Improving Argos Doppler location using multiplemodel smoothing
 Rémy Lopez^{1}Email author,
 JeanPierre Malardé^{1},
 Patrick Danès^{2, 3} and
 Philippe Gaspar^{1}
Received: 3 December 2014
Accepted: 11 September 2015
Published: 29 September 2015
Abstract
Background
Argos is a dedicated system for geolocalization and data collection of platform terminal transmitters (PTTs). The system exploits a constellation of polarorbiting satellites recording the messages transmitted by the PTTs. The localization processing takes advantage of the Doppler effect on the carrier frequency of messages received by the satellites to estimate platform locations. It was recently demonstrated that the use of an Interacting Multiple Model (IMM) filter significantly increases the Argos location accuracy compared to the simple Least Square adjustment technique that had been used from the beginning of the Argos localization service in 1978. The accuracy gain is especially large in cases when the localization is performed from a small number of messages (n ≤ 3). The present paper shows how it is possible to further improve the Argos location accuracy if a processing delay is accepted. The improvement is obtained using a fixedinterval multiplemodel smoothing technique.
Results
The location accuracy of the smoother is evaluated with a data set including over 200 platforms equipped with an Argos transmitter and a GPS receiver, providing the ground truth. The use of the smoother reduces the platforms’ location error. On average, compared with the IMM filter, the smoother achieves an error reduction of about onethird for locations based on two or three messages. For onemessage locations, the error is typically divided by two.
Conclusion
The smoother proves to reduce the platforms’ location error compared to the IMM filter. The error reduction is all the more significant as the number of messages involved in the location is small. This new processing technique targets Argos applications with a limited emitting power or operating in difficult environmental conditions, such as wildlife tracking, for which obtaining more accurate locations is more important than obtaining locations in realtime.
Keywords
Argos system Doppler location Multiplemodel smoothing Rauch–Tung–Striebel formulae Target trackingBackground
The Argos system has been used since 1978 for geolocalization and data collection of platform terminal transmitters (PTTs) in the fields of wildlife tracking, oceanography and maritime safety. The system is based on a constellation of lowaltitude polarorbiting satellites, which record messages transmitted by the PTTs in a dedicated bandwidth around the 401.650MHz frequency. The Argos localization exploits the Doppler shift on the carrier frequency of the messages, induced by the relative motion of the satellite and the platform. When a message is received by a satellite, the shifted carrier frequency is measured before being transmitted to the Argos processing centers via a network of ground stations. All frequency measurements acquired during a satellite pass over a platform are used to estimate the platform’s position.
Between 1978 and 2011, a classical nonlinear Least Squares (LS) estimation technique was used to compute Argos positions. In March 2011, an Interacting Multiple Model (IMM) filter was implemented in the Argos operational processing center [1] and is now the nominal algorithm used by Argos for platforms’ localization in realtime. This new method reduces the Argos positioning error compared to the LS estimates. The error reduction is especially large when less than four messages are received during a satellite pass, a situation mostly encountered with small, low output power transmitters used in difficult environmental conditions (dense forests, rough seas…). Such transmitters are mostly used for animal tracking. The IMM filter also systematically provides a characterization of the positioning error (which was not the case with the LS positioning algorithm) and increases the amount of locations delivered to Argos users [1].
The IMM filter computes locations recursively by combining the frequency measurements of a satellite pass with a set of M realistic prior dynamics and observation models [2]. In practice, the IMM handles a bank of M unscented Kalman filters (KF) [3, 4] to adapt the dynamics model to the active platform behavior or mode (a random walk or a directed movement for Argos). Filtering assimilates past and present frequency measurements to estimate positions. This is an adequate approach when information is needed in realtime, such as in fishing vessel monitoring systems. However, many Argos applications, such as wildlife tracking, do not usually require information provision in realtime. In that case, a Kalman smoother can be used instead of a filter [5]. Filters are indeed devised to make use of measurements acquired before and at the estimation time while smoothers also use subsequent observations. This means that each location can be inferred with a greater amount of information, and thus a better accuracy can be achieved, at the cost of a delayed estimation.
