# A Linear Strong Constraint Joint Solution Method Based on Angle Information Enhancement
## 1 Introduction
Filter-based feature fusion methods use different types of observation information as measurement inputs to the filter, with the terminal position as the system state of the filter. The state is updated through filtering algorithms [15]. Optimization-based feature fusion methods combine various observation information to construct an objective function, solve for the global optimal solution of the objective function, and obtain terminal positioning results [16]. [PERSON] et al. used the simulated annealing algorithm for feature fusion positioning calculation of the TDOA and AOA. Through a probabilistic jump mechanism, they avoided local optimal solutions, improved global convergence capability, showed insensitivity to initial values, and enhanced positioning robustness [17]. [PERSON] et al. used the genetic algorithm for solving, achieving population iterative optimization through selection, crossover, and mutation operations, promoting extensive search in the solution space [18]. [PERSON] used the particle swarm optimization algorithm to solve feature fusion positioning of the TDOA, TOA, and DOA. By retaining historical optimal solutions and avoiding loss of high-quality solutions, they improved convergence speed while ensuring positioning performance [19]. These heuristic algorithms ensure that positioning results converge to the global optimal solution but incur significant computational time consumption. To improve computational efficiency, [PERSON] derived a closed-form solution for distance and angle fusion positioning. By treating the distance from the terminal to the reference base station as a redundant variable, they avoided iterative convergence problems [20]. However, all the above methods perform position calculation by constructing a single observation model. In complex environments, the amount of observation data on line-of-sight paths is limited, redundant observation information is scarce, and scenarios exhibit multimodal characteristics. Each scenario has different types and quantities of observation information, requiring classification and specific modeling for each scenario. To solve the above problems, this paper makes the following contributions:  
(1) A three-stage time-frequency synchronization method based on group peak time sequence tracing is proposed. Timing coarse synchronization is achieved through sliding window group peak identification, frequency offset estimation is performed using cyclic prefixes, and finally, chip-level fine timing synchronization is realized through PSS sliding cross-correlation. (2) A multimodal positioning algorithm for 5G heterogeneous measurement fusion is proposed: Using high-precision angle observation information as intermediate variables, a linear observation model is constructed for modeling and analysis of multimodal scenarios. Closed-form solution position information is obtained, enabling high-precision robust positioning even when the types and quantities of observations change. The chapter arrangement of this paper is as follows: Section 2 introduces reference symbols for 5G positioning; Section 3 introduces fine synchronization based on 5G signals and the PRS tracking algorithm to obtain precise distance observations; Section 4 proposes a multimodal positioning algorithm for 5G heterogeneous measurement fusion, constructing a closed-form solution model using high-precision angle observations as intermediate variables to achieve robust positioning under sparse observation conditions; Section 5 conducted experimental simulation verification; Section 6 provides a summary.