KOSLM: A Kalman-Optimal Hybrid State-Space Memory Network for Long-Term Time Series Forecasting

Long-term time series forecasting (LTSF) remains challenging, as models must capture long-range dependencies and remain robust to noise accumulation. Traditional recurrent models, such as Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM), often suffer from instability and information degradation over extended horizons. The state-of-the-art method xLSTMTime improves memory retention through exponential gating and enhanced memory-transition rules, but it still lacks principled guidance. To address these issues, we propose the Kalman-Optimal Selective Long-Term Memory (KOSLM) model, which embeds a Kalman-optimal selective mechanism driven by the innovation signal within a structured state-space reformulation of LSTM. KOSLM dynamically regulates information propagation and forgetting to minimize state estimation uncertainty, providing both theoretical interpretability and practical efficiency. Extensive experiments across energy, finance, traffic, healthcare, and meteorology datasets show that KOSLM reduces mean squared error (MSE) by 14.3–38.9% compared with state-of-the-art methods, with larger gains at longer horizons. The model is lightweight, scalable, and achieves up to 2.5× speedup over Mamba-2. Beyond benchmarks, KOSLM is further validated on real-world Secondary Surveillance Radar (SSR) tracking under noisy and irregular sampling, demonstrating robust and generalizable long-term forecasting performance.