JP3744720B2 - Target tracking method and target tracking device - Google Patents

Description

【００２２】
一方、モノスタティック・レーダ局Tx/Rxで計測した目標の仰角と方位角を、それぞれφ_m , θ_m と表す。バイスタティック受信局Rxで計測した目標の仰角、方位角をφ_b , θ_b と表す。
【００２３】
次いで、上記▲２▼の、上記観測諸元を用いた目標測位処理について、図２を参照して説明する。
図２に示すように、目標の絶対位置を表すための基準座標系24を設定する。
この座標系で表したモノスタティック・レーダ局およびバイスタティック受信局の絶対位置は既知であると仮定する。
上記得られた観測諸元の内、距離rと角度φ_m , θ_mにより構成される観測諸元ベクトルu^{(c )}を式(5)で定義する（Tは行列の転置を表す）。
この観測諸元ベクトルｕ^{(c )}の情報を使用すれば、モノスタティック・レーダ局Tx/Rxを中心とする円周上での目標の測位（以下、円測位と呼ぶ）が可能である。円測位によって得られる目標位置ベクトルz^{(c )}（基準座標系24で表す）を式(6)で定義する。 上記ｕ^{(c )}より上記z^{(c )}を求める算出式を式(7)で表す。
また、距離ρと角度φ_b , θ_bで構成される観測諸元ベクトルu^(e) を式(8)で定義すれば、この観測諸元ベクトルu^(e) の情報より、モノスタティック・レーダ局Tx/Rxと、バイスタティック受信局Rxを焦点とする楕円上での測位（以下、楕円測位と呼ぶ）が可能である。楕円測位による目標位置ベクトルz^(e) を式(9)とし、 上記u^(e) より上記z^(e) を求める算出式を式(10)で表す。
さらに、距離差δと角度φ_b , θ_bで構成される式(11) の観測諸元ベクトルu^(h)を使用すれば、Tx/RxとRxを焦点とする双曲線上での測位（以下、双曲線測位と呼ぶ）が行える。双曲線測位による目標位置ベクトルｚ^(h)を式(12)とし、上記 u^(h)より上記ｚ^(h)の算出式を式(13)で表す。
【００２４】
【数２】

【００２５】
次いで、上記▲３▼の、上記観測諸元の誤差が目標測位誤差に及ぼす影響について説明する。
上記の観測諸元r , ρ , δ, φ_m , θ_m , φ_b , θ_bに含まれる観測誤差をそれぞれΔr , Δρ, Δδ, Δφ_m , Δθ_m , Δφ_b , Δθ_bと表す。
距離rの誤差は式(1)におけるTx/Rxでの受信波到来時刻t_mの計測誤差に起因して発生する。Δrは平均０、分散σ _r ² のガウス分布に従うと仮定する。
また、距離ρの誤差は式(2)におけるRxでの受信波到来時刻t_bの計測誤差に起因する。Δρは平均０，分散σ_ρ ² のガウス分布に従うと仮定する。
一方、距離差δの誤差は、式(3)におけるt_mの計測誤差とt_bの計測誤差の双方の影響を受ける。この結果 Δδは、式(4)より次式のように表せる。
【００２６】
【数３】

【００２７】
上記Δr , Δρに対するガウス分布の仮定と式(14)より、Δδは平均０、分散σ_δ ² のガウス分布となる。ただし、分散ρ_δ ²は次式で与えられる。
【００２８】
【数４】

【００２９】
ところで、Δrと Δρは、それぞれ異なる計測量t_m , t_bの誤差に起因するため、互いに無相関な誤差であり、式(16)を仮定できる（E[・]は平均演算を表す記号である）。これに対し、ΔrとΔδは共にt_mの計測誤差に影響を受けるため、互いに相関を持つ誤差である。式(14)より、これらの誤差の相互相関に関する共分散は式(17)となる。
【００３０】
【数５】

【００３１】
目標角度の観測誤差Δφ_m , Δθ_m , Δφ_b , Δθ_bは、いずれも平均０で、分散が各々 σ_{φ m} ², σ_{θ m} ² , σ_{φ b} ² , σ_{θ b} ² のガウス分布に従うと仮定する。
これらの誤差は互いに無相関である。
以上のことから、式(5),(8),(11)で定義した各観測諸元ベクトルu^{(c) ,} u^{(e) ,} u^(h) の誤差共分散行列が式(18)〜(22)のように得られる。ここで、式(18),(19),(20)は、それぞれ観測諸元ベクトルの各誤差Δu^(c) , Δu^(e) , Δu^(h) の共分散行列であり、式(21),(22)は、それぞれΔu^(c) と Δu^(e) 、およびΔu^(c) と Δu^(h) の相互相関行列である。なお、diag(a,b,c)は、a,b,cを対角項とする3×3の対角行列を、また、0_{3 × 3}は3ラ3の零行列を表す。
【００３２】
【数６】

【００３３】
上記の観測諸元の誤差が目標の測位誤差に及ぼす影響は、以下のように評価できる。
上記観測諸元ベクトルu^(c) が誤差Δu^(c)を持っている場合の、円測位による目標位置ベクトルz^(c) の誤差をv^(c) とする。同様に、上記観測諸元ベクトルu^(e) が誤差Δu^(e)を持っている場合の、楕円測位による目標位置ベクトルz^(e)の誤差をv^(e)、
上記観測諸元ベクトルu^(h) が誤差Δu^(h)を持っている場合の、双曲線測位による目標位置ベクトルz^(h)の誤差をv^(h)と表す。
式(7),(10),(13)を線形化一次近似することにより、以下のように評価する。
【００３４】
【数７】

【００３５】
ここで、F^(c)は式(7)の関数f ^(c)のu^(c)による一次微分係数を示す3×3行列の真値u ₀ ^(c)における値である。また、F^(e), F^(h) についても同様である。
ここで、真値u₀ ^(c)を実際に得ることはできないが、追尾処理の過程で得られる目標の予測位置や推定位置を使用すれば、近似値を算出することができる。
上記式(18)〜式(22)および式(23)〜式(25)より、測位誤差 v^(c), v^(e) , v^(h)の共分散行列が以下の式(26)〜(30)のように得られる。
ここで、Ｓ^(c)，Ｓ^(e) ，Ｓ^(h)は、測位誤差 v^(c), v^(e) , v^(h)の共分散行列であり、C^(ce) , C^(ch) は、相互相関行列である。
【００３６】
【数８】

【００３７】
ここで、上記の式(29),(30)が示すように、円測位による目標位置ベクトルz^(c)と楕円測位による目標位置ベクトルz^(e)は、互いに誤差が無相関な測位結果であるのに対し、 z^(c)と双曲線測位による目標位置ベクトルz^(h)は互いに誤差が相関を持つ測位結果である。
【００３８】
次いで、上記▲４▼の、上記の解析結果に基づいて追尾フィルタ処理で仮定する目標の運動モデルと入力データのモデルについて説明する。
まず、目標の運動モデルについて説明する。
例えば、図２の基準座標系24でのサンプリングkにおける目標位置と速度の成分により、目標の状態ベクトルを次の式(31)で表す。
【００３９】
【数９】

【００４０】
このとき、目標の運動モデルを式(32)で定義する。ここで、Φ_k-1はサンプリングk-1からサンプリングkへの状態ベクトルｘ_kの推移行列で、例えば、目標の運動を等速直進と仮定する場合、サンプリング間隔をτとして、式(33)で与えられる。ここで、I_{3 × 3}は3×3の単位行列を表す。
ｗ_{k -1}は目標運動を等速直進と見なしたことによる誤差を表すために導入された加速度相当の駆動雑音ベクトルであり、平均０、共分散行列がQ_kのガウス性白色雑音であるとする。
【００４１】
【数１０】

【００４２】
次に、追尾フィルタへの入力データのモデルを以下のように定義する。
円測位による目標位置ベクトルz^(c)を追尾フィルタへの入力データとする場合のモデルを式(34)とする。同様に、楕円測位による目標位置ベクトルz^(e)、双曲線測位による目標位置ベクトルz^(h)を入力データとする場合のモデルを、各々式(35)， (36)とする。ここで、観測行列Hは式(37)で与えられる定数行列である。
また、 v^(c), v^(e), v^(h)は式(23)〜式(25)で定義した各測位誤差であり、これらの誤差は平均０で共分散行列が式(26)〜式(30)で与えられるガウス性白色雑音であると仮定する。
【００４３】
【数１１】

【００４４】
以上で、この発明の目標追尾方法の実施の形態１の背景理論の説明を終る。
【００４５】
次に、図１を参照して、この発明の目標追尾方法の実施の形態１を示す処理手順を詳しく説明する。
この実施の形態１では、サンプリングkまでのモノスタティック・レーダ局およびバイスタティック受信局よりの観測情報に基づき、サンプリングkに対する式(31)の状態ベクトルの推定値を求める。
まず、図１のST1において、通常の追尾処理の場合と同様に、初期２回のサンプリングの目標位置ベクトルから算出した目標の位置および速度を状態ベクトル推定値の初期値に設定し、また、上記算出した位置および速度の誤差共分散を算出して、これを推定誤差共分散行列の初期値に設定し、追尾処理を開始する。
なお、上記初期値を算出するための目標位置ベクトルとしては、モノスタティック・レーダ局における円測位の結果を使用すれば良い。
以降、３回目のサンプリングより、ST2〜ST14の一連の処理ステップを各サンプリングにおいて実行する。これらの処理ステップは、サンプリングk-1に対する状態ベクトル推定値ハット x _k -_1|k -₁ と推定誤差共分散行列P_k -_1|k -₁の値を、サンプリングkの観測情報を用いて、サンプリングkに対する状態ベクトル推定値ハット x _k|kと推定誤差共分散行列P_k|kの値に更新するための処理ステップである。
【００４６】
まず、ST2において、モノスタティック・レーダ局での、円測位による目標位置ベクトルz_k ^(c)を入力し、また、バイスタティック受信局での、楕円測位による目標位置ベクトルz_k ^(e) 、あるいは、双曲線測位による目標位置ベクトルz_k ^(h) のいずれかを入力する。ここで、本実施の形態の目標追尾方法では、楕円測位と双曲線測位のいずれの目標位置ベクトルを入力するかは、各サンプリングにおいて、予め選択されているものとする。
次に、ST3において、このサンプリングにおける距離r,ρ、角度φ_m , θ_m, φ_b , θ_bの観測誤差分散σ _r ² , σ_ρ ² , σ_{φ m} ², σ_{θ m} ², σ_{φ b} ² , σ_{θ b} ²のデータ群を入力する。
【００４７】
次に、ST4に進む。この処理ステップでは、以下に示すカルマンフィルタの予測アルゴリズムに従って、サンプリング間隔分の予測処理を行う。
ここで、ハットx _k|k -₁は状態ベクトル予測値を、また、 P_k|k -₁は予測誤差共分散行列を表す。
【００４８】
【数１２】

【００４９】
次に、ST5では、前記式(26)により、円測位の目標位置ベクトルz_k ^(c)の測位誤差共分散行列S^(c)を算出する。
次に、ST6において、モノスタティック・レーダ局で得られた、円測位による目標位置ベクトルz_k ^(c)を用いて、状態ベクトル推定値の更新処理を実行する。この更新処理では、以下の、カルマンフィルタの更新アルゴリズムを使用することができる。ここで、ハットx _k|k ^(c)は z_k ^(c)による更新後の状態ベクトル、 P_k|k ^(c)はハットx _k|k ^(c)の誤差共分散行列である。また、式(40)のK_k ^(c)はカルマンゲイン行列である。なお、この更新アルゴリズムにおいて、ST4で算出した状態ベクトル予測値ハットx _k|k -₁ と予測誤差共分散行列P_k|k-₁ 、および、ST5で算出した円測位の測位誤差共分散行列S^(c)を使用する。
【００５０】
【数１３】

【００５１】
次に、バイスタティック受信局で得られた、楕円測位による目標位置ベクトルz_k ^(e)、あるいは双曲線測位による目標位置ベクトル z_k ^(h) を用いて、上記ハットx _k|k ^(c)をさらに更新するための処理ステップに進む。
ST7では、バイスタティック受信局での測位結果として、楕円測位または双曲線測位のいずれの目標位置ベクトルが入力されたかを判断する。楕円測位の目標位置ベクトルが入力された場合にはST8に進み、双曲線測位の目標位置ベクトルが入力された場合にはST10に進む。
【００５２】
まず、楕円測位の目標位置ベクトルが入力された場合は、ST8において、前記式(27)により楕円測位の目標位置ベクトルz_k ^(e)の測位誤差共分散行列S_k ^(e)を算出する。
次にST9において、楕円測位の目標位置ベクトルz_k ^(e)を用いて更新処理を行う。ここで、楕円測位の目標位置ベクトルが入力された場合は、上記円測位の場合と同様に、以下に示すカルマンフィルタの更新アルゴリズムを使用することが可能である。この更新アルゴリズムでは、ST8で算出したz_k ^(e)の測位誤差共分散行列S_k ^(e)を使用する。
【００５３】
【数１４】

【００５４】
なお、上記のように、楕円測位の場合に、カルマンフィルタの更新アルゴリズムを適用できるのは、 z_k ^(e) の誤差が、先に用いた円測位の目標位置ベクトルz_k ^(c)との誤差と無相関であるためである。
【００５５】
一方、双曲線測位による目標位置ベクトルが入力された場合は、ST10に進む。ST10では、前記式(28)により、双曲線測位の目標位置ベクトル z_k ^(h) の測位誤差共分散行列S_k ^(h) を算出する。
さらに、ST11において、円測位の目標位置ベクトルz_k ^(c)の誤差と双曲線測位の位置ベクトルz_k ^(h) の誤差との相互相関行列 C_k ^(ch) を、前記式(30)により算出する。次に、ST12〜ST14の３つの処理ステップによる更新処理に進む。
【００５６】
双曲線測位の目標位置ベクトルz_k ^(h) を用いて前記ハットx _k|k ^(c) の更新を行う場合、 z_k ^(h) の誤差が、ST6で用いた円測位の目標位置ベクトルz_k ^(c)の誤差と相関を持つため、カルマンフィルタの更新アルゴリズムが使用できない。
このため、ST12〜ST14においては、以下に示す式(46)〜(48)に従い更新処理を実行する。
ここで、式(46)〜(48)の算出式は、この発明において新たに導出されたアルゴリズムであり、 z_k ^(h)の誤差がz_k ^(c)の誤差と相関を持つ場合に、２乗平均誤差を最小化する最適な推定値を算出することができる。
【００５７】
まず、ST12において、式(46)に従い、フィルタゲイン行列 K_k ^(h) を算出する。このフィルタゲイン行列は、上記z_k ^(h)の誤差とz_k ^(c)の誤差の相関を考慮して更新処理を行うためのゲイン行列であり、その算出にあたっては、ST10で算出したz_k ^(h)の誤差共分散行列S_k ^(h)、ST11で算出したz_k ^(c)とz_k ^(h)の相互相関行列 C_k ^(ch) と、さらに、ST6で算出したカルマンゲイン行列K_k ^(c)および推定誤差共分散行列P _k|k ^(c) を用いている。
【００５８】
次に、ST13では、式(47)に従い、上記算出したフィルタゲイン行列 K_k ^(h)と双曲線測位による目標位置ベクトルz_k ^(h)を用いて、ST6で算出した状態ベクトル推定値ハットx _k|k ^(c) を新たな推定値ハットx _k|k ^(h)に更新する。
さらに、ST14では、ST11で算出したC_k ^(ch) 、ST12で算出したフィルタゲイン行列 K_k ^(h)、ST6で算出したカルマンゲイン行列K_k ^(c) を用いて、推定誤差共分散行列P_k|k ^(c) をP_k|k ^(h)に更新する。 P_k|k ^(h)は式(47)の状態ベクトル推定値ハットx _k|k ^(h)の誤差共分散行列に相当する。
【００５９】
【数１５】

【００６０】
以上が、サンプリングkにおける更新処理である。なお、サンプリングkの更新処理は、楕円測位の目標位置ベクトルを用いた更新処理の結果によるハットx _k|k ^(e) とP _k|k ^(e) 、あるいは、双曲線測位の目標位置ベクトルを用いた更新処理の結果によるハットx _k|k ^(h)とP _k|k ^(h) を、このサンプリングにおける最終的な状態ベクトル推定値ハットx _k|k 、および推定誤差共分散行列P _k|k として終了する。即ち、式(49),(50)あるいは式(51),(52)とする。
【００６１】
【数１６】

