Frequency estimation techniques for high dynamic trajectories

A comparison is presented of four different estimation techniques applied to the problem of continuously estimating the rapidly varying parameters of a sinusoidal signal, observed in the presence of additive noise. Frequency estimates are emphasized, although phase and/or frequency rate are also estimated by some of the algorithms. These parameters are related to the velocity, position, and acceleration of the maneuvering receiver or transmitter. Estimated performance at low carrier-to-noise ratios and high dynamics is investigated for the purpose of determining the useful operating range of an approximate maximum likelihood estimator, an extended Kalman filter, a cross-product automatic frequency loop and a phase-locked loop. Numerical simulations are used to evaluate performance while tracking a common trajectory exhibiting high dynamics     

Digital accumulators in phase and frequency tracking loops

Results on the effects of digital accumulators in phase and frequency tracking loops are presented. Digital accumulators or summers are used extensively in digital signal processing to perform averaging or to reduce processing rates to acceptable levels. For tracking the Doppler of high-dynamic targets at low carrier-to-noise ratios, it is shown through simulation and experiment that digital accumulators can contribute an additional loss in operating threshold. This loss was not considered in any previous study and needs to be accounted for in performance prediction analysis. Simulation and measurement results are used to characterize the loss due to the digital summers for three different tracking loops: a digital phase-locked loop, a cross-product automatic frequency tracking loop, and an extended Kalman filter. The tracking algorithms are compared with respect to their frequency error performance and their ability to maintain lock during severe maneuvers at various carrier-to-noise ratios. It is shown that failure to account for the effect of accumulators can result in an inaccurate performance prediction, the extent of which depends highly on the algorithm used     

The split symbol moments SNR estimator in narrow-band channels

The split symbol moments estimator (SSME) is an algorithm that is designed to estimate symbol signal-to-noise ratio (SNR) in the presence of additive white Gaussian noise (AWGN). The performance of the SSME algorithm in bandlimited channels is examined, and the effects of the resulting intersymbol interference (ISI) are quantified. All results obtained are in closed form and can be easily evaluated numerically for performance-prediction purposes. The results are also validated through digital simulations     

Two novel automatic frequency tracking loops

Two automatic-frequency-control loops are introduced and analyzed in detail. The algorithms are generalizations of the well-known cross-product automatic-frequency-control loop with improved performance. The first estimator uses running overlapping discrete Fourier transforms (DFTs) to create a discriminator curve proportional to the frequency estimation error, whereas the second one preprocesses the received data and then uses an extended Kalman filter to estimate the input frequency. The algorithms are tested by computer simulations in a low carrier-to-noise-ratio (CNR) and highly dynamic environment. The algorithms are suboptimum tracking schemes with a larger frequency error variance compared to an optimum strategy, but they offer simplicity of mechanization and a CNR with a very low operating threshold