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This study is concerned with the estimation of two key parameters in a stochastic non-linear second-order state-space model of traffic flow using the maximum likelihood approach while employing a recursive Monte Carlo-based filtering and smoothing to solve related expectation maximisation (EM) algorithm. A maximum likelihood (ML) framework is employed in the interests of statistical efficiency. EM algorithm may be used to compute these ML estimates and Monte Carlo approach is used to compute required conditional expectations. Considered parameters, free flow speed and critical density are traffic flow characteristics which are key parameters used for traffic control, ramp metering, incident management etc. A set of field traffic data from the Interstate-494 highway located in Metro Freeway Network Area at Minnesota is used to demonstrate the effectiveness of the proposed approach.