【００６２】
最後にST15では、追尾終了か否かを判断し、追尾終了の場合には処理を終了し、追尾継続の場合にはST2に戻り、以降、追尾終了まで、上記ST2〜ST14の処理ステップを各サンプリングにおいて繰り返す。
【００６３】
ところで、上記処理手順では、まず円測位による結果で推定値の更新処理を行った後、次に楕円測位または双曲線測位の結果による更新処理を行ったが、逆に、まず楕円測位または双曲線測位を用い、次に円測位を使用することも可能である。この場合、楕円測位または双曲線測位の結果による更新処理でカルマンフィルタの更新アルゴリズムを用いた後、円測位の結果による更新処理において、先に楕円測位による結果を用いた場合にはカルマンフィルタの更新アルゴリズムを、また、先に双曲線測位による結果を用いた場合には上記式(46)〜(48)の形式のアルゴリズムを使用すればよい。
【００６４】
以上のように、この発明の目標追尾方法の実施の形態１によれば、円測位と、楕円測位または双曲線測位の、両方の結果を用いて状態ベクトル推定値の更新を行うことによって、モノスタティック・レーダ局による観測情報とバイスタティック受信局による観測情報が共に推定値の中に取り込まれる結果となって、追尾精度の向上が可能である。
特に、バイスタティック受信局の情報として双曲線測位による結果を使用する場合にも、式(46)〜(48)のアルゴリズムを使用することにより、円測位結果の誤差と双曲線測位結果の誤差の相互相関による影響を考慮した最適な推定値が算出されるため、両局の情報の融合による精度向上効果を一層高めることができる。
【００６５】
実施の形態２
図３はこの発明の目標追尾装置の実施の形態２を示す構成ブロック図である。コこの実施の形態２は、上記実施の形態１に示した目標追尾方法を実施する目標追尾装置の構成例を示すものである。
図において、1は目標追尾処理装置、2は円測位を行うモノスタティック・レーダ局のデータ処理器、3は双曲線測位を行う第1のバイスタティックデータ処理器、4は楕円測位を行う第2のバイスタティックデータ処理器、5は選択器、6は表示器、7は観測誤差分散設定器である。これらの内、2,3,4,5,6は図６の従来の装置の各対応部位に相当する。
【００６６】
目標追尾装置1は、推定部8およびゲイン設定部9により構成される。
さらに、推定部8は、目標の位置、速度の成分から構成される状態ベクトルの推定値を格納する推定値用メモリ10、１サンプリング後の状態ベクトルの値を予測する予測処理器11、予測位置と測位結果による目標位置の残差を算出する残差算出器12、現サンプリング時刻の状態ベクトルを推定する更新処理器13により構成される。
【００６７】
また、ゲイン設定部9は、状態ベクトル推定値の誤差共分散行列を格納する推定誤差共分散行列用メモリ14、状態ベクトル予測値の誤差共分散行列を算出する予測誤差共分散行列算出器15、測位誤差共分散行列算出器16、測位誤差相互相関行列算出器17、カルマンフィルタのゲイン行列を算出する第1のゲイン行列算出器18、カルマンゲインを用いて更新を行った場合の推定値の誤差共分散行列を算出する第1の推定誤差共分散行列算出器19、カルマンフィルタとは異なる新たなフィルタのゲイン行列を算出する第2のゲイン行列算出器20、このフィルタゲインを用いて更新を行った場合の推定値の誤差共分散行列を算出する第２の推定誤差共分散行列算出器21により構成される。
【００６８】
次に図３を参照して、この発明の本実施の形態２の動作について説明する。
図において、推定値用メモリ10に状態ベクトル推定値の初期値ハットｘ_0|0 を設定し、また推定誤差共分散行列用メモリ14に推定誤差共分散行列の初期値Ｐ_0|0を設定して追尾処理が開始される。
サンプリングkにおいて、モノスタティック・レーダ局およびバイスタティック受信局により目標の新たな観測が為されると、まずモノスタティック・レーダ局のデータ処理器2において、円測位が行われ目標位置ベクトルz_k ^(c) が算出される。
さらに、第1のバイスタティックデータ処理器3において、双曲線測位が行われて目標位置ベクトルz_k ^(h) が、また第2のバイスタティックデータ処理器4において、楕円測位が行われて目標位置ベクトルz_k ^(e)が算出される。
２つのバイスタティックデータ処理器3,4による目標位置ベクトルz_k ^(h) , z_k ^(e)は、選択器5においていずれか一方が選択された後、データ処理器2からの目標位置ベクトルz_k ^(c) と共に、目標追尾装置1に入力される。
【００６９】
一方、観測誤差共分散設定器7では、このサンプリングにおける距離r,ρ、角度φ_m , θ_m , φ_b , θ_bの観測誤差分散σ _r ² , σ_ρ ² , σ_{φ m} ², σ_{θ m} ²,σ_{φ b} ² ,
σ_{θ b} ²が設定され、目標追尾装置1に入力される。
これらの観測誤差分散は、予め目標の存在領域に応じてデータベース化されたものを参照して設定することもできれば、また、各観測毎に入力信号のＳ／Ｎ比等から推定して設定することもできる。
【００７０】
上記データ群が入力されると、目標追尾装置1では、まず推定部8において、推定値用メモリ10より前サンプリングk-1の状態ベクトル推定値 ハットx _{k -1|k -1} が読み出され、予測処理器11が、式(38)に従い状態ベクトル予測値を算出する。
また、ゲイン設定部9において、推定誤差共分散行列用メモリ14より前サンプリングk-1の推定誤差共分散行列Ｐ_{k -1|k -1}が読み出され、予測誤差共分散行列算出器15が式(39)に従い予測誤差共分散行列Ｐ_{k|k -1}を算出する。
【００７１】
次に、円測位の目標位置ベクトルを用いた状態ベクトル推定値の更新処理に進む。
まず、測位誤差共分散行列算出器16において、式(26)に従って、円測位の目標位置ベクトルの誤差共分散行列S^(c)を算出する。
次に第１のゲイン行列算出器18において、予測誤差共分散行列P_k|k-1と測位誤差の共分散行列S^(c)とを入力し、式(40)に従いゲイン行列K _k ^{(c )} を算出して、更新処理器13および第１の推定誤差共分散行列算出器19に送る。
第１の推定誤差共分散行列算出器19では、式(42)に従い、更新後の推定誤差共分散行列Ｐ_{k |k} ^{(c )} を算出しておく。
【００７２】
一方、残差算出器12では、予測処理器11による状態ベクトル予測値と円測位の目標位置ベクトル z_k ^{(c )}を入力し、予測位置と測位結果の目標位置の差z _k ^(c)−Ｈハットx _{k -1|k -1} （いわゆる残差）を算出して、更新処理器13に送る。
更新処理器13は、ゲイン設定部9より送られてきたゲイン行列K_k ^{(c )} を用い、式(41)に従って更新を行う。更新後の状態ベクトル推定値ハットx_k|k ^{(c )}は再び残差算出器12に送出しておく。
【００７３】
次に、楕円測位または双曲線測位による目標位置ベクトルを用いた更新処理に移る。
この処理では、選択器5において、楕円測位の結果が選択されたか、双曲線測位の結果が選択されたかによって、推定部8の動作は変わらないものの、ゲイン設定部9の動作が変更される。
【００７４】
まず、ゲイン設定部9の動作について説明する。ゲイン設定部9では選択器5より、楕円測位あるいは双曲線測位のいずれの結果が選択されたかの指令信号を受けることにより、以下のように動作が切り換わる。
まず、楕円測位の結果が選択された場合は、以下のように動作する。測位誤差共分散行列算出器16において、式(27)に従って、楕円測位による目標位置ベクトル z^(e) _k の誤差共分散Ｓ^(e) が算出される。
【００７５】
次に、第１のゲイン行列算出器18において、第１の推定誤差共分散行列算出器19より、円測位結果による更新処理後の推定誤差共分散行列 Ｐ_k|k ^{(c )}を入力し、これと上記Ｓ^(e) を用い、式(43)に従ってゲイン行列 Ｋ_k ^(e) を算出する。このゲイン行列は推定部8の更新処理器13に送られる。
また、第１の推定誤差共分散行列算出器19では、式(45)に従って楕円測位結果による更新処理後の推定誤差共分散行列 Ｐ_k|k ^(e) を算出し、これをこのサンプリングの最終的な推定誤差共分散行列 Ｐ_k|kとして、推定誤差共分散行列用メモリ14に書き込んで処理を終了する。
【００７６】
これに対し、選択器5において双曲線測位の結果が選択された場合は、以下のように動作する。まず、測位誤差共分散行列算出器16において、式(28)に従い、双曲線測位の目標位置ベクトルの誤差共分散行列S^(h)を算出すると共に、測位誤差相互相関行列算出器17において、式(30)に従い、双曲線測位の誤差と円測位の誤差の相互相関行列Ｃ^(ch)を算出する。
【００７７】
次に第２のゲイン行列算出器20において、第１のゲイン行列算出器18より円測位結果による更新処理で用いたゲイン行列 Ｋ_k ^{(c )}を入力し、第１の推定誤差共分散行列算出器19より、円測位結果による更新処理後の推定誤差共分散行列Ｐ_k|k ^{(c )} を入力し、これらの値と上記S^(h), Ｃ^(ch)より、式(46)に従ってゲイン行列Ｋ_k ^(h)を算出する。このゲイン行列は推定部8の更新処理器13に送出する。
【００７８】
また、第２の推定誤差共分散行列算出器21では、上記S^(h), Ｃ^(ch)とゲイン行列Ｋ_k ^{(c )} , Ｋ_k ^(h)およびＰ _k|k ^{(c )}を入力して、式(48)に従い、双曲線測位の結果による更新処理後の推定誤差共分散行列Ｐ _k|k ^(h)を算出し、これをこのサンプリングの最終的な推定誤差共分散行列Ｐ _k|k として、推定誤差共分散行列用メモリ14に書き込んで処理を終了する。
【００７９】
次に、推定部8の動作について説明する。推定部8では、残差算出器12において、上記の円測位結果による更新処理後の状態ベクトル推定値ハットx_k|k ^{(c )} が示す目標位置と、選択器5より送られてきた楕円測位の目標位置ベクトル z_k ^(e)（ または双曲線測位による目標位置ベクトル z_k ^(h) ）との残差 z_k ^(e)−Hハットx_k|k ^{(c )} （ または z_k ^(h)−Hハットx_k|k ^{(c )} ) を算出し、更新処理器13に送る。
更新処理器13では、ゲイン設定部9よりゲイン行列 Ｋ_k ^(e)（ またはＫ_k ^(h) ）を入力し、式(44)（ または式(47) ）に従って更新を行う。更新処理器13による更新後の状態ベクトル推定値ハット x_k|k ^(e) （ またはハット x _k|k ^(h) ）は、このサンプリングにおける最終的な状態ベクトル推定値ハット x _k|k として推定値用メモリ10に書き込まれると共に、表示器6に送出されて運用者に示される。
以上で、サンプリングkにおける動作が終了する。以降、追尾終了まで、各サンプリング毎に上記処理が繰り返し実行される。
【００８０】
以上のように、この発明の目標追尾装置の実施の形態２によれば、円測位と、楕円測位または双曲線測位の、両方の結果を用いて状態ベクトル推定値の更新を行うことによって、モノスタティック・レーダ局による観測情報とバイスタティック受信局による観測情報が共に推定値の中に取り込まれる結果となって、追尾精度の向上が可能である。
特に、バイスタティック受信局の情報として双曲線測位による結果を使用する場合にも、式(46)〜(48)のアルゴリズムを使用することにより、円測位結果の誤差と双曲線測位結果の誤差の相互相関による影響を考慮した最適な推定値が算出されるため、両局の情報の融合による精度向上効果を一層高めることができる。
【００８１】
実施の形態３
図４はこの発明の目標追尾方法の実施の形態３を説明するフローチャートである。
図において、ST16はモノスタティック・レーダ局での円測位による目標位置ベクトルと、バイスタティック受信局での楕円測位および双曲線測位による目標位置ベクトルを入力するステップ、
ST17は楕円測位の目標位置ベクトルを用いて更新処理を行った場合の推定誤差共分散行列を算出するステップ、
ST18は楕円測位の目標位置ベクトルを用いて更新処理を行った場合の推定誤差共分散行列の評価値を算出するステップ、
ST19は双曲線測位の目標位置ベクトルを用いて更新処理を行った場合の推定誤差共分散行列の評価値を算出するステップ、
ST20は上記二つの評価値の大小を判断するステップ、ST21は楕円測位の目標位置ベクトルを用いて状態ベクトル推定値を算出するするステップである。
また、図１の実施の形態１で説明したフローチャートと同一の処理ステップには、同一符号を付して説明を省く。
【００８２】
この発明の目標追尾方法の実施の形態３の処理手順を詳しく説明するのに先立ち、この実施の形態の背景理論を説明する。
前記実施の形態１で説明したように、楕円測位の目標位置ベクトルz_k ^(e)を用いて更新処理を行う場合、式(43)〜(45)の更新アルゴリズムが使用できる。
ここで、式(45)による推定誤差共分散行列P _k|k ^(e) は、式(43)によるゲイン行列K _k ^(e) を算出した後、実際に式(44)による状態ベクトル推定値の更新処理を行う以前に算出することが可能である。即ちP _k|k ^(e) は、式(44)により更新処理を行った場合の推定誤差に係わる見積もり値を示している。
同様に、双曲線測位による目標位置ベクトル z_k ^(h)を用いて更新処理を行う場合の更新アルゴリズムは式(46)〜(48)であるが、式(48)による推定誤差共分散行列P _k|k ^(h) は、式(46)によるゲイン行列K_k ^(h)を算出した後、式(47)による状態ベクトル推定値の更新処理を行う以前に算出することができる。 P _k|k ^(h)は、式(44)による更新処理を行った場合の推定誤差に係わる見積もり値を示している。
【００８３】
上記のことから、事前に、式(45),(48)の推定誤差共分散行列P _k|k ^(e) , P _k|k ^(h)を算出し、これらの値を比較することによって、楕円測位の目標位置ベクトルによる状態ベクトル推定値の更新（式(44)）を実行するか、双曲線測位による目標位置ベクトルによる状態ベクトル推定値の更新（式(47)）を実行するかを選択することが可能である。
なお、２つの推定誤差共分散行列P _k|k ^(e) , P _k|k ^(h)の大小を比較するためには、これらの行列の大きさをスカラ値によって評価することが必要であるが、このような評価値として、例えば、以下の式に示す値が採用できる。ただし、β^(e) は楕円測位の場合の評価値、β^(h)は双曲線測位の場合の評価値であり、detは行列の行列式をとることを表す。
【００８４】
【数１７】

