Precision Limits of Low-Energy GNSS Receivers

K.M. Pesyna, Jr., R.W. Heath, Jr., T.E. Humphreys

Abstract:	Optimal tradeoffs between sampling rate, number of quantization bits, number of satellites tracked, and the code tracking integration time are explored for maximizing GNSS receiver position-time precision subject to an energy constraint. Analytical expressions relating these tradeoffs to a lower-bound on the receiver’s position-time precision and to the energy consumed are developed and used as objective and constraint functions in a constrained optimization framework. There is an increasing demand for small, portable, energy-efficient GNSS receivers. Small- scale applications such as locating an individual or locating a pair of keys and large-scale applications such as traffic analysis and remote sensing are all made possible by portable, energy-constrained GNSS receivers and the increasing demand for these devices continues to push down device energy constraints. This paper has two contributions along these lines. The first is the identification of a theoretical relationship between the four parameters of interest and two metrics: (1) the attainable precision of a single-shot code-phase GNSS solution and (2) the energy consumed by this solution – to within a scale factor. The second contribution is to reveal the optimal parameter values which maximize the precision under a specified energy constraint. There has been much recent work in the area of energy efficient GNSS receivers. One tech- nique that has been investigated uses cloud offloading, where the burden of signal acquisition, signal tracking, and position determination is borne entirely by the cloud [1]. However, this work does not consider the cost of retrieving the data in a practical way, e.g. by wirelessly transmitting the raw RF samples over a cellular or Wi-Fi connection. A proper evaluation of the advantages of a cloud-based approach must make a fair comparison of the energy required for transmitting the raw bits to the energy required for locally processing these raw bits. So far as the authors are aware, there has been no previous research exploring the limits of en- ergy use if the processing is performed locally. Trends in state-of-the-art GNSS chipsets have led to power consumption levels on the order of 50 milliwatts for continuous tracking and 15 milliwatts for duty-cycled tracking [2], however, one naturally questions whether there exists a fundamental limit to the position-time precision attainable at these power levels. Along these lines, there has been research studying the joint effect that two of the parameters of inter- est, the number of quantization bits and the sampling rate, have on a signal’s carrier-to-noise (C/N0 ) ratio [3, 4]. Additionally, there has been work deriving the Cramer-Rao lower-bound on code-tracking precision as a function of the C/N0 and another paraeter of interest, the code tracking integration time [5, 6]. Lastly, there has been work relating the code-tracking preci- sion and the final parameter of interest, the number of tracked satellites, to the precision of the position-time navigation solution [7]. Using this previous work, the present paper derives one coherent analytical relationship between the parameters of interest of the precision of the navigation solution. This relationship is then used as the objective function in a constrained optimization framework. After deriving the objective function, it becomes necessary to incorporate the energy constraint into the optimization framework. The present work will initially only consider the energy consumed by the baseband processing, e.g. the correlation algorithms, and not of the RF front-end, e.g. downcoversion and the analog-to-digital converter. Existing work has shown that baseband processing accounts for over half of the energy consumed in modern GNSS receivers [8]. Research has shown that baseband energy consumption is proportional to number multiply-and-accumulate (MAC) operations performed during signal correlation [8]. Three of the four parameters of interest in this study: the number of SVs tracked, the sampling rate, and the code tracking integration time, directly effect the number of MAC operations. The final parameter, the number of quantization bits per sample, determines the amount of energy each individual MAC consumes. Consequently, because baseband energy consumption can be reduced to the product of the number of MAC operations and the energy consumption per MAC, all four parameters of interest are functionally related to total energy consumed. This functional relationship is derived in the present work and becomes the constraint function in the constrained optimization framework. Once the objective and constraint functions have been properly derived, a constrained opti- mization solver is used to quickly and efficiently determine values of the receiver parameters that produce the maximal position-time precision while adhering to the energy constraint. Pre- liminary analysis suggest that for a receiver tracking GPS signals under a tight energy budget, maximizing the sampling rate at the expense of minimizing the other parameters will allow for the greatest precision. On the other hand, analysis suggests that a receiver under a relaxed energy budget should maximize the product of the sampling rate and code-tracking integration time to enable the greatest precision. The above preliminary analysis has been performed under ideal circumstances, i.e. it ignores multipath effects and assumes optimal satellite geometry. Next steps by the authors will incor- porate multipath effects and realistic satellite geometry into the problem. These should have a noticeable effect on the optimal parameter values. For example, in the absence of multipath, there is little to be gained in the precision of the position-time solution by increasing the number of tracked satellites [9]. However, in multipath environments there is much more improvement to be gained, as position-time errors are dominated by multipath [10] and much of this can be mitigated by increasing the number of tracked satellites. The aforementioned analysis has been performed assuming signal tracking. To offer a complete picture, this analysis will be extended to study optimal parameter values during signal acquisition as well. [1] J. Liu, B. Priyantha, T. Hart, H. S. Ramos, A. A. Loureiro, and Q. Wang, “Energy efficient gps sensing with cloud offloading,” 2012. [2] u-Blox, Datasheet: NE0-7 GPS/GNSS Module. [3] C. Hegarty, “Analytical model for gnss receiver implementation losses,” NAVIGATION, Journal of the Institute of Navigation, vol. 58, no. 1, p. 29, 2011. [4] J. Curran, D. Borio, and C. Murphy, “Front-end filtering and quantisation effects on gnss signal process- ing,” in Wireless Communication, Vehicular Technology, Information Theory and Aerospace & Electronic Systems Technology, 2009. Wireless VITAE 2009. 1st International Conference on, pp. 227–231, IEEE, 2009. [5] C. Knapp and G. Carter, “The generalized correlation method for estimation of time delay,” Acoustics, Speech and Signal Processing, IEEE Transactions on, vol. 24, no. 4, pp. 320–327, 1976. [6] J. Betz and K. Kolodziejski, “Generalized theory of code tracking with an early-late discriminator part i: lower bound and coherent processing,” Aerospace and Electronic Systems, IEEE Transactions on, vol. 45, no. 4, pp. 1538–1556, 2009. [7] P. Axelrad and R. G. Brown, Global Positioning System: Theory and Applications, ch. 8: GPS Navigation Algorithms, pp. 329–408. Washington, D.C.: American Institute of Aeronautics and Astronautics, 1996. [8] B. Z. Tang, S. Longfield, S. A. Bhave, and R. Manohar, “A low power asynchronous gps baseband pro- cessor,” in Asynchronous Circuits and Systems (ASYNC), 2012 18th IEEE International Symposium on, pp. 33–40, IEEE, 2012. [9] M. Zhang and J. Zhang, “A fast satellite selection algorithm: beyond four satellites,” Selected Topics in Signal Processing, IEEE Journal of, vol. 3, no. 5, pp. 740–747, 2009.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	2828 - 2834
Cite this article:	Pesyna, K.M., Jr.,, Heath, R.W., Jr.,, Humphreys, T.E., "Precision Limits of Low-Energy GNSS Receivers," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 2828-2834.
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