Filtring of coordinates of a maneuvering object in three-dimensional space based on frequency and goniometric measurements

Abstract

The Markov theory of discrete-time nonlinear filtering was used to develop and analyse filtering algorithms for the Cartesian coordinates and for the frequency and Cartesian coordinates of a manoeuvring object. The filtering is performed by a multiposition radio-location system in three-dimensional space, using goniometric measurements and frequency and goniometric measurements respectively, and taking into account the non-detection probability and outlying observations. The maximum set of the state vector components of a mobile radio emission source includes the frequency, the Cartesian coordinates, and projections of speed in three-dimensional space. The maximum set of the observation vector components contains the measured values of frequency, azimuth and elevation of the radio emission source. The measurement data comes from the output ends of the radio-receiving devices in the radio direction finders of the multiposition radio-location system. The observation vector takes into account the possibility of receiving abnormal measurements. When the signal is lost, the data from the corresponding radio direction finder is extrapolated. The filtering of the state vector is based on a quasi-linear filter of the lost signals. The initial estimate of the state vector and its covariance matrix can be set using the a priori information. The suggested method takes into account the changes in the angular coordinates of the manoeuvring radio emission source, as well as the changes in the frequency of its signal occurring due to the Doppler effect, which results in significantly reduced positioning errors as compared to the extended Kalman filter.