The ultimate goal is to determine the tracking target position at the minimum error, and in the wireless sensor network to achieve this object the related art requires a lot of support, such as location technology, target detection, estimation, energy-saving technologies. Target tracking problem solving There are many ways, from the direction of the algorithm is considered can be divided into two categories: top-down and bottom-up algorithm of algorithms. Since the core idea of top-down target tracking algorithm is to first target to be tracked properly modeling, starting from the model to achieve the purpose of tracking, state-space method is a typical top-down approach. The so-called bottom-up approach, meaning there is no ready theoretical framework, starting from the real problems, starting from data obtained on track to achieve the target. In effect, track the performance of the two methods is not particularly significant differences, but since the top-down method has strict theoretical framework to facilitate the study of this method herein, the main consideration.
After the wireless sensor networks, wireless sensor networks laid good detection in a specific area, the network be initialized, all the nodes in the network to locate, and then can track the object of interest.
Detection and target tracking problem description
for target detection and tracking problem in wireless sensor networks, i.e., a target movement state transition equation of the first order can generally Markov
Cove state equations to describe
Wherein, the target state vector xk xk -1 indicates time, typically may contain information of the target position, velocity and acceleration; f (xk -1) represents a target state from the state xk xk -1 time to time the transfer function (linear or nonlinear); wk represents process noise vector. Accordingly, the general form of the time measurement equation:
Wherein, zk represents the observation vector obtained node xk time, h (xk) denotes the observation function (linear or nonlinear), vk represents measurement noise. Process noise and measurement noise are unknown, and not necessarily mean zero Gaussian white noise, but they are generally aware of the probability density. With these two models, the target tracking problem is to be solved according to the state before the target and the observation sequences obtained to solve the current state of the target amount.
Particle filter
Appears particle filter which lasted half a century, the earliest dating back to Monte Carlo (Monte Carlo method) 20 1940's Metropolis, who proposed in the 1970s for the first time MC method for solving nonlinear filtering problem, was using sequential importance sampling method: using a sample set of weighted values sampled from distribution to approximate the recommended target state distribution, there is a very serious degradation of the sample weight problem with this approach, the actual application is very limited ; in 1993, Gordon, who put forward the concept [6] re-sampling, re-sampling and introduced into the Monte Carlo importance sampling process effectively solve the problem of degradation of the value of the sample weights, based on particle opened the Monte Carlo integration research boom filtering algorithm. After twenty years of research and development, now the particle filter is already quite mature, become nonlinear, one of the most important solutions to non-Gaussian estimation system, widely used in autonomous navigation, robot vision and target tracking problems in.
Known initial target state distribution p (x0), in which k - 1 time the posterior probability density distribution p (xk -1 z1: k -1 ) = {xi k -1, wi k -1} N i = 1, importance sampling and resampling binding general particle filter estimates the state vector xk target specific steps in the following time k
- (1) Initialization: k = 0, randomly selected from p (x0) of N initial particles {x0i, i = 1,2, ..., N}, and to make the initial weight of each particle are 1 / N.
- (2) The proposal distribution (SIS algorithm is generally used, i.e. taken prior proposed distribution of the probability density function) update particles
- (3) After observation value obtained at time k zk, the weight of each particle is calculated according to the formula
- (4) re-sampling process, the effective number of particles is calculated according to a formula, performing resampling algorithms (e.g. polynomial resampling), otherwise skip to step (5).
- (5) obtained at time k target state estimation value according to the Monte Carlo integration:
- (6) Let k = k + 1, go to step to give the observed value of the time k + 1 (2), until the end.
Simulation results
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