Efficient particle filter node positioning method for ocean sensor networks

An efficient particle filter node positioning method for ocean sensor networks, comprising following steps:

• S1, establishing a state model of a nonlinear system according to motion characteristics of a velocity field in a sea area and considering an interaction force between a tidal field and a residual field;
• S2, modeling a signal intensity received by each node in the ocean sensor networks based on a signal intensity attenuation model to obtain an observation model of the nonlinear system;
• S3, obtaining a first state vector ū+k-1 of a mean value of a posterior probability at a k−1 moment, calculating a second state vector ū+k at a k moment, representing a state vector
• u
• k
• -
• 1
• i
• of an i-th particle at the k−1 moment by the first state vector, and then performing a Taylor expansion on a state vector
• u
• k
• i
• of the i-th particle at the first state vector
• u
• k
• -
• 1
• i
• to calculate second particle state vectors of all particles approximate to a first-order Taylor series term at the k moment;
• then, performing the Taylor expansion on the second particle state vectors in two steps by a multidimensional Richardson extrapolation method to obtain third particle state vectors of all the particles approximate to a second-order Taylor series term at the k moment;
• S4, based on a normalized weight at the k−1 moment, calculating a normalized weight at the k moment in a recursive way, and realizing a normalization based on observed values obtained by the observation model;
• S5, judging whether the particles are degraded based on a number of effective particles, if the particles are degraded based on the number of effective particles, executing S6, if the particles are not degraded based on the number of effective particles, taking the normalized weight at the k moment and a particle set at this time as a result weight and a result particle set, and executing S8;
• S6, performing a resampling, then dividing a whole particle set into a small-weight particle set and a large-weight particle set according to a weight threshold, keeping state vectors and weight values of particles in the large-weight particle set unchanged, modifying state vectors of particles in the small-weight particle set, and further modifying and normalizing weights of small-weight particles to obtain modified particles, and taking modified and normalized weights of the small-weight particles as result weights;
• S7, performing a residual resampling according to the modified particles to obtain a replicated particle set, and taking the replicated particle set as the result particle set;
• and
• S8, combining the result particle set and the result weight, calculating posterior probability distributions of unknown nodes at the k moment, and calculating expected values of positions according to obtained posterior probability distributions to obtain estimated positions of the unknown nodes at the k moment.