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Continuing with the likelihood: n |x n ) ∝ p1n (yu,k k n |x n ) ∝ p0n (yu,k k 1 e σ12 1 e σ02 − n yu,k σ12 if target present yn − u,k σ02 if target not present. Since the value of σ12 = 2σA2 Es2 As (τ¯ − τu,k , νu,k − ν¯ ) + 2N0 Es is not known as the true target location τu,k , νu,k is not known, thresholding of the matched filter output is required: n ≥T 1, if yu,k n

N, u = 1, . . , U where n =| yu,k 1 M Md −1 n s ∗ (m − τλ,u,k )e− du,k (m) m=0 n j 2π mνλ,u,k M |2 ⇒ λ=1 L n yu,k =| n n Al,k Es AFs (τλ,u,k − τl,u,k , νl,u,k − νλ,u,k ) l=1 λ=1 Md −1 + 1 M n s ∗ (m − τλ,u,k )e− vu,k (m) m=0 n j 2π mνλ,u,k M |2 . λ=1 The likelihood function for each proposed particle n = 1, . . 3. SCHEME FOR ADAPTIVE WAVEFORM SELECTION USING IPLPF 53 n p n (yu,k |Xk1 , . . , Xkn , . . , XkN ), n = 1, . . , N, u = 1, . . , U . n , n = 1, . . , N, u = Here, the hypothesis of particle n is that the state equals Xkn , while yu,k 1, .

Unlike the case of the LFM, in the case of the Björck CAZAC, σ12 is known. This allows us to use unthresholded measurements in the case of the Björck CAZAC for greater measurement accuracy. After calculating the necessary likelihood values, we sample from it using the following process. 8) . In We normalize {{βinτ ,iν ,u,k }iττ =0 }iνν=0 . 10) . The resulting sampled n = cτ n T /2, r˜˙ n = cν n ν/(−2f ), b˜ n = range and range rate and the bias are, respectively, r˜u,k c u,k u,k k˜τ k˜ν . bn˜ ˜ kτ ,kν ,u,k Although, the use of a CAZAC offers accuracy in the range and range rate, this does not imply accuracy in the location and velocity in the x − y plane.

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