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receiver and satellite biases are eliminated and the equations simplify to = R+ = R + + N (8151) (8152)

where R is the vector of user-to-satellite geometric ranges In the case of double di erences, the covariance matrix for denoted as is not diagonal; instead, [ ]ij =

2 2 2

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Absolute-Value Impedance You ll occasionally read or hear that the impedance of some device or component is a certain number of ohms For example, in audio electronics, there are 8- speakers and 600- amplifier inputs How, you ask, can manufacturers quote a single number for a quantity that is two-dimensional and needs two numbers to be completely expressed That s a good question, and there are two answers First, figures like this refer to devices that have purely resistive impedances, also known as nonreactive impedances Thus, the 8- speaker really has a complex impedance of 8 + j0, and the 600- input circuit is designed to operate with a complex impedance at, or near, 600 + j0 Second, you can talk about the length of the impedance vector (that is, the absolute value of the complex impedance), calling this a certain number of ohms If you talk about impedance this way, however, you are being ambiguous There can exist an infinite number of different vectors of any given length in the RX plane Sometimes, the uppercase italic letter Z is used in place of the word impedance in general discussions This is what engineers mean when they say things like Z = 50 or Z = 300 nonreactive In this context, if no specific impedance is given, Z = 8 can theoretically refer to 8 + j0, 0 + j8, 0 j8, or any other complex impedance point on a half circle consisting of all points 8 units from 0 + j0 This is shown in Fig 15-7 Problem 15-4 Name seven different complex impedances that can theoretically be meant by the expression Z = 10 It s easy name three: 0 + j10, 10 + j0, and 0 j10 These represent pure inductance, pure resistance, and pure capacitance, respectively A right triangle can exist having sides in a ratio of 6:8:10 units This is true because 62 + 82 = 2 10 (Check it and see!) Therefore, you can have 6 + j8, 6 j8, 8 + j6, and 8 j6, all complex impedances whose absolute value is 10.

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(8153)

and a set of (m + 1) satellites will be required to generate a set of m measurements The integer ambiguity resolution problem can be applied in various scenarios: L1, L2, L1 and L2, and widelane The number of possible scenarios increases further with the advent of a third frequency in the modernized signal structure Therefore, in this section, we will discuss general characteristics of the problem and means for its solution The solution process will be structured as follows 1 Initialization The main objective of this step is to provide an initial estimate p0 of the position that is su ciently accurate so that the hot s of the approximation = H p + + N (8154)

Impedance Transfer Ratio In RF and AF systems, transformers are employed to match impedances Thus, you will sometimes hear or read about an impedance step-up transformer or an impedance step-down transformer The impedance transfer ratio of a transformer varies according to the square of the turns ratio, and also according to the square of the voltage-transfer ratio If the primary (source) and secondary (load) impedances are purely resistive and are denoted Zpri and Zsec, then the following relations hold:

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