【００８５】
以上より、２つの評価値β^(e) , β^(h) を式(49),(50)により算出し、β^(e) がβ^(h) より小さい場合には、式(44)による楕円測位の目標位置ベクトル z_k ^(e) を用いた更新処理を実行し、逆に、β^(h)がβ^(e) より小さい場合には、式(47)による双曲線測位の目標位置ベクトルz_k ^(h) を用いた更新処理を実行すればよい。
以上で、この実施の形態３の処理手順の背景理論の説明を終わる。
【００８６】
次に、図４を参照して、この発明の目標追尾方法の実施の形態３を示す処理手順を詳しく説明する。
まず、ST1において、実施の形態１の場合と同様に、初期２回のサンプリングの目標位置ベクトルから、状態ベクトル推定値と推定誤差共分散行列の初期値を設定し、追尾処理を開始する。以降、３回目のサンプリングから、ST16以下の一連の処理ステップを各サンプリングにおいて実行する。
各サンプリングでは、まず、ST16において、モノスタティック・レーダ局での、円測位による目標位置ベクトルz_k ^(c)と、バイスタティック受信局での、楕円測位による目標位置ベクトルz_k ^(e) 、及び双曲線測位による目標位置ベクトルz_k ^(h) とを入力する。
ここで、実施の形態１の場合と異なるのは、バイスタティック受信局での測位結果として、楕円測位による目標位置ベクトルと、双曲線測位による目標位置ベクトルの双方を入力する点である。
【００８７】
次に、ST3,ST4,ST5,ST6までの処理手順は、実施の形態１の図１の場合と同様である。さらに、ST8では、前記式(27)により楕円測位の目標位置ベクトルz_k ^{(e )} の測位誤差共分散行列S_k ^(e) を算出し、ST10では、前記式(28)により、双曲線測位の目標位置ベクトル z_k ^(h) の測位誤差共分散行列S_k ^(h) を算出し、ST11では、前記式(30)により、円測位の目標位置ベクトルz_k ^(c) の誤差と双曲線測位の目標位置ベクトル z_k ^(h) の誤差との相互相関行列 C_k ^(ch) を算出する。
【００８８】
次にST17では、楕円測位による目標位置ベクトル z_k ^(e) を用いて、ST6で算出した状態ベクトル推定値ハットx _k|k ^(c) をさらに更新した場合の、推定誤差共分散行列のみを算出する。即ち、ST6で算出した推定誤差共分散行列Ｐ_k|k ^(c)とST8で算出した楕円測位の測位誤差共分散行列S_k ^(e) を用いて、前記式(43)により、カルマンゲイン行列K_k ^(e) を算出し、更に、式(45)に従い、推定誤差共分散行列P _k|k ^(e) を算出する。
【００８９】
次に、ST12とST14は、双曲線測位による目標位置ベクトル z_k ^(h) を用いて、ST6で算出した状態ベクトル推定値ハットx _k|k ^(c) を更新した場合の、推定誤差共分散行列を算出するための処理ステップである。即ち、ST12において、ST6で算出したカルマンゲイン行列K_k ^(c) および推定誤差共分散行列Ｐ_k|k ^(c)、ST10で算出した z_k ^(h) の誤差共分散行列S_k ^(h)、ST11で算出した z_k ^(c)とz ^(h) の相互相関行列 C_k ^(ch) を用い、式(46)に従い、フィルタゲイン行列K_k ^(h)を算出し、更に、ST14において、ST6で算出したカルマンゲイン行列K_k ^(c) 、ST11で算出した C_k ^(ch) 、ST12で算出したフィルタゲイン行列K_k ^(h)を用いて推定誤差共分散行列Ｐ_k|k ^(h)を算出する。
なお、上記までの処理において、式(44)または式(47)による、状態ベクトル推定値自体の更新は、まだ行われていない。
【００９０】
次に、ST18では、式(53)に従い、楕円測位による目標位置ベクトルで状態ベクトル推定値を更新した場合の推定誤差共分散行列Ｐ_k|k ^(e) の評価値β^(e) を算出する。また、ST19で、双曲線測位による目標位置ベクトルで状態ベクトル推定値を更新した場合の推定誤差共分散行列Ｐ_k|k ^(h)の評価値β^(h)を算出する。
【００９１】
次に、ST20において、上記算出した二つの評価値β^(e)，β^(h)の大小を判断し、β^(e)の方が小さい場合は、楕円測位による目標位置ベクトルで状態ベクトル推定値を更新するためのST21に進み、逆にβ^(h)の方が小さい場合には、双曲線測位による目標位置ベクトルで状態ベクトル推定値を更新するためのST13に進む。
ST21では、式(44)により、楕円測位の目標位置ベクトル z_k ^(e) を用いて、ST6で算出した状態ベクトル推定値ハットx _k|k ^(c)を更新する。この際、ST17で算出したカルマンゲイン行列K_k ^(e) を使用する。一方、ST13では、式(47)により、双曲線測位の目標位置ベクトルz_k ^(h) を用いて、ST6で算出した状態ベクトル推定値ハットx _k|k ^(c)を更新する。この際、ST12で算出したフィルタゲイン行列K_k ^(h) を使用する。
【００９２】
以上で、サンプリングkにおける更新処理が終了する。なお、ST20において、楕円測位の目標位置ベクトルを用いた更新処理（ST21）が選択された場合には、ST21の結果によるハットx _k|k ^(e) とST17の結果によるＰ_k|k ^(e) を、このサンプリングにおける最終的な状態ベクトル推定値ハットx _k|k 、および推定誤差共分散行列Ｐ_k|k とし、また、双曲線測位の目標位置ベクトルを用いた更新処理（ST13）が選択された場合には、ST13の結果によるハットx _k|k ^(h) とST14の結果による Ｐ_k|k ^(h) を、このサンプリングにおける最終的な状態ベクトル推定値ハットx _k|k 、および推定誤差共分散行列Ｐ_k|k として、サンプリングkにおける更新処理を終了する。
最後にST15では、追尾終了か否かを判断し、追尾終了の場合には処理を終了し、追尾継続の場合にはST2に戻り、以降、追尾終了まで、上記一連の処理ステップを各サンプリングにおいて繰り返す。
【００９３】
以上のように、この発明の目標追尾方法の実施の形態３によれば、円測位の結果と楕円測位の結果を用いて状態ベクトルの更新を行った場合の推定誤差と、円測位の結果と双曲線測位の結果を用いて状態ベクトルの更新を行った場合の推定誤差の、それぞれの誤差を事前に評価し、推定誤差の小さい方を選択することにより、楕円測位または双曲線測位のいずれの結果を使用するかを決定することができる。
このため、各サンプリング毎に、上記２つのうちの、期待される追尾精度の高い方の測位結果が選択されて、結果的に、モノスタティック・レーダ局とバイスタティック受信局の観測情報の融合効果を、より一層高めることができる。
【００９４】
実施の形態４．
図５はこの発明の目標追尾装置の実施の形態４を示す構成ブロック図である。この実施の形態４は、上記実施の形態３に示した目標追尾方法を実施する目標追尾装置の構成例を示すものである。
また、図５において、図３に示した実施の形態２では、外部の選択器5で楕円測位による目標位置ベクトルか、双曲線測位による目標位置ベクトルかを選択して入力するのに対して、目標追尾装置1の中に選択機能を有する選択部25を持たせた構成となっている。
図において、選択部25は、第１の推定誤差評価器26、第２の推定誤差評価器27、比較器28、選択処理器29より構成され、他の部位は図３の装置の場合と同様の構成である。
【００９５】
図５を参照して、この目標追尾装置の実施の形態４の動作について説明する。
図において、推定値用メモリ10に状態ベクトル推定値の初期値ハットｘ_0|0を設定し、また推定誤差共分散行列用メモリ14に推定誤差共分散行列の初期値Ｐ_0|0を設定して追尾処理が開始される。
サンプリングkにおいて、モノスタティック・レーダ局およびバイスタティック受信局により目標の新たな観測がなされると、データ処理器2により円測位による目標位置ベクトルz_k ^{(c )} が算出され、さらに、第1のバイスタティックデータ処理器3により、双曲線測位による目標位置ベクトル z_k ^(h) が算出され、また第2のバイスタティックデータ処理器4により、楕円測位による目標位置ベクトルz_k ^(e) が算出される。目標位置ベクトルz_k ^{(c )} _, z_k ^(h) _, z_k ^(e) は共に、目標追尾装置1に入力される。
【００９６】
また、観測誤差共分散設定器7では、このサンプリングにおける距離r,ρ、角度φ_m , θ_m , φ_b , θ_bの観測誤差分散σ_r ² _,σ_ρ ² , σ_{φ m} ² , σ_{θ m} ² , σ_{φ b} ²,
σ_{θ b} ² が設定され、目標追尾装置1に入力される。
次に、目標追尾装置1は、式(38),(39)の予測処理および式(40)〜(42)の円測位の目標位置ベクトルによる更新処理を行うまでは、図３の実施の形態２の場合と同様に動作する。
【００９７】
即ち、予測処理器11が、推定値用メモリ10より前サンプリングの状態ベクトル推定値ハットｘ_k-1|k-1 を読み出し、状態ベクトル予測値ハットｘ_k|k-1を算出する。また、予測誤差共分散行列算出器15が、推定誤差共分散行列用メモリ14より前サンプリングの推定誤差共分散行列Ｐ_{k -1|k -1} を読み出し、予測誤差共分散行列Ｐ_{k |k -1}を算出する。
【００９８】
次に、円測位の目標位置ベクトルを用いた状態ベクトル推定値の更新処理に進み、ゲイン設定部9では、測位誤差共分散行列算出器16が、円測位の目標位置ベクトルの誤差共分散行列Ｓ^{(c )}を算出し、次に第１のゲイン行列算出器18が、式(40)のゲイン行列Ｋ_k ^{(c )} を算出して、更新処理器13および第１の推定誤差共分散行列算出器19に送る。また、第１の推定誤差共分散行列算出器19が、更新後の推定誤差共分散行列Ｐ _k|k ^{(c )} を算出しておく。
一方、推定部8では、残差算出器12が、状態ベクトル予測値による予測位置と円測位結果の目標位置との残差z_k ^{(c )}−Ｈハットｘ_k|k-1 を算出し、更新処理器13において、ゲイン設定部9より入力したゲイン行列Ｋ_k ^{(c )} を用いて、更新を行って、更新結果の状態ベクトル推定値ハットx_k|k ^{(c )}を得る。
【００９９】
この段階で、更新処理器13では円測位結果による更新処理後の状態ベクトル推定値ハットx_k|k ^{(c )} が、第１の推定誤差共分散行列算出器19ではハットx_k|k ^{(c )}の誤差共分散行列 Ｐ_k|k ^(c)が得られている。また、第１のゲイン行列算出器18ではゲイン行列 Ｋ_k ^{(c )}が得られている。
【０１００】
次に、楕円測位または双曲線測位による目標位置ベクトルを用いた更新処理について、本実施の形態は以下のように動作する。
まず、ゲイン設定部9の動作から説明する。前記実施の形態１のゲイン設定部が、楕円測位と双曲線測位のいずれの目標位置ベクトルが装置に入力されたかによって動作を切り換え、楕円測位結果用のゲイン行列 Ｋ _k ^(e)あるいは双曲線測位結果用のゲイン行列Ｋ_k ^(h)の、いずれか一方を算出するよう動作したのに対し、本実施の形態のゲイン設定部9は、上記ゲイン行列の両方を算出する。
【０１０１】
まず、円測位結果による更新処理で用いたゲイン行列 Ｋ_k ^{(c )} は、第１のゲイン行列算出器18から第２のゲイン行列算出器20に送出しておく。また、測位誤差共分散行列算出器16において、式(27),(28)に従い、楕円測位による目標位置ベクトルz_k ^(e) の誤差共分散Ｓ^(e) と双曲線測位の目標位置ベクトルの誤差共分散行列Ｓ^(h)を算出し、さらに、測位誤差相互相関行列算出器17において、式(30)に従い、双曲線測位の誤差と円測位の誤差の相互相関行列C^(ch) を算出する。
【０１０２】
次に、第１のゲイン行列算出器18において、第１の推定誤差共分散行列算出器19より、円測位結果による更新処理後の推定誤差共分散行列 P_k|k ^{(c )} を入力し、これと上記Ｓ^(e) を用い、式(43)に従い、ゲイン行列K_k ^(e) を算出する。このゲイン行列K_k ^(e) は選択部25の選択処理器29に送る。
また、第１の推定誤差共分散行列算出器19が、式(45)に従い、楕円測位結果による更新処理を行った場合の推定誤差共分散行列 P_k|k ^(e) を算出する。
この P_k|k ^(e) は選択部25の第１の推定誤差評価器26に送る。
【０１０３】
さらに、第２のゲイン行列算出器20において、第１の推定誤差共分散行列算出器19より円測位結果による更新処理後の推定誤差共分散行列 P _k|k ^{(c )} を入力し、これらの値と上記Ｓ^(h) , C^(ch) 、および、予め第１のゲイン行列算出器18より入力しておいたゲイン行列 Ｋ_k ^{(c )} を用い、式(46)に従って、ゲイン行列Ｋ_k ^(h)を算出する。このゲイン行列は選択部25の選択処理器29に送出する。
また、第２の推定誤差共分散行列算出器21では、上記Ｓ^(h) , C^(ch) とゲイン行列Ｋ_k ^{(c )}, Ｋ _k ^(h) およびP_k|k ^{(c )} を入力して、式(48)に従い、双曲線測位の結果による更新処理を行った場合の推定誤差共分散行列P_k|k ^(h) を算出する。
この P _k|k ^(h) は選択部25の第２の推定誤差評価器27に送る。
【０１０４】
次に選択部25に移り、第１の推定誤差評価器26が、式(53)に従い、楕円測位結果による更新処理を行った場合の推定誤差共分散行列 Ｐ _k|k ^(e)の評価値β^(e)を算出し、
また、第２の推定誤差評価器27が、式(54)に従い、双曲線測位の結果による更新処理を行った場合の推定誤差共分散行列P_k|k ^(h) の評価値β^(h) を算出する。これらの評価値は比較器28に送られる。
比較器28は、上記入力した２つの評価値のいずれが小さいかを判断して、比較結果の識別信号を選択処理器29に送る。
選択処理器29は、上記識別信号に従い、楕円測位または双曲線測位のいずれかを選択して、目標位置ベクトル z_k ^(h) または z_k ^(e)のいずれか一方を残差算出器12に、また、ゲイン行列Ｋ_k ^(e) または Ｋ_k ^(h)のいずれか一方を更新処理器13に送る。
【０１０５】
最後に、推定部8が z_k ^(h) または z_k ^(e) を用いた状態ベクトル推定値の更新を行う。この際の推定部8の動作は、図3の実施の形態１の場合と同様である。即ち、残差算出器12が、円測位結果による更新処理後の状態ベクトル推定値ハットx_k|k ^{(c )} の目標位置と、選択処理器29より送られてきた目標位置ベクトル z_k ^(h) （またはz_k ^(e) ）との残差 z_k ^(e) −Ｈハットx_k|k ^{(c )}（ またはz_k ^(h) −Ｈハットx_k|k ^{(c )} ）を算出し、更新処理器13に送る。更新処理器13は、選択処理器29より送られてきたゲイン行列 K_k ^(e)（またはＫ_k ^(h) ）を入力し、式(44)（または式(47) ）に従って更新を行う。
【０１０６】
更新処理器13による更新後の状態ベクトル推定値 ハットx_k|k ^(e) （またはハットx_k|k ^(h) ）は、このサンプリングにおける最終的な状態ベクトル推定値ハットx _k|k として推定値用メモリ10に書き込まれると共に、表示器6に送出されて運用者に示される。
以上が、サンプリングkにおける動作である。以降、追尾処理まで、各サンプリングにおいて上記一連の動作が繰り返される。
【０１０７】
以上のように、この発明の目標追尾装置の実施の形態４によれば、円測位の結果と楕円測位の結果を用いて状態ベクトルの更新を行った場合の推定誤差と、円測位の結果と双曲線測位の結果を用いて状態ベクトルの更新を行った場合の推定誤差の、それぞれの誤差を事前に評価し、推定誤差の小さい方を選択することにより、楕円測位または双曲線測位のいずれの結果を使用するかを決定することができる。
このため、各サンプリング毎に、上記楕円測位または双曲線測位のうちの、期待される追尾精度の高い方の測位結果が選択されて、結果的に、モノスタティック・レーダ局とバイスタティック受信局の観測情報の融合効果を、より一層高めることができる。
【０１０８】
【発明の効果】
以上のように、請求項１の発明によれば、モノスタティック・レーダ局とバイスタティック受信局からの測位情報を融合しながら目標追尾処理を行うのに、バイスタティック受信局からの測位情報として、双曲線による測位情報を使用する場合に、この測位情報とモノスタティック・レーダ局からの測位情報との誤差の相関を考慮して、目標位置、速度の最適な推定値を算出することができるフィルタアルゴリズムにより、追尾精度を向上した目標追尾方法を得ることが出来る。
【０１０９】
また、請求項２の発明によれば、モノスタティック・レーダ局とバイスタティック受信局からの測位情報を融合しながら目標追尾処理を行うのに、バイスタティック受信局からの測位情報として、双曲線による測位情報を使用する場合に、この測位情報とモノスタティック・レーダ局からの測位情報との誤差の相関を考慮して、目標位置、速度の最適な推定値を算出することができるフィルタアルゴリズムを備え、追尾精度を向上した目標追尾装置を得ることが出来る。
【０１１０】
また、請求項３の発明によれば、モノスタティック・レーダ局とバイスタティック受信局からの測位情報を融合しながら目標追尾処理を行うのに、バイスタティック受信局での測位情報として、双曲線による測位と楕円による測位のいずれか条件の良い方の測位情報を選択するため、上記の両測位情報を使用して追尾処理を行った場合に期待される追尾精度を観測条件に応じて評価して選択を行う、追尾精度を向上した目標追尾方法を得ることが出来る。
【０１１１】
また、請求項４の発明によれば、モノスタティック・レーダ局からの測位情報とバイスタティック受信局からの測位情報を融合しながら目標追尾処理を行うのに、バイスタティック受信局での測位情報として、双曲線による測位と楕円による測位のいずれか条件の良い方の測位情報を選択するため、上記の両測位情報を使用して追尾処理を行った場合に期待される追尾精度を観測条件に応じて評価して上記選択を行う手段を備え、追尾精度を向上した目標追尾装置を得ることが出来る。
【図面の簡単な説明】
【図１】 この発明の目標追尾方法の実施の形態１を説明するフローチャートである。
【図２】 この発明の実施の形態に共通のモノスタティック・レーダ局、バイスタティック受信局による目標測位とその座標系を説明する図である。
【図３】 この発明の目標追尾装置の実施の形態２を示す構成ブロック図である。
【図４】 この発明の目標追尾方法の実施の形態３を説明するフローチャートである。
【図５】 この発明の目標追尾装置の実施の形態４を示す構成ブロック図である。
【図６】 従来の装置を示す構成ブロック図である。
【図７】 従来の装置、およびこの発明の目標追尾装置の目標測位の動作原理を説明するための図である。（モノスタティック受信波とバイスタティック受信波の到来時間差による目標測位の場合）
【図８】 従来の装置、およびこの発明の目標追尾装置の目標測位の動作原理を説明するための図である。(モノスタティック送信波とバイスタティック受信波の時間差による目標測位の場合）
【符号の説明】
１ 目標追尾装置、２ データ処理器、３ バイスタティックデータ処理器、４ バイスタティックデータ処理器、５ 選択器、６ 表示器、７ 観測誤差分散設定器、８ 推定部、９ ゲイン設定部、１０ 推定値用メモリ、 １１ 予測処理器、１２ 残差算出器、１３ 更新処理器、１４ 推定誤差共分散行列用メモリ、１５ 予測誤差共分散行列算出器、１６ 測位誤差共分散行列算出器、１７ 測位誤差相互相関行列算出器、１８ 第１のゲイン行列算出器、１９ 第１の推定誤差共分散行列算出器、２０ 第2のゲイン行列算出器、２１ 第２の推定誤差共分散行列算出器、２５ 選択部、２６ 第１の推定誤差評価器、２７第2の推定誤差評価器、２８ 比較器、２９ 選択処理器。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a target tracking method and target tracking for estimating a target position, velocity, etc. by using the observation results of a monostatic radar and a bistatic radar for detecting a target of an aircraft, a ship, a vehicle, etc. The present invention relates to an apparatus, and more particularly to improvement of target tracking accuracy.
[0002]
[Prior art]
Conventionally, as this type of apparatus, for example, there is one disclosed in Japanese Patent Laid-Open No. 4-29080. FIG. 6 is a block diagram showing the configuration of the apparatus disclosed in the above document.
In the figure, 51, 52, 53, 54, 55, 56, 2 constitute a monostatic radar station 57, 51 is a transmitter, 52 is a transmission / reception switch, 53 is a transmission / reception antenna, 54 is a receiver, 55 is a A signal detector that performs target detection and distance measurement, 56 is a beam pointing angle detector, and 2 is a data processor that performs target positioning.
On the other hand, 58, 59, 60 and 61 constitute a bistatic receiving station 62, 58 is a receiving antenna, 59 is a receiver, 60 is a signal detector, and 61 is a beam pointing angle detector.
Furthermore, 63 is a detector for the arrival time difference between the monostatic reception wave and the bistatic reception wave, 3 is a first bistatic data processor that performs bistatic positioning using this arrival time difference, and 64 is a transmission wave and bistatic signal. Received wave time difference detector, 4 is a second bistatic data processor that performs bistatic positioning using this time difference, 5 is a selector, 65 is a correlation process between monostatic positioning information and bistatic positioning information The correlation positioning processor 6 performs precise measurement and tracking of the target position, and 6 is a display. Reference numeral 66 denotes a target such as an aircraft.
[0003]
The operation of the apparatus shown in FIG. 6 will be described. High-power electromagnetic waves generated by the transmitter 51 of the monostatic radar station 57 are radiated from the transmitting / receiving antenna 53 via the transmission / reception switch 52 to the space. The reflected wave by the target 66 of the transmission wave is received by both the transmission / reception antenna 53 of the monostatic radar station and the reception antenna 58 of the bistatic reception station.
The received signal at the monostatic radar station is subjected to reception processing such as amplification by the receiver 54 via the transmission / reception switch 52, and then the target is detected by the signal detector 55 and the arrival time of the received wave The distance information from the time difference between transmission and reception to the target is detected (so-called distance measurement). Further, the beam directivity angle detector 56 detects the directivity angle of the antenna beam by the transmission / reception antenna 53, and this angle information becomes a reference for detection of the target direction (so-called angle measurement). The distance measurement and angle measurement information is sent to the data processor 2, and the target position is calculated (so-called positioning).
[0004]
On the other hand, the reception signal obtained by the bistatic reception station 62 is subjected to reception processing such as amplification by the receiver 59, and then the target is detected by the signal detector 60 and the arrival time of the received wave is measured.
Next, the arrival time difference detector 63 detects the arrival time difference between the monostatic reception wave and the bistatic reception wave, and based on this information and the angle information from the beam directivity angle detector 61 of the bistatic reception antenna 58, the first difference is detected. Positioning is performed with the bistatic data processor 3.
The time difference detector 64 detects the time difference between the transmission wave from the monostatic radar station and the bistatic reception wave, and based on this information and the angle information from the beam pointing angle detector 61, the second bistatic data. Positioning is performed with the processor 4. The selector 5 selects one of the positioning results of the first and second bistatic data processors 3 and 4 according to the target area, and outputs it to the correlation positioning processor 65. The correlation positioning processor 65 performs precise measurement and tracking processing of the target position by correlation processing between the bistatic positioning information and the positioning information obtained by the monostatic radar station. This result is displayed on the display 6.
[0005]
The operation principle of the above apparatus will be described with reference to FIGS. FIG. 7 is a diagram for explaining the operation principle when positioning the target using information on the arrival time difference between the monostatic reception wave and the bistatic reception wave, and FIG. 8 uses information on the time difference between the transmission wave and the bistatic reception wave. It is a figure explaining the principle of operation in the case of positioning. 7 and 8, when the target is first observed from the transmission / reception antenna Tx / Rx of the monostatic radar station, the target is positioned as a point in the transmission / reception beam 68 on the circumference 67 centering on Tx / Rx. Is done. At this time, the position accuracy in the line of sight as viewed from the target Tx / Rx, that is, the distance measurement accuracy DR is determined by the measurement accuracy of the arrival time of the received signal in the signal detector 55, and this amount is relatively easy to achieve high accuracy. realizable.
On the other hand, the position accuracy ΔL in the tangential direction of the circle as viewed from Tx / Rx is proportional to the distance R to the target and can be expressed by the following equation.
ΔL = R ・ Δθ
Here, Δθ is the angle measurement accuracy, and this angle measurement accuracy basically depends on the antenna beam width although there is an accuracy improvement means such as monopulse angle measurement. In general, there is a limit to narrowing the antenna beam width (a very large-diameter antenna is required to form a narrow beam), so ΔL increases as the target becomes far and absolute positional accuracy is increased. Deteriorates. As a result of the above, the target positioning accuracy is a region that is short in the line-of-sight direction and long in the tangential direction, as in the hatched region 69 in the figure.
[0006]
Next, in FIG. 7, when the target is observed from the receiving antenna Rx of the bistatic receiving station, if the target is determined from the difference between the arrival times of the received waves of Rx and Tx / Rx, the target locus is from Rx and Tx / Rx. The distance difference is a constant curve, that is, a hyperbola 70 focusing on Rx and Tx / Rx, and the positioning accuracy is a region 72 that is hatched in the figure as a crossing region of the hyperbola and the reception beam 71. Here, the width of the hyperbola depends on the expected angle when Rx and Tx / Rx are viewed from the target, but basically the measurement accuracy of the arrival time of the received wave at the bistatic receiver station and monostatic radar station If selected appropriately, it can be made sufficiently small.
On the other hand, the accuracy of the tangential direction of the hyperbola depends on the angle measurement accuracy, and therefore deteriorates as the target becomes a long distance. That is, the region 72 is also a region that is short in the width direction of the hyperbola and long in the tangential direction.
On the other hand, in FIG. 8, when the target is observed from the receiving antenna Rx of the bistatic receiving station and the target is determined from the time difference between the transmission time of the transmission wave and the arrival time of the reception wave at Rx, the target locus is Rx and The sum of the distances from Tx / Rx is a constant curve, that is, an ellipse 73 whose focal point is Rx and Tx / Rx, and the positioning accuracy is a hatched region 74 as a crossing region of this ellipse and the received beam 71. This region 74 is short in the width direction of the ellipse and long in the tangential direction for the same reason as described above.
[0007]
Thus, the difference between the bistatic positioning in FIGS. 7 and 8 is whether the target is positioned on the hyperbola or the ellipse. Here, the tangent of the hyperbola and the tangent of the ellipse at the target position are orthogonal to each other.
By the way, in either case of FIG. 7 and FIG. 8, if the correlation processing of the monostatic positioning result and the bistatic positioning result is performed, the target position accuracy is the crossing region of the two hatched regions 69, 72 or 69, 74. In principle, the positioning accuracy can be improved. Furthermore, as the crossing angle between the target trajectory on the circumference by monostatic positioning and the target trajectory on the hyperbola or ellipse by bistatic positioning becomes closer to a right angle, the effect of improving positioning accuracy increases. Therefore, the positioning accuracy can be increased by selecting either hyperbola or ellipse positioning according to the target location.
[0008]
[Problems to be solved by the invention]
The conventional apparatus is configured as described above, and the principle of positioning accuracy improvement brought about by the fusion of positioning information by a monostatic radar station and a bistatic receiving station is shown, but a specific target tracking processing method is shown. Not.
[0009]
In target tracking using a monostatic radar, a Kalman filter, an α-β filter, or an α-β-γ filter obtained by simplifying the Kalman filter is generally applied. When the target tracking process is performed using both the positioning information of the monostatic radar station and the hyperbolic positioning information of the bistatic receiving station, the positioning information from the monostatic radar station and the bistatic receiving station are correlated with each other. Therefore, a general filter such as a Kalman filter cannot be theoretically applied, or if these are applied, the tracking accuracy deteriorates and the effect of fusing the positioning information of the two stations is sufficiently obtained. There was a problem that it was not possible.
[0010]
In addition, the conventional apparatus is configured to select information having a better condition of hyperbolic positioning or elliptical positioning as positioning information at the bistatic receiving station. There has been a problem that a specific processing method is not shown.
[0011]
The present invention has been made in order to solve the above-described problems, and in particular, for performing target tracking processing while merging positioning information from a monostatic radar station and a bistatic receiving station, in particular, bistatic reception. When using hyperbolic positioning information as the positioning information from the station, the optimum estimated values of the target position and speed are calculated in consideration of the correlation between the positioning information and the positioning information from the monostatic radar station. It is an object of the present invention to obtain a target tracking method with improved tracking accuracy and a target tracking device that implements the target tracking method with a filter algorithm that can perform the above.
[0012]
In addition, in order to perform target tracking processing while merging the positioning information from the monostatic radar station and the bistatic receiving station, as the positioning information at the bistatic receiving station, either hyperbolic positioning or elliptical positioning is required. Target tracking method with improved tracking accuracy by evaluating the tracking accuracy expected when tracking processing is performed using both of the above positioning information in order to select the better positioning information. And it aims at obtaining the target tracking apparatus which implements it.
[0013]
[Means for Solving the Problems]
In order to achieve the above object, a target tracking method according to claim 1 of the present invention is installed separately from a monostatic radar station and the monostatic radar station. In the target tracking method of performing the target tracking process using the positioning results of the target by both stations of the bistatic receiving station that receives the reflected wave from
Set the initial value of the estimated value of the state vector and the estimated error covariance matrix composed of the motion parameters such as the target position, velocity, etc., and thereafter at each sampling time,
Positioning result on the elliptical locus based on the measurement result on the circumferential locus by the monostatic radar station and the measurement result of the time difference between the bistatic reception wave and the transmission wave by the bistatic reception station, or Input one of the positioning results on the hyperbolic locus based on the measurement result of the arrival time difference between the static reception wave and the reception wave at the monostatic radar station, and the distance between the monostatic radar station and the bistatic reception station Input the observation error variance data group related to the angle observation parameters, calculate the predicted value of the state vector and the prediction error covariance matrix using the Kalman filter prediction algorithm, and perform positioning on the circumferential trajectory. The positioning error covariance matrix of the result is calculated, and the Kalman filter update algorithm is used using the positioning result on the circumferential trajectory. When the state vector estimation value and the estimation error covariance matrix are calculated based on the golism, and the positioning result on the elliptical locus is input as the positioning result at the bistatic receiving station, The positioning error covariance matrix of the positioning result of is calculated, and the state vector estimation value and the estimation error covariance matrix are updated based on the Kalman filter update algorithm using the positioning result on the elliptical trajectory. When the positioning result on the hyperbolic locus is input as the positioning result at the bistatic receiving station, the positioning error covariance matrix of the positioning result on the hyperbolic locus is calculated, and the positioning result on the circumferential locus is calculated. The cross-correlation matrix between the error in the positioning result and the error in the positioning result on the hyperbolic locus is calculated, and the error in the positioning result on the circumferential locus and the measurement on the hyperbolic locus are calculated. In consideration of the cross-correlation with the error of the result, a filter gain matrix for calculating the optimum state vector estimation value that minimizes the mean square of the estimation error is calculated, and the filter gain matrix and the hyperbolic locus are calculated. Update the state vector estimate using the positioning result at, calculate the estimated error covariance matrix of the updated state vector estimate using the positioning result on the hyperbolic locus, and The process is repeated until the end of tracking.
[0014]
A target tracking device according to claim 2 of the present invention is
Using the positioning results of the targets of both the monostatic radar station and the bistatic receiving station that is installed away from the monostatic radar station and receives the reflected wave from the target of the monostatic radar transmission wave In the target tracking device that performs target tracking processing by
An estimated value memory for storing and holding an estimated value of a state vector composed of motion parameters such as the target position and speed; prediction processing means for predicting the state vector for a sampling interval; and the state vector prediction A residual calculation means for calculating a residual between a target position based on a value or the state vector estimated value and a target position based on a positioning result from the monostatic radar station or the bistatic receiving station, and the state vector predicted value Alternatively, update processing means for updating the state vector using the state vector estimated value, the residual and the filter gain matrix, and an estimated error covariance matrix for storing and holding the estimated error covariance matrix of the state vector estimated value. A variance matrix memory, a prediction error covariance matrix calculating means for calculating a prediction error covariance matrix of the state vector prediction value, The positioning error covariance matrix of the positioning result by the monostatic radar station and the bistatic receiving station based on the setting values of the distance and angle error dispersion of the monostatic radar station and the bistatic receiving station , Positioning error covariance matrix of positioning result on elliptical locus based on measurement result of time difference between bistatic received wave and transmitted wave, received wave at bistatic receiving station and received wave at monostatic radar station A positioning error covariance matrix calculating means for calculating a positioning error covariance matrix of a positioning result on a hyperbolic locus based on a measurement result of an arrival time difference with respect to a distance from the monostatic radar station and the bistatic receiving station The positioning error by the monostatic radar station and the bistati Updated by a positioning error cross-correlation matrix calculating means for calculating a cross-correlation matrix with a positioning error on the hyperbola by the receiving station, a first gain matrix calculating means for calculating a gain matrix of the Kalman filter, and an update algorithm of the Kalman filter Using the first estimated error covariance matrix calculating means for calculating the estimated error covariance matrix and the cross-correlation matrix, the optimal state vector estimated value that minimizes the mean square of the estimated error Second gain matrix calculating means for calculating a filter gain matrix for calculating the error, and second estimated error covariance matrix calculating means for calculating an estimated error covariance matrix when updating is performed using this gain matrix It is characterized by comprising.
[0015]
Further, the target tracking method according to claim 3 of the present invention is:
Using the positioning results of the targets of both the monostatic radar station and the bistatic receiving station that is installed away from the monostatic radar station and receives the reflected wave from the target of the monostatic radar transmission wave In the target tracking method of performing target tracking processing by
Set the initial value of the estimated value of the state vector and the estimated error covariance matrix composed of the motion parameters such as the target position, velocity, etc., and thereafter at each sampling time,
Positioning result on the elliptical locus based on the measurement result on the circumferential locus by the monostatic radar station and the measurement result of the time difference between the bistatic reception wave and the transmission wave by the bistatic receiving station, and bistatic Input the positioning result on the hyperbolic locus based on the measurement result of the arrival time difference between the received wave and the received wave at the monostatic radar station, and the distance and angle of the monostatic radar station and the bistatic receiving station are input. Input the observation error variance data group related to the observation specifications, calculate the predicted value of the state vector and the prediction error covariance matrix using the Kalman filter prediction algorithm, and the positioning error of the positioning result on the circumferential trajectory Calculate the covariance matrix and use the positioning results on the above circular trajectory, based on the Kalman filter update algorithm Calculating a state vector estimate and the estimated error covariance matrix,
The positioning error covariance matrix of the positioning result on the elliptical locus is calculated, the positioning error covariance matrix of the positioning result on the hyperbolic locus is calculated, and the error of the positioning result on the circumferential locus and the hyperbola are calculated. Calculate the cross-correlation matrix with the error of the positioning result on the trajectory, calculate the estimated error covariance matrix when the state vector estimated value is updated using the positioning result on the elliptical trajectory, and the circle In order to calculate an optimum state vector estimated value that minimizes the mean square of the estimation error in consideration of the cross-correlation between the error of the positioning result on the circumferential locus and the error of the positioning result on the hyperbolic locus. The filter gain matrix is calculated, and the estimated error covariance matrix when the state vector estimation value is updated is calculated using the filter gain matrix and the positioning result on the hyperbolic locus, and the positioning on the elliptic locus is performed. Using the results above The evaluation value of the estimation error covariance matrix when the vector estimation value is updated is calculated, and the estimation error content when the state vector estimation value is updated is calculated using the filter gain matrix and the positioning result on the hyperbolic locus. Estimating when the evaluation value of the variance matrix is calculated, the magnitude of the two evaluation values calculated above is determined, and as a result of the determination, the state vector estimation value is updated using the positioning result on the elliptical locus When the evaluation value of the error covariance matrix is smaller, the state vector estimation value is updated using the positioning result on the elliptical locus, and the positioning result on the hyperbolic locus is used as a result of the determination. When the estimated value of the estimated error covariance matrix is smaller when the state vector estimated value is updated, the state vector estimation is performed using the filter gain matrix and the positioning result on the hyperbolic locus. The value is updated, and the series of processing at each sampling time is repeated until the end of tracking.
[0016]
A target tracking device according to claim 4 of the present invention is:
Using the positioning results of the targets of both the monostatic radar station and the bistatic receiving station that is installed away from the monostatic radar station and receives the reflected wave from the target of the monostatic radar transmission wave In the target tracking device that performs target tracking processing by
An estimated value memory for storing and holding an estimated value of a state vector composed of motion parameters such as the target position and speed; prediction processing means for predicting the state vector for a sampling interval; and the state vector prediction A residual calculation means for calculating a residual between a target position based on a value or the state vector estimated value and a target position based on a positioning result from the monostatic radar station or the bistatic receiving station, and the state vector predicted value Alternatively, update processing means for updating the state vector using the state vector estimated value, the residual and the filter gain matrix, and an estimated error covariance for storing and holding an estimated error covariance matrix of the state vector estimated value A matrix memory, a prediction error covariance matrix calculating means for calculating a prediction error covariance matrix of the state vector prediction value, and the above The positioning error covariance matrix of the positioning result by the monostatic radar station and the bistatic receiving station based on the setting values of the distance and angle error variance of the nostatic radar station and the bistatic receiving station , Positioning error covariance matrix of positioning result on elliptical locus based on measurement result of time difference between bistatic received wave and transmitted wave, received wave at bistatic receiving station and received at monostatic radar station A positioning error covariance matrix calculating means for calculating a positioning error covariance matrix of a positioning result on a hyperbolic locus based on a measurement result of an arrival time difference with a wave, and measurement of the monostatic radar station and the bistatic receiving station. Based on the setting values of distance and angle error variance, the positioning error by the monostatic radar station and the bistat A positioning error cross-correlation matrix calculating means for calculating a cross-correlation matrix with a positioning error on the hyperbola by a signal receiving station, a first gain matrix calculating means for calculating a gain matrix of the Kalman filter, and an update algorithm for the Kalman filter An optimal state vector in which the mean square of the estimation error is minimized by using the first estimation error covariance matrix calculation means for calculating the estimation error covariance matrix when updated in step 1 and the cross-correlation matrix Second gain matrix calculating means for calculating a filter gain matrix for calculating an estimated value, and a second estimated error covariance matrix for calculating an estimated error covariance matrix when updating is performed using this gain matrix A calculation means, a first estimation error evaluation means for calculating an evaluation value of an estimation error covariance matrix when updated by the Kalman filter update algorithm, Second estimation error evaluation means for calculating an evaluation value of an estimation error covariance matrix when updating is performed with an algorithm using a filter gain matrix for calculating an optimum state vector estimation value using the cross-correlation matrix And a comparison means for comparing the magnitudes of the evaluation values by the first and second estimation error evaluation means, and a positioning result on the elliptical locus or a hyperbolic locus on the basis of the comparison result by the comparison means. A filter gain matrix for selecting one of the positioning results and calculating an optimal state vector estimate value that minimizes the mean square of the estimation error using the Kalman filter gain matrix or the cross-correlation matrix Selection processing means for selecting any one of the above and outputting the selected positioning result and filter gain matrix.
[0017]
DETAILED DESCRIPTION OF THE INVENTION
Embodiment 1 FIG.
FIG. 1 is a flowchart for explaining a first embodiment of the target tracking method of the present invention.
FIG. 2 is a diagram for explaining the target positioning by the monostatic radar station and the bistatic receiving station common to the embodiment of the present invention and its coordinate system.
In FIG. 1, ST1 is a step of setting an initial value of a target state vector estimated value and an estimated error covariance matrix that is an error covariance matrix of the estimated value;
ST2 is a step of inputting a target position vector by circular positioning at a monostatic radar station and a target position vector by elliptical positioning or hyperbolic positioning at a bistatic receiving station,
ST3 is a step to input the observation error variance data group of distance and angle observed by monostatic radar station and bistatic receiving station.
ST4 calculates a prediction error covariance matrix that is a state vector prediction value and an error covariance matrix of the prediction value according to a Kalman filter prediction algorithm;
ST5 is a step of calculating a positioning error covariance matrix for circular positioning;
ST6 is a step of calculating a state vector estimated value and an estimated error covariance matrix using a circular positioning target position vector according to a Kalman filter update algorithm.
[0018]
Furthermore, ST7 is a step of determining whether the target position vector input from the bistatic receiving station is of elliptical positioning or hyperbolic positioning,
ST8 is a step of calculating a positioning error covariance matrix for elliptical positioning,
ST9 is a step of calculating a state vector estimated value and an estimated error covariance matrix using an elliptical positioning target position vector according to a Kalman filter update algorithm.
ST10 is a step of calculating a positioning error covariance matrix for hyperbolic positioning,
ST11 is a step of calculating a cross-correlation matrix of the positioning error of circular positioning and the positioning error of hyperbolic positioning;
ST12 is a step of calculating a filter gain according to a calculation algorithm that takes into account the cross-correlation between the positioning error of circular positioning and the positioning error of hyperbolic positioning,
ST13 is a step of calculating a state vector estimated value using a hyperbolic positioning target position vector,
ST14 is a step of calculating an estimation error covariance matrix of the state vector estimation value.
ST15 is a step for determining whether or not the tracking is finished.
[0019]
Prior to detailed description of the processing procedure of the first embodiment of the target tracking method of the present invention, the background theory of this embodiment will be described with respect to the following (1), (2), (3) and (4).
(1) Observing specifications at monostatic radar station and bistatic receiving station.
(2) Target positioning process using the above observation specifications.
(3) Regarding the effect of the above-mentioned measurement specifications error on the target positioning error.
(4) About the target motion model and input data model assumed in the tracking filter processing based on the above analysis results.
[0020]
First, the observation specifications of the monostatic radar station and the bistatic receiving station of (1) will be described with reference to FIG.
In FIG. 2, the arrival time t of the received wave at the monostatic radar station Tx / Rx_m, The round-trip distance 22 from the monostatic radar station Tx / Rx to the target Tgt is obtained according to the equation (1). This distance is represented as r.
Also, the arrival time t of the received wave at the bistatic receiving station Rx_bIf the time difference from the transmission time is used, the distance 23 from the monostatic radar station Tx / Rx to the bistatic receiving station Rx via the target Tgt is obtained according to the equation (2). Let this distance be ρ.
Furthermore, the received wave arrival time at the monostatic radar station and the received wave arrival time t at the bistatic receiving station_bIs used, the difference between the distance from the target to the monostatic radar station and the distance to the bistatic receiving station is obtained according to equation (3). Let this distance difference be δ. Here, from the expressions (1) to (3), the distance difference δ can be equivalently expressed as the expression (4).
[0021]
[Expression 1]