This paper is the direct sequel of [1] in which the LS estimation technique previously used for Argos positioning was compared to the IMM filter. The comparison was performed on a large data set obtained from over 200 mobiles carrying both an Argos transmitter and a GPS receiver used as ground truth. After a brief reminder of the Argos Doppler positioning problem and its solution based on an IMM filter, the new smoothing method is presented and its performances are evaluated using the same data set as [1].
Methods
Notations are standard: P(·), p(·) and E[·] represent a probability, a probability density function (pdf) and an expectation, respectively. \(N\left( {.;\bar{x},P} \right)\) stands for the real Gaussian distribution function with mean \(\bar{x}\) and covariance P. The transpose operator is denoted by ·^{T}.
Multiplemodel filtering
Multiplemodel smoothing
We are interested in obtaining the smoothed Argos locations within a fixed interval 0 ≤ k ≤ T of satellite passes. The integer T is the terminal time index of the interval or, equivalently, the last satellite pass of the emitting period of the PTT. The aim is to compute the first two moments \(\hat{x}_{k\left T \right.} = E\left[ {x_{k} \left {z_{1:T} } \right.} \right]\) and \(P_{k\left T \right.} = E\left[ {\left( {x_{k}  \hat{x}_{k\left T \right.} } \right)\left( {x_{k}  \hat{x}_{k\left T \right.} } \right)^{T} \left {z_{1:T} } \right.} \right]\) of the smoothed state density \(p\left( {x_{k} z_{ 1:T} } \right)\) of the satellite pass k conditioned on all the frequency measurements z _{1:T } over the fixed interval ending at T.
In the singlemodel case, two approaches are generally considered to build the smoothed mean and covariance. The first solution, called the “twofilter smoother”, combines the posterior mean and covariance computed from a classical forwardtime Kalman filter with the predicted mean and covariance produced by a backwardtime filter initialized at time T with no information [8]. Another mathematically equivalent solution is the Rauch–Tung–Striebel smoother that runs a conventional forwardtime Kalman filter until time T, then smartly recombines the forwardtime moments into the smoothed estimates inside a backward recursion [9]. This recursion is straightforwardly initialized with the forwardtime moments at time T.
Test data set
List and characteristics of the PTTs included in the dataset
Type of mobile  Number of platforms  Number of locations  Data owner and references  

Argos  GPS  
Marabou stork (Leptoptilos crumeniferus)  5  3759  8250  Neil and Liz Baker (Tanzania Bird Atlas, P.O. Box 1605, Iringa, Tanzania) 
Goose (Anser indicus)  55  21,220  80,980  Lucy Hawkes (University of Exeter, Penryn Campus, Cornwall, TR10 9EZ, UK), Charles Bishop (Bangor University, Bangor, Gwynedd, LL57 2DG, UK) and Pat Butler (University of Birmingham, Birmingham, B15 2TT, UK) [18] 
Blue wildebeest (Connochaetes taurinus)  10  2180  4144  Moses Selebatso (Western Kgalagadi Conservation Corridor Project) 
Bighorn (Ovis canadensis)  13  2159  1704  Norv Dallin (Nevada Department of Wildlife, Eastern Region, 60 Youth Center Drive, 89801 Elko, NV, USA) 
Flatback turtle (Natator depressus)  19  24,205  21,809  Kellie Pendoley (Pendoley Environmental Pty Ltd, 2/1 Aldous Place, Booragoon, WA 6154) 
Green turtle (Chelonia mydas)  24  15,959  13,340  Simon Benhamou (Centre d’Ecologie Fonctionnelle et Evolutive, U.M.R. 5175 Montpellier, France) [19] 
Galapagos sea lion (Zalophus wollebaeki)  9  1680  3027  Daniel Costa (Department of Ecology and Evolutionary Biology Institute of Marine Sciences, Long Marine Lab University of California, Santa Cruz Santa Cruz, California, USA) [20] 
Elephant seal (Mirounga angustirostris, Mirounga leonina)  26  13,120  62,664  Daniel Costa [21] Christophe Guinet (Centre d’Etudes Biologiques de Chizé, 79360 VilliersenBois, France) [22, 23] 
Ship  23  23,404  36,425  Various 
Drifter  44  54,817  175,633  Luca Centurioni (Scripps Institution of Oceanography, Physical Oceanography Research Division, 9500 Gilman Drive, Mail Code 0213, La Jolla, CA, 92093 USA) 
Total  228  162,503  430,370 
Results and discussion

C1: the platform is located from 5° to 15° left or right of the subsatellite track (using the Earth centered angular distance),

C2: messages are numerous and uniformly distributed within the satellite pass (the platform is observed under multiple angles by the satellite).
