# Adaptive Doppler Centroid Estimation Algorithm Based on Curve Fitting

In order to improve the performance of the energy balancing method in the non-homogeneous scene, the prominent point targets must be eliminated. Figure 3.4 shows the azimuth power spectrum of real airborne SAR system in non-homogeneous scene. According to Fig. 3.4, there are mainly two kinds of prominent point targets that deteriorate the homogeneity of the scene. Target A represents targets with extremely high power that severely affects energy distribution of the spectrum, and Target B represents targets with considerable power, but relatively lower peak.

In [6], an algorithm is proposed to remove the impact of Target A by setting up rigid threshold. However, the value of threshold is given manually, and the impact of Target B is neglected.

**Fig. 3.4 ****Azimuth power spectrum of airborne SAR**

According to the shapes of power spectra of prominent point targets, an improved energy balancing algorithm based on Gaussian curve fitting of down-sampled power spectrum is proposed. In this section, the principle and specific processing steps of the proposed algorithm are introduced.

Prominent point targets, such as Target A and B can be considered as disturbances of the Gaussian-shape azimuth spectrum. Moreover, their spectra are keen-edged and narrow, whereas the azimuth spectrum is relatively flat. After operate down-sample to the azimuth spectrum, only a few samples are located in Target A and B. On the contrary, most of the samples obey Gaussian distribution. Therefore, after Gaussian curve fitting, samples of ideal azimuth spectrum are preserved, and samples of prominent point targets will be abandoned adaptively. The proposed algorithm consists of six steps as follows:

Step 1: Operating down-sample of the azimuth spectrum to get the discrete spectrum data;

Step 2: Operating Gaussian curve fitting of the discrete azimuth spectrum, thus samples of prominent point targets will be far from the fitting curve, which is defined as exceptional samples;

Step 3: Calculating the fitting errors of each sample, and calculate the mean and standard deviation of the fitting errors. Compare the fitting error of each sample with the sum of mean and standard deviation, the samples with fitting errors larger than the sum are regarded as exceptional samples and should be abandoned;

Step 4: Operating Gaussian curve fitting of the new spectrum without exceptive samples, the new fitting curve is considered to be the ideal azimuth power spectrum;

**Fig. 3.5 ****Flowchart of the proposed algorithm**

Step 5: Processing traditional energy balancing method to estimate Doppler centroid *f _{dc}*

Step 6: Operating linear curving fitting of each range cell to further eliminate random estimation error [7].

The flowchart of the proposed algorithm is shown in Fig. 3.5.