<![CDATA[This paper presents an adaptive approximation method for detecting anomalous patterns in extensive data streams gathered by mobile robots operating in rough terrain. Detecting anomalies in such dynamic environments poses a significant challenge, as it requires continuous monitoring and adjustment of robot movement, which can be resource intensive. To address this, a cost-effective solution is proposed that incorporates a threshold mechanism to track transitions between different regions of the data stream. The approach utilizes stochastic differential approximation (SDA) and optimistic optimization of Brownian motion to determine optimal parameter values and thresholds, ensuring efficient anomaly detection. This method focuses on minimizing the movement cost of the robots while maintaining accuracy in anomaly identification. By applying this technique, robots can dynamically adjust their movements in response to changes in the data stream, reducing operational expenses. Moreover, the temporal performance of the data stream is prioritized, a key factor often overlooked by conventional search engines. This paper demonstrates how the approach enhances the precision of anomaly detection in resource-constrained environments, making it particularly beneficial for real-time applications in rugged terrains.]]>
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