[0022]
On the other hand, the target elevation angle and azimuth angle measured by the monostatic radar station Tx / Rx are_m , θ_m It expresses. The target elevation angle and azimuth angle measured by the bistatic receiving station Rx is φ_b , θ_b It expresses.
[0023]
Next, the target positioning process (2) using the above-mentioned observation specifications will be described with reference to FIG.
As shown in FIG. 2, a reference coordinate system 24 for representing the absolute position of the target is set.
It is assumed that the absolute positions of the monostatic radar station and the bistatic receiving station expressed in this coordinate system are known.
The distance r and angle_m , θ_mObservation vector u consisting of^(c )Is defined by equation (5) (T represents the transpose of the matrix).
This observation vector u^(c )By using the above information, it is possible to perform target positioning on the circumference centered on the monostatic radar station Tx / Rx (hereinafter referred to as circular positioning). Target position vector z obtained by circular positioning^(c )(Represented by the reference coordinate system 24) is defined by equation (6). U^(c )More than z^(c )The calculation formula for obtaining is expressed by equation (7).
Also, distance ρ and angle φ_b , θ_bObservation vector u consisting of^(e)  Is defined by equation (8),^(e) From this information, positioning on the ellipse with the monostatic radar station Tx / Rx and the bistatic receiving station Rx as the focal point (hereinafter referred to as elliptical positioning) is possible. Target position vector z by ellipsometry^(e) Is the formula (9), and the above u^(e) More than z^(e) The calculation formula for obtaining is expressed by equation (10).
Furthermore, the distance difference δ and the angle φ_b , θ_bObservation vector u in equation (11) consisting of^(h)Can be used for positioning on a hyperbola focusing on Tx / Rx and Rx (hereinafter referred to as hyperbola positioning). Target position vector z by hyperbolic positioning^(h)Is given by equation (12), and u^(h)More than z^(h)The calculation formula is expressed by formula (13).
[0024]
[Expression 2]

