The ultimate goal of target tracking is to determine the location of the target with the smallest error, and to achieve this goal in wireless sensor networks requires the support of many related technologies, such as positioning technology, target detection technology, estimation technology, and energy saving technology. There are many ways to solve the target tracking problem, which can be divided into two categories from the perspective of the algorithm: top-down algorithms and bottom-up algorithms. The core idea of the top-down target tracking algorithm is to first properly model the target to be tracked, starting from the model to achieve the tracking purpose, the state space method is a typical top-down method. The so-called bottom-up method means that there is no existing theoretical framework, starting from actual problems and starting from the data obtained to realize the tracking of the target. From the effect point of view, the tracking effect of the two methods is not particularly obvious. However, since the top-down method has a strict theoretical framework and is convenient for research, this method is mainly considered in this article.
In a wireless sensor network, after the wireless sensor network is deployed in a specific detection area, the network first initializes, locates all nodes in the network, and then can track the target of interest.
Description of the problem of target tracking and detection For the problem of target tracking and detection in
wireless sensor networks, the movement process of the target, that is, the state transition equation can usually be described by the first-order
Markov equation of state
In the formula, xk represents the target state vector at time xk -1, which may generally contain information such as the target's position, speed, acceleration, etc.; f(xk -1) represents the state transfer function (linearly) of the target state from xk -1 to xk Or nonlinear); wk represents the process noise vector. Correspondingly, the general form of the observation equation at time:
In the formula, zk represents the observation vector obtained from the node at time xk, h(xk) represents the observation function (linear or nonlinear), and vk represents the observation noise. Both process noise and observation noise are unknown, and not necessarily Gaussian white noise with zero mean, but their probability density is generally known. With these two models, the problem to be solved by target tracking is to solve the current state quantity of the target according to the previous state of the target and the obtained observation sequence.
Particle filter algorithm
The emergence of particle filter algorithms lasted more than half a century, and can be traced back to the Monte Carlo method proposed by Metropolis et al. in the 1940s. The MC method was first used to solve nonlinear filtering problems in the 1970s. At that time, the sequential importance sampling method was used: a set of weighted samples sampled from the proposed distribution were used to approximate the target state distribution. This method has a serious problem of sample weight degradation, and its practical application is very limited. ; In 1993, Gordon et al. proposed the concept of resampling [6], and introduced resampling into the Monte Carlo importance sampling process to effectively solve the problem of sample weight degradation and opened the Monte Carlo integration based particle Research boom in filtering algorithms. After more than 20 years of research and development, particle filter algorithms are now quite mature and become one of the most important solutions to estimation problems in nonlinear and non-Gaussian systems. They are widely used in autonomous navigation, robot vision, and target tracking. in.
The initial distribution of the target state is known as p(x0), and its posterior probability density distribution at k -1 is p(xk -1 z1: k -1) = {xi k -1, wi k -1} N i = 1, combined with importance sampling and resampling, the specific steps of a general particle filter algorithm to estimate the target state vector xk at time k are as follows
- (1) Initialization: k = 0, randomly select N initial particles {x0i, i = 1, 2,..., N} from p(x0), and set the initial weight of each particle to 1/N.
- (2) Update the particles according to the proposal distribution (usually using the SIS algorithm, that is, taking the prior probability density function as the proposal distribution)
- (3) After obtaining the observation value zk at time k, calculate the weight of each particle according to the formula
- (4) In the re-sampling process, first calculate the effective number of particles according to the formula, and execute the re-sampling algorithm (such as polynomial resampling, etc.), otherwise skip to step (5) directly.
- (5) Obtain the estimated value of the target state at time k according to the Monte Carlo integration:
- (6) Let k = k + 1, get the observation value at k + 1 and then go to step (2) until the end.
Simulation results
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