A Survey on Wireless Position Estimation <s> Geometric Techniques <s> From the Publisher: ::: Wireless Location in CDMA Cellular Radio Systems investigates methods for wireless location in CDMA networks and analyzes their performances. Techniques for measuring location parameters (AoAs, ToAs, etc.) are presented along with algorithms for calculating position from those parameters. Several impairments to accurate location are covered and analyzed including multipath propagation, non-line-of-sight propagation, and multiple-access interference. Many of the topics in this book are also applicable to FDMA- and TDMA-based communication networks. <s> BIB001 </s> A Survey on Wireless Position Estimation <s> Geometric Techniques <s> This paper proposes a mobile user location scheme for wideband code-division multiple-access (CDMA) wireless communication systems. To achieve high location accuracy and low cost of the mobile receiver, the location scheme combines the time difference of arrival (TDOA) measurements from the forward link pilot signals with the angle of arrival (AOA) measurement from the reverse link pilot signal. High chip rates in wideband CDMA systems facilitate accurate TDOA measurements, and a smart antenna used at the home base station (BS) can provide accurate AOA measurement in a macrocell environment. A two-step least square location estimator is developed based on a linear form of the AOA equation in the small error region. Numerical results demonstrate that the proposed hybrid TDOA/AOA location scheme gives a much higher location accuracy than TDOA only location, when the number of base stations is small and/or when the TDOA measurements have a relatively poor accuracy. <s> BIB002
Geometric techniques solve for the position of the target node as the intersection of position lines obtained from a set of position related parameters at a number of reference nodes. As studied in Section 2, an RSS or a TOA parameter defines a circle for the position of the target node; hence three parameter estimates can be used to determine the position via trilateration, as shown in Figure 5 . On the other hand, an AOA parameter defines a straight line passing through the target node and the reference node, as shown in Figure 3 . Therefore, two AOA parameters are sufficient to locate the target node via triangulation as shown in Figure 6 . In the case of TDOA based positioning, each TDOA parameter determines a hyperbola for the position of the target node. For three reference nodes, two range differences (obtained from TDOA parameters) define two hyperbolas, the intersection of which yields the position of the target node, as shown in Figure 7 , However, the position may not always be determined uniquely depending on the geometrical conditioning of the nodes  , BIB001 . The geometric techniques can also be applied to hybrid systems, in which multiple types of position related parameters, such as TDOA/AOA BIB002 or TOA/TDOA  , are employed in position determination. For example, for a hybrid AOA/TOA system as shown in Figure 8 , in which the reference node can estimate both AOA and TOA of the signal from the target node, the position can be calculated as where (x 1 , y 1 ) is the position of the reference node, ψ is the AOA, and d is the range obtained via TOA estimation. In other words, the minimum number of nodes that are required to determine the position of the target node can change depending on the capabilities of the target and/or the reference nodes. One of the disadvantages of geometric techniques is that they do not provide a theoretical framework in the presence of noise in position related parameters. In other words, when the position lines intersect at multiple points, instead of a single point, due to random errors in the parameter estimation step, the geometric approach does not provide any inside as to which point to choose as the position of the target node. In addition, as the number of parameters increases, the number of intersections increases even further. For example, Figure 9 illustrates three erroneous AOA parameter estimates related to three reference nodes, which results in multiple intersections of the position lines, without all three lines intersecting at a single point. As this example illustrates, the geometric approach does not provide an efficient data fusion mechanism; i.e., cannot utilize multiple parameter estimates efficiently.