**6. Conclusions and future work**

16 Will-be-set-by-IN-TECH

**Figure 15.** A typical WSN in normalized three dimensional space.

and thus form a three dimensional sensor network.

works for all possible dimensions.

after normalization along three axial directions), such as building monitoring [35], underwater acoustic sensor networks[2], may be encountered. For example, the localization problem of sensors for building monitoring is actually defined in a three dimensional space since sensors are deployed in two dimensions on each floor and the whole network constructed by sensors on different floors forms a three dimensional one. Also, sensors in the underwater acoustic sensor networks are often deployed at different depth, with different longitude and latitude

The presented two models in this chapter admit the higher dimensional localization problems as we did not specify the number of dimensions in the problem formulation and the model

As demonstrated in simulations, Model II outperforms Model I in the sense of estimation error for the cases with the same simulation setup. However, it is notable that Model II requires an extra dynamic model for the initialization, which is at the cost of implementation complexity and longer computation time. Fortunately, the dynamic models can be implemented with either digital or analog devices and thus the computation can be completed in a very short time. For example, the simulation examples for the two dimensional localization problem

In this chapter, we overviewed our recent work on range-free localization of sensors in WSNs via dynamic models. The range-free localization problem is formulated as two different optimization problems, each of which corresponds to a dynamic model, namely Model I and Model II, for the solution. Simulations in both one dimensional case and two dimensional case are performed and the two models are compared in both sceneries. The simulation results demonstrate effectiveness of the dynamic models.

Compared with conventional range-free localization algorithms, a prominent advantage of ODE based solutions is that the models are implementable by parallel hardware. As a promising direction for WSN localization, the following aspects are of fundamentally importance in both theory and practise and are open to all researchers,


• Can the presented models be used in range-base WSN localization, if not applicable directly, is the results helpful to supply a good "warm start", which accelerates the convergence?

• The presented models are essentially ODE models for solving nonlinear inequalities defined on a network. Are the models extendable to other network applications, such as robotic networks, smart grids, the internet of things, etc?
