# An Improved PSO Algorithm and Its Application in GNSS Ambiguity Resolution
## 1 Introduction  
The carrier phase observation of global navigation satellite systems (GNSS), such as the American Global Positioning System (GPS), Russian Global Navigation Satellite System (GLONASS), European Galileo, and Chinese Beilou Navigation Satellite System (BDS), is characterized by limited noise and high precision, and is usually applied in high-precision positioning. Ambiguity resolution (AR) is crucial for processing GNSS data, given the initial integer ambiguity of GNSS observations. The correct integer ambiguity must be obtained to transform GNSS observations into high-precision receiver-satellite ranging signals [1; 2; 3]. Conventional AR methods first obtain the ambiguity float resolution from GNSS observations. Subsequently, the rounding method, confidence region method, or least-squares method is applied to obtain the correct integer ambiguity [4; 5; 6; 7]. The least-squares ambiguity decorrelation (LAMBDA) method has been widely applied in the GNSS AR [8; 9; 10]. Numerous intelligent optimization algorithms, such as the neural network algorithm, genetic algorithm, and particle swarm optimization (PSO) algorithm, have attracted increasing attention with the rapid development of computer technology over the past few years [11; 12; 13]. The PSO algorithm is a novel evolutionary computation technique that is inspired by social behavior simulation [14; 15; 16]. Given its strong global search capability, limited adjustment parameters, and fast computational speed,the PSO algorithm has attracted considerable research interest. The development of novel applications for the PSO algorithm is currently an important research hotspot. The PSO algorithm is widely used in several fields, such as function optimization or fuzzy control [17; 18; 19; 20; 21]. GNSS AR is essentially a procedure for mapping the relationship between the float solution and integer solution. In the absence of a definite mathematical analytical formula for constructing the relationship between the float solution and the integer solution, some integer ambiguity candidates can be selected and considered in the objective function. The candidate that can satisfy the set condition will be identified as the optimal integer solution. Thus, the integer linear optimal programming problem in mathematics is the core principle of GNSS AR. The PSO algorithm can solve this problem. Therefore, the application of the PSO algorithm in GNSS AR is an interesting topic that nevertheless has received limited research attention. A method for GPS attitude determination based on a discrete PSO algorithm was introduced by [22]. This method lacks ambiguity decorrelation and ignores the defects of the PSO algorithm. An improved PSO algorithm for GPS integer AR was introduced by [23]. However, the performance of this method has not been analyzed in detail, and the relationship between its performance and the property of the ambiguity float solution has been ignored. In this study, we developed a novel method for GNSS AR by using an improved PSO (IPSO) algorithm, namely, improved particle swarm optimization-ambiguity resolution (IPSO-AR). The ambiguity float resolution and corresponding covariance matrix can be estimated from GNSS observations. Then, we used the PSO algorithm to search for the optimal integer solution by applying a decorrelating Z-transformation [24; 25] that is based on the minimum criterion of the weighted residual sum of squares in the corresponding search space. The standard PSO (SPSO) algorithm exhibits some defects, such as proneness to prematurity and to falling into a local optimum. In fact, these defects are common problems of all intelligent optimization algorithms. Thus, the PSO algorithm must be optimized prior to its application. Many previous researchers, such as [26; 27; 28], have focused on the improvement of the PSO algorithm. We introduced population maturity for the adaptive adjustment of inertia weight.