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Tropospheric Propagation At frequencies above about 30 MHz, the lower atmosphere bends radio waves toward the surface Tropospheric banding occurs because the index of refraction of air, with respect to EM waves, decreases with altitude The effect is similar to the way sound waves sometimes travel long distances over the surface of a calm lake in the early morning or early evening, letting you hear a conversation more than a mile away Tropospheric propagation makes it possible to communicate for hundreds of miles when the ionosphere will not return waves to the earth Another type of tropospheric propagation is called ducting It takes place when EM waves are trapped in a layer of cool, dense air sandwiched between two layers of warmer air Like bending, ducting occurs almost entirely at frequencies above 30 MHz Still another tropospheric-propagation mode is known as troposcatter This takes place because air molecules, dust grains, and water droplets scatter some of the EM field This effect is commonly seen at VHF and UHF Tropospheric propagation in general, without mention of the specific mode, is sometimes called tropo Auroral Propagation In the presence of unusual solar activity, the aurora (northern lights or southern lights) can return radio waves to the earth This is known as auroral propagation The aurora occur at altitudes of about 40 to 250 mi (65 to 400 km) Theoretically, auroral propagation is possible, when the aurora are active, between any two points on the surface from which the same part of the aurora lie on a line of sight Auroral propagation seldom occurs when one end of the circuit is at a latitude less than 35 north or south of the equator Auroral propagation is characterized by rapid and deep fading This almost always renders analog voice and video signals unintelligible Digital modes are most effective for communication via auroral propagation, but the carrier is often spread out over several hundred hertz as a result of phase modulation induced by auroral motion This severely limits the maximum data transfer rate Auroral propagation is often accompanied by deterioration in ionospheric propagation Meteor Scatter Meteors produce ionized trails that persist for approximately 05 s up to several seconds, depending on the size of a particular meteor, its speed, and the angle at which it enters the atmosphere This is not enough time for the transmission of much data, but during a meteor shower, multiple trails can result in almost continuous ionization for a period of hours Such ionized regions reflect radio waves at certain frequencies This is meteor scatter propagation It can take place at frequencies considerably.

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CHAPTER 11 AIDED INERTIAL NAVIGATION as de ned following eqn (1156), Hi = [hi Re D, 0, 0], n e n

and 0 is the 3 1 vector In an alternative approach, a similarity transform could be used to transform the error state, F and matrices so that the error state included pe instead of p Note that the north error n and east error e are not the horizontal error in vehicle position in geographic frame; instead, they are the error in the location of the origin of the geographic frame 11823 Lever Arm Compensation

above 30 MHz, and occurs over distances ranging from just beyond the horizon up to about 1500 mi (2400 km), depending on the altitude of the ionized trail and the relative positions of the trail, the transmitting station, and the receiving station

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Aided initialization and error estimation methods are complicated by the fact that the aiding system and INS are separated by a lever arm The lever arm adds complication in at least two forms First, the lever arm length and alignment will not be perfectly known due to manufacturing tolerances, di erent possible system con gurations, lever arm ex, and vibration Second, the measurement prediction and residual measurement models will depend on the lever arm o set vector The rst set of e ects can only be accommodated by changing the mechanical structure to enhance rigidity, by augmenting calibration states, or by arti cially increasing the variance of the measurement noise Those approaches are not discussed herein Assuming that the body frame o set vector is known, the lever arm e ects should be modeled at the design state to determine their e ect on accuracy and observability Often the lever arm must be accounted for to achieve high accuracy This section discusses the topic in general Several speci c instance are used in 12 Consider the situation shown in Figure 117 where pn and pa denote the position vectors of the navigation system and aiding sensor, respectively The point O denotes the navigation frame origin The o set vector r between the two positions is de ned as r = pa pn (11166)

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Moonbounce The moon, like the earth, reflects EM fields This makes it possible to communicate by means of earth-moon-earth (EME), also called moonbounce High-powered transmitters, sophisticated antenna systems, and sensitive receivers are needed for EME Some moonbounce communication is done by radio amateurs at frequencies from 50 MHz to over 2 GHz

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