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

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.