^{*}

^{*}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In the case of through-the-wall localization of moving targets by ultra wideband (UWB) radars, there are applications in which handheld sensors equipped only with one transmitting and two receiving antennas are applied. Sometimes, the radar using such a small antenna array is not able to localize the target with the required accuracy. With a view to improve through-the-wall target localization, cooperative positioning based on a fusion of data retrieved from two independent radar systems can be used. In this paper, the novel method of the cooperative localization referred to as joining intersections of the ellipses is introduced. This method is based on a geometrical interpretation of target localization where the target position is estimated using a properly created cluster of the ellipse intersections representing potential positions of the target. The performance of the proposed method is compared with the direct calculation method and two alternative methods of cooperative localization using data obtained by measurements with the M-sequence UWB radars. The direct calculation method is applied for the target localization by particular radar systems. As alternative methods of cooperative localization, the arithmetic average of the target coordinates estimated by two single independent UWB radars and the Taylor series method is considered.

Localization capability is becoming one of the most attractive features of a wireless sensor network. Ultra wideband (UWB) radar systems as a special kind of wireless sensor network allow one to detect and track authorized or unauthorized moving targets with an advantage in critical environments or under hindered conditions. This results from the fact that UWB radars operating in the frequency range up to 4 GHz are characteristic of a good penetration of emitted electromagnetic waves through various materials, such as wood, brick, concrete, plastic, rock, ground, snow,

In these applications, handheld sensors for through-the-wall monitoring are applied by security forces directly to the place of operation. Here, the monitoring results should be available for the radar operator immediately. It is also expected that the operator can change the sensor location permanently. It follows from the outlined requirements that the handheld radar systems have to operate in a stand-alone mode and to be small-sized and light-weight. Therefore, they usually use only a small antenna array necessary for motion detection and basic spatial positioning of the targets.

It is well-known that the ability to detect moving targets and target positioning precision depend inter alia on the number of the radar antennas and their size, types and spatial layout. However, in the case of handheld sensors, the radar system performance improvement based on the application of a complex antenna array is naturally limited. The alternate approach on how to improve the detection and positioning is to use at the same time two or more handheld sensors for monitoring the same area. Here, diversity is the keyword behind the outlined idea. By spacing the particular radar systems, including their transmitting and receiving antenna elements, in such a way that the target angular spread is manifested, the sensor network can exploit the spatial diversity of target scatters and mitigate to environment complexity, opening the way to a variety of new techniques that can improve radar performance [

Motivated by the outlined scenarios of the UWB radar applications, we will focus on through-the-wall localization and tracking of a moving person by two independent UWB radar systems in this paper (hereinafter, the basic scenario). In the mentioned scenario, the handheld M-sequence UWB radars equipped with one transmitting and two receiving antennas will be used as UWB sensors [

Moving target localization and tracking by two independent UWB radar systems is a complex procedure that includes signal processing phases, such as background subtraction, detection, time-of-arrival (TOA) estimation, wall effect compensation, localization and tracking. The significance of the particular phases has been explained, e.g., in [

In the case of the single radar system equipped with one transmitting and two receiving antennas, the direct calculation (DC) method is the basic method of target localization [

In addition to these papers, several interesting contributions (e.g., [

In [

Target localization by a multistatic UWB radar system has been studied in [

Another interesting approach to target localization by UWB sensor networks represented by multistatic UWB radar has been introduced in [

The mentioned localization methods applied for scenarios with a general number of nodes are essentially based on an appropriate solution of the overdetermined set of nonlinear equations and/or a proper optimization task solution. The particular equations are created by means of the known coordinates of the radar antennas and TOA estimations corresponding to the target to be localized. Because of the optimization approach application, the performance properties of these localization methods depend strongly on the number of the nodes. The more nodes are used, the better the performance of the localization methods will be obtained. On the other hand, if the number of the equations is small, the target localization precision is very sensitive to TOA estimation accuracy. In this case, even a single TOA estimated with a large error results in a large error of the target position estimation. Unfortunately, this scenario is just a typical one for through-the-wall localization of the target by means of two independent radar systems. In this case, only four nonlinear equations are available for the target localization problem description [

The alternative solution of the target localization problem by two independent radar systems referred to as joining intersections of the ellipses (JIEM) has been originally proposed in [