Ratio of the signed tangential error on the error modulus
Type of mobile  4 mess. or more  2 and 3 mess.  1 mess.  

Filter (%)  Smoother (%)  Filter (%)  Smoother (%)  Filter (%)  Smoother (%)  
Marabou  1  1  10  10  37  71 
Goose  4  4  −1  −2  −8  −1 
Blue wildebeest  3  2  −16  −11  −25  −36 
Bighorn  −2  −1  7  12  −19  9 
Flatback turtle  −13  −5  −9  10  −14  11 
Green turtle  5  16  −15  15  −22  9 
Galapagos sea lion  15  17  −4  18  −2  6 
Elephant seal  −2  13  −8  17  −18  13 
Ship  −1  1  −18  0  −24  −6 
Drifter  −14  1  −38  8  −59  9 
Probabilities that computed locations fall within the error confidence ellipses (headers contain the theoretical values)
Type of mobile  1σ (39.3 %)  \(\sqrt 2\) σ (63.2 %)  3σ (98.9 %)  

Filter (%)  Smoother (%)  Filter (%)  Smoother (%)  Filter (%)  Smoother (%)  
Marabou  15  14  22  23  51  51 
Goose  20  20  27  28  49  50 
Blue wildebeest  21  21  34  34  70  70 
Bighorn  33  34  45  47  70  72 
Flatback turtle  25  28  37  40  65  68 
Green turtle  28  32  41  45  67  71 
Galapagos sea lion  22  24  34  35  60  61 
Elephant seal  18  20  26  29  50  54 
Ship  21  22  31  33  59  61 
Drifter  30  34  45  50  80  84 
Conclusion
Smoothing is a deferredtime processing that assimilates all frequency measurements within the platform emitting period to estimate each point of the associated trajectory. The multiplemodel smoother proved to be a new step forward in enhancing the overall quality of the Argos tracks. Compared to the IMM filter, average location errors are indeed reduced by onethird with two or three messages and by half with a single message. The standard deviations of the error also decrease similarly. The smoother displays more uniform performances regardless of the observation geometry associated to the satellite pass, particularly when the PTT is close to the subsatellite track or at the edge of the satellite visibility circle. Moreover, the smoother eliminates the bias effect along the track observed with the filter on onemessage locations due to the use of a random walk dynamics in the model set. The users can take advantage of this new approach through a dedicated reprocessing service made available on the official Argos website (www.argossystem.org). This service is able to deliver upon request and independently of the realtime processing the smoothed estimates for a list of platforms and their associated tracking periods since January 1st 2008.
Platform terminal transmitters with a limited emitting power or operating in difficult environmental conditions, like wildlife tracking applications, markedly benefit of this new approach. The Argos community has always been extremely prolific and ingenious to develop tools detecting abnormal locations or correcting tracks of this kind of PTTs (see for example [24–29] among many others). These methods are particularly efficient for locations computed with very few messages where the accuracy is limited. The aim of this new processing is not only to improve the overall location accuracy but also to simplify the posterior analysis conducted by the Argos users and to limit the use of multiple postprocessing tools.
