Real-time Doppler/Doppler Rate Derivation for Dynamic Applications

Jason Zhang, Kefei Zhang, Ron Grenfell, Yong Li, Rod Deakin

School of Mathematical and Geospatial Sciences, RMIT University.

DOI:                 

Abstract

Precise GPS velocity and acceleration determination relies on Doppler and/or Doppler rate observations. There are no direct Doppler rate measurements in GPS. Although every GPS receiver measures Doppler shifts, some receivers output only “raw” Doppler shift measurements and some don’t output any at all. In the absence of raw Doppler and Doppler rate measurements, a differentiator is necessary to derive them from other GPS measurements such as the carrier phase observations. For real-time dynamic applications, an ideal differentiator should have a wideband frequency response to cover all the dynamics. It should also have a group delay as short as possible. In addition, a low-order differentiator is more favourable for easy implementation. This paper provides an overview of methods in differentiator design for applications of GPS velocity and acceleration determination. Low-order Finite Impulse Response (FIR) differentiators proposed by Kavanagh are introduced. A class of first-order Infinite Impulse Response (IIR) differentiators are developed on the basis of Al-Alaoui’s novel differentiator. For noise attenuation, it is proposed to selectively use Kavangagh’s FIR differentiators, and the first-order IIR filters derived for adaptation to different dynamics.

Keywords

GPS velocity determination, GPS acceleration determination, differentiator design, FIR filter, IIR filter, Doppler.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Al-Alaoui M.A. (1992): Novel Approach to Designing Digital Differentiators. Electronics Letters 28(15): 1376-1378.
[2]	Al-Alaoui M.A. (1993): Novel Digital Integrator and Differentiator. Electronics Letters 29(4): 1376-1378.
[3]	Al-Alaoui M.A. (1994): Novel IIR Differentiator from the Simpson Integration Rule. IEEE Transactions on Circuits and System-I Fundamental , Theory and Applications 41(2).
[4]	Antoniou A. (1993): Digital Filters: Analysis, Design and Appications. New York, McGraw-Hill 0-07-002121X.
[5]	Bona P. (2000): Precision, Cross Correlation, and Time Correlation of GPS Phase and Code Observations. GPS solutions 4(2): 3-13.
[6]	Borre K. and Tiberius C. (2000): Time Series Analysis of GPS Observables. proceedings of the ION GPS 2000, Salt Lake City, UT, 1885-1894.
[7]	Brown R.G. and Hwang P.Y.C. (1992): Introduction to Random Signals and Applied Kalman Filtering. New York, John Wiley &Sons, INC 0471-52573-1.
[8]	Bruton A.M., Glennie C.L. and Schwarz K.P. (1999): Differentiation for High-Precision GPS Velocity and Acceleration Determination. GPS solutions 2(4): 7-21.
[9]	Cannon M.E., Lachapelle G., Szarmes M.C., Hebert J.M., Keith J. and Jokerst S. (1998): DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Velocity and Position Determination. Journal of the Institute of Navigation 44(2): 231-245.
[10]	Carlsson B., Ahlen A. and Sternad M. (1991): Optimal Differentiation Based on Stochastic Signal Models. IEEE Transactions on Signal Processing 39(2): 341-353.
[11]	Chen C.-K. and Lee J.-H. (1995): Design of High-Order Digital Differentiators using L1 Error Criteria. IEEE Transactions on Circuits and Systems II: Analogy and Digital Signal Processing 42(4): 287-291.
[12]	Chen C.-T. (2001): Digital Signal Processing: Spectral Computation and Filter Design. New York, Oxford, Oxford University Press 0-19-513638-1.
[13]	Farlex (2004): TheFreeDictionaryCom: Kaiser Window. http:// encyclopedia.thefreedictionary.com/Kaiser%20window.
[14]	Fenton P. and Townsend B. (1994): NowAtel Communications Ltd,-What's New? Proceedings of KIS'94, Banff, AB, CA, 25-29.
[15]	Hamming R.W. (1977): Digital Filters. Englewood Cliffs, Prentice-Hall, Inc. 0-13-212571-4.
[16]	Harvey N. (2004): Doppler and Carrier Phase Measures in Trimble 5700 GPS Receiver. Christchurch, New Zealand (Personal communication).
[17]	Hebert C.J. (1997): High Accuracy GPS Velocity Using the Carrier Phase Observable. Proceedings of KIS'97, Banff, AB, Canada, 265-269.
[18]	Hebert C. J., Keith J., Ryan S., Szarmes M., Lachapelle G. and Canon M. E. (1997): DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Aircraft Velocity Determination. Proceedings of the ION GPS-97, Albuquerque, NM.
[19]	Jekeli C. and Garcia R.. (1997): GPS Phase Accelerations for Moving-base Vector Gravimetry. Journal of Geodesy 71(10): 630-639.
[20]	Kavanagh R.C. (2001): FIR Differentiators for Quantized Signals. IEEE Transactions on Signal Processing 49(11): 2713-2720.
[21]	Kennedy S. (2002): Precise Acceleration Determination from Carrier Phase Measurements. Proceeding of the ION GPS-2002, Portalnd Oregon, USA, 962-972.
[22]	Kennedy S.L. (2003): Precise Acceleration Determination from Carrier-Phase Measurements. Navigation, Journal of the Institute of Navigation 50(1): 9-19.
[23]	Khan I.R. and Ohba R. (1999): New Design of Full Band Differentiators Based on Taylor Series. IEEE Proceedings-Vision, Image and Signal Processing 146(4): 185-189.
[24]	Khan I. R., Ohba R. and Hozumi N. (2000): Mathematical Proof of Explicit Formulas for Tap-coefficients of Fullband FIR Digital Differentiators. IEE Proceedings-Vision, Image and Signal Processing 147(6): 553-555.
[25]	Kumar B. and Dutta S. C. R. (1988): Coefficients of Maximally Linear, FIR Digital Differentiators for Low Frequencies. Electronics Letters 24(9): 563-565.
[26]	Kumar B. and Dutta S.C.R. (1988): Design of Digital Differentiators for Low Frequencies. Proceedings of the IEEE 76(3): 287-289.
[27]	Kumar B. and Dutta S.C.R. (1989): Design of Efficient FIR Digital Differentiators and Hilbert Transforms for Midband Frequency Ranges. Internal 36(6).
[28]	Kumar B. and Dutta S.C.R. (1989): Maximally Linear FIR Digital Differentiators for Midband Frequencies. Int. J. Circuit Theory Appl. 17: 483-488.