In this paper, JIEM will be derived in detail. In order to compare the performance of JIEM and a method based on the direct solution of a nonlinear overdetermined equation set, a new modification of the Taylor-Series method (TSM) adapted for the basic scenario problem will be introduced also in our contribution. Then, the performance of the DC (applied for each radar system independently), MEAN, TSM and JIEM will be compared based on the processing of the signals obtained by through-the-wall measurement with two independent M-sequence UWB radar systems. For raw radar data processing, the complex UWB radar signal procedure proposed in [

To fulfill the outlined intention, our paper will have the following structure. In Section 2, the problem statement for the target localization by means of two independent UWB radar systems considered in this paper will be given. In Section 3, the particular phases of radar signal processing will be outlined. Section 4 is the core of our contribution. In this section, TSM and JIEM will be introduced. Subsequently, the performance of DC, MEAN and the introduced localization methods will be illustrated, compared and discussed in Section 5. Finally, conclusions and final remarks to this contribution are made in Section 6.

Let us consider the fundamental scenario of through-the-wall localization of a moving target by means of two UWB radar systems, denoted as the radar system A (RS_{A}) and the radar system B (RS_{B}) (

Here, every radar system is equipped with one transmitting and two receiving antennas. In the scenario, it is assumed that the antenna positions are known, and their coordinates are given as follows:

coordinates of the transmitting antenna of the RS_{A}(_{A}_{A}_{A,t},y_{A,t}

coordinates of the first receiving antenna of the RS_{A}:(_{A}_{,1}): _{A}_{,1} = (x_{A}_{,1}, _{A}_{,1}),

coordinates of the second receiving antenna of the RS_{A}(_{A}_{,2}): _{A}_{,2} = (_{A}_{,2},_{A}_{,2}),

coordinates of the transmitting antenna of the RS_{B} (_{B}_{B}_{B,t}_{B,t}

coordinates of the first receiving antenna of the RS_{B}(_{B}_{,1}): _{B}_{,1} = (x_{B}_{,1}, _{B}_{,1}),

coordinates of the second receiving antenna of the RS_{B}(_{B}_{,2}): _{B}_{,2} = (_{B}_{,2}, _{B}_{,2}).

Raw radar signals retrieved from the particular radar systems can be interpreted as a set of impulse responses of the surroundings through which the electromagnetic waves emitted by the radar are propagated. They are aligned to each other, creating a 2D picture called a radargram, where the vertical axis is related to the propagation time (

Hereinafter, we will assume that the radar systems applied for target tracking are synchronized in such a way that both radar devices are controlled approximately by the same system clock. Therefore, we can assume that the radargrams obtained by the measurements by all four receiving antennas have the same propagation and observation time axes and that their radargram samples are taken in the same time instants. The other kind of radar system synchronization is not assumed.

Taking into account the above-mentioned assumption, the problem to be solved within our paper is to estimate the target trajectory based on processing of raw radar signals retrieved from two independent radar systems. The solution of that problem will consist of two stages. Within the former stage, TOA corresponding to the target for each pair of transmitting and receiving antennas of the same radar system will be estimated. For that purpose, the UWB radar signal processing procedure described in the next section will be applied. The latter stage of the target localization will consist in the target coordinate estimation based on the fusion of the data (_{A} and RS_{B}. For that purpose, TSM and JIEM will be proposed in Section 4. The further improvement of target positioning accuracy will be reached by target tracking. The tracking algorithms applied in our paper will be mentioned in Section 3.

In the case of UWB radar signal processing for through-the-wall localization of moving persons, target positioning is a complex procedure that includes such signal processing phases as background subtraction, target detection, TOA estimation, wall effect compensation, target localization and tracking. The particular phases are implemented using appropriate methods of signal processing. In the following parts of this section, we would like to provide the reader with a short outline of the mentioned procedure. It should help for readers to see clearly the connections of the target localization methods developed and discussed in this paper with their applications for through-the-wall localization of moving persons by UWB radar systems. Ea intentione, the significance of the particular phases of the mentioned procedure will be outlined, and the lists of signal processing methods that are most frequently used within the particular phases will be given. Because of the complexity of the discussed procedure of moving target positioning, its detailed description is beyond this paper, and hence, it will not be presented here. The reader can find its comprehensive description, especially, in [