[0025]
Next, the effect of the error in the above item 3 on the target positioning error will be described.
The above observation parameters r, ρ, δ, φ_m  , θ_m  , φ_b , θ_bThe observation errors contained in are respectively Δr, Δρ, Δδ, Δφ_m  , Δθ_m  , Δφ_b , Δθ_bIt expresses.
The error of distance r is the received wave arrival time t at Tx / Rx in equation (1)._mOccurs due to the measurement error. Δr is mean 0, variance σ_r ²  Suppose that it follows a Gaussian distribution of.
The error of the distance ρ is the received wave arrival time t at Rx in the equation (2)._bDue to measurement error. Δρ is mean 0, variance σ_ρ ² Suppose that it follows a Gaussian distribution of.
On the other hand, the error of the distance difference δ is t in Equation (3)._mMeasurement error and t_bAffected by both measurement errors. As a result, Δδ can be expressed by the following equation from Equation (4).
[0026]
[Equation 3]

[0027]
From the assumption of Gaussian distribution for Δr and Δρ and Equation (14), Δδ is 0 on average and variance σ_δ ² With a Gaussian distribution. Where variance ρ_δ ²Is given by:
[0028]
[Expression 4]

[0029]
By the way, Δr and Δρ are different measured quantities t._m , t_bTherefore, Equation (16) can be assumed (E [•] is a symbol representing an average operation). In contrast, Δr and Δδ are both t_mSince these are affected by the measurement error, the errors are correlated with each other. From Equation (14), the covariance regarding the cross-correlation of these errors is Equation (17).
[0030]
[Equation 5]

[0031]
Target angle observation error Δφ_m , Δθ_m , Δφ_b , Δθ_bAre all mean 0 and the variance is σ_{φ m} ², σ_{θ m} ² , σ_{φ b} ² , σ_{θ b} ² Suppose that it follows a Gaussian distribution of.
These errors are uncorrelated with each other.
From the above, each observation specification vector u defined by Equations (5), (8), and (11)^(c) , u^(e) , u^(h)    The error covariance matrix is obtained as shown in equations (18) to (22). Here, Eqs. (18), (19), and (20) are respectively the errors Δu^(c) , Δu^(e) , Δu^(h) Equations (21) and (22) are respectively Δu^(c) And Δu^(e) , And Δu^(c) And Δu^(h) Is the cross-correlation matrix. Note that diag (a, b, c) is a 3 × 3 diagonal matrix with a, b, c as diagonal terms, and 0_{Three × Three}Represents a 3-by-3 zero matrix.
[0032]
[Formula 6]

[0033]
The influence of the above-mentioned observation item error on the target positioning error can be evaluated as follows.
Above observation vector u^(c) Is the error Δu^(c)Target position vector z by circular positioning^(c) Error of v^(c) And Similarly, the above observation specification vector u^(e) Is the error Δu^(e)Target position vector z by ellipsometric positioning^(e)Error of v^(e),
Above observation vector u^(h) Is the error Δu^(h)Target position vector z by hyperbolic positioning^(h)Error of v^(h)It expresses.
Expressions (7), (10), and (13) are evaluated as follows by linearly linear approximation.
[0034]
[Expression 7]

[0035]
Where F^(c)Is the function f in equation (7)^(c)U^(c)True value of 3 × 3 matrix indicating the first derivative by₀ ^(c)Is the value at. F^(e), F^(h) The same applies to.
Where true value u₀ ^(c)Cannot be actually obtained, but an approximate value can be calculated by using the target predicted position or estimated position obtained in the course of the tracking process.
From the above formula (18) to formula (22) and formula (23) to formula (25), positioning error v^(c), v^(e) , v^(h)Are obtained as in the following equations (26) to (30).
Where S^(c), S^(e) , S^(h)Is the positioning error v^(c), v^(e) , v^(h)Is the covariance matrix of C^(ce) , C^(ch) Is a cross-correlation matrix.
[0036]
[Equation 8]

[0037]
Here, as shown in the above equations (29) and (30), the target position vector z by circular positioning^(c)And target position vector z by ellipsometry^(e)Are positioning results whose errors are uncorrelated with each other, whereas z^(c)And target position vector z by hyperbolic positioning^(h)Is a positioning result in which errors are correlated with each other.
[0038]
Next, the target motion model and the input data model assumed in the tracking filter processing based on the analysis result of (4) will be described.
First, the target exercise model will be described.
For example, the target state vector is expressed by the following equation (31) based on the target position and velocity components at the sampling k in the reference coordinate system 24 of FIG.
[0039]
[Equation 9]

[0040]
At this time, the target motion model is defined by equation (32). Where Φ_k-1Is the state vector x from sampling k-1 to sampling k_kFor example, if the target motion is assumed to be straight at a constant speed, the sampling interval is τ and is given by Equation (33). Where I_{Three × Three}Represents a 3 × 3 identity matrix.
w_k -1Is a driving noise vector equivalent to acceleration introduced to represent the error caused by considering the target motion to be straight ahead at constant speed, with mean 0 and covariance matrix Q_kIs a Gaussian white noise.
[0041]
[Expression 10]

[0042]
Next, a model of input data to the tracking filter is defined as follows.
Target position vector z by circular positioning^(c)A model in which is used as input data to the tracking filter is represented by Expression (34). Similarly, target position vector z by elliptical positioning^(e), Target position vector z by hyperbolic positioning^(h)Equations (35) and (36) are respectively used when the model is input data. Here, the observation matrix H is a constant matrix given by Expression (37).
And v^(c), v^(e), v^(h)Are the positioning errors defined in Eqs. (23) to (25). These errors are assumed to be Gaussian white noise whose mean is 0 and the covariance matrix is given by Eqs. (26) to (30). To do.
[0043]
## EQU11 ##

