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Magnetic particle tracking is a recently developed technology that can measure the translation and rotation of a particle in an opaque environment like a turbidity flow and fluidized-bed flow. The trajectory reconstruction usually relies on numerical optimization or filtering, which involve artificial parameters or thresholds. Existing analytical reconstruction algorithms have certain limitations and usually depend on the gradient of the magnetic field, which is not easy to measure accurately in many applications. This paper discusses a new semi-analytical solution and the related reconstruction algorithm. The new method can be used for an arbitrary sensor arrangement. To reduce the measurement uncertainty in practical applications, deep neural network (DNN)-based models are developed to denoise the reconstructed trajectory. Compared to traditional approaches such as wavelet-based filtering, the DNN-based denoisers are more accurate in the position reconstruction. However, they often over-smooth the velocity signal, and a hybrid method that combines the wavelet and DNN model provides a more accurate velocity reconstruction. All the DNN-based and wavelet methods perform well in the orientation reconstruction.