Tracking a Target on a 450 Degree Turn with the Multi-fractional Order Estimator (MFOE)

Abstract

This paper presents a method of tracking a maneuvering target during a 450 turn with the polynomial multi-fractional order estimator (MFOE) from statistically corrupted measurement samples. The novel concept of the MFOE is to trade-off noisy measurements for fractions of estimated position, velocity, acceleration, jerk, etc. (fractions of estimated polynomial coefficients) to improve tracking accuracy by reducing the size of the MSE (variance plus bias-squared). Although the direct or ostensible trade-off is between the number of measurement samples vs. fractions of polynomial coefficients, the secondary or actual trade-off is between the variance and bias-squared. The MFOE creates a set of weights and applies them to the noisy measurement samples to yield the predicted position and MSE. MFOE features: The sum of the weights equals 1 and the sum of the squares of the weights is the variance normalized with respect to the noise variance. Of course, the bias is the square root of the difference between the MSE and the variance. Plots included are the target trajectory, the range and azimuth of the target as seen by the sensor (radar), as well as the individual range and azimuth tracking errors: measurement noise standard deviation (SD), prediction noise SD, RMSE, and bias. Particularly surprising is that the azimuth MFOE predictor SD is smaller during constant velocity after the turn than is the SD of the conventional polynomial second order predictor; i.e., first degree polynomial representing a constant velocity trajectory. (Note: Estimator order equals polynomial degree plus 1 from the Kalman filter.