This paper addresses the problem of robust tracking of small objects in infrared (IR) video streams under non-Gaussian noise conditions. Classical methods based on the Kalman filter are suboptimal, as they ignore higher-order statistics of the noise caused by atmospheric turbulence and detector errors. To overcome these limitations, we propose a nonlinear processing algorithm based on the Truncated Polynomial Maximization Method (TPMM). The core of the method is an approach in which a high-degree stochastic polynomial is used to estimate the object’s trajectory parameters, while truncated polynomials of the minimal required degrees are used for the joint estimation of noise cumulants (variance, skewness, and kurtosis). The primary result is the synthesis of a computationally efficient system of nonlinear equations for this joint estimation. This provides a theoretical foundation for robust tracking algorithms that explicitly utilize information about the non-Gaussian nature of the noise, thereby improving accuracy and stability.