CAN LORAN MEET GPS BACKUP REQUIREMENTS?

To be presented at the 11 th Saint Petersburg International Conference on Integrated Navigation Systems, 24 26 May 24 CAN LORAN MEET GPS BACKUP REQUIREMENTS? Gregory Johnson, MSEE, Ruslan Shalaev, BSCS John J. McMullen Associates, New London, CT 86-71-256 gwjohnson@jjma.com, rshalaev@jjma.com Richard Hartnett, PhD US Coast Guard Academy, New London, CT 86-444-8542 rhartnett@exmail.uscga.edu Peter Swaszek, PhD University of Rhode Island, Kingston, RI 41-874-582 swaszek@ele.uri.edu Mitch Narins, MS Eng. Mgt. Federal Aviation Administration, Washington, DC 22-493-4336 mitchell.narins@faa.gov Abstract Key words: Loran, Additional Secondary Factor (ASF), GPS backup The Federal Aviation Administration (FAA) is currently leading a team consisting of members from Industry, Government, and Academia to provide guidance to the policy makers in their evaluation of the future of Loran-C in the United States. In a recently completed Navigation Transition Study, the FAA concluded that Loran-C, as an independent radionavigation (RNAV) system, is theoretically the best backup for the Global Positioning System (GPS). However, in order for Loran-C to be considered a viable back-up system to GPS, it must be able to meet the requirements for non-precision approaches (NPA s) for the aviation community, and the Harbor Entrance and Approach (HEA) requirements for the maritime community. Through FAA sponsoring, the U.S. Coast Guard Academy (USCGA) is responsible for conducting some of the tests and evaluations to help determine whether Loran can provide the accuracy, availability, integrity, and continuity to meet these requirements. A major part of assessing the suitability of Loran is in understanding the nature of Loran ground wave propagation over paths of varying conductivities and terrain. Propagation time adjustments, called additional secondary factors (ASFs), are used to adjust receiver times of arrival (TOAs) to account for propagation over non-seawater path(s). These ASFs vary both spatially and temporally, and unless understood and/or modeled, we lose accuracy and may not be able to guarantee a hazardously misleading information (HMI) probability of less than 1x1-7. During the summer of 23, the Coast Guard Academy, with flight support from the FAA Technical Center, conducted a series of tests to measure ASF variations in the vicinity of several selected airfields in Colorado, Arkansas, Florida, and California. In addition, approaches were flown at several airports in each of these areas. ASF and TOA data collected during these trials has been analyzed through post-processing to determine the Loran position accuracy during approaches. The accuracy of raw (uncorrected Loran), as well as ASF-corrected Loran positions are shown for a variety of ASF profiles. Using the BALOR ASF modeling software produced by the University of Wales at Bangor, we have also done some simulations of best-case performance analysis for receivers with little or no noise. In addition, we present some ideas for using a Kalman-filtered integrated Loran-INS receiver in order to smooth out Loran position errors. Finally, how all of these efforts lead towards meeting the accuracy requirements is shown. Introduction/Goals In 21, the Volpe National Transportation Systems Center completed an evaluation of GPS vulnerabilities and the potential impacts to transportation systems in the United States [1]. One of the recommendations of this study was for the operation of backup system(s) to GPS. One possible backup system was identified as Loran-C. The Federal Aviation Administration (FAA) observed in its recently completed Navigation and Landing Transition Study [2] that Loran-C, as an independent radio navigation system, is theoretically the best backup for the Global Positioning System (GPS). However, this study also observed that Loran-C s potential benefits hinge upon the level of position accuracy actually realized (as measured by the 2 drms error radius): for aviation applications this is the ability to support non-precision approach (NPA) at a Required Navigation Performance (RNP) of.3 which equates to a 2 drms error of 39 meters for maritime applications this is the ability to support harbor entrance and approach (HEA) requirements which equates to a 2 drms error of 8-2 meters. The recently released report of the DOT Radionavigation Task Force [3] details the results of a multi-modal capabilities assessment and alternatives analysis of radionavigation systems. This report is based on current US policy for radionavigation systems as contained in the 21 Federal Radionavigation Plan [4] and detailed descriptions of the various radionavigation systems are contained in the 21 Federal Radionavigations System [5]. In the task force

