How LORAN-C Works

In this section, we describe the LORAN-C standard. We don't explain any other LORAN-type standard (i.e., LORAN-A, LORAN-B, LORAN-D, or LORAN-F) because they are already discontinued.

LORAN-C signals are transmitted as a series of pulse chains. Generally, a LORAN-C chain (i.e., a specific set of transmitters) propagates anywhere between three and six pulse chains. One of these pulse chains must be a Master, whereas the other pulse chains must be Secondaries. The Master pulse chain is different from the Secondary pulse chains because it contains a series of nine pulses, whereas the Secondary pulse chains only contain eight. Thus, each LORAN-C chain transmits exactly one nine-pulse Master and between two and four eight-pulse Secondaries.

The Master is transmitted at regular intervals. The period at which these Masters are transmitted is known as the Group Repetition Interval (GRI). Each LORAN-C chain has its own GRI; therefore, the GRI can be used to distinguish between different LORAN-C chains. The United States Coast Gaurd publishes the GRIs for every LORAN-C chain in microseconds divided by ten. Thus, a LORAN-C chain with a published GRI of 9960 transmits the Master every 99600 microseconds.

The Secondaries are used to determine position. Thus, they are not transmitted at pre-published intervals. However, they are transmitted after a pre-published Coding Delay (CD). These delays are necessary to seperate Secondary pulse chains within the GRI; that is, without the CDs, the Secondary pulse chains would overlap in time. The Coast Gaurd publishes the CD for each Secondary transmitter in microseconds. Thus, a Secondary with a CD of 11000 transmits its pulse chain no less than 11000 microseconds after it receives the Master; and, a Secondary with a CD of 25000 transmits its pulse chain no less than 25000 microseconds after it receives the Master.

Let us consider the "Northeast U.S." (NE) LORAN-C chain. It contains one Master transmitter (in Seneca, NY) and four Secondary transmitters (in Caribou, ME; Nantucket, MA; Carolina Beach, NC; and, Dana, IN). Generally, the LORAN-C literature designates the Master and Secondary transmitters with letters. Thus, the Master is specified as M (for Master), whereas the Secondaries are specified as W (Whiskey), X (X-Ray), Y (Yankee), and Z (Zulu). The South Central U.S. chain is the only LORAN-C chain to also have a Secondary specified as V (Victor). Thus, for the NE chain, the Seneca, NY transmitter is known as M; Caribou, ME, as W; Nantucket, MA, as X; Carolina Beach, NC, as Y; and Dana, IN, as Z.

The GRI for the NE chain is 9960. Thus, it transmits the Master pulse chain every 99600 microseconds. The Master signal propagates omni-directionally throughout the region, and eventually hits a Secondary transmitter. The CD comes into effect only after it receives the Master signal. Thus, the Secondary transmitter broadcasts its pulse chain a certain number of microseconds after the Master, which includes both the time it took the Master to reach the Secondary transmitter and the Secondary transmitter's CD. In other words, the Emission Delay (ED) - that is, the delay in microseconds between the time the Master and Secondary signals are transmitted - is the sum of the time the Master signal took to reach the Secondary and the Secondary's CD. Because we can calculate the distance between the Master and Secondary transmitters, we can attempt to estimate the ED for each transmitter. Unfortunately, this is a deceptively difficult estimation to calculate, because we must take into account not only the Earth's pseudo-spherical shape, but also the conductivity of the Earth between the transmitters, which typically decreases the speed of the signals' progagation. Luckily, the Coast Guard also publishes the EDs for each transmitter in microseconds. These EDs were determined experimentally, and are therefore very accurate.

In the NE chain, the Whiskey's ED is 13797.20 microseconds. Thus, our receiver will not obtain the Whiskey's pulse chain until at least 13797.20 microseconds after it has obtained the Master's pulse chain. Generally, the receiver will obtain the Whiskey's pulse chain after a longer period of time - perhaps, at around 15000 microseconds - because its signal must also travel between the Whiskey transmitter and the Receiver. Thus, at a high level, we can imagine using the time delay (TD) between the Receiver's reception of the Master and Secondary pulse chains to compute the distance between the Secondary transmitter and the Receiver.

This calculation is also deceptively complex. That is, although we know that the Receiver cannot obtain the Secondary signal before the ED, we do not know when the Receiver obtains the Master signal. For example, if the Receiver and Master are very close to one another, the Receiver will obtain the Master signal much sooner than the Secondary obtains it. Thus, from the Receiver's point of view, the delay between the Master and Secondary signals will be quite large. Similarly, if the Receiver and Master are very far from each other, the Receiver will obtain the Master signal much later than the Secondary obtains it. Thus, the delay between the Master and Secondary signals at the Receiver will be comparitively small. Therefore, we can only be certain that a particular time delay corresponds to the Receiver's position with respect to both the Master and Secondary transmitters.

It turns out that hyperbolic Lines of Position (LOPs) can be drawn with respect to a Master-Secondary pair that specify locations resulting in a particular TD. That is, a hyperbola can be drawn between a Master and Secondary transmitter such that every point upon it results in a single TD. Thus, by determining the TD at a Receiver between a Master and Secondary pulse chain, we can determine the hyperbola upon which our Receiver lies. Then, by measuring the TD between another Master-Secondary pair, we can determine the intersection point of two hyperbolas. That intersection point is the location of our Receiver. Thus, at least one Master and two Secondaries are required to fix a particular position with the LORAN-C system.