[0044]
This is the end of the description of the background theory of the first embodiment of the target tracking method of the present invention.
[0045]
Next, with reference to FIG. 1, the process procedure which shows Embodiment 1 of the target tracking method of this invention is demonstrated in detail.
In the first embodiment, based on observation information from the monostatic radar station and the bistatic receiving station up to sampling k, an estimated value of the state vector of Expression (31) for sampling k is obtained.
First, in ST1 of FIG. 1, as in the case of the normal tracking process, the target position and speed calculated from the target position vector of the initial two samplings are set as the initial values of the state vector estimated values. The error covariance of the calculated position and velocity is calculated, set to the initial value of the estimated error covariance matrix, and the tracking process is started.
As a target position vector for calculating the initial value, a circular positioning result in a monostatic radar station may be used.
Thereafter, from the third sampling, a series of processing steps ST2 to ST14 is executed in each sampling. These processing steps consist of a state vector estimate hat x for sampling k-1._k -_{1 | k} -₁ And the estimated error covariance matrix P_k -_{1 | k} -₁Using the observation information of sampling k, the state vector estimate hat x for sampling k_{k | k}And the estimated error covariance matrix P_{k | k}It is a processing step for updating to the value of.
[0046]
First, in ST2, the target position vector z by circular positioning at the monostatic radar station_k ^(c)And the target position vector z by ellipsometry at the bistatic receiving station_k ^(e) Or target position vector z by hyperbolic positioning_k ^(h) Enter one of the following. Here, in the target tracking method according to the present embodiment, it is assumed that the target position vector of either elliptical positioning or hyperbolic positioning is input in advance at each sampling.
Next, in ST3, the distance r, ρ, angle φ in this sampling_m , θ_m, φ_b , θ_bObservation error variance σ_r ² , σ_ρ ² , σ_{φ m} ², σ_{θ m} ², σ_{φ b} ² , σ_{θ b} ²Enter the data group.
[0047]
Next, proceed to ST4. In this processing step, prediction processing for the sampling interval is performed according to the following Kalman filter prediction algorithm.
Where hat x_{k | k} -₁Is the state vector prediction, and P_{k | k} -₁Represents the prediction error covariance matrix.
[0048]
[Expression 12]

[0049]
Next, in ST5, the target position vector z for circular positioning is calculated by the equation (26)._k ^(c)Positioning error covariance matrix S^(c)Is calculated.
Next, in ST6, the target position vector z obtained by the circular positioning obtained by the monostatic radar station_k ^(c)Is used to update the state vector estimated value. In this update process, the following Kalman filter update algorithm can be used. Where hat x_{k | k} ^(c)Is z_k ^(c)State vector updated by P,_{k | k} ^(c)Is hat x_{k | k} ^(c)The error covariance matrix of Also, K in formula (40)_k ^(c)Is the Kalman gain matrix. In this update algorithm, the state vector predicted value hat x calculated in ST4_{k | k} -₁ And the prediction error covariance matrix P_{k | k}-₁ , And positioning error covariance matrix S of circular positioning calculated in ST5^(c)Is used.
[0050]
[Formula 13]

[0051]
Next, the target position vector z obtained by elliptical positioning obtained at the bistatic receiving station_k ^(e), Or target position vector z by hyperbolic positioning_k ^(h) Use the above hat x_{k | k} ^(c)Proceed to processing steps for further updating.
In ST7, it is determined whether an elliptical positioning or a hyperbolic positioning target position vector is input as a positioning result at the bistatic receiving station. When the target position vector for ellipse positioning is input, the process proceeds to ST8, and when the target position vector for hyperbolic positioning is input, the process proceeds to ST10.
[0052]
First, when an elliptical positioning target position vector is input, in ST8, the elliptical positioning target position vector z_k ^(e)Positioning error covariance matrix S_k ^(e)Is calculated.
Next, in ST9, the target position vector z for elliptical positioning_k ^(e)Update processing is performed using. Here, when a target position vector for elliptical positioning is input, it is possible to use the following Kalman filter update algorithm as in the case of circular positioning. In this update algorithm, z calculated in ST8_k ^(e)Positioning error covariance matrix S_k ^(e)Is used.
[0053]
[Expression 14]

[0054]
As mentioned above, the Kalman filter update algorithm can be applied in the case of elliptical positioning._k ^(e) Is the target position vector z of the circular positioning used earlier_k ^(c)This is because there is no correlation with the error.
[0055]
On the other hand, when the target position vector by hyperbolic positioning is input, the process proceeds to ST10. In ST10, the target position vector z for hyperbolic positioning is calculated by the above equation (28)._k ^(h) Positioning error covariance matrix S_k ^(h) Is calculated.
Further, in ST11, the target position vector z for circular positioning_k ^(c)Error and hyperbolic positioning position vector z_k ^(h) Cross-correlation matrix C with error_k ^(ch) Is calculated by the equation (30). Next, it progresses to the update process by three process steps of ST12-ST14.
[0056]
Hyperbolic positioning target position vector z_k ^(h) Using the hat x_{k | k} ^(c) Z to update_k ^(h) Is the target position vector z for circular positioning used in ST6._k ^(c)Therefore, the Kalman filter update algorithm cannot be used.
For this reason, in ST12 to ST14, update processing is executed according to the following equations (46) to (48).
Here, the calculation formulas of formulas (46) to (48) are algorithms newly derived in the present invention, and z_k ^(h)Error is z_k ^(c)When there is a correlation with the error, it is possible to calculate an optimum estimated value that minimizes the mean square error.
[0057]
First, in ST12, the filter gain matrix K according to Equation (46)_k ^(h) Is calculated. This filter gain matrix is_k ^(h)Error and z_k ^(c)This is a gain matrix for performing update processing in consideration of the error correlation of_k ^(h)Error covariance matrix S_k ^(h)Z calculated in ST11_k ^(c)And z_k ^(h)Cross-correlation matrix C_k ^(ch) And the Kalman gain matrix K calculated in ST6._k ^(c)And the estimated error covariance matrix P_{k | k} ^(c) Is used.
[0058]
Next, in ST13, according to the equation (47), the calculated filter gain matrix K_k ^(h)And target position vector z by hyperbolic positioning_k ^(h)Using state vector estimated value hat x calculated in ST6_{k | k} ^(c) The new estimated hat x_{k | k} ^(h)Update to
Furthermore, in ST14, C calculated in ST11_k ^(ch) , Filter gain matrix K calculated in ST12_k ^(h), Kalman gain matrix K calculated in ST6_k ^(c) Is used to estimate the error covariance matrix P_{k | k} ^(c) P_{k | k} ^(h)Update to P_{k | k} ^(h)Is the state vector estimate hat x in equation (47)_{k | k} ^(h)Is equivalent to the error covariance matrix.
[0059]
[Expression 15]

[0060]
The above is the update process in sampling k. Note that the sampling k update process is performed by the hat x based on the result of the update process using the target position vector for ellipse positioning._{k | k} ^(e) And P_{k | k} ^(e) Or hat x based on the result of the update process using the target position vector for hyperbolic positioning_{k | k} ^(h)And P_{k | k} ^(h) To the final state vector estimate hat x in this sampling_{k | k} , And the estimated error covariance matrix P_{k | k} End as That is, the expressions (49) and (50) or the expressions (51) and (52) are used.
[0061]
[Expression 16]

[0062]
Finally, in ST15, it is determined whether or not the tracking is finished.If the tracking is finished, the process is terminated.If the tracking is continued, the process returns to ST2, and thereafter, the processing steps of ST2 to ST14 are repeated until the tracking is finished. Repeat in sampling.
[0063]
By the way, in the above processing procedure, the update process of the estimated value is first performed with the result of the circular positioning, and then the update process is performed with the result of the elliptical positioning or the hyperbolic positioning, but conversely, the elliptical positioning or the hyperbolic positioning is performed first. It is also possible to use and then use circular positioning. In this case, after using the update algorithm of the Kalman filter in the update process based on the result of the elliptical positioning or the hyperbolic positioning, in the update process based on the result of the circular positioning, the update algorithm of the Kalman filter is used when the result of the elliptical positioning is used first. Further, when the result of hyperbolic positioning is used first, an algorithm of the above formulas (46) to (48) may be used.
[0064]
As described above, according to the first embodiment of the target tracking method of the present invention, the state vector estimation value is updated using both the results of the circular positioning and the elliptical positioning or the hyperbolic positioning, so that the monostatic・ Observation information from the radar station and observation information from the bistatic receiving station are both taken into the estimated value, and the tracking accuracy can be improved.
In particular, even when using the result of hyperbolic positioning as information of the bistatic receiving station, the correlation between the error of the circular positioning result and the error of the hyperbolic positioning result is obtained by using the algorithm of equations (46) to (48). Since the optimum estimated value in consideration of the influence of the information is calculated, the accuracy improvement effect by the fusion of information of both stations can be further enhanced.
[0065]
Embodiment 2
FIG. 3 is a block diagram showing the configuration of the second embodiment of the target tracking apparatus according to the present invention. This Embodiment 2 shows a configuration example of a target tracking device that implements the target tracking method shown in Embodiment 1 above.
In the figure, 1 is a target tracking processor, 2 is a data processor of a monostatic radar station that performs circular positioning, 3 is a first bistatic data processor that performs hyperbolic positioning, and 4 is a second that performs elliptical positioning. A bistatic data processor, 5 is a selector, 6 is a display, and 7 is an observation error variance setting device. Of these, 2, 3, 4, 5, and 6 correspond to the corresponding portions of the conventional apparatus of FIG.
[0066]
The target tracking device 1 includes an estimation unit 8 and a gain setting unit 9.
Further, the estimation unit 8 includes an estimated value memory 10 that stores an estimated value of a state vector composed of target position and velocity components, a prediction processor 11 that predicts a value of a state vector after sampling, a predicted position And a residual calculator 12 for calculating the residual of the target position based on the positioning result, and an update processor 13 for estimating the state vector at the current sampling time.
[0067]
The gain setting unit 9 includes an estimation error covariance matrix memory 14 that stores an error covariance matrix of state vector estimation values, a prediction error covariance matrix calculator 15 that calculates an error covariance matrix of state vector prediction values, Positioning error covariance matrix calculator 16, positioning error cross-correlation matrix calculator 17, first gain matrix calculator 18 that calculates the gain matrix of the Kalman filter, and error value of the estimated value when updating using the Kalman gain The first estimation error covariance matrix calculator 19 that calculates the variance matrix, the second gain matrix calculator 20 that calculates the gain matrix of a new filter different from the Kalman filter, and when updating is performed using this filter gain The second estimated error covariance matrix calculator 21 calculates an error covariance matrix of the estimated values.
[0068]
Next, the operation of the second embodiment of the present invention will be described with reference to FIG.
In the figure, the initial value hat x of the state vector estimated value is stored in the estimated value memory 10._{0 | 0} And the initial value P of the estimated error covariance matrix is stored in the estimated error covariance matrix memory 14._{0 | 0}Is set and the tracking process is started.
When a new target is observed by the monostatic radar station and the bistatic receiving station at sampling k, first, circular positioning is performed in the data processor 2 of the monostatic radar station, and the target position vector z_k ^(c) Is calculated.
Further, in the first bistatic data processor 3, hyperbolic positioning is performed and the target position vector z_k ^(h) In the second bistatic data processor 4, ellipse positioning is performed and the target position vector z_k ^(e)Is calculated.
Target position vector z by two bistatic data processors 3 and 4_k ^(h) , z_k ^(e)Is selected by the selector 5 and then the target position vector z from the data processor 2 is selected._k ^(c) At the same time, it is input to the target tracking device 1.
[0069]
On the other hand, in the observation error covariance setting device 7, the distance r, ρ, angle φ in this sampling_m  , θ_m , φ_b , θ_bObservation error variance σ_r ² , σ_ρ ² , σ_{φ m} ², σ_{θ m} ², σ_{φ b} ² ,
σ_{θ b} ²Is set and input to the target tracking device 1.
These observation error variances can be set by referring to a database previously prepared according to the target existing area, or set by estimating from the S / N ratio of the input signal for each observation. You can also.
[0070]
When the above data group is input, in the target tracking device 1, first, in the estimation unit 8, the state vector estimated value of the pre-sampling k-1 from the estimated value memory 10 Hat x_{k -1 | k -1}  Is read, and the prediction processor 11 calculates the state vector prediction value according to the equation (38).
Further, in the gain setting unit 9, the estimated error covariance matrix P-1 of the pre-sampling k-1 from the estimated error covariance matrix memory 14 is used._{k -1 | k -1}Is read out, and the prediction error covariance matrix calculator 15 calculates the prediction error covariance matrix P according to the equation (39)._{k | k -1}Is calculated.
[0071]
Next, the process proceeds to a state vector estimated value update process using a circular positioning target position vector.
First, in the positioning error covariance matrix calculator 16, the error covariance matrix S of the target position vector for circular positioning according to equation (26).^(c)Is calculated.
Next, in the first gain matrix calculator 18, the prediction error covariance matrix P_{k | k-1}And positioning error covariance matrix S^(c)And gain matrix K according to equation (40)_k ^(c ) Is sent to the update processor 13 and the first estimated error covariance matrix calculator 19.
In the first estimated error covariance matrix calculator 19, the updated estimated error covariance matrix P is updated according to the equation (42)._{k | k} ^(c ) Is calculated in advance.
[0072]
On the other hand, in the residual calculator 12, the state vector predicted value by the prediction processor 11 and the circular target position vector z_k ^(c )Enter the difference between the predicted position and the target position of the positioning result z_k ^(c)-H hat x_{k -1 | k -1} (So-called residual) is calculated and sent to the update processor 13.
The update processor 13 receives the gain matrix K sent from the gain setting unit 9._k ^(c ) Is updated according to the equation (41). Updated state vector estimate hat x_{k | k} ^(c )Is sent to the residual calculator 12 again.
[0073]
Next, the process proceeds to update processing using a target position vector by elliptical positioning or hyperbolic positioning.
In this process, although the operation of the estimation unit 8 does not change depending on whether the selector 5 selects the result of elliptical positioning or the result of hyperbolic positioning, the operation of the gain setting unit 9 is changed.
[0074]
First, the operation of the gain setting unit 9 will be described. When the gain setting unit 9 receives from the selector 5 a command signal indicating which result of elliptical positioning or hyperbolic positioning has been selected, the operation is switched as follows.
First, when an elliptical positioning result is selected, the following operation is performed. In the positioning error covariance matrix calculator 16, the target position vector z by ellipsometric positioning according to the equation (27)^(e) _k Error covariance S^(e) Is calculated.
[0075]
Next, in the first gain matrix calculator 18, the estimated error covariance matrix P after the update processing based on the circular positioning result is received from the first estimated error covariance matrix calculator 19._{k | k} ^(c )And enter this and S^(e) And gain matrix K according to equation (43)_k ^(e) Is calculated. This gain matrix is sent to the update processor 13 of the estimation unit 8.
Further, the first estimated error covariance matrix calculator 19 calculates the estimated error covariance matrix P after the update processing based on the elliptical positioning result according to the equation (45)._{k | k} ^(e) And this is the final estimated error covariance matrix P of this sampling_{k | k}Is written in the estimated error covariance matrix memory 14, and the process is terminated.
[0076]
On the other hand, when the hyperbolic positioning result is selected by the selector 5, the operation is as follows. First, in the positioning error covariance matrix calculator 16, according to the equation (28), the error covariance matrix S of the hyperbolic positioning target position vector^(h)In the positioning error cross-correlation matrix calculator 17, the cross-correlation matrix C between the hyperbolic positioning error and the circular positioning error is calculated according to the equation (30).^(ch)Is calculated.
[0077]
Next, in the second gain matrix calculator 20, the gain matrix K used in the update process by the circular positioning result from the first gain matrix calculator 18._k ^(c )And the estimated error covariance matrix P after the update processing based on the circular positioning result from the first estimated error covariance matrix calculator 19_{k | k} ^(c ) Enter these values and above S^(h), C^(ch)From the equation (46), the gain matrix K_k ^(h)Is calculated. This gain matrix is sent to the update processor 13 of the estimation unit 8.
[0078]
In the second estimation error covariance matrix calculator 21, the above S^(h), C^(ch)And gain matrix K_k ^(c ) , K_k ^(h)And P_{k | k} ^(c )And the estimated error covariance matrix P after the update processing according to the hyperbolic positioning result according to the equation (48)_{k | k} ^(h)And this is the final estimated error covariance matrix P of this sampling_{k | k} Is written in the estimated error covariance matrix memory 14, and the process is terminated.
[0079]
Next, the operation of the estimation unit 8 will be described. In the estimation unit 8, in the residual calculator 12, the state vector estimated value hat x after the update processing based on the circular positioning result is performed._{k | k} ^(c ) And the target position vector z of ellipse positioning sent from the selector 5_k ^(e)(Or target position vector z by hyperbolic positioning_k ^(h) ) Residual z_k ^(e)-H hat x_{k | k} ^(c ) (Or z_k ^(h)-H hat x_{k | k} ^(c ) ) Is calculated and sent to the update processor 13.
In the update processor 13, the gain matrix K is input from the gain setting unit 9._k ^(e)(Or K_k ^(h) ) And update according to equation (44) (or equation (47)). State vector estimated value hat x after update by the update processor 13_{k | k} ^(e) (Or hat x_{k | k} ^(h) ) Is the final state vector estimate hat x in this sampling_{k | k} Is written in the estimated value memory 10 and sent to the display 6 to be shown to the operator.
This completes the operation at sampling k. Thereafter, the above processing is repeatedly executed for each sampling until the end of tracking.
[0080]
As described above, according to the second embodiment of the target tracking device of the present invention, the state vector estimation value is updated using both the results of the circular positioning and the elliptical positioning or the hyperbolic positioning.・ Observation information from the radar station and observation information from the bistatic receiving station are both taken into the estimated value, and the tracking accuracy can be improved.
In particular, even when using the result of hyperbolic positioning as information of the bistatic receiving station, the correlation between the error of the circular positioning result and the error of the hyperbolic positioning result is obtained by using the algorithm of equations (46) to (48). Since the optimum estimated value in consideration of the influence of the information is calculated, the accuracy improvement effect by the fusion of information of both stations can be further enhanced.
[0081]
Embodiment 3
FIG. 4 is a flow chart for explaining the third embodiment of the target tracking method of the present invention.
In the figure, ST16 is a step of inputting a target position vector by circular positioning at a monostatic radar station, and a target position vector by elliptical positioning and hyperbolic positioning at a bistatic receiving station,
ST17 is a step of calculating an estimated error covariance matrix when performing update processing using a target position vector for elliptical positioning;
ST18 is a step of calculating an evaluation value of an estimated error covariance matrix when update processing is performed using a target position vector for elliptical positioning;
ST19 is a step of calculating an evaluation value of an estimated error covariance matrix when update processing is performed using a target position vector of hyperbolic positioning;
ST20 is a step for determining the magnitude of the two evaluation values, and ST21 is a step for calculating a state vector estimated value using the target position vector for elliptical positioning.
Also, the same processing steps as those in the flowchart described in the first embodiment in FIG.
[0082]
Prior to detailed description of the processing procedure of the third embodiment of the target tracking method of the present invention, the background theory of this embodiment will be described.
As described in the first embodiment, the target position vector z for ellipsometric positioning_k ^(e)When the update process is performed using, the update algorithms of equations (43) to (45) can be used.
Here, the estimated error covariance matrix P by Equation (45)_{k | k} ^(e) Is the gain matrix K according to equation (43)_k ^(e) Can be calculated before actually performing the state vector estimated value update processing according to the equation (44). Ie P_{k | k} ^(e) Indicates an estimated value related to the estimation error when the update process is performed according to the equation (44).
Similarly, target position vector z by hyperbolic positioning_k ^(h)The update algorithm when performing the update process using Eq. (46) to (48) is the estimated error covariance matrix P according to Eq. (48)_{k | k} ^(h) Is the gain matrix K according to equation (46)_k ^(h)Can be calculated before the state vector estimated value update process according to equation (47) is performed. P_{k | k} ^(h)Indicates an estimated value related to the estimation error when the update process according to the equation (44) is performed.
[0083]
From the above, in advance, the estimated error covariance matrix P in Eqs. (45) and (48)_{k | k} ^(e) , P_{k | k} ^(h)By calculating and comparing these values, update the state vector estimated value (formula (44)) with the target position vector for elliptical positioning, or update the state vector estimated value with the target position vector by hyperbolic positioning It is possible to select whether to execute (Expression (47)).
Note that the two estimated error covariance matrices P_{k | k} ^(e) , P_{k | k} ^(h)In order to compare the magnitudes of these, it is necessary to evaluate the sizes of these matrices with scalar values. As such evaluation values, for example, values shown in the following equations can be adopted. However, β^(e) Is the evaluation value for elliptical positioning, β^(h)Is an evaluation value in the case of hyperbolic positioning, and det represents taking a determinant of a matrix.
[0084]
[Expression 17]