report, the following conclusions were reached about Loran: The evaluation of enhanced Loran needs to be completed before making a firm commitment to that system. Termination of Loran would eliminate the only available crossmodal radionavigation backup to GPS. The report also recommends Complete the evaluation of enhanced Loran to validate the expectation that it will provide the performance to support aviation NPA and maritime HEA operations. If enhanced Loran meets the NPA and HEA performance criteria, and is cost effective across multiple modes, the Federal Government should operate Loran as an element of the long-term US radionavigation system mix. A significant factor limiting the accuracy of a Loran system is the spatial and temporal variation in the times of arrival (TOAs) observed by the receiver. A significant portion of these variations are due to the signals propagating over paths of varying conductivity; these TOA corrections which compensate for propagating over non-seawater paths are called additional secondary factors (ASFs) [6]. Hence, a key component in evaluating the utility of Loran as a GPS backup is a better understanding of ASFs and a key goal is deciding how to mitigate the effects of ASFs to achieve more accurate Loran-C positions while ensuring that the possibility of providing hazardous and misleading information (HMI) will be no greater than 1x1-7. The U.S. Coast Guard Academy, as a part of the FAA s government, industry, and academia team, is striving to improve the understanding of the temporal, spatial, and directional variations in time of arrival (TOA) that could be mitigated. The intent is to develop a differential or enhanced Loran system that estimates and removes these ASFs to allow for higher precision position solutions. Our Loran system for 23 and beyond is based on a multi-station, multi-chain, all-in-view, DSP-based receiver observing TOA measurements with an H-field antenna. To improve performance, this new system separates the ASF errors (where this ASF error includes all TOA errors) into spatial, temporal, and directional components; specifically, as described in [7], our approach is to model each of the three components of the ASF errors, estimate parameter values for the models, and then correct the TOA observations using the models before applying the position solution algorithm. For an aviation receiver the approach is to use a single set of ASF values (one for each Loran tower) for a given airport. This value may have seasonal adjustments applied to it. The Loran receiver will use this set of static ASF values to improve position accuracy when conducting a non-precision approach (NPA). The issue to be resolved is whether the ASF gradients are sufficiently small in the location of a given airport that use of a single static value will meet RNP.3 requirements. For a maritime receiver in a harbor entrance and approach environment, a grid of ASF values will be used. This grid may have temporal adjustments applied by using a static reference site in a differential Loran scenario. The issue to be resolved here is how accurate and how dense the grid needs to be in order to meet the HEA accuracy requirements. During the summer of 23, the Coast Guard Academy, with flight support from the FAA Technical Center, conducted a series of tests to measure ASF variations in the vicinity of several selected airfields in Colorado, Arkansas, Florida, and California. Approaches were also flown at several airports in each of these areas. ASF and TOA data collected during these trials has been analyzed through post-processing to determine the Loran position accuracy during approaches. The accuracy of raw (uncorrected Loran), as well as ASF-corrected Loran positions are shown for a variety of ASF profiles. In addition, maritime data has been collected over several weeks in the Fall of 23 on the Thames River in Connecticut using a training vessel from the USCG Academy. These two data collections are described in the sections following. However, one of the issues currently impacting performance is limitations and errors in the receivers; specifically, there have been issues with receiver noise performance and the H-field antennas. Some of the errors introduced with current H-field antennas have been investigated by the authors and are discussed in [8]. In order to focus on the possible performance with the Loran system and not be limited by receiver errors, we have used a simulation approach in order to answer the question of whether Loran can meet the accuracy requirements. The simulation approach is described in a later section followed by the results of predicted performance. Flight Tests A series of flight tests were conducted in conjunction with the FAA Technical Center during July, August, and September of 23. This testing covered airports in four areas: Grand Junction, CO; Little Rock, AR; Pensacola, FL; and Monterey, CA (see Figure 1). In each area, data was collected with the FAA s Convair 58, with a mobile unit on the ground, and from a static reference site set up at one of the airports. The goals of the in-flight data were to measure ASF variations in the vicinity of the airports and to fly approaches for later post-processing of the TOA data. The goal of the ground mobile data collection was to collect ASF data at static locations around each airport that could be used to assess ASF gradients and also used as a reference to assess the accuracy of the flight measurement data. The static reference site was used in order to factor out the temporal variations in the ASFs. Details on our data collection