We propose a method to estimate unknown parameters of coupled dynamical systems from observed data using a merging particle filter. The particle filter is a method to estimate the probability density function (PDF) of the system state by approximating the PDF using many particles that change their locations according to the observational data, and the merging particle filter is an extension of the particle filter. As an example, we consider a mathematical model of CPG (Central Pattern Generator) that generates rhythmic gait patterns in the spinal cord of animals. The mechanism of CPG has not been unraveled yet and various mathematical models have been proposed. Artificial robots that generates gait patterns, which can adapt to complex environment and exhibit stable walk and movement, has also been developed based on the CPG model. Using the data obtained by simulating a coupled-oscillator model proposed by Golubitsky et al., we estimate the parameters of the CPG model. We confirm that the merging particle filter can successfully estimate most of the parameters of representative gate patterns. In some cases, different parameter sets that generate the same gait patterns were also found. We also discuss that some of the parameters can be more easily estimated when the system noise is stronger.
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