Interacting multiple model in the alert class radar tracking study (1)

Yin Rui, Wang Yam Samuel, Wang Feng

(Institute, Nanjing, Jiangsu Province, Nanjing 210013)

0 introduction

IMM (interacting multiple model) approach is Blom h.a.p. in 1984.

Multiple-model method is mainly used for properties at any time ask the State estimates of changes in the system, so it is especially suitable for maneuvering target tracking. A typical example is the tactical flight of the aircraft's track. At the IMM method, it is assumed that there is a finite number of target model exists, each model corresponds to different mobile input level. In calculating the various models to correct a posteriori probability, you can pass on the model of the correct status to the estimated weighted sum to the final destination state estimation, the weighting factor for model correct a posteriori. IMM estimator is known best single scan State estimator, are widely applied in various fields, but not yet applied in airborne early warning radar target tracking. This article picks a surveillance radar product of a few tracks by IMM method filtering, filtering results and it is now practical engineering is using .Kalman (Singer model) filtering accuracy comparison, implementation model optimization.

1 algorithm processes

This simulation is mainly divided into data reading people, multiple model filter, data output in three parts.

Data read into the process including track with drop after machine system data reading people, track the corresponding GPS data read and put into the pending data coordinate system transformations. Multiple model filter is read in the last step and converted to inertial data respectively in x, y, z axis multiple model filter. Data output process include the multi-model track output filtering, and put this trajectory and measured by GPS (global positioning system) trajectory and Kalman (Singer model) filtering trajectories, the size of the error. Specific flowchart see figure l.

　　

　　

2 simulation data transmission and human

This simulation of random selected radar two track record, combined with a different model for filtering, analysis corresponding to the different mobility adopted two model combination Oh to maximize filtering accuracy and GPS data to benchmark their filtering results and present common Kalman (Singer model) filtering accuracy, came to the conclusion of a reference value.

Target track l roughly: in time 42 138 s goals from longitude 120.667.

, Latitude 40.250 ° uniform flight to latitude longitude 123.172 °, and then target 62.465 ° in time at 360 s 43 065. Big turning point for longitude, latitude 123.118 ° 62.521 °. Destination of the flight track 1 Reference inertial measurement of two-dimensional coordinates for the graph shown in Figure 2, with the goal of flight speed diagram shown in Figure 3.

　　

　　

　　

　　

Target path 2 roughly: in time 39 163 s objectives in longitude 121.456 °, latitude 65.525 ° longitude at uniform speed flying to 123.24l °, latitude 61.89l ° turning maneuvers to longitude l 22.25 l °, latitude 62.215 °.

Destination of the flight track 2 reference inertial measurement of two-dimensional coordinates for the graph shown in Figure 4, the target flight speed diagram as shown in Figure 5.

　　

　　

　　

　　

3 simulation output data

3.1 track l

On track 1 using CV model and CA model interaction, CV model and Singer ' model of interaction, CV model and "current" statistical model of interaction, Singer ' model and "current" statistical model of interaction, get a set of simulation and a set of simulation data.

Including CV model and cA model portfolio simulation results are as follows: CV model interaction CA model filter, measured GPs, Kalman (Singer model) filtering two-dimensional longitude orbit as shown in Figure 6, CV model interaction CA model filtering and Kalman (Singer model) filter range error as shown in Figure 7, longitude error shown in Figure 8, latitude error as shown in Figure 9. 4 model two two interactive, a total of 6 effective model portfolio. Track 1 of the 6 model combination filter range error statistics such as shown in table l, longitude error statistics as shown in table 2, distance error statistics such as shown in table 3. Track 1 using Kalman (Singer model) filter range error 64.453 8 m, longitude 2 ° error 0.002, latitude error 0.011 l °.

