermore, like other swarm intelligence al gorithms, the standard DBO still tends to get trapped in a local optimum when faced with high-dimensional, strongly nonlinear problems like DPE. To address these issues, we propose an adaptive DBO algorithm (ADBO) based on the concept of Fitness Landscape Analysis (FLA), which is connected to auto-tuning and the development of intelligent algorithms for complex systems [26; 27]. This allows the ADBO algorithm to dynamically adjust its search strategy more effectively to varying optimization landscapes, with two key enhancements. The ADBO algorithm adjusts the proportion of foraging and spawning dung beetles and the convergence factor based on Fitness Distance Correlation (FDC). This approach adapts the balance between global and local search capabilities based on the landscape characteristics encountered by the population. Additionally, a hybrid mutation strategy combining Cauchy and Gaussian mutations is applied, with coefficients adjusted according to the ruggedness of the optimization problem. This approach enhances local exploration capabilities and reduces premature convergence risk. The main contributions of this article are as follows. First, we propose a DPE-SI framework, which incorporates a low-complexity correlation approach and a swarm intelligence-based navigation solution search approach, effectively reducing the computational cost required for DPE. It is worth mentioning that this is the first attempt to apply swarm intelligence algorithms to DPE. Second, a novel ADBO algorithm is proposed, including a detailed explanation of its dynamic search strategy adjustments based on FLA. Benchmark function tests validate that the proposed ADBO algorithm outperforms other swarm intelligence algorithms. Next, the ADBO and other algorithms are applied to the proposed DPE-SI framework, with their performance compared against MRG, ARS, and 2 SP methods in simulated signal experiments. Finally, the proposed framework is validated using real GNSS data in both static and dynamic receiver scenarios. Experimental results indicate that the DPE-SI framework with the ADBO algorithm provides higher positioning accuracy and improved stability with lower computational costs. The rest of this paper is organized as follows. Section 2.1 describes the optimization model of DPE and proposes a DPE-SI framework for implementing DPE with a low-computation correlation approach. In Section 2.3.2, the proposed ADBO algorithm is presented and discussed in detail. Section 2.3.3 evaluates the convergence performance of ADBO against seven popular swarm intelligence algorithms using benchmark test functions. Section 3 provides the positioning results based on both simulated signals and real GNSS data. Finally, we conclude this paper in Section 5.