Simplified Solution for a Class of Fading Memory Filters

A fading memory filter is a least squares estimator (LSE) thatapplies an exponentially decaying weight to past measurements.When compared with a standard Kalman filter, its key advantagesare asymptotic stability and reduced sensitivity to modeling errors.This paper derives a simple solution for a class of fading memoryfilters, resulting in a reduction in computational complexity. Steadystate filter solutions are obtained for second-and third-order filtersused in a global positioning system (GPS) receiver for high dynamicvehicles.     

High Dynamic GPS Receiver Using Maximum Likelihood Estimationand Frequency Tracking

A new high dynamic global positioning system (GPS) receiver ispresented and its performance characterized by analysis,simulation, and demonstration. The demonstration receiver is abreadboard model capable of tracking a single simulated satellitesignal in pseudorange and range rate. Pseudorange and range rateestimates are made once every 20 ms, using a maximum likelihoodestimator, and are tracked by means of a third-order fadingmemory filter in a feedback configuration. The receiver trackspseudorange with rms errors of under 1 m when subjected tosimulated 50 g, 40 g/s circular trajectories. The tracking thresholdis approximately 28 dB·Hz, which provides 12 dB margin relativethe the minimum specified signal strength, assuming 3.5 dB systemnoise figure and 0 dB antenna gain.     

Parameter Estimation Based on Doppler Frequency Shifts

An acoustic source generates an amplitude-modulated tone, with Doppler variations due to the relative motion between source andreceiver. A method is presented for real-time estimation of tone restfrequency and minimal distance between source and receiver, usingdigital signal processing techniques. The algorithm presented herewas implemented using a Texas Instruments TMS32010 processor.     

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