　　

　　

　　

　　

　　

　　

Analysis of track l simulation chart you can see, the CV model and CA model interaction, CV model and Singer model interaction, CV model and "current" statistical model interactive filter range error 62.4 m, distance from the error than is currently the popular Kalman (Singer model) filter range error about small 2 m.

CA model and Singer model interaction, CA model and "current" statistical model for interactive distance errors than Kalman (Singer model) filter range error big l m or so. Singer model and "current" statistical model for interactive distance errors than the Kalman filter (Singer model)Wave range error small l m or so. Longitude and latitude of great dimensions, interaction model includes CV model combination longitude can improve 0.000 l ° latitude can improve 0.000 9 °. Singer model and "current" statistical model interaction increase O.000 2 ° latitude, longitude accuracy did not improve. Thus, for this track, i.e. the target made 927 s after the turn of uniform motion, CV model and the remaining three model two two combinations and Singer model and the current statistical model combination improves filtering accuracy, with cV model and "current" statistical model interactive filter improved precision.

　　

　　

3.2 track 2

On track 2 is also available using cV model and CA model interaction, CV model and Singer model interaction, CV model and "current" statistical model of interaction, Singer model and "current" statistical model of interaction, get a set of simulation and a set of simulation data.

Where cA model and "current" statistical model portfolio simulation results are as follows: cA model interaction "current" statistical model filter, measured GPS, Kalman (Singer model) filtering two-dimensional longitude orbit as shown in Figure 10, CA model interaction "current" statistical model of filtering and Kalman (Singer model) filter range error as shown in Figure l l, longitude error as shown in Figure 12, latitude error as shown in Figure 13. 4 model two two interactive, a total of 6 effective model portfolio.

　　

　　

　　

　　

　　

　　

　　

　　

Track 2 of 6 kinds of model combination filter range error statistics such as shown in table 4, longitude error statistics such as shown in table 5, distance error statistics as shown in table 6.

Track 2 using Kalman filtering (Singer model) distance error 103.600 3 m, longitude 4 ° error 0.006, latitude error 0.011 6 °.

Analysis of track 2 of the chart you can see, the cV model and CA model interaction, CV model and Singer model interaction, CV model and "current" statistical model interactive filter range error 106.7 m, distance from the error ratio currently works on using Kalman (Singer model) filtering error 3 m distance.

CA model and Singer model interactive distance errors than Kalman (Singer model) filter range error about small 3 m, CA model and "current" statistical model for interactive distance errors than Kalman (Singer model) filter range error small 4 m or so. Singer model and "current" statistical model for interactive distance errors than Kal.

Man (Singer model) filter range error about small 2 m.

Longitude and latitude of great dimensions, cA model and "current" statistical model for interaction of longitude and latitude errors are errors reduces 0.000 1 °. Thus, for the track, that is the target to do some l 037 s uniform motion after doing some 800 s mobile, CA model and Singer model portfolio, cA model and "current" statistical model portfolio, Singer and "current" statistical model combination improves the precision of r filter. Contains a combination of CA model improves the accuracy of the more obvious, with CA model and current statistics ' model interactive filter to improve the accuracy of the most high.

4 conclusions

This article uses the cV model, cA model, Singel ' model as well as the "current" statistical model two two interactive multiple model algorithm to deal with a guard class radar one day test flight of two tracks, the simulation results of a series and the current project to handle track filtering Kalman (Singer model) algorithm to draw the following knot was:

A) Kalman (Singer model) tracking simple, convenient, real-time computing, target tracking filter has a certain meaning.

B) do non-motorised sports plane or small tactical movement, using Kalman (Singer model) to process the track can achieve better results, but precision than contains CV model interaction algorithm accuracy and low.

C) aircraft for highly mobile, with multiple model filter for tracking has its advantages, to a certain extent to improve filtering accuracy.

D) model algorithms improve filtering accuracy, target motion model must include the multi-model the prior model, and its hypothetical since the relevant time constant to and tactical campaign related time constant close, so you can maximize the filter [1] [2]