Since the low security of sensors, poor detection area and resource limitation in Wireless Sensor Network (WSN) cause outlier data collected by nodes, an algorithm of the outlier node detection in WSN based on graph signal processing was proposed. Firstly, according to the sensor position features, a K-Nearest Neighbors ( KNN) graph signal model was established. Secondly, the statistical test quantity was built based on the smoothness ratio of the graph signal before and after low-pass filtering. Finally, the judgement of the existence of outlier nodes was realized through the statistical test quantity and decision threshold. Experiments on the public temperature dataset and PM2.5 dataset demonstrate that compared with algorithm of outlier node detection based on graph frequency domain, the proposed algorithm has the detection rate increased by 7% under the condition of single outlier node and has the detection rate of 98% under the condition of multiple outlier nodes, and keep high detection rate under the condition of outlier node with small deviation value.

A new fast algorithm was proposed to solve the heavy computational load of coherent wideband signal DOA (Direction Of Arrival) estimation. Firstly, through Toeplitz technique of matrix, incoherent wideband signals were obtained without any division for the array. Secondly, according to the character of Hermitian matrix of received data, utilized the unitary transformation matrix, the real matrix could be acquired and the computation of eigendecomposition could be decreased. Finally, through the orthogonality technique of projected subspaces, new space spectrum was acquired with noise subspace and conjugate noise subspace, and the DOA could be obtained just through the angle search from zero to ninety degree in semi-spectrum according to the symmetrical spectrum, while the computational complexity for the search of spectrum peak was reduced by half. The theoretical analysis and simulation results show that the new algorithm has higher precision and smaller computational load, and it is effective for wideband coherent signals.