efforts and equipment used can be found in [9]. For the purposes of this paper, the data from the airport approaches has been separated out and analyzed. As described above, the goal is to meet 39 meter accuracy along the approach paths. The total flight path with the four airport approaches for one of the airports is shown in Figure 2. The position accuracies along these approach paths are shown in Figure 3. The red dots are the position errors for positions calculated using raw Loran TOAs, while the blue dots are the position errors for the case of Loran TOAs adjusted by using a single set of airport ASF values (one for each station). In each case the WAAS GPS position of the aircraft is used as the ground truth position in order to calculate the position error. The performance observed in this case was acceptable; at other airports the data was not as good due

to poor receiver performance. The aircraft receivers we used suffer from poor noise performance as well as the heading dependent variations in the measured TOAs due to issues with the H-field antennas used. These results led us to investigate a simulation approach for the short term while awaiting improved receivers and H-field antennas. Monterey, CA FAA Tech Ctr Grand Junction, CO Little Rock, AR Pensacola, FL Figure 1 Flight tracks for summer 23 ASF mapping; the 4 test areas are circled and labeled in red Ground track for DDC Approaches, Monterey, 25 Sep 3 36.9 Leg 1 Leg 2 Leg 3 Leg 4 36.8 Latitude 36.7 36.6 36.5 36.4-122.5-122.4-122.3-122.2-122.1-122 -121.9-121.8-121.7 Longitude Figure 2 Flight track for flights on 25 Sep 23 showing the 4 approaches flown into Monterey airport

1 DDC Approaches, Monterey, 25 Sep 3 9 8 Position Error, m 7 6 5 4 3 Uncorrected Loran ASF Corrected Loran 2 1 17.5 17.6 17.7 17.8 17.9 18 18.1 UTC, HH.hh Figure 3 Position errors observed along approach paths: uncorrected Loran and ASF corrected Loran Simulation Strategy In order to investigate the performance of the Loran system without being distracted by performance limitations of individual receivers, we have developed a simulation approach. In this simulation we have used the GPS track from the actual approaches as the flight path combined with grids of predicted Additional Secondary Factors (ASFs) calculated using BALOR. BALOR is a software model developed by the University of Wales at Bangor and modified under an FAA-funded contract for the Loran Evaluation team. This software is designed for calculating predicted ASFs using the Monteath method [1-12]. It uses a terrain elevation database (DTED Level 1 format), a ground conductivity database (from the FCC), and a coastline database (World Vector Shorelines) for the ASF computations. Additional details on our use of the software are contained in [9]. The BALOR software is used to create evenly spaced, rectangular grids of predicted ASF values. The grids for the Monterey area are shown in Figures 4a-4c (one for each of the three closest Loran stations), with the three airports (MRY = Monterey, SRS = Salinas, and WVI = Watsonville) and approach paths marked in black. The dotted black line is the coastline. Since the BALOR model generates ASF values on evenly spaced grid points, a two-dimensional interpolation is done to estimate a more precise ASF value at each individual GPS location. In order to create the simulated Loran TOAs that would be measured by a receiver at each location, we have used the predicted TOA (primary factor secondary factor) for each GPS position plus the published Emission Delay plus the predicted ASF value calculated using the BALOR model. Simulation Results Flight The procedure described above has been used to calculate expected position errors along the approach path to each of the airports in the study. Similar results are seen at all airports; since the ASF value used for all positions is the ASF that is valid at the airport, the position error is minimum (zero) at the airport and increases with distance from the airport as a function of how much the ASFs vary with distance and in relationship to each other. For the sake of space only one example is shown here, for Monterey airport. In Figure 5, we have shown the position errors along the flight path for four cases: perfect ASF knowledge (red), no ASFs (blue), single set of ASF values (green), and single set of ASF values with additive Gaussian noise (maroon). In this case the raw Loran performance has errors in the range of 45-55m. With the use of the set of airport ASF values, the performance is improved to less than 1m of error. The additive noise has minimal impact on the solution. The perfect knowledge ASF case shows almost zero error as expected; this was our check that the algorithm was working correctly. The four approaches can be seen in the four ramps of error minimum error at the airport and maximum at the start of the approach. This can be seen better in Figure 6 where we have plotted error as a function of distance from the airport both for the uncorrected Loran case (blue) and the ASF-corrected Loran case (green). The cumulative distribution of position errors is shown in Figure 7; 5% of the position errors are less than 6m and 95% are less than 1m.

