Radar coincidence imaging is an instantaneous imaging technique which does not depend on the relative motion between targets and radars. High-resolution, fine-quality images can be obtained using a single pulse either for stationary targets or for complexly maneuvering ones. There are two image-reconstruction algorithms used for radar coincidence imaging, that is, the correlation method and the parameterized method. In comparison with the former, the parameterized method can achieve much higher resolution but is seriously sensitive to grid mismatch. In the presence of grid mismatch, neither of the two algorithms can obtain recognizable high-resolution images. The above problem largely limits the applicability of radar coincidence imaging in actual imaging scenes where grid mismatch generally exists. This paper proposes a joint correlation-parameterization algorithm, which uses the correlation method to estimate the grid-mismatch error and then iteratively modifies the results of the parameterized method. The proposed algorithm can achieve high resolution with fine imagery quality under the grid mismatch. Examples are provided to illustrate the improvement of the proposed method.

Radar coincidence imaging is developed as the extension of classical coincidence imaging in microwave radar systems [

Because of the different imaging principles, the radar coincidence imaging technique has two advantages over most of the RD imaging methods. Firstly, radar coincidence imaging does not depend on the aspect-angle integration or the Doppler gradient to achieve high azimuth resolution. Thus, it does not require relative motion between radars and targets and can obtain images of the targets which remain stationary with respect to radars. Furthermore, radar coincidence imaging can achieve high-resolution using a single pulse. The extremely short imaging time, which is shorter than a pulse width, considerably decreases the impact of the noncooperative motion to imagery quality. Therefore, radar coincidence imaging can obtain high-resolution, fine-quality images either for stationary targets or for the ones in complex maneuvers.

In radar coincidence imaging, the target area needs to be discretized to a grid and target-scattering centers are assumed to be located at the grid points. If scattering centers are located off the grid points, then the grid mismatch yields. There are two main image-reconstruction methods used in radar coincidence imaging. One is the correlation method with lower resolution. The other is the parameterized method which can produce much higher resolution but is too sensitive under grid mismatch to give recognizable target images. Furthermore, current algorithms that are applicable to solve the sensitivity to basis mismatch are unfortunately ineffective for the grid mismatch in radar coincidence imaging [

The paper is organized as follows. Section

Coherent signals, which are widely employed by most of the imaging radars, generally produce detecting signals that show significant spatial correlation, as shown in Figure

(a) The spatial distribution of time-space detecting signals. (b) The spatial distribution produced by coherent transmitted signals.

Generally, the target location can be firstly estimated based on the detection and localization techniques [

Geometry of the target area grid.

The ideal transmitted signals for radar coincidence imaging are supposed to be group-orthogonal and time-independent as denoted in (

Note that the detecting signal

The excellent point-to-point relationship in (

The imaging equation presented in (

To illustrate the grid-mismatch impact, we give an example to show how the position bias affects the modeling error and how the modeling error affects the imaging quality. In the quantitative manner, the imaging quality discussed here is firstly indicated by the relative imaging error, expressed as

The example employs an

The arrangement of antennas and the target model.

The grid-mismatch impact to imaging quality of the parameterized method. (a) The imaging error versus

In this example, the target image in Figure

Consider another example to compare the correlation method with the parameterized method under grid mismatch. In the example, target images will be reconstructed via the two methods with and without the grid mismatch. Herein, the grid mismatch leads to

The imaging results recovered by different methods. (a) The correlation-method result without grid mismatch. (b) The parameterized-method result without grid mismatch. (c) The correlation-method result when

As shown in Figure

In conclusion, neither of the two image-reconstruction methods can achieve both high resolution and good imaging quality in the presence of grid mismatch. According to their respective limitations, there are two ways to solve the image reconstruction under grid mismatch. One way is to improve the resolution of the correlation method. The other one is to decrease the grid-mismatch impact in the parameterized method. As stated previously, however, microwave signal does not have adequate time-independence in nature, resulting in a limited resolution. Thus, the latter might be a possible way to solve the problem of grid mismatch.

A direct idea to decrease grid-mismatch impact in the parameterized method is to estimate the modeling error. Note that the modeling error is relevant to the scattering center number, scattering intensity, and the position-bias level of all scattering centers. If there is no prior information of the target shape, the modeling error will be quite difficult to estimate. Then for the targets that are unknown in advance, the obtainable shape information could be sought from the imaging results of the two reconstruction methods. Thus, a possible source to provide the desired knowledge would be the correlation-method result, considering the seriously distorted images of the parameterized method caused by grid mismatch.

The knowledge that can be used by the imaging equation should be quantitative and precise. However, the result of the correlation method, as observed in Figure

Firstly, still under the grid-match assumption, we estimate the target scattering-coefficient vector via the two reconstruction methods:

If the result remains unsatisfactory, we can repeat the computation of (

The flow of the joint correlation-parameterization method.

Step 1 | Set the iteration step maximum |

Step 2 | Discretize the target area and compute the reference signal. |

Step 3 | Obtain the scattering-coefficient vector |

Step 4 | Set a threshold |

Step 5 | Compose the coincidence imaging equation. Obtain the initial estimation |

Step 6 | Compute the inverse matrix of the reference matrix |

Step 7 | Derive |

Step 8 | Compute the modeling noise |

Step 9 | Update the scattering-coefficient vector as |

Step 10 | Stop if |

To examine the correlation-parameterization method, target images are reconstructed according to the iteration process of Table

The imaging results of the joint correlation-parameter method. (a) The imaging result of the first iteration. (b) The imaging result of the second iteration. (c) The imaging result of the third iteration.

As shown in Figure

Radar coincidence imaging can achieve excellent high-resolution target images on the condition of grid match, but the imagery quality gets degraded beyond recognition in the presence of the modeling error caused by grid mismatch. Therefore, the paper proposes the joint correlation-parameterization method for image reconstruction. The proposed algorithm iteratively modifies the parameterized-method result with the estimated modeling error, which is obtained based on the correlation-method result. Consequently, the grid-mismatch impact on the imaging quality is considerably reduced. The example shows that the joint correlation-parameterization method can achieve high resolution and maintain the robustness under grid mismatch.

The authors declare that there is no conflict of interests regarding the publication of this paper.