Note that, for a given repetition period of the platform, a lower number of received messages means also they are likely to be unevenly distributed within the satellite pass.
Declarations
Authors’ contributions
All authors contributed equally to the design, conduct, and analysis of this study and to the preparation of this manuscript. All authors read and approved the final manuscript.
Acknowledgements
The authors would like to thank all Argos users who kindly provided access to their data so as to qualify the smoothing algorithm presented here. The GPS drifters that provided the data used in the validation analysis were funded by Office of Naval Research Grant N000140810557 and by National Oceanic and Atmospheric Administration Grant NA10OAR4320156.
All data displayed in this paper remain the property of the different scientists/laboratories listed in Table 1. They provided their Argos/GPS data to the authors for the sole purpose of this paper. People wishing to access these data shall first request them from their data owners. CLS will then gladly provide reprocessed data featured in this paper given the agreement of their owners.
Compliance with ethical guidelines
Competing interests Rémy Lopez, JeanPierre Malardé and Philippe Gaspar are employees of Collecte Localisation Satellites which operates the Argos System.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
References
 Lopez R, Malarde JP, Royer F, Gaspar P. Improving Argos Doppler location using multiplemodel Kalman filtering. IEEE Trans Geosci Remote Sens. 2014;52:4744–55.View ArticleGoogle Scholar
 Blom HAP, BarShalom Y. The interacting multiple model algorithm for systems with Markovian switching coefficients. IEEE Trans Autom Control. 1988;33:780–3.View ArticleGoogle Scholar
 Kalman RE. A new approach to linear filtering and prediction problems. J Basic Eng. 1960;82(Series D):35–45.View ArticleGoogle Scholar
 Wan EA, Van Der Merwe R. The unscented Kalman filter for nonlinear estimation. In: IEEE symposium on adaptive systems for signal communications, and control (ASSPCC’2000); 2000. p. 153–8.Google Scholar
 Anderson BDO, Moore JB. Optimal filtering. Courier Corporation; 2012.Google Scholar
 Li XR, Jilkov VP. Survey of maneuvering target tracking. Part V: multiplemodel methods. IEEE Trans Aerosp Electron Syst. 2005;41:1255–321.View ArticleGoogle Scholar
 Gustafsson F. Adaptive filtering and change detection. New York: Wiley; 2000.Google Scholar
 Fraser D, Potter J. The optimum linear smoother as a combination of two optimum linear filters. IEEE Trans Autom Control. 1969;14:387–90.View ArticleGoogle Scholar
 Rauch HE, Tung F, Striebel CT. Maximum likelihood estimates of linear dynamic systems. AIAA J. 1965;3:1445–50.View ArticleGoogle Scholar
 Helmick RE, Blair WD, Hoffman SA. Fixedinterval smoothing for Markovian switching systems. IEEE Trans Inf Theory. 1995;41:1845–55.View ArticleGoogle Scholar
 Barber D. Expectation correction for smoothing in switching linear Gaussian state space models. J Mach Learn Res. 2005;7:2515–40.Google Scholar
 Mesot B, Barber D. A simple alternative derivation of the expectation correction algorithm. IEEE Signal Process Lett. 2009;16:121–4.View ArticleGoogle Scholar
 Barber D. Bayesian reasoning and machine learning. Cambridge: Cambridge University Press; 2012.Google Scholar
 Ackerson G, Fu K. On state estimation in switching environments. IEEE Trans Autom Control. 1970;15:10–7.View ArticleGoogle Scholar
