**3.3. Model performance**

14 Will-be-set-by-IN-TECH

These parameters are estimated from the measurements. The derivation approach is described

For the derivation of the model parameters, a series of measurements with synthetic arrays at both transmitter (Tx) and receiver (Rx) have been conducted in three different office and lab scenarios in the IHE building of the Karlsruhe Institute of Technology. Two are office scenarios (scenario B and D), where the number of details in both rooms is small. The third scenario (scenario C) is a cluttered lab scenario [25]. Here, a large number of small details such as cables, tools, books etc. is distributed over the tables and shelves. These small objects were neglected in the scenario model. The transmitter is placed within a 0.12 m long linear positioner, and the receiver is moved on a 1.2 m by 0.6 m rectangle. Thus, a linear and a rectangular virtual array are obtained. The spacing between two consecutive antenna positions in both Tx and Rx arrays is 3 cm. With the exception of the antennas, the measurement setup used is identical with the setup described before. The simulation settings

For the derivation of the model parameters, the behavior of the channel characteristics (path loss *L* and delay spread *σ*D) in the measurements and the simulations are analyzed and compared [25]. To find adequate model parameters, simulations with different parameter sets are conducted and compared with the measurements. As the test of all possible parameter combinations would be computationally prohibitive, an initial parameter set has been chosen based on previous work findings in [23] and the parameters have been varied one by one. The scatterer generation is done only once in each realization for Tx position in the middle of the Tx array and for Rx position in the middle of the Rx arrays. For each other Tx/Rx

Due to the statistical nature of the model, some variation of the simulated channel parameters for consecutive simulations with the same model parameter set is to be expected. Hence, for each parameter set 5 realizations are then simulated and the channel parameters derived from them are averaged. This number is small enough to be simulated quickly, and large enough

To derive the model parameters, their influence on the chosen channel characteristics is



Considering this observation, first *p* is set to 0.03 because it has the strongest influence on the error. Thus, values of *a* = 0.2 and *N* = 16 are chosen which give a good tradeoff between path

Another indirect model parameter is the order of reflection which is considered in the scatterer placement. The influence of the considered reflection order on the delay spread is shown for a

loss and delay spread errors. Finally, the scattering radius is set to *r* = 1 m.


**3.2. Derivation of the model parameters**

configuration the same scatterers are used.

*p*. The error minimum is at *p* = 0.025.

analyzed. It can be observed that:

to give approximate mean values for a given parameter set.

in the following Sections.

are also the same.

To test the parameterized model, it is compared with measurements with respect to path loss, delay spread, azimuth spread, power delay profiles and azimuth spectra at the receiver [25]. For the estimation of the power delay profiles and azimuth spectra, the first Tx position and a rectangular track along the edges of the positioning table at Rx is considered. Each edge of the rectangular track is placed 9 cm (3 Rx positions) away from the edge of the positioning table. The estimation of azimuth angle is done using the sensor-CLEAN algorithm [8] using 4×4 elements with a spacing of 6 cm, with the midpoint at each comparison-track point. In contrast to the measurement the simulations can provide also the angle of arrival of individual paths. However, due to the enormous amount of data obtained if the properties of each individual path are recorded, it is more convenient to apply the estimation also to the simulation data. In this case, only the coherent sum of all paths for a particular Tx/Rx position has to be recorded.

The placement of the comparison points and of the arrays used for calculating the angles of arrival (AoA) at the receiver is shown in Fig. 13 .

**Figure 13.** Placement of the comparison points and of the arrays used for the calculation of AoA at the rectangular positioner.

The "array X" configuration is used for positions along the shorter edge, whereas the "array Y" configuration is used for positions along the longer edge of the rectangular positioner. The elevation is neglected here as the measurements with a 2-D array do not allow for resolution of paths impinging from below and above the array.

The analysis of the corresponding PDPs shows that the impulse responses simulated with the hybrid approach bear much more similarity to the measurements. Although the scatterers are generated in a statistical way, their properties are tightly bound to the properties of underlying reflections so that their contributions do not dominate in the channel impulse response but fill the missing dense components of the impulse responses and angular spectra.