[0085]
From the above, the two evaluation values β^(e) , β^(h) Is calculated by equations (49) and (50), and β^(e) Is β^(h) If it is smaller, the target position vector z for elliptical positioning according to equation (44)_k ^(e) Update process using^(h)Is β^(e) If it is smaller, the target position vector z for hyperbolic positioning according to equation (47)_k ^(h) It is sufficient to execute update processing using.
This is the end of the explanation of the background theory of the processing procedure of the third embodiment.
[0086]
Next, with reference to FIG. 4, the process procedure which shows Embodiment 3 of the target tracking method of this invention is demonstrated in detail.
First, in ST1, as in the case of the first embodiment, the state vector estimated value and the initial value of the estimated error covariance matrix are set from the target position vector of the initial two samplings, and the tracking process is started. Thereafter, from the third sampling, a series of processing steps from ST16 onward are executed in each sampling.
In each sampling, first, in ST16, the target position vector z by circular positioning at the monostatic radar station_k ^(c)And the target position vector z by elliptical positioning at the bistatic receiving station_k ^(e) , And target position vector z by hyperbolic positioning_k ^(h) Enter.
Here, the difference from Embodiment 1 is that both a target position vector based on elliptical positioning and a target position vector based on hyperbolic positioning are input as positioning results at the bistatic receiving station.
[0087]
Next, the processing procedures up to ST3, ST4, ST5, and ST6 are the same as those in FIG. 1 of the first embodiment. Furthermore, in ST8, the target position vector z for elliptical positioning is calculated by the above equation (27)._k ^{(e )} Positioning error covariance matrix S_k ^(e) In ST10, the target position vector z for hyperbolic positioning is calculated by the above equation (28)._k ^(h) Positioning error covariance matrix S_k ^(h) In ST11, the target position vector z for circular positioning is calculated by the above equation (30)._k ^(c) Error and hyperbolic positioning target position vector z_k ^(h) Cross-correlation matrix C with error_k ^(ch) Is calculated.
[0088]
Next, in ST17, the target position vector z by elliptical positioning_k ^(e) Using state vector estimated value hat x calculated in ST6_{k | k} ^(c) Only the estimated error covariance matrix is calculated when. That is, the estimated error covariance matrix P calculated in ST6_{k | k} ^(c)And the positioning error covariance matrix S of ellipse positioning calculated in ST8_k ^(e) Using the above equation (43), the Kalman gain matrix K_k ^(e) Further, according to equation (45), the estimated error covariance matrix P_{k | k} ^(e) Is calculated.
[0089]
Next, ST12 and ST14 are the target position vector z by hyperbolic positioning._k ^(h) Using state vector estimated value hat x calculated in ST6_{k | k} ^(c) Is a processing step for calculating an estimated error covariance matrix when. That is, in ST12, the Kalman gain matrix K calculated in ST6_k ^(c) And the estimated error covariance matrix P_{k | k} ^(c)Z calculated in ST10_k ^(h)  Error covariance matrix S_k ^(h)Z calculated in ST11_k ^(c)And z^(h) Cross-correlation matrix C_k ^(ch) And filter gain matrix K according to equation (46)_k ^(h)Further, in ST14, the Kalman gain matrix K calculated in ST6 is calculated in ST14._k ^(c) , C calculated in ST11_k ^(ch) , Filter gain matrix K calculated in ST12_k ^(h)Is used to estimate the error covariance matrix P_{k | k} ^(h)Is calculated.
In the processing up to the above, the state vector estimated value itself is not yet updated by the equation (44) or the equation (47).
[0090]
Next, in ST18, the estimated error covariance matrix P in the case where the state vector estimated value is updated with the target position vector by elliptical positioning according to the equation (53)._{k | k} ^(e) Evaluation value β^(e) Is calculated. In ST19, the estimated error covariance matrix P when the state vector estimated value is updated with the target position vector by hyperbolic positioning is used._{k | k} ^(h)Evaluation value β^(h)Is calculated.
[0091]
Next, in ST20, the two calculated evaluation values β^(e), Β^(h)Judge the magnitude of β^(e)If is smaller, proceed to ST21 for updating the state vector estimated value with the target position vector by elliptical positioning, and conversely β^(h)If is smaller, the process proceeds to ST13 for updating the state vector estimated value with the target position vector by hyperbolic positioning.
In ST21, the target position vector z for elliptical positioning is obtained by equation (44)._k ^(e) Using state vector estimated value hat x calculated in ST6_{k | k} ^(c)Update. At this time, Kalman gain matrix K calculated in ST17_k ^(e) Is used. On the other hand, in ST13, the target position vector z for hyperbolic positioning is calculated by Equation (47)._k ^(h) Using state vector estimated value hat x calculated in ST6_{k | k} ^(c)Update. At this time, the filter gain matrix K calculated in ST12_k ^(h) Is used.
[0092]
This completes the update process for sampling k. In ST20, when update processing (ST21) using a target position vector for ellipsometry is selected, hat x based on the result of ST21_{k | k} ^(e)  And P by the result of ST17_{k | k} ^(e) To the final state vector estimate hat x in this sampling_{k | k} , And estimated error covariance matrix P_{k | k} If update processing (ST13) using the target position vector for hyperbolic positioning is selected, the hat x based on the result of ST13_{k | k} ^(h) And P by the result of ST14_{k | k} ^(h) To the final state vector estimate hat x in this sampling_{k | k} , And estimated error covariance matrix P_{k | k} Then, the update process at sampling k is terminated.
Finally, in ST15, it is determined whether or not the tracking is finished.If the tracking is finished, the process is terminated, and if the tracking is continued, the process returns to ST2.After that, the above series of processing steps are performed in each sampling until the tracking is finished. repeat.
[0093]
As described above, according to the third embodiment of the target tracking method of the present invention, the estimation error when the state vector is updated using the circular positioning result and the elliptical positioning result, the circular positioning result, By evaluating each error of the estimation error when updating the state vector using the result of hyperbolic positioning in advance and selecting the one with the smaller estimation error, the result of either elliptical positioning or hyperbolic positioning is obtained. You can decide what to use.
Therefore, for each sampling, the expected positioning result with the higher tracking accuracy of the above two is selected, and as a result, the effect of merging the observation information of the monostatic radar station and the bistatic receiving station is obtained. Can be further increased.
[0094]
Embodiment 4 FIG.
FIG. 5 is a block diagram showing the configuration of the fourth embodiment of the target tracking apparatus according to the present invention. This Embodiment 4 shows the structural example of the target tracking apparatus which implements the target tracking method shown in the said Embodiment 3. FIG.
In FIG. 5, in the second embodiment shown in FIG. 3, the external selector 5 selects and inputs a target position vector based on elliptical positioning or a target position vector based on hyperbolic positioning. The tracking device 1 includes a selection unit 25 having a selection function.
In the figure, the selection unit 25 is composed of a first estimation error evaluator 26, a second estimation error evaluator 27, a comparator 28, and a selection processor 29, and the other parts are the same as in the case of the apparatus of FIG. It is the composition.
[0095]
With reference to FIG. 5, the operation of the fourth embodiment of the target tracking device will be described.
In the figure, the initial value hat x of the state vector estimated value is stored in the estimated value memory 10._{0 | 0}And the initial value P of the estimated error covariance matrix is stored in the estimated error covariance matrix memory 14._{0 | 0}Is set and the tracking process is started.
When a new target is observed by the monostatic radar station and bistatic receiving station at sampling k, the target position vector z by circular positioning is obtained by the data processor 2._k ^(c ) Is calculated by the first bistatic data processor 3, and the target position vector z by hyperbolic positioning is calculated._k ^(h) Is calculated, and the second bistatic data processor 4 calculates the target position vector z by ellipse positioning._k ^(e) Is calculated. Target position vector z_k ^(c ) _, z_k ^(h)  _, z_k ^(e) Are both input to the target tracking device 1.
[0096]
In addition, the observation error covariance setter 7 uses the distance r, ρ and angle φ in this sampling._m , θ_m , φ_b , θ_bObservation error variance σ_r ²  _,σ_ρ ²  , σ_{φ m} ² , σ_{θ m} ² , σ_{φ b} ²,
σ_{θ b} ² Is set and input to the target tracking device 1.
Next, the target tracking device 1 performs the prediction processing of the equations (38) and (39) and the update processing by the circular positioning target position vector of the equations (40) to (42) until the embodiment of FIG. The operation is the same as in the case of 2.
[0097]
In other words, the prediction processor 11 performs a state vector estimated value hat x that is pre-sampled from the estimated value memory 10._{k-1 | k-1} And state vector predicted value hat x_{k | k-1}Is calculated. In addition, the prediction error covariance matrix calculator 15 performs the pre-sampling estimated error covariance matrix P than the estimated error covariance matrix memory 14._{k -1 | k -1} And the prediction error covariance matrix P_{k | k -1}Is calculated.
[0098]
Next, the process proceeds to a state vector estimated value update process using the circular positioning target position vector. In the gain setting unit 9, the positioning error covariance matrix calculator 16 performs an error covariance matrix S of the circular positioning target position vector.^(c )Next, the first gain matrix calculator 18 calculates the gain matrix K of the equation (40)._k ^(c ) Is sent to the update processor 13 and the first estimated error covariance matrix calculator 19. Further, the first estimated error covariance matrix calculator 19 performs an updated estimated error covariance matrix P_{k | k} ^(c ) Is calculated in advance.
On the other hand, in the estimation unit 8, the residual calculator 12 calculates the residual z between the predicted position based on the state vector predicted value and the target position of the circular positioning result._k ^(c )-H hat x_{k | k-1} And the gain matrix K input from the gain setting unit 9 in the update processor 13_k ^(c ) And update the state vector estimated value hat x of the update result_{k | k} ^(c )Get.
[0099]
At this stage, the update processor 13 performs the state vector estimated value hat x after the update processing based on the circular positioning result._{k | k} ^(c ) However, in the first estimation error covariance matrix calculator 19, hat x_{k | k} ^(c )Error covariance matrix P_{k | k} ^(c)Is obtained. In the first gain matrix calculator 18, the gain matrix K_k ^(c )Is obtained.
[0100]
Next, in the update process using the target position vector by the elliptical positioning or the hyperbolic positioning, the present embodiment operates as follows.
First, the operation of the gain setting unit 9 will be described. The gain setting unit of the first embodiment switches the operation depending on which target position vector of elliptical positioning or hyperbolic positioning is input to the apparatus, and the gain matrix K for elliptical positioning results_k ^(e)Or gain matrix K for hyperbolic positioning results_k ^(h)However, the gain setting unit 9 of the present embodiment calculates both of the gain matrices.
[0101]
First, the gain matrix K used in the update process based on the circular positioning result_k ^(c ) Is sent from the first gain matrix calculator 18 to the second gain matrix calculator 20. Further, in the positioning error covariance matrix calculator 16, the target position vector z by elliptical positioning is obtained according to equations (27) and (28)._k ^(e) Error covariance S^(e) And covariance matrix S of hyperbolic positioning target position vector^(h)Further, the positioning error cross-correlation matrix calculator 17 calculates the cross-correlation matrix C of the hyperbolic positioning error and the circular positioning error according to the equation (30).^(ch) Is calculated.
[0102]
Next, in the first gain matrix calculator 18, the estimated error covariance matrix P after the update processing based on the circular positioning result is received from the first estimated error covariance matrix calculator 19._{k | k} ^(c ) And enter this and S^(e) And gain matrix K according to equation (43)_k ^(e) Is calculated. This gain matrix K_k ^(e) Is sent to the selection processor 29 of the selection unit 25.
In addition, the estimated error covariance matrix calculator 19 when the first estimated error covariance matrix calculator 19 performs the updating process based on the elliptical positioning result according to the equation (45)._{k | k} ^(e) Is calculated.
This P_{k | k} ^(e) Is sent to the first estimation error evaluator 26 of the selection unit 25.
[0103]
Further, in the second gain matrix calculator 20, the estimated error covariance matrix P after the update processing based on the circular positioning result from the first estimated error covariance matrix calculator 19_{k | k} ^(c ) Enter these values and the above S^(h) , C^(ch) , And a gain matrix K previously input from the first gain matrix calculator 18_k ^(c ) And gain matrix K according to equation (46)_k ^(h)Is calculated. This gain matrix is sent to the selection processor 29 of the selection unit 25.
In the second estimation error covariance matrix calculator 21, the above S^(h) , C^(ch) And gain matrix K_k ^(c ), K_k ^(h) And P_{k | k} ^(c ) , And according to equation (48), the estimated error covariance matrix P_{k | k} ^(h) Is calculated.
This P_{k | k} ^(h) Is sent to the second estimation error evaluator 27 of the selection unit 25.
[0104]
Next, the process proceeds to the selection unit 25, where the first estimation error evaluator 26 performs the update process based on the elliptical positioning result according to the equation (53), and the estimated error covariance matrix P_{k | k} ^(e)Evaluation value β^(e)To calculate
The estimated error covariance matrix P when the second estimation error evaluator 27 performs the updating process according to the hyperbolic positioning result according to the equation (54)._{k | k} ^(h) Evaluation value β^(h) Is calculated. These evaluation values are sent to the comparator 28.
The comparator 28 determines which of the two input evaluation values is smaller and sends a comparison result identification signal to the selection processor 29.
The selection processor 29 selects either elliptical positioning or hyperbolic positioning according to the identification signal, and sets the target position vector z_k ^(h) Or z_k ^(e)Either one of them to the residual calculator 12 and the gain matrix K_k ^(e) Or K_k ^(h)Any one of these is sent to the update processor 13.
[0105]
Finally, the estimator 8 is z_k ^(h) Or z_k ^(e) The state vector estimated value using is updated. The operation of the estimation unit 8 at this time is the same as that in the first embodiment shown in FIG. That is, the residual calculator 12 calculates the state vector estimated value hat x after the update processing based on the circular positioning result._{k | k} ^(c ) And the target position vector z sent from the selection processor 29_k ^(h) (Or z_k ^(e) ) Residual z_k ^(e) -H hat x_{k | k} ^(c )(Or z_k ^(h) -H hat x_{k | k} ^(c ) ) And sent to the update processor 13. The update processor 13 receives the gain matrix K sent from the selection processor 29._k ^(e)(Or K_k ^(h) ) And update according to equation (44) (or equation (47)).
[0106]
State vector estimate after update by update processor 13 Hat x_{k | k} ^(e) (Or hat x_{k | k} ^(h) ) Is the final state vector estimate hat x in this sampling_{k | k} Is written in the estimated value memory 10 and sent to the display 6 to be shown to the operator.
The above is the operation at sampling k. Thereafter, the above series of operations is repeated in each sampling until the tracking process.
[0107]
As described above, according to the fourth embodiment of the target tracking device of the present invention, the estimation error when the state vector is updated using the circular positioning result and the elliptic positioning result, and the circular positioning result By evaluating each error of the estimation error when updating the state vector using the result of hyperbolic positioning in advance and selecting the one with the smaller estimation error, the result of either elliptical positioning or hyperbolic positioning is obtained. You can decide what to use.
For this reason, for each sampling, the expected positioning result of the higher elliptical positioning or hyperbolic positioning is selected, and as a result, observation of the monostatic radar station and the bistatic receiving station is performed. The information fusion effect can be further enhanced.
[0108]
【The invention's effect】
As described above, according to the invention of claim 1, in order to perform the target tracking process while merging the positioning information from the monostatic radar station and the bistatic receiving station, as positioning information from the bistatic receiving station, When using hyperbolic positioning information, a filter algorithm that can calculate the optimum estimated values of the target position and speed in consideration of the error correlation between this positioning information and the positioning information from the monostatic radar station Thus, a target tracking method with improved tracking accuracy can be obtained.
[0109]
According to the invention of claim 2, in order to perform the target tracking process while integrating the positioning information from the monostatic radar station and the bistatic receiving station, the positioning information from the bistatic receiving station is determined by the hyperbolic positioning. When using information, it is equipped with a filter algorithm that can calculate the optimum estimated value of the target position and speed in consideration of the error correlation between this positioning information and the positioning information from the monostatic radar station, A target tracking device with improved tracking accuracy can be obtained.
[0110]
According to the invention of claim 3, in order to perform target tracking processing while merging positioning information from a monostatic radar station and a bistatic receiving station, positioning by a hyperbola is used as positioning information at the bistatic receiving station. In order to select the positioning information with the better one of the positioning by the ellipse and the ellipse, the tracking accuracy expected when tracking processing is performed using both positioning information above is selected according to the observation conditions A target tracking method with improved tracking accuracy can be obtained.
[0111]
According to the invention of claim 4, as the positioning information at the bistatic receiving station, the target tracking process is performed while fusing the positioning information from the monostatic radar station and the positioning information from the bistatic receiving station. In order to select positioning information with a better condition of either hyperbolic positioning or elliptical positioning, the tracking accuracy expected when tracking processing is performed using both positioning information above depends on the observation conditions. It is possible to obtain a target tracking device that includes means for evaluating and making the selection, and that has improved tracking accuracy.
[Brief description of the drawings]
FIG. 1 is a flowchart for explaining a first embodiment of a target tracking method according to the present invention;
FIG. 2 is a diagram for explaining target positioning and its coordinate system by a monostatic radar station and a bistatic receiving station common to the embodiments of the present invention.
FIG. 3 is a configuration block diagram showing a second embodiment of the target tracking device of the present invention.
FIG. 4 is a flowchart for explaining a third embodiment of the target tracking method of the present invention.
FIG. 5 is a block diagram showing the configuration of a fourth embodiment of the target tracking device according to the present invention;
FIG. 6 is a configuration block diagram showing a conventional apparatus.
FIG. 7 is a diagram for explaining an operation principle of target positioning of a conventional device and a target tracking device of the present invention. (Target positioning based on arrival time difference between monostatic and bistatic reception waves)
FIG. 8 is a diagram for explaining an operation principle of target positioning of a conventional device and a target tracking device of the present invention. (Target positioning based on time difference between monostatic transmission wave and bistatic reception wave)
[Explanation of symbols]
1 target tracking device, 2 data processor, 3 bistatic data processor, 4 bistatic data processor, 5 selector, 6 display, 7 observation error variance setter, 8 estimation unit, 9 gain setting unit, 10 estimation Memory for value, 11 Prediction processor, 12 Residual calculator, 13 Update processor, 14 Memory for estimation error covariance matrix, 15 Prediction error covariance matrix calculator, 16 Positioning error covariance matrix calculator, 17 Positioning error Cross correlation matrix calculator, 18 first gain matrix calculator, 19 first estimated error covariance matrix calculator, 20 second gain matrix calculator, 21 second estimated error covariance matrix calculator, 25 selection 26, a first estimation error evaluator, 27 a second estimation error evaluator, 28 a comparator, 29 a selection processor.