The analysis of raw radar data has shown that it is impossible to directly identify any moving targets in the obtained radargrams. This comes from the fact that the components of the impulse responses represented by the target echo are much smaller than those of the signals reflected by the front wall or large or metal static objects or signals representing the cross-talk between transmitting and receiving antennas. In order to detect a moving target, the ratio of signals scattered by a target (

It has been shown that the signal processing methods, such as basic averaging (mean, median) [

Detection is the next phase of the radar signal processing procedure, which comes after the background subtraction. Detection methods analyze the radargram with the subtracted background and reach the decision of whether a signal scattered by a moving target is present or absent in the analyzed impulse response.

The detector output corresponding to the receiving antenna in the observation time instant, _{k}_{d}_{k}_{j}_{k}_{kj}_{kj}_{j}_{k}_{j}

The detailed structure of a detector depends on the selected strategy and optimization criteria of detection [

CFAR detectors can be especially assigned between detectors capable of providing a good and robust performance for through-the-wall detection of moving targets by the UWB radar system. They are based on the Neymann-Person optimum criterion, providing the maximum probability of detection for a given false alarm rate. There are a number of varieties of CFAR detectors [

If a target is represented by only one non-zero sample of the detector output, then the target is referred to as a simple target. However in the case of the scenario analyzed in this contribution, the radar range resolution is finer than the physical dimensions of the target. This results in the detector output, due to such a target, usually not being expressed by only one non-zero sample of _{d}_{k}_{k}

The TOA estimation is quite complex, and therefore, it is not fully described in this paper. An algorithm of this kind can be found, e.g., in [

On the other hand, the low complexity TOA estimation for UWB systems based on model selection by information theoretic criteria has been developed in [

The propagation of electromagnetic waves through-the-wall results in a delayed time of signals reflected by targets moving behind the wall, which means that TOA estimated by the previous phase of the radar signal processing are time shifted, because of the wall presence. Their correction can be achieved by the subtraction of the mentioned delay time, whereby its estimation is the task of the wall effect compensation phase. The method referred to as the target trace correction of the second kind [

The aim of the target localization phase is to determine the target coordinates in a defined coordinate system. The target positions estimated in the consecutive observation time instants create a target trajectory. The analyses of the target localization by M-sequence UWB radar equipped with one transmitting and two receiving antennas based on DC presented in [

Target tracking provides a new estimation of the target location based on its foregoing positions. Target tracking usually results in the target trajectory estimation error decreasing, including trajectory smoothing. Most of tracking systems use a number of basic or advanced modifications of Kalman filters (e.g., linear, nonlinear and extended Kalman filters [

In this section, we will deal with the problem of the cooperative localization of the target for the basic scenario. Firstly, the basic equations describing the target localization will be introduced. Then, TSM and JIEM as the possible approaches of the mentioned equation set solution will be derived.

Let _{R,i}_{R}_{R,i}_{R,i}_{R,i}_{R}_{R,i}^{8} ms^{−1}. On the other hand, the distance, _{R,,i}_{R}_{R,i}. Finally, _{R,i} represents the additive noise component expressing the random errors of the TOA estimation.

Then, the target localization problem can be defined as the estimation of the target coordinates, (

The TSM method is a popular and very often used iterative method for object localization by UWB systems [

Let us define the functions:
_{R,i}_{v}_{v}_{x}_{y}_{R,i}(^{(i)}‖ and ^{th}^{th}

Let us assume for a moment a perfect estimate of _{R,i},i.e., if _{R,i} = 0. Then, the Equation set _{R}_{R,t}, _{R,t}) and _{R,i}_{R,i}_{R,i}_{R,i}_{R}_{R,1}_{R}_{R,i}_{R,i}_{R}_{R,i}

Let us return now to the basic scenario outlined in _{R,i}_{i}_{i}_{i}_{R,i}

Unfortunately, _{R,i}_{R,i}_{A} labeled as _{A}_{1} and _{2}. On the other hand, the intersection of _{3} and _{4}, labeled as _{B}_{B}. It can be observed from _{A}_{B}_{B} (_{B}_{B}_{,1}, it was not possible to create the ellipse, _{3}, and hence, RS_{B} was not able to localize the target. In both scenarios, better results can be provided by RS_{A} (