Middletown 2 6 Monterey 5 37. N 1.5 4 Perfect ASF knowledge no ASFs single airport ASF airport ASF w/rcvr noise WVI Position Error, m 3 SRS 2 36.5 N MRY 1 1 5 1 15 2 25 3 35 4 45 122. W 121.5 W.5 Figure 5 Position errors as a function of position number, four approaches into Montrose airport (a) Loran Station Middletown 6 Monterey Searchlight 4 5 3.5 4 Loran solution - no ASFs Loran solution using airport ASF 37. N WVI 3 2.5 Position Error, m 3 min ASFs: 2.665.7453 2.7457 max ASFs: 2.3378.86279 2.9874 range of ASFs: 2.27139.1175.24173 SRS 2 MRY 1 36.5 N 1.5 2 4 6 8 1 12 Distance from airport, SM 1 Figure 6 Position errors along plotted as a function of distance from the airport.5 122. W 121.5 W Cumulative distribution of position errors out to 1 miles from the airport 1 (b) Loran Station Searchlight 9 Fallon 4 8 37. N WVI 3.5 3 2.5 Percent of errors less than or equal to x 7 6 5 4 3 SRS 2 2 1 MRY 36.5 N 1.5 1 2 3 4 5 6 7 8 9 1 Position Error, m 1 Figure 7 Cumulative Distribution of Position Errors 122. W 121.5 W.5 (c) Loran Station Fallon Figure 4 BALOR ASF grids for Monterey, CA area

To be presented at the 11 th Saint Petersburg International Conference on Integrated Navigation Systems, 24 26 May 24 Simulation Results - Maritime Data In [7] we considered the impact of the spatial variation of the ASF for the 996 chain on navigation performance on the Thames River in New London, CT and on Narragansett Bay in RI. Similar to the idea described above for airport navigation, we employed a single static ASF value (one per Loran station) for the entire harbor area and tested navigation performance along typical ship tracks. Specifically, these static ASF values were subtracted from the observed TOAs at each time step and the Loran position was calculated. While for these harbors the error in the raw Loran position was on the order of 4 to 6m, the static ASF corrected Loran position error was reduced to the 3-1 meter range. While this result more than meets the RNP.3 accuracy requirement of 39 meters, it does not meet the Coast Guard requirement for Harbor Entrance Area (HEA) of 2 meters. Since a single ASF value does not provide the desired accuracy for maritime users, our current approach is to create a coarse grid of the ASF contours in relevant harbor and harbor-entrance areas and to interpolate ASF values from these grids. Specifically, the interpolation can be based upon a recent position or in a boot-strap mode in which we iteratively interpolate (i.e. start with static ASFs for the harbor area, then repeatedly compute a Loran position and interpolate the ASF grid at that point until the position solution converges). To test the feasibility of such a grid-based scheme, we have developed a simulation approach using actual ship tracks combined with ASFs calculated using BALOR. In this case, BALOR generates both the fine grid to simulate the measured TOAs as well as the coarse grid for interpolation. The ASF grid spacing for the fine grid was.1 degrees in both latitude and longitude (a spatial separation on the order of 1 meters at our location). Combined with the predicted TOAs (including the primary and secondary factors) and the Emission Delay, this allows for calculation of the expected Loran TOAs along the tracks. Gaussian noise (with variance dependent upon the expected SNR of the station) is added to the TOAs. The ASF grid for the Loran receiver is constructed by subsampling the original ASF grids. For the simulation results below, we used 7-by-12 point grids which corresponds to one ASF value every 5-1m. While other size grids could be easily constructed, we picked a relatively coarse size (fewer than 1 ASF values per station) to demonstrate the level of performance achievable with small parameter sets. Our test area is the Thames River in Southeastern Connecticut (the site of the U. S. Coast Guard Academy). As can be seen from the map of the Northeastern US in Figure 8, the test location is centrally located with respect to the four Loran stations in the 996 NEUS chain. While others stations and chains can be tracked at this location, our simulation focuses on this simple geometry. Further, the relative closeness of Nantucket (with its steep ASF profile on the river) and the long distances to Caribou and Carolina Beach make for an interesting scenario. A typical 7-by-12 ASF grid for the receiver for our test region, shown as a mesh plot, appears in Figure 9. The four full resolution ASF grids for this area are shown as colored contour plots in Figure 1. The North-South track used for simulation is also shown in black on each plot. Caribou Seneca Nantucket Wildwood Figure 9 A typical 7-by-12 ASF grid for the Thames River area. Carolina-B Figure 8 The locations of the 996 NEUS chain relative to the Thames River area.

