In this paper, we investigate a long state vector Kalman filter for the enhancement of speech that has been corrupted by white and coloured noise. It has been reported in previous studies that a vector Kalman filter achieves better enhancement than the scalar Kalman filter and it is expected that by increasing the state vector length, one may improve the enhancement performance even further. However, any enhancement improvement that may result from an increase in state vector length is constrained by the typical use of short, non-overlapped speech frames, as the autocorrelation coefficient estimates tend to become less reliable at higher lags. We propose to overcome this problem by incorporating an analysis-modification-synthesis framework, where long, overlapped frames are used instead. Our enhancement experiments based on the NOIZEUS corpus show that the proposed long state vector Kalman filter achieves higher mean SNR and PESQ scores than the scalar and short state vector Kalman filter, therefore fulfilling the notion that a longer state vector can lead to better enhancement.