Blanqueamiento material: «¿Qué se hicieron los africanos de Cartagena?» 21

To study the efficiency of the proposed TROA approach, the MSE’s were com- pared to a derived CRLB for the problem at hand (details of the CRLB deriva- tion are given in Appendix B). Figures 4.22 and 4.23 illustrate the estimation performance of our approach for the x coordinate and y coordinate of the NOI, respectively on both the conventional and logarithm scales. The position estima- tion performance has been studied for 3 different position of the NOI within the in- door environment of interest; the considered positions are: [x, y] = [5, 5; 12, 4; 9, 14]. In these three cases, the TROA approach shows good performances where the MSEs are close to their respective CRLBs.

1 2 3 4 5 6 7 8 9 10 11 x 10−10 0 0.5 1 1.5 2 x 10−3 Standard Deviation (s) Error (m)

CRLB vs. MSE plot for x coordinates CRLB (5,5) MSE (5,5) CRLB (12,4) MSE (12,4) CRLB (9,14) MSE (9,14)

Figure 4.22: CRLB vs. MSE comparison for x coordinates of (5,5), (12,4) and (9,14) 1 2 3 4 5 6 7 8 9 10 11 x 10−10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10 −3 Standard Deviation (s) Error (m)

CRLB vs. MSE plot for y coordinates CRLB (5,5) MSE (5,5) CRLB (12,4) MSE (12,4) CRLB (9,14) MSE (9,14)

Figure 4.23: CRLB vs. MSE comparison for y coordinates of (5,5), (12,4) and (9,14)

4.6

Conclusion

4.6.1

Summary

In conclusion, a novel UWB-driven multilateration technique for position estima- tion in an indoor environment has been presented in this chapter. The presented technique exploits the inherent properties of UWB signal propagation; and its def- inition is in conjunction with the operational principles of the widely overlooked and under-studied TSOA position estimation technique. The accuracy of the proposed approach for a network of three receivers and one transmitter has been studied and presented. By means of a series of statistically driven MSE analyses, it has been shown that in comparison with TOA and TSOA, the proposed TROA technique possesses a much higher accuracy with regards to position estimation. The CRLBs have been computed using TROA measurement set; and it has also been shown that the proposed TROA technique shows good performances when the CRLB is directly compared with the MSE.

4.6.2

Contributions

The main research contributions presented in this chapter can be summarised as follows:

• Explicit definition and description of a novel time-based position estimation technique which is coined as Time Reflection of Arrival (TROA). TROA is wholly UWB-driven and unlike conventional position estimation techniques, it does not require the NOI to be either active or semi-passive.

indoor environment shapes (i.e. square and rectangle).

• Derivation of a new theoretical lower bound on the covariance of the TROA estimator based on the Cram´er-Rao lower bound (CRLB) to determine the efficiency of TROA.

These research contributions have been documented and reported in a technical journal paper titled “A Novel UWB-based Multilateration Technique for Indoor Localisation”. In February 2014, it was accepted for publication by the IET Communications Journal and has recently been included in the July 2014 edition [119].

Case Study: Fall Detection

Algorithm for Alzheimer’s

Disease (AD) Patients

5.1

Introduction & Problem Statement

In this chapter, an inherently novel and Ultra-Wideband (UWB) driven algorithm that performs the task of detecting unrecovered falls by an Alzheimer’s Disease (AD) patient is presented. The proposed algorithm achieves this by cleverly us- ing an element of the AD patient’s location information in a 3-D solution space to determine their real-time postural orientation (i.e. fallen down, standing up, lying down) in a specified indoor environment. The utilised element is the ‘z’ co- ordinate of the patient’s location information and it is obtained from a known point on the patients body. When this element is measured relative to the ground plane of coordinates (0, 0, 0), the height of the patient or the vertical distance

(Vd) between the patient and the floor is defined. Based on the specified AD pa- tient’s physical attributes, Vd is subsequently compared with a set of pre-defined heights that correspond to postural activities exclusively carried out by the pa- tient. As it is shown in the following sections, this is done in order to facilitate the determination of the real-time postural orientation of the patient and ultimately ascertain if they have fallen down. Once a fall has been inferred and ascertained, the duration in which the patient’s Vd value remains in the fall defining range is monitored for a fixed time to determine if they have recovered from the fall1_.

In the event that the Vd value either fails to increase within the allocated time or fluctuates sporadically within the allocated time, an alarm is triggered and a medical personnel is notified. For the entirety of this work, TSOA is employed as the underlying position estimation technique. TSOA is chosen because as im- plied in chapter 3, even though there is an additional receiver requirement for its implementation in comparison to both TOA and TDOA, it offers a better accuracy2_.

5.2

Background

Dementia to all intents and purposes is an unremitting disease that affects people that are of the ages of 65 and above (i.e. elderly people) [120–122]. One of the most common forms of dementia that is usually observed in this category of people is Alzheimer’s Disease (AD) [120, 121]. With AD, the sufferer’s reduced

1_{A V}

d value that gradually increases with time is an indicator that the patient attempting

to recover from the fall while a Vd value that remains constant over a period of time indicates

no recovery attempt.

2_{It is noteworthy to mention that at the time this algorithm was formulated, TROA was yet}

to be conceptualised. Hence future work could entail a comparison between a fully defined 3-D TROA and TSOA to determine the better technique accuracy-wise.

brain capacity and functionality which is as a direct result of a combination of the adverse effect of this disease and the drugs being administered to combat it, makes them a lot more prone to a constant deterioration in their cognitive functions. Notably, this ultimately leads to a high occurrence of involuntary falling. In some cases, the involuntary fall is relatively mild and the patient is able to recover from it in a timely manner, while in other cases, the severity of the fall results in the inability of the patient to recover from it. In this work, we focus wholly on unrecovered falls and explicitly define an algorithm that detects such falls by using the patient’s location information.