How to estimate a macaque's moving finger position through neuron spikes in its mortor cortex is an issue about neural decoding. For the issue, most of existing methods is a supervised training algorithm and require supervised data to obtain the relationship between the spikes and the finger's moving position. Therefore, the performance of the existing methods depends on the training data. This paper proposes an unsupervised decoding method, which is based on a state space model (SSM), adopts neural networks to obtain the weights between the neuron spikes and the finger's moving position, and then estimates the finger's position through sequential state estimator. To reduce computational complexity and enhance estimation accuracy, a nonlinear cubature Kalman filter (CKF) is used to train the neural network and estimate the sequential moving position. Compared with the existing methods, the proposed method's advantage is to be unsupervised. It could estimate the finger's position only through the spike vector instead of the supervised training data. Experiment results show that the existing methods have more estimation errors than the proposed method when a small amount of supervised data is adopted, and the exiting ones have similar estimation errors only when more supervised data adopted.