The massive deployment of low-end wireless Internet of things (IoT) devices opens the challenge of finding de-centralized and lightweight alternatives for secret key distribution. A possible solution, coming from the physical layer, is the secret key generation (SKG) from channel state information (CSI) during the channel's coherence time. This work acknowledges the fact that the CSI consists of deterministic (predictable) and stochastic (unpredictable) components, loosely captured through the terms large-scale and small-scale fading, respectively. Hence, keys must be generated using only the random and unpredictable part. To detrend CSI measurements from deterministic components, a simple and lightweight approach based on Kalman filters is proposed and is evaluated using an implementation of the complete SKG protocol (including privacy amplification that is typically missing in many published works). In our study we use a massive multiple input multiple output (mMIMO) orthogonal frequency division multiplexing outdoor measured CSI dataset. The threat model assumes a passive eavesdropper in the vicinity (at 1 meter distance or less) from one of the legitimate nodes and the Kalman filter is parameterized to maximize the achievable key rate.