The analyses of the scenarios given in _{A}_{B}

Generally, four ellipses, _{i}_{1}, _{2}), (_{1}, _{3}), (_{1}, _{4}), (_{2}, _{3}), (_{2}, _{4}) and (_{3}, _{4}). For every pair of the ellipses, _{ij}_{i}_{j}_{i}_{j}_{k}_{k}_{i}_{j}_{i}_{j}

The decision algorithm can be described as follows. Let us consider the ellipses, _{m}_{n}_{l}_{k}_{m}_{n}_{m}_{n}_{m}_{n}_{v}

The main idea of _{v}_{v}_{v}_{v}_{v}_{v}_{v}|_{v}

Taking into account the significance of the metrics _{m}_{m}_{n}_{n}_{m}_{n}_{m}_{n}_{m}_{m}_{n}_{m}_{n}_{m}_{m}_{n}_{m}_{n}

The described decision algorithm will be applied step by step for all pairs of the ellipses, _{mn}

For the basic scenario, there are also situations when the four ellipses cannot be created. Then, the following approach is used by JIEM. If there are only three ellipses with more than one intersection in the monitored area, the target position is estimated as the intersection of the ellipses belonging to the same radar system. If there is only one intersection in the monitored area, its coordinates represent the estimated coordinates of the target. Finally, if at least two ellipses cannot be created or if no intersection can be found in the monitored area, the target cannot be localized.

In order to evaluate JIEM performance, the scenario outlined in

The raw radar data analyzed in this contribution were acquired by means of two M-sequence UWB radar systems (_{RD}

The first radar system, denoted as RS_{A}, has been equipped with three spiral antennas (_{B}, has been equipped with three double-ridged horn antennas (_{A} and RS_{B}, respectively.

In the case of our measurements, the synchronization of RS_{A} and RS_{B} has been created by the interconnection of RS_{A} and RS_{B} through the local area network (LAN). The outlined application of LAN has allowed one to start the measurement of the particular impulse responses by RS_{A} and RS_{B} theoretically in the same time instant (practically, almost in the same time). No additional signal processing has been applied for the purpose of the synchronization of the data provided by RS_{A} and RS_{B}. Taking into account the rate of measurement (10 impulse response per second) and the speed of the target movement (approximately 0.80–1.00 ms^{−1}), we believe that this form of RS_{A} and RS_{B} synchronization can be acceptable for the cooperative localization of the moving target.

In the basic scenario, both radar systems have operated simultaneously over the same frequency band. They have emitted the same M-sequence, but the initial conditions of their M-sequence generators have been set randomly. Hence, the M-sequences generated by the first and second radar system are theoretically the same, but they are mutually shifted. Because the radar receiver is based on an application of the correlation between the transmitting M-sequence and the received signal, we have expected that it should result in additional correlation peaks, due to the transmitting of the second radar system. These peaks should be delayed only according to the initial conditions in comparison to the first radar system. However, this effect and, therefore, no mutual interference of the radar systems have been identified in our measurement. The deeper analyses of this effect provided by [

The raw radar data acquired by the described measurement have been processed by the procedure described in Section 3. Here, the exponential averaging method, CFAR detector, the method introduced in [_{A} and RS_{B}, the DC method has been used. On the other hand, MEAN, TSM and JIEM have been applied for cooperative positioning of the moving target by using two independent radar systems.

It is well known that TSM performance depends on the initial guess of the target location (_{v}_{v}_{A} and RS_{B} [

The results obtained in the particular phases of UWB radar signal processing for the basic scenario are given in _{A} and RS_{B} are given in _{A} and RS_{B} are denoted as DCA and DCB, respectively. Finally, the target tracks obtained by KF applied to the target trajectories obtained by DC (KF DCA, KF DCB), MEAN (KF MEAN), TSM (KF TSM) and JIEM (KF JIEM) are given in

The target position estimation accuracy corresponding to the particular methods of target localization is illustrated also by the time evolution of target localization errors for the estimated trajectories and tracks (

Now, after this short summary of the obtained results, we can discuss some outcomes in detail. Let us begin with the target trajectories received as the localization phase output by DC for the RS_{A} and RS_{B} (

The improved accuracy of the target localization can be obtained by MEAN,

The target trajectory estimated by TSM within the localization phase is presented in