 Koch W. Fixedinterval retrodiction approach to Bayesian IMMMHT for maneuvering multiple targets. IEEE Trans Aerosp Electron Syst. 2000;36:2–14.View ArticleGoogle Scholar
 Lopez R, Danès P. Exploiting Rauch–Tung–Striebel formulae for IMMbased smoothing of Markovian switching systems. In: 2012 IEEE international conference on acoustics, speech and signal processing (ICASSP); 2012. p. 3953–6.Google Scholar
 Lopez R, Danès P. A fixedinterval smoother with reduced complexity for jump Markov nonlinear systems. In: 2014 17th international conference on information fusion (FUSION); 2014. p. 1–8.Google Scholar
 Hawkes LA, Balachandran S, Batbayar N, Butler PJ, Frappell PB, Milsom WK, Tseveenmyadag N, Newman SH, Scott GR, Sathiyaselvam P, Takekawa JY, Wikelski M, Bishop CM. The transHimalayan flights of barheaded geese (Anser indicus). PNAS. 2011;108:9516–9.PubMed CentralView ArticlePubMedGoogle Scholar
 Benhamou S, Sudre J, Bourjea J, Ciccione S, De Santis A, Luschi P. The role of geomagnetic cues in green turtle open sea navigation. PLoS One. 2011;6:e26672.PubMed CentralView ArticlePubMedGoogle Scholar
 VillegasAmtmann S, Simmons SE, Kuhn CE, Huckstadt LA, Costa DP. Latitudinal range influences the seasonal variation in the foraging behavior of marine top predators. PLoS One. 2011;6:e23166.PubMed CentralView ArticlePubMedGoogle Scholar
 Robinson PW, Costa DP, Crocker DE, GalloReynoso JP, Champagne CD, Fowler MA, Goetsch C, Goetz KT, Hassrick JL, Hückstädt LA, Kuhn CE, Maresh JL, Maxwell SM, McDonald BI, Peterson SH, Simmons SE, Teutschel NM, VillegasAmtmann S, Yoda K. Foraging behavior and success of a mesopelagic predator in the Northeast Pacific Ocean: insights from a datarich species, the Northern Elephant Seal. PLoS One. 2012;7:e36728.PubMed CentralView ArticlePubMedGoogle Scholar
 Dragon AC, Monestiez P, BarHen A, Guinet C. Linking foraging behaviour to physical oceanographic structures: southern elephant seals and mesoscale eddies east of Kerguelen Islands. Prog Oceanogr. 2010;87:61–71.View ArticleGoogle Scholar
 Dragon A, BarHen A, Monestiez P, Guinet C. Horizontal and vertical movements as predictors of foraging success in a marine predator. Mar Ecol Prog Ser. 2012;447:243–57.View ArticleGoogle Scholar
 Douglas DC, Weinzierl R, Davidson SC, Kays R, Wikelski M, Bohrer G. Moderating Argos location errors in animal tracking data. Methods Ecol Evol. 2012;3(6):999–1007. doi:10.1111/j.2041210X.2012.00245.x.View ArticleGoogle Scholar
 Tremblay Y, Shaffer SA, Fowler SL, Kuhn CE, McDonald BI, Weise MJ, Bost CA, Weimerskirch H, Crocker DE, Goebel ME, Costa DP. Interpolation of animal tracking data in a fluid environment. J Exp Biol. 2006;209:128–40.View ArticlePubMedGoogle Scholar
 Royer F, Lutcavage M. Filtering and interpreting location errors in satellite telemetry of marine animals. J Exp Mar Biol Ecol. 2008;359:1–10.View ArticleGoogle Scholar
 Jonsen ID, Flemming JM, Myers RA. Robust statespace modeling of animal movement data. Ecology. 2005;86:2874–80.View ArticleGoogle Scholar
 McConnell BJ, Chambers C, Nicholas KS, Fedak MA. Satellite tracking of grey seals (Halichoerus grypus). J Zool. 1992;226:271–82.View ArticleGoogle Scholar
 Austin D, McMillan JI, Bowen WD. A threestage algorithm for filtering erroneous Argos satellite locations. Mar Mamm Sci. 2003;19:371–83.View ArticleGoogle Scholar