# Passive state estimation of air vehicles

### Multi-sensor tracking

The paper 6 describes a commercial multi-sensor tracking (MST) system, that is able to process an arbitrary mix of radar data and passive sensor data. The radar data consists of range and azimuth angles together with optional elevation angles, while the passive sensor data lacks the range information. When data arrives, association to existing tracks representing air-vehicles is attempted. The association is performed in the measurement space of each sensor after which the tracks are updated in a Cartesian earth tangential coordinate system. The tracking filters are interacting multiple model (IMM) filters that switch smoothly between one constant velocity model and another high noise maneuver model, both implemented by extended Kalman filters (EKFs). Measurements that cannot be associated to existing tracks are used for initiation of new tracks. Notably, the initiation of tracks from passive sensor data is performed by advanced Bayesian cross computation and deghosting algortithm. A block diagram of the MST is available in Fig. 1.

*Figure 1. Block diagram of the multi-sensor tracker. *

### Noncooperative type estimation

The contributions 3, 4 and 7 describe techniques tailored to augment the kinematic tracking algorithms of the MST, to include processing of arbitrary type information. Such functionality serves not only to derive enhanced information, if properly used it also dramatically increases the performance of the data association, the cross computation and the deghosting. This follows since type information is connected to measurements of azimuth and elevation angles with infra-red search and track (IRST) and electronic surveillance measures (ESM) sensors. The IRST image data may e.g. generate information on the number of engines, missile counts and similar. In addition, flight envelope information (5) may contribute by analysis of the kinematic track.

These publication first design a recursive Bayesian algorithm for update and propagation of target type, within a pre-defined set. All above information sources and more may be fused via the likelihood of the data. Notably, the algorithms allow ambiguous scenarios. Fig. 2 illustates the target type filtering for an angular track where the available information allows non-ambiguous traget type estimation while Fig. 3 illustrates an ambiguous case.

*Figure 2. Recursive target type estimation in a non-ambiguous case. *

*Figure 3. Recursive traget type estimation in an ambiguous case. *

Based on the estimated types for the angular track, tentative crosses can be formed. Fig.4 shows how not only a Cartesian state can be computed, but also a refined type probability. This is described in detail in 3 and 4, where also the calculation of a cross quality in the type domain is derived, thereby enhancing de-ghosting algorithms.

*Figure 4. Combining of strobe track type probabilities into track probabilities. *

In addition, 3 and 4 contain methods for data association and track supervision where type information is used to enhance performance.

### UAV tracking in cellular networks

Tracking of UAVs that fly using cellular resources represents an increasing need. The European U-space will provide a complete framework for this. UAV tracking functionality is then needed, to support e.g. conflict alert. However, a main problem when using ADS-B type functionality is that GPS data over links like ADS-B may be tampered with, since it is possible for the pilot to disable the transfer of the satellite navigation data. Additional data sources therefore need to be used for kinematic state estimation, or unwanted drone operation may pass undetected. One possibility is to use active primary radar. Another possibility would be to use cellular systems for UAV tracking, as discussed here.

Cellular measurements that cannot be disabled by UAV operators need to be selected as measurements depending on the mandatory parts of the cellular communication standards, or as measurements that do not require standardisation at all. Doppler shift measurements in the 4G and 5G cellular standards constitute such measurements. Doppler shift measurements can also be performed in neighbour cells, by exploiting the X2 and Xn interfaces between base stations of these standards. Other mandatory measurements include the round trip time timing advance measurement of the serving cell. Measurements of angle of arrival (AoA) require antenna arrays that may not be generally deployed. The scope here is therefore focused on UAV tracking based on Doppler shift measurements in multiple 4G and 5G base stations. An observability analysis of 2 proves that Doppler shift measurements in 4 base stations is the minimum number that renders a solvable estimation problem, see Fig. 5.

*Figure 5. Minimal singular value of the observability matrix for the case with Doppler shift measurement in four base station sites. *

The first contribution of 2 is an interacting multiple model (IMM) UAV tracking algorithm with a number of novel properties. Joint state estimation of the Cartesian 3D velocity, 3D position and the cellular carrier clock frequency bias of the UAV is performed. The use of Doppler shift measurements is advantageous since accurate frequency synchronization is available in the base stations. Time difference of arrival based tracking on the other hand, would require network-wide high accuracy time synchronization, which is expensive to achieve. The data fusion is performed by two extended Kalman filters, that handle the nonlinear Doppler shift measurement models. Furthermore, the IMM filtering algorithm is derived in continuous time which allows processing of irregularly sampled measurements.

An example of the achievable performence appears in Fig. 6 and Fig. 7.

*Figure 6. Estimated UAV position (red) and ground truth (blue) using Doppler shift measurements in 4 sites. *

*Figure 7. Estimated UAV velocity (red) and ground truth (blue) using Doppler shift measurements in 4 sites. *

Another alternative is to use the standardized 5G measurement of multiple round trip times between a mobile transceiver and a set of base stations. Each such round trip time measurement generates a range related measurement, usable for UAV state estimation as noted in the paper 1.

The state estimation of 1 is also based on IMM-filtering, however 3 movement modes are used since the round trip time measurement is statically related to a range. The first movement mode is a six state constant velocity model, while the second movement mode is a nine state constant acceleration model. The third movement mode is unconventional and models hovering with a constant position model with three states. The mode mixing is also novel, with a requirement that a transition from constant velicity movement to hovering is over a time period with acceleration. Three extended Kalman filters handle the nonlinear measurement processing. See 1 for further details.

### References

1. S. Yasini and T. Wigren, "Round trip time based UAV state estimation", to appear in Proc. European Control Conference, Stockholm, Sweden, June 25-28, 2024.

2. T. Wigren and S. Yasini, Passive UAV tracking in wireless networks", IEEE Trans. Aerospace and Electronic Systems, vol. 58, no. 5, pp. 4101-4118, 2022. DOI 10.1109/TAES.2022.3158640.

3. T. Wigren, "Remote aircraft type probablity estimation and combining using distributed sensors - an application of Bayesian estimation", Docent Lecture, Uppsala University, 2002.

4. T. Wigren, "Target type probability combining algorithms for multi-sensor tracking", Proc. Aerosense 2001, SPIE, Orlando, FL, vol 4380, pp. 46-62, April 16-20, 2001.

5. T. Wigren, "Noncooperative target type identification in multi-sensor tracking", Proc. IRCTR Colloquium on Surveillance Sensor Tracking , Delft Technical University, Delft, the Netherlands, pp. 1-12, June 26, 1997. Invited paper.

6. T. Wigren, E. Sviestins and H. Egnell, "Operational multi-sensor tracking for air defense", Proc. First Australian Data Fusion Symposium , Adelaide, Australia, pp. 13-18, Nov. 21-22, 1996.

7. T. Wigren and H. Egnell, "Automatic target identification and multi-sensor data fusion in air defense command and control systems", Proc. Milinf 1996 , Swedish Defense Material Organization, Enköping, Sweden, June 1996.