## 1 Introduction  
Airborne passive radars exploit the existing transmitters as emitters of opportunity, having attracted widespread attention in recent years [1, 2, 3, 4, 5, 6, 7]. Compared with airborne active radars, the lack of dedicated transmitters offers the advantages of low cost, strong survivability, and antijamming. However, the moving airborne platform leading to the received ground clutter is extended in terms of the Doppler frequencies and angle. Thus, it is difficult for a traditional spatial or temporal filter to detect targets. Space-time adaptive processing (STAP), which uses multichannel spatial information across a sequence of temporal pulses to form a two-dimensional filter, is a crucial technology in airborne passive radar for clutter cancellation. However, the application of STAP is restricted by practical problems, such as excessively high computational complexity and a large number of the required training snapshots. Subsequently, extensive research on STAP mainly considered how to reduce the computational burden and enhance the convergence speed. However, the practical implementation of STAP in airborne passive radar is based on the assumption that the reference signal is uncontaminated. When this condition is not satisfied, the clutter caused by the direct-path (DP) signal (DP clutter) and multipath (MP) signal (MP clutter) affects the covariance matrix estimation. Consequently, the target self-nulling phenomenon may exist [8]. The MP clutter cancellation approach before STAP can eliminate the influence of impure reference signals in airborne passive radars. Existing MP clutter suppression techniques can be categorized into two groups. One is signal equalization, which relies heavily on precise prior information [9]. Another is the sparse reconstruction of MP clutter that does not require prior knowledge [8; 10; 11]. However, the pulse-to-pulse fluctuations in MP signals, also known as the intrinsic clutter motion (ICM) [12], degrade the reconstruction quality. Thus, it is a challenge to suppress MP clutter with ICM errors in airborne passive radar systems. In the current paper, to enhance the MP clutter suppression performance with ICM errors, we present a novel suppression algorithm with ICM error calibration and off-grid effects mitigation. In the proposed algorithm, the ICMs of clutter patches (ICM-CP) and MP scatterers (ICM-MP) are considered. After using reference signals for matched filtering, the DP clutter snapshot involves the temporal fluctuation vector caused by ICM-CP, and the MP clutter snapshot involves the temporal fluctuation vector caused by both ICM-CP and ICM-MP. Consequently, the MP clutter is not only related to the DP clutter snapshot and the modified steering vector, which are mentioned in SRA and LSA, but also related to the ICM-MP fluctuation. Thus, the existing sparse model of MP clutter is disturbed in the presence of ICM-MP. Based on the above analyses, an MP clutter suppression algorithm based on joint optimization is designed. The procedure of the proposed algorithm is described as follows: Initially, the ICM-MP fluctuation is introduced, and the sparse model of MP clutter is revised. Subsequently, by adding a constraint to ICM-MP fluctuation, we modify a traditional reconstruction issue into a joint optimization issue. Thirdly, the ICM-MP fluctuation and MP clutter profile are estimated simultaneously based on the local search technique. Finally, the MP clutter is suppressed with ICM-MP error calibration and off-grid effects mitigation. After the MP clutter cancellation algorithm, the existing STAP is utilized to mitigate the impacts of ICM-DP and cancel DP clutter. The main contributions of the paper are summarized as follows:  
1. We develop a new sparse model of MP clutter and joint optimization problems by considering ICM-MP fluctuation. 2. We propose a joint optimization algorithm for improving the MP clutter suppression performance when ICM-MP fluctuation exists, where the local search technique is incorporated to mitigate off-grid effects. 3.