Practical development of the second-order extended Kalman filter for very long range radar tracking

Abstract

This paper improves the second-order extended Kalman filter (SOF) by accounting the correlation of the first and second-order terms (FSOT) in the measurement Taylor approximation—a matrix assumed to be zero in the conventional SOF. The goal is to achieve consistent estimation results for very long range radar tracking, whereas this correlation term becomes non-negligible. Remarkably, the range element of the correlation term is so significant that it is several times larger than the range variance of the second-order term (SOT) and four orders of magnitude larger than the variance of the range measurement. In the absence of a closed form expression, the correlation of interest is approximated by scaling the variance of SOT using a design parameter. Improved performance of the new method is shown in simulated tests when the parameter is tuned up using the off-line Monte-Carlo averaging. The proposed SOF can process measurements in either the range–direction–sine (r–u–v) coordinates or the spherical (r–a–e) coordinates.