To be presented at the 11 th Saint Petersburg International Conference on Integrated Navigation Systems, 24 26 May 24 3.9 41.4 N Seneca 41.4 N Nantucket.8 2.95 41.38 N 41.38 N.7 41.36 N 2.9 41.36 N.6.5 41.34 N 2.85 41.34 N.4.3 41.32 N 2.8 41.32 N.2 72.12 W 72.1 W 72.8 W 72.6 W 2.75 4.9 72.12 W 72.1 W 72.8 W 72.6 W 2.1 41.4 N Caribou 41.4 N Carolina Beach 4.85 1.9 41.38 N 4.8 41.38 N 1.8 4.75 41.36 N 41.36 N 4.7 1.7 41.34 N 4.65 41.34 N 1.6 4.6 41.32 N 41.32 N 1.5 4.55 72.12 W 72.1 W 72.8 W 72.6 W 4.5 72.12 W 72.1 W 72.8 W 72.6 W 1.4 Figure 1 BALOR predictions of the ASFs for the Thames River area. We performed the simulation under two scenarios: no additive noise on the TOA values and with additive noise of the expected variance. The performance with no noise shows the variation in position accuracy as a function of the mismatch between the estimated and actual ASFs to show what level of precision is needed from the ASF grids; adding noise more realistically demonstrates achievable performance. Figure 11 shows the error performance as a scatter plot showing individual North-South and East-West errors for approximately 27 track locations. The plot to the left shows the performance of the interpolated ASF grid alone, no noise. It is clear from the diagram that the ASF profiles along the ship track considered wander about the piecewise linear fit from the interpolation operation. The 95% circle, shown in red, is well under 2 meters. The plot to the right shows the effect of additive noise (on the TOA measurements) of the correct variance. Again, the 95% circle shows that even only a 7-by-12 ASF grid for this area (which demonstrates wide ASF variation over a short distance) achieves the desired 2 meter accuracy. Figure 12 shows the error magnitude along the simulated ship track (this is the same simulation data as above, but shown as error magnitude along the track), again both with and without additive noise on the TOA values.

25 7x12 ASF grid-no noise 25 7x12 ASF grid- noise 2 2 15 15 Error North-South, m 1 5-5 -1 Error North-South, m 1 5-5 -1-15 95% err: 11.648m -15-2 -2 95% err: 13.2729m -25-2 -1 1 2 Error East-West, m -25-2 -1 1 2 Error East-West, m Figure 11 Scatter plots of Loran position errors for the Thames River area 25 T-boat track for Thames River 7x12 ASF grid-no noise 7x12 ASF grid- noise 2 Position Error, m 15 1 5 5 1 15 2 25 3 Figure 12 Position performance for the Thames River area error magnitude in meters versus time along the track. The two previous figures demonstrate the position accuracy achievable with ASF estimation based upon grid interpolation at a recent location. A natural question is What happens when a recent position is unavailable? Our response is to have the system iteratively, through a bootstrap-like operation, estimate a location and interpolate the ASF grids at that location. To test this approach, we present the following simulation results: 1. Select a random location within the grid area and, using the fine ASF grids, compute the TOAs for that location as a sum of the predicted TOAs, the ASFs, and noise. (This is identical to step one of the maritime simulation above except that we randomly select the position.) 2. Take as an initial estimate for the ASFs the median value for each station on the grid. 3. Offset the TOAs by these ASF estimates and calculate the Loran position solution. 4. Interpolate the ASF grids at the location computed in step 3. 5. Repeat steps 3 and 4 until the position converges. Figure 13 shows the result of 1 such random start-ups. The left hand diagram shows the trajectory of the solution algorithm (the first solution is shown by a star and the stopping solution is a circle); we note that the stopping position