In the next step, the mean error *μ*e and the standard deviation of the error between the measurement and the hybrid model *σ*<sup>e</sup> is calculated for the path loss *L*, delay spread *σ<sup>D</sup>* and the angular spread *σψ*R. For this purpose, all possible Tx/Rx positions as described in Subsection 3.2 are used. These values and the corresponding values of the error between the measurement and conventional ray tracing are shown in Table 1 .


Scenario B Scenario C Scenario D .

**Figure 14.** Angle-dependent power delay profile for the transmitter position Tx1 in Scenario A

model delivers very realistic channel impulse responses, azimuth spectra, and resulting channel parameters. The mean error between measurement and simulation is considerably improved in comparison to conventional ray tracing. This includes also the geometrical structure of the channel. Moreover, the deviation of the values of the simulated channel parameters due to the random placement of the scatterers is very small. Thus, a good

Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks 195

In the application scenario envisaged in the introduction, an unknown environment is inspected by a UWB sensor network. Static anchor nodes of the network are placed at strategic positions. They span a local coordinate system and passively localize people or other moving objects just by electromagnetic waves scattered from them. "Electromagnetic images" of the environment are provided by moving nodes of the network. All data extraction algorithms that evaluate data measured by the sensor network require a priori information about the position of corresponding sensor nodes. In this section, basic principles of the cooperative

UWB localization is usually achieved in two steps, parameter extraction and data fusion, [20, 57]. The parameter extraction estimates parameters of signals received by sensor nodes that are required in the data fusion step. Typical parameters that are used in radio based localization systems are time of arrival (ToA), time difference of arrival (TDoA), angle of arrival (AoA) and/or received signal strength (RSS). The range-based schemes, ToA and TDoA, are shown to yield the best localization accuracy due to the excellent time resolution of UWB signals [19]. The range based ToA approach appears to be the most suitable approach for localization in UWB sensor networks. However, there are still many challenges in developing a real-time ToA based indoor UWB localization system. Due to the number of error sources, such as thermal noise, multipath propagation, direct path (DP) blockage and DP excess delay, the accuracy of the range estimation may get worse. In indoor environments, it is proven that the major sources of errors are multipath components (MPCs) and the NLOS situation [54, 56] that strongly influence the parameter estimation step - the range estimation. The quality of the range estimation is related to the SNR (or distance between Tx and Rx) and the LOS/NLOS

simulated with the hybrid method.

reproducibility of the results is given.

localization of sensor nodes are described.

**4. Cooperative localization of mobile sensor nodes**

**Table 1.** Mean values and standard deviations of the error between the measurement and ray tracing simulation (RT) and between the measurement and hybrid simulation (Hyb.) .

Except for azimuth spread, the standard deviation values are very small. In the case of azimuth spread, however, additional errors are imposed due to path estimation. In a few cases, an insignificant rise is observed. The mean values are improved simultaneously for all considered channel characteristics.

The spread of the error values of path loss, delay spread and capacity resulting from the statistical nature of the model is analyzed also. For this purpose 40 realizations of the channel with the same parameter set are generated. For each realization, the mean error of each channel parameter is calculated. To describe the spread, the standard deviation over all mean values is adopted.

Finally, the derived model is applied to scenario A from Subsection 6.4 to prove the space-time distribution of the additional contributions. The angle dependent PDP simulated with the hybrid method is shown in Fig. 14 . The comparison with Fig. 8 shows that the additional contributions are properly placed in the azimuth-delay space, thus, depicting better the clustering effects in the scenario.

With this, a simple and effective modeling approach for directional UWB channels is proposed. The ray tracing method is combined with a simple geometric-stochastic model which represents the dense part of the channel.

The parameters of the stochastic model are connected to the properties of reflected paths so that they form a cluster with a certain delay and angle range around the reflected contribution. The stochastic clusters are also implemented around the points of multiple reflections. The

**Figure 14.** Angle-dependent power delay profile for the transmitter position Tx1 in Scenario A simulated with the hybrid method.

model delivers very realistic channel impulse responses, azimuth spectra, and resulting channel parameters. The mean error between measurement and simulation is considerably improved in comparison to conventional ray tracing. This includes also the geometrical structure of the channel. Moreover, the deviation of the values of the simulated channel parameters due to the random placement of the scatterers is very small. Thus, a good reproducibility of the results is given.
