Source localization has been an important research subject in radar and sonar. Traditional source localization technique assumes stationary source and receivers. Source localization can be based on Angle of Arrival (AOA), Time of Arrival (TOA) or Time Difference of Arrival (TDOA) measurements, or a combination of them. TDOA technique is more popular than others in passive localization, because it does not require time stamp when the signal is transmitted, and can achieve relatively good location accuracy.

In the near future, the target location scenario will be dynamic. That is, the source is not stationary and the receivers will be in airborne platforms such as UAVs. Due to the relative motion between the source and the receivers, Frequency Differences of Arrival (FDOAs) can be used in addition to TDOA for localization. A sample location scenario is shown below, where several UAVs and fighter jets are used to locate a moving source on the ground through TDOA and FDOA measurements.

Target localization based on TDOA and FDOA measurements is known to be a challenging task because the target location, both position and velocity, are nonlinearly related to the measurements. The Taylor-series method can provide an accurate solution. It is, however, iterative and hence computationally expensive. Most importantly, it requires a very good initial solution guess to reach a solution and convergence is not guaranteed.

Recently, the CGI has developed a very efficient and effective closed-form solution to locate a moving target based on TDOA and FDOA measurement. The solution requires only two weighted least-squares minimization, and the solution accuracy achieves the CRLB before the thresholding effect occurs. Figure 2 show the target location accuracy of the developed technique, where 5 receivers, separated by about 0.5 km, are used to locate a target source that is about 4.5 km away. Both the target source and receivers are moving at speeds in the order of 10 m/s. In the figure, "c" is the signal propagation speed and "sigma d ^2" is the TDOA measurement noise power. The FDOA measurement noise power is ten times smaller than that of TDOA. It is clear that the proposed technique achieves the CRLB, and has a higher noise threshold than the Taylor-series technique where it is initialized at the true solution with variance twice the CRLB.

One limitation of using airborne receivers is that their precise positions and velocities will not be available. The uncertainty in the receiver locations can significantly degrade the performance of the source location accuracy. Figure 3 illustrates the decrease in location accuracy due to random errors in the position and velocity of the receivers. If a location algorithm assumes the receiver locations are correct but in fact they have errors, the target location accuracy is reduced by about 6 dB even if the receiver location error variance is only 0.001.

To improve this situation, the CGI is currently investigating different methods to achieve better source location accuracy by taking the uncertainty of the receiver locations into account. Figure 4 present some preliminary results from the proposed technique. The technique under development is not iterative, and most importantly, is able to reach the CRLB.

Figure 5 gives the "bullseye" view of the improvement in estimation accuracy of the proposed method. At 5 cm receiver position error, the previous method without accounting for the receiver position uncertainty has an RMS error of about 200 m, whereas the proposed technique reduces the RMS error by a factor of two.

In some practical scenario, only a single sensor is available for localization. Bearing-Only Tracking (BOT) and Doppler-Bearing Tracking (DBT) attempts to track a constant velocity target based on a sequence of bearing measurements only or Doppler and bearing measurements. Figure 6 illustrates the BOT and DBT scenario. The challenge for BOT and DBT is to obtain an unbiased solution that achieves the CRLB accuracy. Quite often, the bearing angles and the Doppler measurements are obtained from the time history of UAV video and/or electronic signal interception.

CGI has developed a BOT and DBT technique that significantly improves the performance of previous methods. Figure 7 compares the proposed tracking method with the Instrumental Variable method. In the simulation scenario, the Instrumental Variable method experiences divergence behavior, whereas the proposed method is able to estimate and follow the target track well. Most importantly, the proposed method achieves an asymptotically unbiased solution estimate that reaches the CRLB.

One problem for the existing BOT and DBT approach is that the target is assumed to be moving at a constant velocity. As a consequence, the estimated target track diverges when the target maneuvers. To improve the tracking behavior, CGI is working on BOT and DBT technique with maneuver detection so that we will be able to capture the target track again after the target has maneuvered. Figure 8 gives some preliminary results on DBT with maneuver detection. The traditional approach loses tracking after the target maneuvers, and the new approach is able to re-capture the desired target track.