Coordinates determination based on multimodal filtration of ambiguous phase measurements

Radiolocation and radio navigation


Kishko D. V.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



In our days phase signal measurements are used in many radio systems. For example, in GPS, GLONASS or pseudolite navigation system (like Locata) carrier phase measurements allows to determine three-dimensional vector of coordinates with centimetre accuracy.

Carrier phase measurements have cycle ambiguity property. One of the most common algorithms for ambiguity resolution is the LAMBDA method. However, for correct operation of LAMBDA method requires a large number of measurements. For example, it requires at least 12 satellites for good quality operation in GPS when operating in the L1 band frequency.

In the article describes filter algorithm for determining three-dimensions coordinates vector of a static object. The algorithm is based on processing ambiguous phase measurements and allows minimizing number of measurements. In the proposed algorithm, the likelihood function of state vector is represented as a set of modes (points, particles) as is done in particle filter. In the paper are presented formulas for calculating the characteristics of each mode (point or particle) on a prediction and correction filter steps: position, value of the likelihood function and an integer ambiguity vector. On correction step is performed ambiguity resolution using the LAMBDA method.

In the article is shown results of work the algorithm on the example of processing signals from pseudolites navigation systems with small bases between transmitters. The size of the convergence region of the algorithm for case with 4...8 transmitters and different number of modes involved in the filtering process are shown. It is shown that already at 5 transmitters the convergence time of the algorithm is determined by 10 time samples. Also the case of using contrast ratio (the ratio of height of the two adjacent height mod) as an indicator of true ambiguity resolution was discussed.


carrier phase, ambiguity resolution, LAMBDA, nonlinear filtration, pseudolite, local navigation system, GPS, GLONASS, Locata


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