Recent works on deep non-linear spatially selective filters demonstrate exceptional enhancement performance with computationally lightweight architectures for stationary speakers of known directions. However, to maintain this performance in dynamic scenarios, resource-intensive data-driven tracking algorithms become necessary to provide precise spatial guidance conditioned on the initial direction of a target speaker. As this additional computational overhead hinders application in resource-constrained scenarios such as real-time speech enhancement, we present a novel strategy utilizing a low-complexity tracking algorithm in the form of a particle filter instead. Assuming a causal, sequential processing style, we introduce temporal feedback to leverage the enhanced speech signal of the spatially selective filter to compensate for the limited modeling capabilities of the particle filter. Evaluation on a synthetic dataset illustrates how the autoregressive interplay between both algorithms drastically improves tracking accuracy and leads to strong enhancement performance. A listening test with real-world recordings complements these findings by indicating a clear trend towards our proposed self-steering pipeline as preferred choice over comparable methods.