An ideal pulse within a LORAN-C pulse chain is defined by the equation: i(t) = A(t - tau)² * exp(-2(t - tau)/65) * sin(.2(pi)t + PC), where A() is the Normalization Constant; tau is the envelope-to-cycle difference; and, PC is the phase code parameter. In simple terms, the LORAN-C signal operates at 100 kHz and has pulses defined by the envelope t²exp(-2t/65). As mentioned, Secondary pulse chains consist of eight pulses; each pulse is seperated by approximately 100 microseconds. Master pulse chains consist of nine pulses; the first eight are seperated by approximately 100 microseconds, whereas the ninth pulse appears approximately 200 microseconds after the eighth pulse.

The pulse chains are also defined by phase code parameters. Essentially, a positive phase code (specified by a "+") does not affect the location of a pulse in time; however, a negative phase code (specified by a "-") shifts a pulse forward in time by 180 degrees. At 100 kHz, each LORAN-C cycle lasts 10 microseconds; thus, a negative phase code shifts a pulse forward in time by 5 microseconds. The phase code parameters follow simple patterns that repeat every two GRIs; each pattern is specified by the letters A or B. Thus, for Master pulse chains, Phase Code A is {+ + - - + - + - +}, and Phase Code B is {+ - - + + + + + -}. Similarly, for Secondary pulse chains, Phase Code A is {+ + + + + - - +}, and Phase Code B is {+ - + - + + - -}. These phase code patterns allow engineers to easily distinguish between neighboring GRIs.

This information is vital in a LORAN-C positioning system because the signal obtained by the Receiver is usually very noisy. To increase the signal-to-noise ratio (SNR), LORAN-C receivers generally perform pointwise summations across several GRIs of the obtained signal. Because the LORAN-C signal is phase coded, it is usually simpler to sum the obtained signal two GRIs at a time. In other words, the Receiver adds a point in the LORAN-C signal with another point that is exactly two GRIs away. Thus, the Receiver sums several periods of the obtained signal that are phase coded in exactly the same manner. This method works because the summations cause the pulse chains to constructively interfere with one another; and, if we assume that the propagation noise is Gaussian (i.e., random), the summations cause the noise to cancel out. Thus, these summations simultaneously increase the strength of LORAN-C pulses and decrease that of the noise, thereby increasing the SNR.

To further increase a pulse's SNR, the Receiver typically sums the pulses within a pulse chain. That is, every pulse within a Master or Secondary pulse chain is added together to form a single clean pulse. With this clean pulse, the Receiver begins to calculate the TD. However, the Receiver must define a common reference point within this pulse to accurately measure the TD. This reference point must be sufficiently contained by the pulse; in addition, it must also be unaffected by skywave propagation. Skywaves occur when a transmitted signal reflects off the ionosphere before hitting the Receiver. Thus, the Receiver actually obtains two signals: one that came directly from the transmitter, and another that reflected off the ionosphere. Typically, skywave propagation causes distortion at the end of a pulse; in addition, skywaves generally have an amplitude much larger than the direct signal, thereby causing significant distortion.

It turns out that skywaves do not arrive at the Receiver less than 30 microseconds after the direct signal. Thus, a suitable reference point for TD measurements exists 30 microseconds into the obtained signal. At 100 kHz, each LORAN-C cycle last 10 microseconds; thus, the third zero crossing of a LORAN-C pulse corresponds to suitable reference point. In other words, LORAN-C receivers determine the third zero crossing of the first pulse in each pulse chain, and subtract the times that the zero crossings occurred in each Master-Secondary pair to determine the TDs.

These TDs are converted to latitude-longitude coordinates to aid users with navigation. However, as already mentioned, TD-coordinate conversions are very complex. First, the Earth's shape is not precisely spherical; thus, precise calculations must account for the planet's complex pseudo-spherical geometry. Also, the Earth's conductivity varies with location; typically, this conductivity decreases the signals' propagation speed. There are several techniques to account for this conductivity; the Coast Guard even provides conductivity tables to aid engineers with their algorithms. However, such techniques can only approximate the signals' propagation speed; therefore, a certain degree of error will always exist in any TD-coordinate conversion. Care must also be taken with the algorithm that determines the Receiver's hyperbolic intersection point; in rare cases, these hyperbolic LOPs intersect in two places.

Today, DSP technologies can be used to perform most of these tasks. These technologies have reportedly improved the absolute accuracy of LORAN-C to approximately 50 feet. Earlier generations did not have access to such techniques. For example, in the 1970s, the first digital LORAN-C receivers measured TDs by using a local oscillator to sync with the input pulses. At the time, analog-to-digital conversion (ADC) was so primitive that engineers could only determine whether a point on the LORAN-C signal was positive or negative. Despite these limitations, engineers built receivers that were accurate to 200 feet. Engineers in the 1950s had it even worse: digital technology wasn't even invented, so signals were obtained and manipulated with analog circuits. Yet, these receivers were still accurate to 1500 feet. Clearly, today's technology provides advantages and opportunities that LORAN's architects never had.

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