Underwater acoustic telemetry positioning is widely used to track the fine-scale movements of aquatic animals. In study areas near acoustically reflective surfaces, reflected transmissions may cause large detection outliers that can severely reduce the accuracy of positioning models. A novel time-of-arrival model for telemetry positioning is presented that utilizes a population Monte Carlo algorithm to solve positions (termed PMC-TOA). Telemetry detection error is modelled as a mixture distribution, allowing reflected detections to be identified and positions to be estimated despite their presence. Importantly, the PMC-TOA model provides good measures of positioning uncertainty, facilitating the use of post-processing state-space models to further refine position estimates. A simulated telemetry study is used to validate the PMC-TOA model and compare its performance to a conventional time-difference-of-arrival positioning model. A real case study on Atlantic salmon (Salmo salar) smolt passage behaviour is further used to demonstrate how PMC-TOA can be combined with post-processing models to produce high-resolution tracks. The resulting tracks are compared against those resulting from YAPS and TDOA positioning. The PMC-TOA model was shown to work well as either (i) a pre-processing step to remove reflected transmissions from time-of-arrival datasets, or (ii) a fast and accurate positioning method when paired with a post-processing state-space model. Positions returned by the model can be further used for animal movement statistics, allowing researchers to test the effects of experimental or environmental factors on the fine-scaled movement behaviours of aquatic animals in acoustically challenging environments.