Claims (4)

Using the positioning results of the targets of both the monostatic radar station and the bistatic receiving station that is installed away from the monostatic radar station and receives the reflected wave from the target of the monostatic radar transmission wave In the target tracking method of performing target tracking processing by
Set the initial value of the estimated value of the state vector and the estimated error covariance matrix composed of the motion parameters such as the target position, velocity, etc., and thereafter at each sampling time,
Positioning result on the elliptical trajectory based on the measurement result on the circumferential trajectory by the monostatic radar station and the measurement result of the time difference between the bistatic reception wave and the transmission wave by the bistatic receiving station, or Enter one of the positioning results on the hyperbolic locus based on the measurement result of the arrival time difference between the static reception wave and the reception wave at the monostatic radar station,
Input a group of observation error variance data related to the distance and angle observation specifications at the monostatic radar station and the bistatic receiving station.
Using the Kalman filter prediction algorithm, calculate the predicted value of the state vector and the prediction error covariance matrix,
Calculate the positioning error covariance matrix of the positioning result on the circumferential trajectory,
Using the positioning results on the circumferential trajectory, based on the Kalman filter update algorithm, calculate the state vector estimate and the estimated error covariance matrix,
When the positioning result on the elliptical locus is input as the positioning result at the bistatic receiving station, the positioning error covariance matrix of the positioning result on the elliptical locus is calculated,
Using the positioning result on the elliptical trajectory, based on the Kalman filter update algorithm, update the state vector estimation value and the estimation error covariance matrix,
On the other hand, when the positioning result on the hyperbolic locus is input as the positioning result at the bistatic receiving station, the positioning error covariance matrix of the positioning result on the hyperbolic locus is calculated,
Calculate a cross-correlation matrix between the positioning result error on the circumferential trajectory and the positioning result error on the hyperbolic trajectory,
Considering the cross-correlation between the positioning result error on the circular trajectory and the positioning result error on the hyperbolic trajectory, the optimal state vector estimation value that minimizes the mean square of the estimation error is calculated. To calculate the filter gain matrix for
Update the state vector estimate using the filter gain matrix and the positioning result on the hyperbolic locus,
Calculate an estimation error covariance matrix of the state vector estimate updated using the positioning result on the hyperbolic locus,
A target tracking method characterized by repeating a series of processes at each sampling time until the end of tracking. Using the positioning results of the targets of both the monostatic radar station and the bistatic receiving station that is installed away from the monostatic radar station and receives the reflected wave from the target of the monostatic radar transmission wave In the target tracking device that performs target tracking processing by
An estimated value memory that stores and holds an estimated value of a state vector composed of motion parameters such as the target position and velocity;
Prediction processing means for predicting the state vector for the sampling interval;
A residual calculation means for calculating a residual between a target position based on the state vector predicted value or the state vector estimated value and a target position based on a positioning result from the monostatic radar station or the bistatic receiving station;
Update processing means for updating the state vector using the state vector predicted value or the state vector estimated value, and the residual and filter gain matrix;
An estimation error covariance matrix memory that stores and holds an estimation error covariance matrix of the state vector estimation value;
A prediction error covariance matrix calculating means for calculating a prediction error covariance matrix of the state vector prediction value;
The positioning error covariance matrix of the positioning result by the monostatic radar station based on the setting values of the ranging and angle error dispersion of the monostatic radar station and the bistatic receiving station, and the bistatic receiving station , The positioning error covariance matrix of the positioning result on the elliptical trajectory based on the measurement result of the time difference between the bistatic received wave and the transmitted wave, and the received wave at the bistatic receiving station and the reception at the monostatic radar station A positioning error covariance matrix calculating means for calculating a positioning error covariance matrix of a positioning result on a hyperbolic locus based on a measurement result of an arrival time difference with a wave;
Based on the setting values of ranging and angle error dispersion of the monostatic radar station and the bistatic receiving station, positioning error by the monostatic radar station and positioning on the hyperbola by the bistatic receiving station A positioning error cross-correlation matrix calculating means for calculating a cross-correlation matrix with errors;
First gain matrix calculating means for calculating a gain matrix of the Kalman filter;
A first estimated error covariance matrix calculating means for calculating an estimated error covariance matrix when updating is performed using a Kalman filter update algorithm;
Second gain matrix calculating means for calculating a filter gain matrix for calculating an optimal state vector estimated value that minimizes the mean square of the estimation error using the cross-correlation matrix;
A target tracking apparatus comprising: a second estimated error covariance matrix calculating unit that calculates an estimated error covariance matrix when updating is performed using the gain matrix. Using the positioning results of the targets of both the monostatic radar station and the bistatic receiving station that is installed away from the monostatic radar station and receives the reflected wave from the target of the monostatic radar transmission wave In the target tracking method of performing target tracking processing by
Set the initial value of the estimated value of the state vector and the estimated error covariance matrix composed of the motion parameters such as the target position, velocity, etc., and thereafter at each sampling time,
Positioning result on the elliptical locus based on the measurement result on the circumferential locus by the monostatic radar station and the measurement result of the time difference between the bistatic reception wave and the transmission wave by the bistatic receiving station, and bistatic Input the positioning result on the hyperbolic locus based on the measurement result of the arrival time difference between the received wave and the received wave at the monostatic radar station,
Input a group of observation error variance data related to the distance and angle observation specifications at the monostatic radar station and the bistatic receiving station.
Using the Kalman filter prediction algorithm, calculate the predicted value of the state vector and the prediction error covariance matrix,
Calculate the positioning error covariance matrix of the positioning result on the circumferential trajectory,
Using the positioning results on the circumferential trajectory, based on the Kalman filter update algorithm, calculate the state vector estimate and the estimated error covariance matrix,
Calculate the positioning error covariance matrix of the positioning result on the elliptical trajectory,
Calculate the positioning error covariance matrix of the positioning result on the hyperbolic locus,
Calculate a cross-correlation matrix between the positioning result error on the circumferential trajectory and the positioning result error on the hyperbolic trajectory,
Calculate the estimated error covariance matrix when the state vector estimate is updated using the positioning result on the elliptical trajectory,
Considering the cross-correlation between the positioning result error on the circular trajectory and the positioning result error on the hyperbolic trajectory, the optimal state vector estimation value that minimizes the mean square of the estimation error is calculated. To calculate the filter gain matrix for
Using the filter gain matrix and the positioning result on the hyperbolic locus, calculate an estimated error covariance matrix when the state vector estimate is updated,
Calculate the evaluation value of the estimated error covariance matrix when the state vector estimated value is updated using the positioning result on the elliptical trajectory,
Using the filter gain matrix and the positioning result on the hyperbolic trajectory, the evaluation value of the estimation error covariance matrix when the state vector estimation value is updated is calculated,
The evaluation value of the estimated error covariance matrix when the magnitude of the two evaluation values calculated above is determined and the state vector estimation value is updated using the positioning result on the elliptical trajectory as a result of the determination. Is small, update the state vector estimate using the positioning result on the elliptical locus,
As a result of the determination, when the estimated value of the estimated error covariance matrix is smaller when the state vector estimated value is updated using the positioning result on the hyperbolic locus, the filter gain matrix and the hyperbola Update the state vector estimate using the positioning result on the trajectory,
A target tracking method characterized by repeating a series of processes at each sampling time until the end of tracking. Using the positioning results of the targets of both the monostatic radar station and the bistatic receiving station that is installed away from the monostatic radar station and receives the reflected wave from the target of the monostatic radar transmission wave In the target tracking device that performs target tracking processing by
An estimated value memory that stores and holds an estimated value of a state vector composed of motion parameters such as the target position and velocity;
Prediction processing means for predicting the state vector for the sampling interval;
A residual calculation means for calculating a residual between a target position based on the state vector predicted value or the state vector estimated value and a target position based on a positioning result from the monostatic radar station or the bistatic receiving station;
Update processing means for updating the state vector using the state vector predicted value or the state vector estimated value, and the residual and filter gain matrix;
An estimation error covariance matrix memory that stores and holds an estimation error covariance matrix of the state vector estimation value;
A prediction error covariance matrix calculating means for calculating a prediction error covariance matrix of the state vector prediction value;
The positioning error covariance matrix of the positioning result by the monostatic radar station and the bistatic receiving station based on the setting values of the ranging and angle error dispersion of the monostatic radar station and the bistatic receiving station , The positioning error covariance matrix of the positioning result on the elliptical locus based on the measurement result of the time difference between the bistatic received wave and the transmitted wave, the received wave at the bistatic receiving station, and the monostatic radar station A positioning error covariance matrix calculating means for calculating a positioning error covariance matrix of a positioning result on a hyperbolic locus based on a measurement result of an arrival time difference with a received wave;
Based on the setting values of ranging and angle error dispersion of the monostatic radar station and the bistatic receiving station, positioning error by the monostatic radar station and positioning on the hyperbola by the bistatic receiving station A positioning error cross-correlation matrix calculating means for calculating a cross-correlation matrix with errors;
A first gain matrix calculating means for calculating a gain matrix of the Kalman filter, a first estimated error covariance matrix calculating means for calculating an estimated error covariance matrix when updated by the Kalman filter update algorithm,
Second gain matrix calculating means for calculating a filter gain matrix for calculating an optimal state vector estimated value that minimizes the mean square of the estimation error using the cross-correlation matrix;
Second estimated error covariance matrix calculating means for calculating an estimated error covariance matrix when updating is performed using this gain matrix;
First estimation error evaluation means for calculating an evaluation value of an estimation error covariance matrix when updated by the Kalman filter update algorithm;
Second estimation error evaluation means for calculating an evaluation value of an estimation error covariance matrix when updating is performed with an algorithm using a filter gain matrix for calculating an optimum state vector estimation value using the cross-correlation matrix When,
Comparison means for comparing the magnitudes of the evaluation values by the first and second estimation error evaluation means;
Based on the comparison result by the comparison means, either the positioning result on the elliptical trajectory or the positioning result on the hyperbolic trajectory is selected, and estimation is performed using the gain matrix of the Kalman filter or the cross-correlation matrix Selection processing means for selecting any one of the filter gain matrices for calculating the optimum state vector estimation value in which the mean square error is minimized, and outputting the selected positioning result and the filter gain matrix; A target tracking device comprising:

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