Performance Analysis of Doppler Aided Tracking Loops in Modernized GPS Receivers
The GPS modernization program deploys new generations of satellites designated Block IIR-M, Block IIF and Block III-A, equipped to transmit multiple civil signals. The coexistence of multiple civilian signals in a GPS receiver has been a focus in recent research activities. In the literature to date, correlator outputs of individual channels are combined in ways either to increase the power available for processing or to reduce the error in tracking measurements. These combinations are typically made at the discriminator level, after the discriminator or after the loop filter. The combinations have been considered both for channels operating on the same carrier frequency (e.g. data and pilot channels of L5) as well as channels across different carrier frequencies. In a modernized GPS receiver, tracking multiple civil signals, the relationship between Doppler frequencies (proportional to the corresponding carrier frequencies) of all signals is known and therefore Doppler estimates of one PLL can be utilized by another PLL tracking a different frequency. While such benefits are conventionally achieved through ultra-tight GPS/INS coupling, this paper presents performance analysis of a Doppler-aided tracking loop architecture, where the Doppler assistance is obtained from another loop in the same receiver. L1 C/A and L2C are the two civil signals selected for the analysis, because this pair of signals will be available long before any other combination. The analysis, however, is relevant to any pair of signals from a single satellite. The L2C carrier, having the pilot channel and relatively slower dynamics, is used as aiding source in the considered arrangement. The L2C PLL, operated with a wide loop bandwidth, absorbs the dynamic stress and provides Doppler estimates to the L1 PLL (affected by wide-band interference) operating at narrow-band. The tracking error associated with such collaboration between two tracking loops is analyzed. It is shown that a 7 dB-Hz RFI margin (equivalent to that achieved with a moderate quality inertial sensor), can be achieved through the local Doppler-assistance.
Dual-frequency signal processing architecture for robust and precise positioning applications
Availability of new GPS civil signals L2C and L5 along with existed L1C/A signal and Galileo E1/E5/E6 signals has increased the potential ways to generate linear combination of signals to remove ionosphere errors and improve accuracy in carrier integer ambiguity resolution. Conventionally, a linear combination of dual frequency signals has been used to remove first order ionosphere delays incurred in signal propagation path which is a major source of range error. Out of the three civil signals in GPS and Galileo system, L5/E5 signals have advanced signal features such as higher received power, faster chip rate and lower carrier frequency than L1/E1 and L2C/E6 signals. Hence, dual frequency receiver with combination of L1/L5 and E1/E5 signals is more suitable to remove ionosphere delay and get benefit from L5/E5 signal characteristics. However, the major limitation of linear combination of signal observations is an amplification of receiver noise. To get benefit of two frequency signals, a suitable signal processing architecture is needed. By taking advantage of GPS L5/Galileo E5 signal characteristics, a dual frequency signal processing architecture is proposed with an aim to reduce the ionosphere-free signal observation noise and to enhance the L1/E1 signal tracking loop sensitivity. The L1/E1 signal tracking loop sensitivity can be enhanced by Doppler aiding from L5/E5 signal tracking loop. The low noise L5/E5 signal Doppler aid reduces the noise in the L1/E1 signal tracking loop. Moreover, two frequency signals tracked with common Doppler estimate will have common observation errors, which will get cancel in linear combination of observations i.e. ionosphere-free, wide-lane etc. Further, code phase observations can be smoothed (Hatch filter) using carrier phase observations. The carrier phase observations are limited by cycle slip. Hence, we have investigated an optimum combination of divergence-free and ionosphere-free pseudorange smoothing using dual-frequency carrier Doppler observations for GPS L1/L5 and Galileo E1/E5 signals. The cycle slip in carrier phase observations can be neglected in carrier Doppler observations. The proposed signal processing architecture incorporated in GPS L1/L5 and Galileo E1/E5 dual frequency receiver will ensure robust signal tracking and minimum pseudorange errors, suitable to a range of high accuracy standalone and code differential positioning applications. The performance of the proposed dual frequency signal processing architecture is evaluated with GPS L1/L5 signals collected from Block-IIF satellites.
On the ontology of particle mass and energy in special relativity
Einstein claimed that the fundamental dynamical insight of special relativity was the equivalence of mass and energy. I disagree. Not only are mass and energy not equivalent (whatever exactly that means) but talk of such equivalence obscures the real dynamical insight of special relativity, which concerns the nature of 4-forces and interactions more generally. In this paper I present and defend a new ontology of special relativistic particle dynamics that makes this insight perspicuous and I explain how alleged cases of mass–energy conversion can be accommodated within that ontology.