The comparison of the target trajectory estimations by the localization methods considered in this paper has shown that the best performance is provided by JIEM (

The standard approach for how to improve the target trajectory estimation obtained by the localization phase is to apply tracking filters [

The performance properties of JIEM have been tested also in [

The described procedure of signal processing has been implemented on a standard notebook using MATLAB software. In _{L}_{L}_{0} = 12 ms. Then, the total average time necessary for the target position evaluation corresponding to one impulse response processing is _{SP}_{L}_{0}. As follows from _{L}_{SP}_{RD}_{L}

This paper has been devoted to target localization by two independent UWB radar systems. A novel method of the cooperative localization of the target, referred to as JIEM, has been proposed. The main idea of JIEM consists in the creation of

JIEM can be used for cooperative target positioning with an advantage, especially if the number of radar systems applied for target positioning is not very high. This application scenario represents a trade-off between its good performance and high complexity. On the other hand, conventional methods, such as DC, MEAN or TSM, have a limited ability to provide a robust performance for through-the-wall localization of moving persons. Their high sensitivity to TOA estimation errors is the main reason for their pure performance in such scenarios. Taking into account these facts, JIEM should be preferred for through-the-wall target localization by two radar systems in comparison with that of DC, MEAN or TSM.

JIEM possess the potential to also be easily extended for target localization by a UWB sensor network consisting of more than two sensors, for target localization by a UWB multistatic radar system with

We assume that further improvement of JIEM performance can be obtained by its non-complex modifications. The promising modification of JIEM can be seen in the target coordinates estimation based on the intersections included in

This work was supported by the Slovak Cultural and Educational Grant Agency (KEGA) under contract No. 010TUKE-4/2012 and by the Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic and the Slovak Academy of Sciences (VEGA) under contract No. 1/0563/13.

The authors declare no conflicts of interest.

The target localization by two ultra wideband (UWB) radar systems. The basic scenario.

Geometrical interpretation of target localization. Review of basic scenarios. (_{A}_{B}_{A}_{B}_{A}_{B}_{A}_{B}

The scheme of measurement for the basic scenario.

Room interior. (

M-sequence UWB radar systems with (

Radargram with preprocessed raw radar signals. (_{A}; (b) the first receiving channel of RS_{B}.

Radargram with the subtracted background. (a) The first receiving channel of _{A}_{B}

Detector output. (_{A}_{B}

TOA estimations. (_{A}; (_{A}_{B}_{B}

Target tracks estimated by all considered methods.

Target trajectory estimated by DCA.

Target trajectory estimated by DCB.

Target trajectory estimated by MEAN.

Target trajectory estimated by Taylor-Series method (TSM).

Target trajectory estimated by joining intersections of the ellipses (JIEM).

Localization errors for all estimated trajectories.

Localization errors for all estimated tracks.

Parameters of ellipses.

_{i} |
_{i} | ||
---|---|---|---|

_{A}_{,1} = (_{A}_{,1},_{A}_{,1}) |
_{A}_{A,t}_{A,t} |
_{A}_{,1}/2 | |

_{A}_{,2} = (_{A}_{,2},_{A}_{2}) |
_{A}_{A,t}_{A,t} |
_{A}_{,2}/2 | |

_{B}_{,1} = (_{B}_{,1},_{B}_{,1}) |
_{B}_{B,t}_{B,t} |
_{B}_{,1}/2 | |

_{B}_{,2} = (_{B}_{,2},_{B}_{,2}) |
_{B}_{B,t}_{B,t} |
_{B}_{,2}/2 |

Mean and RMS values of target localization errors for the estimated trajectories.

Mean [m] | 0.5846 | 0.5342 | 0.4418 | 0.5445 | 0.4215 |

RMS [m] | 0.7025 | 0.5858 | 0.4818 | 0.6304 | 0.4776 |

Mean and RMS values of target localization errors for the estimated tracks.

Mean [m] | 0.5187 | 0.5644 | 0.4546 | 0.5606 | 0.3961 |

RMS [m] | 0.6470 | 0.5865 | 0.4881 | 0.6065 | 0.4558 |

Illustration of computational complexity of target localization by DC, MEAN, TSM and JIEM.

Average time of calculation [ms] | 0.18 | 0.18 | 0.37 | 5.79 | 4.85 |