Accurate determination algorithm of swimming trajectory for ultrasonically-tagged fish in natural water

Abstract: An important goal of hydrobiology is the simulation, reconstruction and restoration of important fish habitats, in which fish species form aquatic ecosystems' climax communities, enabling structural and functional restoration of river ecosystems. Traditional methods for identifying key fish habitat locations such as spawning grounds, include fish resource surveys, observation of fish spawning behavior and interviews with fishermen. But these are subject to problems including poor accuracy and large error. Precise positioning of fish can accurately locate key habitats (such as spawning grounds) based on key life cycle phases (such as spawning periods), permitting observation of corresponding habitat parameters. Fish movement trajectory data can also deepen understanding of fish habits and habitats, permitting suitable habitat indicators to be scientifically determined, and providing theoretical and technical support for fish protection and habitat restoration efforts. Ultrasonic tag tracking technology is widely used in fish behavior research due to its long underwater propagation distance and broad applicability. But most existing researches derived fish movement trajectories from hydrophone data using equipment manufacturers' software or services, and few articles concerning fish positioning principles and methods optimized for natural aquatic environments have been published. The Chan's algorithm (1994) in literature24 and robust least squares estimation were combined to get the location of ultrasonically-tagged fish in this paper, leveraging the strengths of these methods to overcome their disadvantages when used singly. Chan's algorithm was first used to obtain approximate coordinates of fish, which were used as initial position estimates from which the final position estimates were obtained with robust least squares. Prior information such as water depth and fish swimming speed could also be taken into account, making the proposed positioning method well-suited for dealing with ultrasonically-tagged fish in natural aquatic environments. The proposed method was suitable for existing ultrasound hydrophones, and effectively solved problems with large observation errors. Based on these research results, the UWP (under water positioning) software package was developed. To verify the effectiveness of the proposed method, an observation network was constructed which consisting of 16 hydrophones uniformly distributed over a area of 120 m×120 m in Huangbai River, Yichang. 4 ultrasonic signal tags were used to evaluate the positioning results, 2 was co-located with hydrophones for static simulation, and the other 2 affixed to a boat hull for dynamic simulation. Comparisons with Beidou/GNSS RTK with centimeter-level accuracy positioning estimates over 115 groups of test results, using millisecond-level accuracy observation data from existing hydrophones, swimming trajectories of ultrasonically-tagged fish could be obtained to an accuracy of about 2.15 m. While complex water environments degraded this accuracy, where single observations contained gross errors exceeding 10 m, 100% of these errors could be identified. The success rate for identification of observations with gross error was a gradually declining function of gross errors, dropping to 84.3% for 3 such observations. With over 3 gross error-bearing observations, the success rate declined significantly. With over 5 gross error-bearing observations where gross error-bearing observations accounted for over 31.25% of all observations, application of the proposed method could detect the error' existence, but was unable to identify the error-bearing observations effectively. The ultrasonic tag precise positioning method of fish proposed in this paper provide an effective method for determining the accurate swimming trajectory of fish in rivers, lakes and seas with low visibility. In addition, by modifying the data communication interface, this method can be effectively applied to ultrasonicall-taggeds fish and hydrophones of different manufacturers. In the future, it can play a more important role in promoting ecological environmental protection, and human beings' understanding of ecological and behavioral evolution in the aquatic environment at the population level.