solution is well within 2 meters for each case. The right hand diagram shows the magnitude of the error after each step in the iteration; we note that each case converged in four or fewer iterations of steps 3 and 4. 6. Figure 13 ASF grid bootstrapping performance. Conclusions / Future Our simulation efforts have shown that the Loran system is capable of meeting the aviation and maritime accuracy requirements. Work needs to be done on receiver and antennas however, to enable the receivers to achieve this performance. For the aviation case, since the approach path of interest is at most 1 miles out from the airport, it appears that even in areas of rough terrain such as Colorado, the ASF variations are not so extreme that a single airport ASF value will not work. For all of the Colorado airports, using the single set of airport ASF values yielded position errors well below 39m in most cases less than 1m. For the maritime case, our simulation efforts have shown that the use of a fairly simple ASF grid can produce excellent results within the 2m limit for HEA. Our future efforts will focus on studying the required grid density; to determine a method for creating the smallest grids for an area that still enable the required accuracy. We will also look at improving our ability to make accurate ASF measurements and thus create real-world ASF grids instead of relying just on the BALOR predictions; though we anticipate using BALOR to help determine the required grid density. We will also be looking at an integrated receiver that will use GPS to track changes in the ASF grid due to seasonal/temporal variations and an IMU to help the receiver track smoothly through poor TOA measurements. References [1] Volpe National Transportation Systems Center, U.S. Department of Transportation, Office of Ass't Sec for Transportation Policy, "Vulnerability Assessment of the Transportation Infrastructure Relying on the Global Positioning System," Boston, MA, August 21. [2] Federal Aviation Administration, Office of Architecture and Investment Analysis, ASD-1, "Navigation and Landing Transition Strategy," Washington, DC, August 22. [3] US Department of Transportation, "Radionavigation Systems: A Capabilities Investment Strategy," January 24. [4] US Department of Defense and Department of Transportation, "21 Federal Radionavigation Plan," December 21. [5] Department of Defense and Department of Transportation, "21 Federal Radionavigation Systems," Washington, DC, Report: DOT-VNTSC-RSPA-1-3.1/DOD-465.5, December 21. [6] R. Hartnett, G. Johnson, P. F. Swaszek, and M. J. Narins, "A Preliminary Study of LORAN-C Additional Secondary Factor (ASF) Variations," presented at 31st Annual Meeting, International Loran Association, Washington, DC,28-3 October 22.

[7] G. Johnson, R. Hartnett, et al., "FAA Loran-C Propagation Studies," presented at Annual Technical Meeting, Institute of Navigation, Anaheim, CA,22-24 January 23. [8] R. Hartnett, G. Johnson, P. F. Swaszek, and K. Dykstra, "Getting a Bearing on ASF Directional Corrections," presented at 32nd Annual Meeting, International Loran Association, Boulder, CO,3-6 November, 23. [9] G. Johnson, R. Hartnett, et al., "Summer Vacation 23 - ASF Spatial Mapping in CO, AR, FL, and CA," presented at 32nd Annual Meeting, International Loran Association, Boulder, CO,3-6 November 23. [1] D. Last and P. Williams, "Loran-C ASF, Field Strength and ECD Modelling," presented at LORIPP meeting, Tysons Corner, VA,29 July 23. [11] P. Williams and D. Last, "Mapping the ASFs of the Northwest European Loran-C System," presented at 28th Annual Convention and Technical Symposium, International Loran Association,October 1999. [12] P. Williams and D. Last, "Modelling Loran-C Envelope-to-Cycle Differences in Mountainous Terrain," presented at 32nd Annual Meeting, International Loran Association, Boulder, CO,3-6 November 23. DISCLAIMER AND NOTE The views expressed herein are those of the authors and are not to be construed as official or reflecting the views of the Commandant, the U.S. Coast Guard, the Federal Aviation Administration, or any agency of the U.S. Government.