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Multistatic continuous active sonar (MCAS) systems involve the transmission and reception of multiple continuous probing sequences and can achieve significantly enhanced target detection and parameter estimation performance through exploiting the advantages of continuous illumination and spatial diversity. The main focuses and contributions of this paper are: 1) spectrally-contained continuous sequence sets with low correlation sidelobe levels are designed for the MCAS transmission so that the so-generated sequences meet the spectral containment restrictions and the weak correlations among the received echoes can be exploited to improve the target detection performance; and 2) a decentralized target parameter (position and velocity) determination method is investigated since its conventional centralized counterpart lacks robustness if there is no fusion center (FC) or the FC fails. This paper casts the target position determination problem based on the range measurements and the directions-of-arrival information (RMDI) as a set of decentralized optimization subproblems with consensus constraints imposed on the target position estimates of the receivers. Based on the alternating-direction method of multipliers (ADMM), we introduce the distributed position estimation algorithm to improve the local estimates of each receiver via local computation and information exchange with its neighbors. A similar method is also applied to obtain enhanced target velocity estimation. The effectiveness of the proposed MCAS signal processing techniques is verified using numerical examples.