Target Tracking with Multiple Radars: Measurement Model and Cramer-Rao Lower Bound Analysis

This paper investigates the measurement model and Cramer-Rao lower bound (CRLB) for target tracking using multiple radars. The measurement model is defined as follows:

• R'n,q,k and V'n,q,k denote the radial distance and speed from target q to radar n, respectively.
• θ'n,q,k ∈ [0, 2π] and φ'n,q,k ∈ [0, π] are the azimuth and elevation angles, respectively.
• d'n,q,k = √((x'g,k - x'n,k)² + (y'g,k - y'n,k)²) is the distance from target q to radar n in the XY-plane.

In the measurement model, u'n,q,k represents the measurement noise, which follows a zero-mean Gaussian distribution with covariance Z'n,q,k(P'n,k, s'n,q,k) = σ²n,q,k * I, where σ²n,q,k denotes the power emitted by radar n to target q. The notation blkdiag( ) represents a block diagonal operator. σ²n,q,k and σ² are the Cramer-Rao lower bounds, where σ is a proportional operator. K'n,q,k is the radar cross-section (RCS) of target q with respect to airborne radar n. P'n,q,k, T'n,q,k, θ'3dB, and φ'3dB are the signal effective bandwidth, dwell time, 3dB receive beamwidth in azimuth, and 3dB receive beamwidth in elevation, respectively.