Allowing for perturbations in speed and turn rate of a target moving in a coordinated turn obeys a non-linear stochastic differential equation. Existing algorithms for coordinated turn tracking avoid this problem by ignoring perturbations in the continuous time model and adding process noise only after discretisation. The dynamic model used here adds small perturbations, modelled as independent Brownian motion processes, to the speed and turn rate. The target state is to be recursively estimated from noisy discrete-time measurements of the target's range and bearing. In particular, this paper examines the effect of the perturbations in speed and turn rate on the coordinated turn motion of the aircraft, and subsequently the stochastic algorithm is developed by deriving the evolutions of conditional means and variances for estimating the state of the aircraft. By linearizing the stochastic differential equations about the mean of the state vector using first-order approximation, the mean trajectory of the resulting first-order approximated stochastic differential model does not preserve the perturbation effect felt by the moving target; only the variance trajectory includes the perturbation effect. For this reason, the effectiveness of the perturbed model is examined on the basis of the second-order approximations of the system non-linearity. The theory of the non-linear filter of this paper is developed using the Kolmogorov forward equation 'between the observation' and a functional difference equation for the conditional probability density 'at the observation'. The effectiveness of the second-order non-linear filter is examined on the basis of its ability to preserve perturbation effect felt by the aircraft. The Kolmogorov forward equation, however, is not appropriate for numerical simulations, since it is the equation for the evolution of the conditional probability density. Instead of the Kolmogorov equation, one derives the evolutions for the moments of the state vector, which in our case consists of positions, velocities and turn rate of the manoeuvring aircraft. Even these equations are not appropriate for the numerical simulations, since they are not closed in the sense that computing the evolution of a given moment involves the knowledge of higher-order moments. Hence we consider the approximations to these moment evolution equations. Simulation results are introduced to demonstrate the usefulness of an analytic theory developed in this paper.